DEVICE FOR EVALUATING CHARACTERISTIC OF INSULATED GATE TRANSISTOR

Abstract

A transistor having a longer channel length and serving as a reference, and a transistor having a shorter channel length and to be subjected to effective channel length extraction are prepared (step ST1.1). A hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a gate overdrive is slightly changed is extracted in a mask channel length versus total drain-to-source resistance plane. The values of a function (F) are calculated which are defined by the difference between the rate of change in the total drain-to-source resistance and the product of a channel resistance per unit length and the rate of change in a mask channel length at the hypothetical points (step ST1.6). A true threshold voltage of the transistor having the shorter channel length is determined by a shift amount (δ) which minimizes the standard deviation of the function (F) determined in the step ST1.7 (step ST1.10). A resistance-based method thus extracts an effective channel length and a series resistance with increased accuracy.

Description

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a device for evaluating a characteristic of an insulated gate transistor which extracts the effective channel length and also the series resistance of the insulated gate transistor.

[0003] 2. Description of the Background Art The resistance-based method is intended for extracting a series resistance Rsd and an effective channel length Leff. However, the resistance-based method determines a channel length reduction DL (=Lm−Leff in place of the effective channel length Leff where Lm is a mask channel length (designed channel length). The resistance-based method carries out the extraction on the assumption that a total drain-to-source resistance Rtot is the sum of the series resistance Rsd and a channel resistance Rch. A relationship which holds between the effective channel length Leff and the channel resistance Rch is such that the channel resistance Rch is the product of the effective channel length Leff and a channel resistance f per unit length. FIG. 24 conceptually shows the relationship between the channel resistance Rch, the series resistance Rsd, the effective channel length Leff, the mask channel length Lm, and the channel length reduction DL. The relationship shown in FIG. 25 approximately holds between the total drain-to-source resistance Rtot and the mask channel length Lm. Specifically, with a gate voltage Vgs or the gate voltage Vgs minus a threshold voltage Vth held constant, the total drain-to-source resistance Rtot changes in constant proportion to the mask channel length Lm. The gate voltage Vgs minus the threshold voltage Vth is referred to hereinafter as a gate overdrive Vgt. It is assumed that Rtot−Lm lines for various values of the gate overdrive Vgt intersect at one point. The mask channel length Lm coordinate of the point of intersection is represented by DL*, and the total drain-to-source resistance Rtot coordinate thereof is represented by Rsd*. The symbol * which follows the reference character representing a value indicates that the value is determined based on such a relationship which holds between the total drain-to-source resistance Rtot and the mask channel length Lm, in other words, based on characteristic curves plotted in the X-Y plane defined by an X-axis which denotes the mask channel length and a Y-axis which denotes the total drain-to-source resistance.

[0004] Many types of resistance-based method have been hithertofore proposed, among which the Terada-Muta-Chem method (referred to hereinafter as the TMC method) and the Shift and Ratio method (referred to hereinafter as the S&R method) are generally used.

[0005] First, the TMC method is described with reference to FIGS. 26 and 27. Expression (1) providing the relationship between the total drain-to-source resistance Rtot, the effective channel length Leff, the resistance f per channel unit length and the series resistance Rsd is transformed into Expression (4) by using Expression (2) providing the relationship between the effective channel length Leff, the mask channel length Lm and the channel length reduction DL and Expression (3) providing a variable A.

R tot =L eff ·f+R sd   (1)

L eff =L m −DL   (2)

A≡−DL·f+R sd   (3)

R tot =L m ·f+A   (4)

[0006] It is found from Expression (4) that the resistance f per unit length and the variable A are determined from the relationship between the total drain-to-source resistance Rtot and the mask channel length Lm. The total drain-to-source resistance Rtot, the mask channel length Lm and the resistance f per unit length which serve as a function of the gate overdrive Vgt must be determined, with the gate overdrive Vgt held constant. As shown in FIG. 26, for example, a plurality of lines may be plotted for different gate overdrives Vgt1, Vgt2, . . . by measuring the total drain-to-source resistance Rtot of MOS transistors having the mask channel length Lm which takes values Lm1 to Lm4. Then, values f1, f2, . . . of the resistance f per unit length and values A1, A2, . . . of the variable A defined in Expression (3) are found from the slopes and Rtot-intercepts of the respective plotted lines.

[0007] With attention focused on Expression (3), the TMC method extracts the channel length reduction DL and the series resistance Rsd based on the slope and Rtot-intercept of the line of the graph of FIG. 27 since the values f1, f2, . . . of the resistance f and the values A1, A2, . . . of the variable A which are found in the above described manner are in the relationship shown in the graph of FIG. 27. The threshold voltage Vth of the MOS transistor which serves as a reference for the calculation of the gate overdrive Vgt is determined by extrapolation from a source-drain current versus gate voltage characteristic as shown in FIG. 28.

[0008] The TMC method is of low extraction accuracy because of the uncertainty of the threshold voltage Vth obtained by the extrapolation, and thus is not adaptable for an application to transistors which are not greater than 0.35 μm in channel length. FIG. 29 shows the influence of the uncertainty of the gate overdrive Vgt in the case where the mask channel length Lm, coordinate value DL* of the point of intersection is determined using two transistors. There is no problem if the gate overdrives Vgt of the two transistors differ by the same amount from the true Vgt. On the other hand, a 0.01 V difference in gate overdrive Vgt between the two transistors, for example, causes an error on the order of slightly less than 0.01 μm. The extraction error of the threshold voltage Vth of one of the transistors which has a shorter gate length due to the series resistance Rsd is about −0.02 V when the extrapolation is used for the extraction of the threshold voltage Vth. Thus, the extraction error of the channel length reduction DL resulting from the uncertainty of the threshold voltage Vth is estimated to be about −0.01 to about −0.02 μm. Additionally, when data obtained by measuring the gate voltage Vgs at intervals of 0.1 V are used, there is a likelihood that a quantization error causes the extraction error of the threshold voltage Vth on the order of ±0.0V, thereby causing the extraction error of the channel length reduction DL.

[0009] Next, the S&R method is described below with reference to FIGS. 30 and 31. The S&R method provides the channel length reduction DL using Expression (5) using two MOS transistors Sh and Lo which are equal in mask channel width Wm but differ in mask channel length Lm. The MOS transistor Lo is a transistor having a channel length long enough to ignore the influence of the channel length reduction DL, and the MOS transistor Sh is a transistor having a shorter channel length. 1$\begin{array}{cc}\mathrm{DL}=L_{\mathrm{mSh}}-\frac{L_{\mathrm{mLo}}}{⟨\mathrm{ri}⟩}\mathrm{where}\mathrm{ri}=\frac{R_{\mathrm{totLo}}^{\prime }\left(V_{\mathrm{gs}}\right)}{R_{\mathrm{totSh}}^{\prime }\left(V_{\mathrm{gs}}+{\delta }_0\right)}& \left(5\right)\end{array}$

[0010] where the marks “<>” denote an average value in a given region of the gate overdrive Vgt, the prime denotes a first derivative with respect to the gate overdrive Vgt, and δ0 is the difference (VthSh-VthLo) between the threshold voltages VthSh and VthLo of the two MOS transistors Sh and Lo.

[0011] In other words, the S&R method results in the problem of determining <ri> for the correct gate overdrive Vgt. An algorithm for determining <ri> is as follows:

[0012] Step 1: extracting the threshold voltage VthLo of the transistor Lo

[0013] Step 2: shifting Rtotsh′ to Rtotsh′+δ to calculate the average value <ri> and a standard deviation σ (ri) in a given region of the gate overdrive VgtLo (=Vgs−VthLo) (See FIG. 30)

[0014] Step 3: repeating Step 2, with the shift amount δ changed

[0015] Step 4: providing <ri> as <ri>δ=δ0 where 670 is the shift amount δ when σ(ri)2 is a minimum, based on the result of Step 3.

[0016] It should be noted that the changes in the shift amount δ are equivalent to changes in the threshold voltage VthSh of the short transistor Sh.

[0017] The S&R method reduces the error resulting from the uncertainty of the threshold voltage Vth which is the problem with the TMC method, but presents another problem in that the region of the gate overdrive Vgt to be calculated must be adequately determined so that the appropriate channel length reduction DL is obtained. The S&R method determines <ri> on the assumption that, when the gate overdrive Vgt is small, ri is a constant value, in spite of the dependence of ri upon the gate overdrive Vgt. As a result, the channel length reduction DL extracted by the S&R method is dependent upon the region of the gate overdrive Vgt (See FIG. 32).

[0018] The S&R method requires the mask channel length LmLo of the long transistor Lo to be sufficiently greater than the mask channel length LmSh of the short transistor Sh. As the mask channel length LmLo of the long transistor Lo approaches the mask channel length LmSh of the short transistor Sh, <ri> approaches “1,” and the value of the channel length reduction DL accordingly approaches “0” as will be found from Expression (5) (See FIG. 33). This problem results from the formulation in defiance of the dependence of the channel length reduction DL and the series resistance Rsd upon the gate overdrive Vgt.

[0019] As above described, the conventional resistance-based method is disadvantageous in the low extraction accuracy of the effective channel length and the series resistance, and in the dependence of the extraction accuracy thereof upon the setting of parameters. For example, the TMC method extracts the effective channel length and the series resistance with low accuracy because of the error resulting from the uncertainty of the threshold voltage determined by the extrapolation. The S&R method reduces the extraction error of the effective channel length resulting from the uncertainty of the threshold voltage, but has the drawback that the value of the effective channel length to be extracted changes greatly depending on the range of the gate overdrive Vgt to be specified for calculation.

SUMMARY OF THE INVENTION

[0020] A first aspect of the present invention is intended for a method of evaluating a characteristic of an insulated gate transistor. According to the present invention, the method comprises the steps of: (a) preparing at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length; (b) extracting a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value of the threshold voltage as a first estimated value; (c) extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve plotted in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance on the condition that the first and second gate overdrives are equal, the value of the mask channel length and the value of the total drain-to-source resistance at the hypothetical point being defined as second and third estimated values, respectively, and also extracting the slope of the characteristic curve at the hypothetical point to define the extracted value of the slope as a fourth estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the second insulated gate transistor and the first estimated value; (d) repeating the step (c) with the first estimated value changed; (e) determining optimum second to fourth estimated values that are respective ones of the second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, to determine an optimum first estimated value associated with the optimum second to fourth estimated values, thereby to determine a true threshold voltage of the second insulated gate transistor based on the optimum first estimated value; and (f) determining the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0021] Preferably, according to a second aspect of the present invention, in the method of the first aspect, the characteristic curve is approximated in the step (e) using a first line drawn in the X-Y plane and passing through first and second points, the first point being given for the first insulated gate transistor when the first gate overdrive has a first value, the second point being given for the second insulated gate transistor when the second gate overdrive has the first value.

[0022] Preferably, according to a third aspect of the present invention, in the method of the second aspect, the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed are determined in the step (e) using the relationship expressed by 2$F\left(\delta ,V_{\mathrm{gtLo}}\right)=d{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)+\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L}^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-{\mathrm{DL}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0023] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, dL* is an X-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, DL* is the X coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0024] Preferably, according to a fourth aspect of the present invention, in the method of the second aspect, the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed are determined in the step (e) using the relationship expressed by 3$F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{f^2\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L}^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0025] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, dL* is an X-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, Rsd* is the Y coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0026] Preferably, according to a fifth aspect of the present invention, in the method of the second aspect, the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed are determined in the step (e) using the relationship expressed by 4$F\left(\delta ,V_{\mathrm{gtLo}}\right)=R^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)-\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0027] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, R* is a Y-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, Rsd* is the Y coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0028] Preferably, according to a sixth aspect of the present invention, in the method of the second aspect, the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed are determined in the step (e) using the relationship expressed by 5$F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}+D{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0029] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, R* is a Y-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, DL* is the X coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0030] A seventh aspect of the present invention is intended for a method of evaluating a characteristic of an insulated gate transistor. According to the present invention, the method comprises the steps of: (a) preparing at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length; (b) extracting a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value of the threshold voltage as a first estimated value; (c) extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve plotted in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y-axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance on the condition that the first and second gate overdrives are equal, the value of the mask channel length at the hypothetical point being defined as a second estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the second insulated gate transistor and the first estimated value; (d) repeating the step (c) with the first estimated value changed; (e) determining an optimum first estimated value among the first and second estimated values associated with the steps (b), (c) and (d), the optimum first estimated value satisfying that a characteristic curve indicating the relationship between the second gate overdrive measured on an X-axis and the second estimated value measured on a Y-axis has a predetermined configuration in a predetermined range of the second gate overdrive, to determine a true threshold voltage of the second insulated gate transistor based on the optimum first estimated value; and (f) determining the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0031] Preferably, according to an eighth aspect of the present invention, in the method of the seventh aspect, the characteristic curve includes a plurality of characteristic curves, and the step (e) comprises the step of determining among the plurality of characteristic curves an optimum characteristic curve exhibiting the second estimated value which converge best on a constant value within the predetermined range to detect the characteristic curve having the predetermined configuration.

[0032] According to a ninth aspect of the present invention, a method of evaluating a characteristic of an insulated gate transistor comprises the steps of: (a) extracting an effective channel length from each of at least two drain current versus gate voltage characteristics differing from each other in source-drain voltage, by using a resistance-based method; and (b) determining an effective channel length by extrapolation from the effective channel lengths extracted for different source-drain voltages.

[0033] According to a tenth aspect of the present invention, a method of fabricating an insulated gate transistor comprises the steps of: producing at least two insulated gate transistors differing from each other only in mask channel length; measuring a drain current characteristic of the two insulated gate transistors, with a gate voltage and a source-drain voltage changed; determining a threshold voltage and an effective channel length of the insulated gate transistors by using a method of evaluating a characteristic of an insulated gate transistor as recited in one of the first to ninth aspects; and judging specification fitness of the drain current characteristic, the threshold voltage and the effective channel length.

[0034] Am eleventh aspect of the present invention is intended for an insulated gate transistor characteristic evaluation device using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, the insulated gate transistor characteristic evaluation device for evaluating a characteristic of the second insulated gate transistor using a characteristic of the first insulated gate transistor as a reference. According to the present invention, the insulated gate transistor characteristic evaluation device comprises: threshold voltage estimation means for extracting a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value as a first estimated value; extraction means for extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when first and second gate overdrives are slightly changed, based on a characteristic curve drawn in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y-axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance, the value of the mask channel length and the value of the total drain-to-source resistance at the hypothetical point being defined as second and third estimated values, respectively, the extraction means also extracting the slope of the characteristic curve at the hypothetical point to define the value of the slope as a fourth estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the first and second insulated gate transistors and the first estimated value; threshold voltage determination means for determining optimum second to fourth estimated values that are respective ones of the second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, to determine an optimum first estimated value associated with the optimum second to fourth estimated values, thereby to determine a true threshold voltage of the second insulated gate transistor based on the optimum first estimated value; and channel length reduction determination means for determining the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0035] Preferably, according to a twelfth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the eleventh aspect, the extraction means approximates the characteristic curve using a first line drawn in the X-Y plane and passing through first and second points, the first point being given for the first insulated gate transistor when the first gate overdrive has a first value, the second point being given for the second insulated gate transistor when the second gate overdrive has the first value.

[0036] Preferably, according to a thirteenth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the twelfth aspect, the threshold voltage determination means determines the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, using the relationship expressed by 6$F\left(\delta ,V_{\mathrm{gtLo}}\right)=d{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)+\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L}^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-{\mathrm{DL}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0037] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, dL* is an X-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, DL* is the X coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0038] Preferably, according to a fourteenth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the twelfth aspect, the threshold voltage determination means determines the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, using the relationship expressed by 7$F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{f^2\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L}^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0039] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, dL* is an X-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, Rsd* is the Y coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo. Preferably, according to a fifteenth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the twelfth aspect, the threshold voltage determination means determines the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, using the relationship expressed by 8$F\left(\delta ,V_{\mathrm{gtLo}}\right)=R^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)-\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0040] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, R* is a Y-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, Rsd* is the Y coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0041] Preferably, according to a sixteenth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the twelfth aspect, the threshold voltage determination means determines the optimum second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, using the relationship expressed by 9$F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}+D{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)$

[0042] where δ is the difference between the first estimated value of the threshold voltage of the second insulated gate transistor and the threshold voltage of the first insulated gate transistor, VgtLo is the first gate overdrive, R* is a Y-intercept provided by extrapolation from the characteristic curve, f is the slope of the characteristic curve at the hypothetical point, DL* is the X coordinate of the hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

[0043] A seventeenth aspect of the present invention is intended for an insulated gate transistor characteristic evaluation device using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, the insulated gate transistor characteristic evaluation device for evaluating a characteristic of the second insulated gate transistor using a characteristic of the first insulated gate transistor as a reference. According to the present invention, the insulated gate transistor characteristic evaluation device comprises: threshold voltage estimation means for extracting a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value as a first estimated value; extraction means for extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve drawn in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y-axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance, the values of the mask channel length at the hypothetical point being defined as a second estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the second insulated gate transistor and the first estimated value; threshold voltage determination means for determining a first estimated value by the second estimated value, the first estimated value satisfying that a characteristic curve indicating the relationship between the second gate overdrive measured on an X-axis and the second estimated values measured on a Y-axis has a predetermined configuration in a predetermined range of the second gate overdrive, to determine the determined first estimated value as a true threshold voltage of the second insulated gate transistor; and channel length reduction determination means for determining the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0044] Preferably, according to an eighteenth aspect of the present invention, in the insulated gate transistor characteristic evaluation device of the seventeenth aspect, the threshold voltage determination means determines a standard deviation of the second estimated value in the predetermined range to detect the characteristic curve having the predetermined configuration.

[0045] According to a nineteenth aspect of the present invention, an insulated gate transistor characteristic evaluation device comprises: calculation means for extracting an effective channel length from each of at least two drain current versus gate voltage characteristics differing from each other in source-drain voltage, by using a resistance-based method; and output means for determining an effective channel length by extrapolation from the effective channel lengths extracted for different source-drain voltages.

[0046] A twentieth aspect of the present invention is intended or a computer readable recording medium storing therein a characteristic evaluation program and using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, the computer readable recording medium for causing a computer to evaluate a characteristic of the second insulated gate transistor using a characteristic of the first insulated gate transistor as a reference. According to the present invention, the computer readable recording medium comprises: means for causing the computer to extract a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value as a first estimated value; means for causing the computer to extract a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve drawn in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y-axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance on the condition that the first and second gate overdrives are equal, the value of the mask channel length and the value of the total drain-to-source resistance at the hypothetical point being defined as second and third estimated values, respectively, the means also causing the computer to extract the slope of the characteristic curve at the hypothetical point to define the value of the slope as a fourth estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the second insulated gate transistor and the first estimated value; means for causing the computer to determine optimum second to fourth estimated values that are respective ones of the second to fourth estimated values which satisfy that the amount of change in the third estimated value equals the product of the amount of change in the second estimated value and the fourth estimated value when the first and second gate overdrives are slightly changed, to determine an optimum first estimated value associated with the optimum second to fourth estimated values, thereby to determine a true threshold voltage of the second insulated gate transistor based on the optimum first estimated value; and means for causing the computer to determine the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0047] An twenty-first aspect of the present invention is intended for a computer readable recording medium storing therein a characteristic evaluation program and using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, the computer readable recording medium for causing a computer to evaluate a characteristic of the second insulated gate transistor using a characteristic of the first insulated gate transistor as a reference. According to the present invention, the computer readable recording medium comprises: means for causing the computer to extract a threshold voltage for the first insulated gate transistor to estimate a threshold voltage for the second insulated gate transistor to define the estimated value as a first estimated value; means for causing the computer to extract a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve drawn in an X-Y plane with the mask channel length measured on an X-axis and the total drain-to-source resistance measured on a Y-axis, the characteristic curve indicating the relationship between the mask channel length of the first and second insulated gate transistors and the total drain-to-source resistance on the condition that the first and second gate overdrives are equal, the value of the mask channel length at the hypothetical point being defined as a second estimated value, the first gate overdrive being defined as the difference between the gate voltage of the first insulated gate transistor and the extracted threshold voltage of the first insulated gate transistor, the second gate overdrive being defined as the difference between the gate voltage of the second insulated gate transistor and the first estimated value; means for causing the computer to determine a first estimated value by the second estimated value, the first estimated value satisfying that a characteristic curve indicating the relationship between the second gate overdrive measured on an X-axis and the second estimated value measured on a Y-axis has a predetermined configuration in a predetermined range of the second gate overdrive, to determine the determined first estimated value as a true threshold voltage of the second insulated gate transistor; and means for causing the computer to determine the difference between the mask channel length and an effective channel length, and a series resistance, based on the true threshold voltage.

[0048] As above described, the method of evaluating the characteristic of the insulated gate transistor according to the first and seventh aspects of the present invention, the insulated gate transistor characteristic evaluation device according to the eleventh and seventeenth aspects of the present invention and the computer readable recording medium storing therein the characteristic evaluation program according to the twentieth and twenty-first aspects of the present invention may accurately extract the threshold voltage of the second insulated gate transistor independently of the range of the second gate overdrive to increase the extraction accuracy of the effective channel length and the series resistance.

[0049] The method of evaluating the characteristic of the insulated gate transistor according to the second aspect of the present invention and the insulated gate transistor characteristic evaluation device according to the twelfth aspect of the present invention approximate the characteristic curve using the line. Then, the hypothetical point may be determined as a point of intersection of lines, and the slope at the point of intersection may be determined as the slope of the lines. This is effective in facilitating the extraction of the hypothetical point and the slope at the hypothetical point.

[0050] The method of evaluating the characteristic of the insulated gate transistor according to the third to sixth aspects of the present invention and the insulated gate transistor characteristic evaluation device according to the thirteenth to sixteenth aspects of the present invention need not determine a derivative of the coordinates of the hypothetical point with respect to the gate overdrive. This might reduce errors since the coordinate of the point of intersection determined from the characteristic curve are more significantly influenced by noises than are the Y- and X-intercepts of the characteristic curve. Thus, the derivative of the coordinates of the hypothetical point with respect to the gate overdrive has a greater error than does the derivative of the intercepts.

[0051] The method of evaluating the characteristic of the insulated gate transistor according to the eighth aspect of the present invention and the insulated gate transistor characteristic evaluation device according to the eighteenth aspect of the present invention facilitate the detection of the characteristic curve having the predetermined configuration to readily increase the speed of the characteristic evaluation.

[0052] The method of evaluating the characteristic of the insulated gate transistor according to the ninth aspect of the present invention and the insulated gate transistor characteristic evaluation device according to the nineteenth aspect of the present invention may eliminate errors resulting from drift velocity saturation to increase the extraction accuracy.

[0053] The method of fabricating the insulated gate transistor according to the tenth aspect of the present invention may extract the threshold voltage and the effective channel length with high accuracy and in a non-destructive manner using the method of evaluating the characteristic of the insulated gate transistor, thereby to reduce the time required for the fabrication.

[0054] It is therefore an object of the present invention to provide a resistance-based method which extracts an effective channel length and a series resistance with increased accuracy.

[0055] These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] FIG. 1 is a flowchart for illustrating the outline of the present invention;

[0057] FIG. 2 conceptually illustrates one step of FIG. 1;

[0058] FIG. 3 is a flowchart showing a procedure of a method of evaluating a characteristic of an insulated gate transistor according to a first preferred embodiment of the present invention;

[0059] FIG. 4 is a graph for illustrating the determination of a true shift amount;

[0060] FIG. 5 is a graph for illustrating an effect of the first preferred embodiment;

[0061] FIG. 6 is a graph for illustrating another effect of the first preferred embodiment;

[0062] FIG. 7 is a graph for illustrating still another effect of the first preferred embodiment;

[0063] FIG. 8 illustrates a high-order approximation;

[0064] FIG. 9 is a block diagram showing an arrangement of a device for evaluating a characteristic of an insulated gate transistor according to the first preferred embodiment;

[0065] FIG. 10 conceptually shows a calculation portion shown in FIG. 9 as implemented using a computer;

[0066] FIG. 11 is a flowchart showing the steps of fabrication of an insulated gate transistor using the method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment;

[0067] FIG. 12 is a graph showing the relationship between a mask channel length and an effective channel length in the fabrication of the insulated gate transistor;

[0068] FIG. 13 is a graph showing the relationship between the effective channel length and a threshold voltage in the fabrication of the insulated gate transistor;

[0069] FIG. 14 is a graph for illustrating the outline of a second preferred embodiment of the present invention;

[0070] FIG. 15 is a flowchart showing a procedure of the method of evaluating the characteristic of the insulated gate transistor according to the second preferred embodiment;

[0071] FIG. 16 is a graph for illustrating the determination of a channel length reduction according to the second preferred embodiment;

[0072] FIG. 17 is a block diagram showing an arrangement of the device for evaluating the characteristic of the insulated gate transistor according to the second preferred embodiment;

[0073] FIG. 18 is a graph showing a relationship between a gate-drain voltage and the effective channel length;

[0074] FIG. 19 is a graph showing another relationship between the gate-drain voltage and the effective channel length;

[0075] FIG. 20 is a graph showing the correction of a gate finished length by KY and S&I methods;

[0076] FIG. 21 is a graph for comparison between measured values and a first simulation result of a drain current versus gate voltage characteristic;

[0077] FIG. 22 is a graph for comparison between the measured values and a second simulation result of the drain current versus gate voltage characteristic;

[0078] FIG. 23 is a graph for comparison between the measured values and a third simulation result of the drain current versus gate voltage characteristic;

[0079] FIG. 24 conceptually shows the relationship between a channel resistance, a series resistance, the effective channel length, the mask channel length, and the channel length reduction;

[0080] FIG. 25 is a graph showing the relationship which approximately holds between a total drain-to-source resistance and the mask channel length;

[0081] FIGS. 26 and 27 are graphs for illustrating the extraction of the effective channel length in the TMC method;

[0082] FIG. 28 is a graph for illustrating the extraction of the threshold voltage;

[0083] FIG. 29 is a graph for illustrating an error caused by the TMC method due to the uncertainty of the threshold voltage;

[0084] FIG. 30 is a graph for illustrating the calculation of a standard deviation in the S&R method;

[0085] FIG. 31 is a graph for illustrating the determination of the true shift amount in the S&R method;

[0086] FIG. 32 is a graph showing an example of the dependence of the channel length reduction upon an upper limit of a gate overdrive region in the S&R method;

[0087] FIG. 33 is a graph showing an example of the dependence of the channel length reduction upon the channel length in the S&R method; and

[0088] FIG. 34 illustrates the definition of Rsd* and Rsd* *

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0089] The outline of a method of evaluating a characteristic of an insulated gate transistor according to the present invention will now be described with reference to FIGS. 1 and 2. FIG. 1 is a flowchart showing the outline of the procedure of the method of evaluating the characteristic of the insulated gate transistor according to the present invention. The insulated gate transistor used herein shall be a MOS transistor. Two ore more MOS transistors are prepared which are equal in mask channel width Wm but differ in mask channel length Lm. An effective channel length Leff for these MOS transistors is extracted from two or more drain-source current versus gate voltage characteristics (Ids-Vgs characteristics) having different drain-source voltages Vds (step ST1). This extraction is performed using a linear region of the Ids-Vgs characteristics. For example, with the drain-source voltage Vds set to 0.05 V, 0.1 V and 0.15 V, the respective effective channel lengths Leff are extracted.

[0090] The value of the effective channel length Leff is provided by extrapolation from the relationship between the effective channel length Leff(0) and the source-drain voltage Vds. For instance, the value of an intercept, that is, Leff(0) in the graph shown in FIG. 2 depicting the relationship between the effective channel length Leff and the source-drain voltage Vds is defined as the effective channel length Leff (step ST2). A series resistance Rsd is given by extraction from the Ids-Vgs characteristics when the source-drain voltage Vds has a minimum value. The value of the series resistance Rsd may be determined by the extrapolation using the relationship between the effective channel length Leff and the source-drain voltage Vds in a manner similar to the determination of the effective channel length Leff.

[0091] First Preferred Embodiment

[0092] The method of evaluating the characteristic of the insulated gate transistor according to a first preferred embodiment of the present invention will be described hereinafter. In the method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment, a channel length reduction DL and the series resistance Rsd are extracted using the drain current in a linear region of two transistors which are equal in mask channel width Wm but differ in mask channel length Lm.

[0093] The step ST1 shown in FIG. 1 in the method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment will be briefly described below. In the method of the first preferred embodiment, two MOS transistors which are equal in mask channel width Wm but differ in mask channel length Lm are prepared. One of the two MOS transistors which has a longer mask channel length Lm is referred to hereinafter as a long transistor Lo or a first insulated gate transistor, and the other MOS transistor having a shorter mask channel length Lm is referred to hereinafter as a short transistor Sh or a second insulated gate transistor. The threshold voltages VthLo and VthSh of the MOS transistors Lo and Sh are extrapolated, for example, from the Ids−Vgs characteristics in the conventional manner described with reference to FIG. 28. The threshold voltage VthSh of the second insulated gate transistor obtained at this time by the extrapolation is a first estimated value.

[0094] With the threshold voltage VthLo of the long transistor Lo fixed, the threshold voltage VthSh (the first estimated value) of the short transistor Sh is changed. Then, coordinates (DL*, Rsd*) of hypothetical points at which changes in the value of a total drain-to-source resistance Rtot is estimated to be approximately zero if a gate overdrive Vgt is slightly changed for the changed values of the threshold voltage VthSh are extracted using the coordinates of points of intersection, for example. At this time, the gate overdrive Vgt of the long transistor Lo is a first gate overdrive, and the gate overdrive Vgt of the short transistor Sh is a second gate overdrive. The values of the coordinate DL* of the hypothetical points are second estimated values, the values of the coordinate Rsd* thereof are third estimated values, and the values of the slope f at the hypothetical points are fourth estimated values.

[0095] Using the threshold voltages VthLo and VthSh, the coordinates (DL*, Rsd*) of the hypothetical point are extracted from the relationship between the total drain-to-source resistance Rtot and the mask channel length Lm. An example of the method of extracting the hypothetical point from the relationship between the total drain-to-source resistance Rtot and the mask channel length Lm includes, for example, a conventional method of extracting the point of intersection of two Rtot−Lm characteristic curves (lines) drawn in the graph shown in FIG. 25, that is, the graph showing the mask channel length Lm on the X-axis versus the total drain-to-source resistance Rtot on the Y-axis. For instance, in FIG. 25, the line indicative of the gate overdrive Vgt is a first line, a point which satisfies the mask channel length Lm=LmLo on the first line is a first point, and a point which satisfies the mask channel length Lm=LmSh on the first line is a second point. However, the estimation of the coordinate of the hypothetical point is not limited to the above described method. For example, a curve determined by three or more points, rather than the line passing through two points, may be used for the estimation, and a point adjacent to the point of intersection may be used in place of the point of intersection. Among the extracted coordinates (DL*, Rsd*) of the hypothetical points are determined those of a hypothetical point estimated to satisfy that the product of the channel resistance f per unit length and the X coordinate component of the hypothetical point, that is, the amount of change in the mask channel length Lm coordinate value DL* is equal to the Y coordinate component of the hypothetical point, that is, the amount of change in the total drain-to-source resistance Rtot coordinate value Rsd* of the hypothetical point.

[0096] Next, the step ST1 of FIG. 1, that is, the step of extracting the effective channel length Leff and the series resistance Rsd of the MOS transistor for the respective values of the drain-source voltages Vds is described in detail with reference to FIG. 3. First, the Ids−Vgs characteristics of the two transistors Lo and Sh which are equal in mask channel width Wm but differ in mask channel length Lm are measured (step ST1.1).

[0097] The threshold voltages VthLo and VthSh of the long and short transistors Lo and Sh are extracted by the extrapolation and the like from the measured Ids−Vgs characteristics (step ST1.2). The difference (VthSh−VthLo) between the threshold voltages VthLo and VthSh is calculated. The difference (VthSh−VthLo) between the threshold voltages VthLo and VthSh calculated in this manner is designated hereinafter by δ guess.

[0098] The lower and upper limits of a range in which a value δ defined as the threshold voltage difference falls are determined as δinf=δguess−K and δsup=δguess+K, respectively, (step ST1.3) where K equals 0.2 V, for example. The initial value δ=δinf is set.

[0099] Whether or not the value δ to be calculated is between δinf and δsup is judged (step ST1.4). That is, whether or not δinf≦δ≦δsup is judged.

[0100] The threshold voltage VthLo of the long transistor Lo is fixed at the value extracted in the step ST1.2. The threshold voltage VthSh of the short transistor Sh is assumed to be the sum of the value δ and the threshold voltage VthLo of the long transistor Lo (step ST1.5).

[0101] The gate overdrive Vgt is measured on the basis of the threshold voltages VthLo and VthLo+δ provided in the step ST1.5. The rates of change DL*′(δ, Vgtn) in the Lm coordinate value of about 20 hypothetical points, the rates of change Rsd*(δ, Vgtn) in the Rtot coordinate values thereof, and the channel resistances f( 8R, Vgtn) per unit length thereof are determined in a given region Ω, for example, a range of the gate overdrive Vgt satisfying 0.3 V≦Vgt≦1.3 V. From the determined values are calculated the values of a function F(δ, Vgtn) expressed by

F (δ, Vgtn)=Rsd*′−f·DL*′  (6)

[0102] where n=1, 2, . . . , 20

[0103] Next, a standard deviation a σ[F(δ)] of the function F is calculated in the region Ω (step ST1.7). The value of the shift amount δ is changed by substituting δ+Ω for δ, and the flow returns to the step ST1.4 (step ST1.8).

[0104] The steps ST1.5 to ST1.8 are repeated if it is judged in the step ST1.4 that δinf≦δ≦δsup. If it is not judged in the step ST1.4 that δinf≦δ≦δsup, the flow proceeds to the step ST1.9. In the step ST1.9, δ=δ0 which minimizes the standard deviation a σ[F(δ)] is determined. At that time, the true threshold voltage VthSh of the short transistor Sh is the sum of the threshold voltage VthLo of the long transistor Lo and δ0 determined in the step ST1.9.

[0105] Using the true threshold voltage VthLo+δ0 of the short transistor Sh which is determined in the step ST1.9, the gate overdrive Vgt of the short transistor Sh is measured to determine the values of the Lm coordinate DL*(Vgt) of the hypothetical points (step ST1.10). It should be noted that the threshold voltage VthLo of the long transistor Lo at this time is based on the value determined in the step ST1.2 as in the step ST1.5.

[0106] The Lm coordinate value DL* of a hypothetical point at a stationary point closest to the point at which the gate overdrive Vgt=0 is determined as the true channel length reduction DL (step ST1.11). The true channel length reduction DL is an optimum second estimated value. At the same time, the effective channel length Leff is determined by the difference between the mask channel length Lm and the true channel length reduction DL, and the series resistance Rsd which is an optimum third estimated value is determined by

R sd (Vgt)=RtotLo(Vgt)−(LmLo−DL)·f(δ0, Vgt)  (7)

[0107] where RtotLo is the total drain-to-source resistance of the long transistor Lo, and LmLo is the mask channel length of the long transistor Lo. An optimum fourth estimated value is the channel resistance f per unit length obtained using the gate overdrive Vgt which gives the true channel length reduction DL.

[0108] The specific procedure of the determination of the true channel length reduction DL and the like from the standard deviation of the function F given in Expression (6) is described below. The method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment employs a variational method particularly to reduce an error resulting from the uncertainty of the extrapolation of the threshold voltage, particularly the uncertainty of the extrapolation of the threshold voltage of a transistor having a short channel length, with attention focused on the relationship given in Expression (8) which holds between the values of the Lm coordinate DL* of the hypothetical point and dL*, for example. 10$\begin{array}{cc}{\mathrm{dl}}^{*}+\frac{f}{f^{\prime }}·d{L}^{*\prime }-{\mathrm{DL}}^{*}=0& \left(8\right)\end{array}$

[0109] where dL* is the value of an X-intercept provided by the extrapolation from an Rtot−Lm characteristic curve (line) drawn in a graph showing the relationship between the total drain-to-source resistance Rtot on the Y-axis and the mask channel length Lm on the X-axis. The value dL* is referred to hereinafter as an Lm-intercept value.

[0110] It is assumed that the threshold voltage difference between the short transistor Sh and the long transistor Lo is the shift amount δ. The Lm coordinate value DL* of the hypothetical point the Lm-intercept value dL*, the rate of change dL*′ thereof, the channel resistance f per unit length, and the rate of change f thereof are determined from RtotSh(VgtLo+δ−VthSh+VthLo) and RtotLo(VgtLo). Expression (8) is satisfied when the shift amount δ equals the true threshold voltage difference δ0 between the short transistor Sh and the long transistor Lo. At that time, the Lm coordinate value DL* of a hypothetical point at which the threshold voltage VthLo is close to zero provides the true channel length reduction DL. Therefore, the true channel length reduction DL and the series resistance Rsd may be extracted in a procedure to be described below.

[0111] Initially, the Lm coordinate value DL* of the hypothetical point, the Lm-intercept value dL*, and the channel resistance f per unit length are provided for a given shift amount δ by 11$\begin{array}{cc}{\mathrm{DL}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)=\left(L_{\mathrm{mSh}}-\frac{\delta R_{\mathrm{totSh}}}{\delta R_{\mathrm{totLo}}}·L_{\mathrm{mLo}}\right)·{\left(1-\frac{\delta R_{\mathrm{totSh}}}{\delta R_{\mathrm{totLo}}}\right)}^{-1}& \left(9\right)\\ d{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)=\left(L_{\mathrm{mSh}}-\frac{R_{\mathrm{totSh}}}{R_{\mathrm{totLo}}}·L_{\mathrm{mLo}}\right)·{\left(1-\frac{R_{\mathrm{totSh}}}{R_{\mathrm{totLo}}}\right)}^{-1}& \left(10\right)\\ f\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{R_{\mathrm{totLo}}-R_{\mathrm{totSh}}}{L_{\mathrm{mLo}}-L_{\mathrm{mSh}}}& \left(11\right)\end{array}$

[0112] The parameters RtotSh, RtotLo, δRtotSh and δRtotLo used in Expressions (9) to (11) are determined by

R totSh =R totSh (VgtLo+δ−VthSh+VthLo)  (12)

R totLo =R totLo   (13)

[0113] 12 $$ δ ⁢   ⁢ R totSh = R totSh ⁡ ( V gtLo + δ - V thSh + V thLo - δ ⁢   ⁢ V gt 2 ) - R totSh ⁡ ( V gtLo + δ - V thSh + V thLo + δ ⁢   ⁢ V gt 2 ) ( 14 ) δ ⁢   ⁢ R totLo = R totLo ⁡ ( V gtLo - δ ⁢   ⁢ V gt 2 ) - R totLo ⁡ ( V gtLo + δ ⁢   ⁢ V gt 2 ) ( 15 )

[0114] The Lm coordinate value DL* of the hypothetical point, the Lm-intercept value dL*, the rate of change dL*′ thereof, the channel resistance f per unit length, and the rate of change f′ thereof are determined, with the shift amount δ changed.

[0115] The function F given in Expression (6), when transformed and redefined into 13$\begin{array}{cc}F\left(\delta ,V_{\mathrm{gtLo}}\right)=d{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)+\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L^{*}}^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-{\mathrm{DL}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)& \left(16\right)\end{array}$

[0116] is easier to determine. The function F defined in Expression (16) equals zero independently of the gate overdrive VgtLo when the shift amount δ equals the threshold voltage difference δ0 between the two transistors Lo and Sh. Then, the shift amount δ which minimizes the standard deviation of the function F in a given region of the gate overdrive VgtLo is determined as the true threshold voltage difference δ0.

[0117] FIG. 4 is a graph showing a relationship between the standard deviation of the function F and the shift amount δ. In the graph of FIG. 4, since the standard deviation of the function F is a minimum when the shift amount δ is 0.095 V, the true threshold voltage difference δ0 is set at 0.095 V.

[0118] The value of the true channel length reduction DL is determined using the value of the above-mentioned threshold voltage difference δ0. For example, the value of the true channel length reduction DL may be determined in the manner performed in the step ST1.11 of FIG. 3. Otherwise, the average of the Lm coordinate values DL*(δ0, VgtLo) of the hypothetical points at which the gate overdrive VgtLo of the long transistor Lo is close to zero may be determined as the true channel length reduction DL. Using the effective channel length LeffSh calculated from the true channel length reduction DL, the series resistance Rsd is determined by

R totSh (Vst)=LeffSh(Vgt)·f(Vgt)+Rsd(Vgt)

[0119] FIGS. 5 to 7 show examples of results of the method of evaluating the characteristic of the MOS transistor according to the first preferred embodiment (referred to hereinafter as a KY method), the S&R method and the TMC method which are applied to a process for fabricating a MOS transistor with a pattern width of 0.3 μm. FIGS. 5 and 6 suggest that the channel length reduction DL and the series resistance Rsd extracted by the TMC method are significantly different from those extracted by the other methods (S&R and KY methods) because of the uncertainty of the threshold voltage Vth. FIG. 7 shows that the channel length reduction DL extracted by the S&R method is significantly dependent upon the region of the gate overdrive Vgt which is set for calculation. The channel length reduction DL extracted by the KY method is stable and is not dependent upon the region of the gate overdrive Vgt which is set for calculation, as compared with those extracted by the TMC and S&R methods.

[0120] The relationship between the KY method and the S&R method can be explicitly shown. The Lm coordinate values DL* of the hypothetical points determined from the two transistors Sh and Lo which differ in mask channel length Lm are given by Expression (10). At a limit as δVgt approaches zero, Expression (18) holds. 14$\begin{array}{cc}\frac{\delta R_{\mathrm{totSh}}}{\delta R_{\mathrm{totLo}}}=\frac{d{R}_{\mathrm{totSh}}}{d{R}_{\mathrm{totLo}}}=\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}\equiv \frac{1}{\mathrm{ri}}& \left(18\right)\end{array}$

[0121] Substituting Expression (18) into Expression (10) provides 15$\begin{array}{cc}{\mathrm{DL}}^{*}={\mathrm{DL}}^{*}\left[S\&R\right]{\left(1-\frac{1}{\mathrm{ri}}\right)}^{-1}\mathrm{where}{\mathrm{DL}}^{*}\left[S\&R\right]\equiv L_{\mathrm{mSh}}-\frac{L_{\mathrm{mLo}}}{\mathrm{ri}}& \left(19\right)\end{array}$

[0122] where [S&R] denotes a solution by the S&R method.

[0123] The Lm coordinate value DL* given by Expression (19) differs by the amount of the correction term (1−1/ri)−1 from the Lm coordinate value DL*[S&R] of the hypothetical point calculated by the S&R method which is disclosed in Y. Taur et al. “A New “Shift and Ratio” Method for MOSFET Channel-Length Extraction,” IEEE Elect. Div. Lett, EDL-13(5), p. 267, 1992 (referred to hereinafter as Reference (1)) where [S&R] denotes a solution obtained by the S&R method. The difference results from the fact that the technique disclosed in Reference (1) neglects the rate of change DL′ in the channel length reduction and the rate of change Rsd′ in the series resistance with respect to the changes in the gate overdrive Vgt when the Lm coordinate value DL* [S&R] is derived. Without such neglect, the result given in Expression (12) is obtained.

[0124] If the mask channel length LmSh of the short transistor Sh is sufficiently small relative to the mask channel length LmLo of the long transistor Lo, the Lm coordinate value DL*[S&R] of the hypothetical point determined by the S&R method asymptotically approaches the Lm coordinate value DL* determined by the KY method. However, there are two differences between the KY method and the S&R method, which allow the KY method to provide a more consistent result than does the S&R method. One of the differences is a difference in method of determining the difference δ0 in threshold voltage Vth between the two transistors. The S&R method assumes that, when the gate overdrive Vgt is small, the Lm coordinate values DL*[S&R] of the hypothetical points have no gate overdrive dependence (Vgt-dependence). It is because the Lm coordinate values DL*(Vgt) of the hypothetical points have a stationary point at or near Vgt=0.7 that the S&R method provides a suitable result in spite of the Vgt-dependence of the Lm coordinate values DL*[S&R]. The second difference is a difference in interpretation of the channel length reduction DL. In the KY method, the extracted Lm coordinate value DL* of the hypothetical point near Vgt=0 is defined as the true channel length reduction DL. The extractable well-defined amount in the resistance-based method is only the channel length reduction DL at Vgt=0.

[0125] The function F may be determined using any one of Expressions (20) to (22) in place of Expression (16) used in the first preferred embodiment. 16$\begin{array}{cc}F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{f^2\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·d{L}^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)& \left(20\right)\\ F\left(\delta ,V_{\mathrm{gtLo}}\right)=R^{*}-\frac{f\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}·R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)-R_{\mathrm{sd}}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)& \left(21\right)\\ F\left(\delta ,V_{\mathrm{gtLo}}\right)=\frac{R^{*\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}{f^{\prime }\left(\delta ,V_{\mathrm{gtLo}}\right)}+D{L}^{*}\left(\delta ,V_{\mathrm{gtLo}}\right)& \left(22\right)\end{array}$

[0126] The parameter R* in Expressions (21) and (22) denotes the value of an Rtot-intercept provided by the extrapolation from the Rtot−Lm characteristics. The use of the Y-intercept R* or the X-intercept dL* provided at X=0 or Y=0 by the extrapolation from the Rtot−Lm characteristic curve (line) drawn in a graph showing the relationship between the mask channel length Lm on the X-axis and the total drain-to-source resistance Rtot on the Y-axis may eliminate the need to differentiate the coordinates (DL*, Rsd*) of the hypothetical points. There is no difference in accuracy if any one of Expressions (16), and (20) to (22) is used, but Rsd* must be calculated if Expressions (20) and (21) are used. Thus, Expression (16) or (22) is preferably used.

[0127] Although the shift amount δ is determined by the minimum value of the standard deviation of the function F in the first preferred embodiment, the shift amount δ may be determined by the average value of the function F which is close to zero or by the minimum value of the sum of squares ΣF2 of the function F. However, the final result determined by these determination methods, unlike the method using the minimum value of the standard deviation, sometimes contains an error resulting from an offset of the value of the function F due to calculation errors.

[0128] Further, although the channel length reduction DL is determined using the stationary point in the first preferred embodiment, the Lm coordinate value DL* of a hypothetical point at which the gate overdrive Vgt has a predetermined value close to zero may be defined as the channel length reduction DL For example, the Lm coordinate value DL* of a hypothetical point at which the gate overdrive Vgt is 0.3 V is defined as the channel length reduction DL

[0129] In the first preferred embodiment, the channel length reduction DL is determined by the Lm coordinate value DL* of the hypothetical point at the stationary point. However, the average value of DL* in a predetermined range of the gate overdrive Vgt may be defined as the channel length reduction DL. For example, the average value of DL* in a range of the gate overdrive Vgt which satisfies 0.5≦Vgt≦1.0 is defined as the channel length reduction DL.

[0130] Further, although the channel length reduction DL is determined by the Lm coordinate value DL* of the hypothetical point at the stationary point in the first preferred embodiment, the maximum value of DL* may be defined as the channel length reduction DL. When the channel length reduction DL is determined by other methods, effects similar to those of the first preferred embodiment are provided.

[0131] Furthermore, although δRtotSh/δRtotLo is used in Expression (9) in the first preferred embodiment to determine the Lm coordinate values DL* of the hypothetical points, RtOtSh′/RtotLo′ may be used in place of δRtotSh/δRtotLo. That is, the calculation of the rate of change in the total drain-to-source resistance Rtot of the long transistor Lo and the short transistor Sh with high accuracy using a high-order approximate formula allows the extraction of the channel length reduction DL with high accuracy. For example, when a curve is drawn through points y−2, y−1, y0, y1, y2 and y3 equally spaced at intervals h as shown in FIG. 8, the slope of the curve at the point y0 may be given by the high-order approximate formula 17$\begin{array}{cc}{y}_0^{\prime }=\frac{1}{12h}\left(y_{-2}-8y_{-1}+8y_1-y_2\right)& \left(23\right)\end{array}$

[0132] The method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment enables the evaluation with higher accuracy than the conventional methods . Accordingly, the increase in the accuracy by the use of RtotSh′/RtotLo′ is reflected in the evaluation result more sufficiently than that of the background art.

[0133] A device for evaluating a characteristic of an insulated gate transistor according to the first preferred embodiment will now be described with reference to FIG. 9. The insulated gate transistor characteristic evaluation device 1 is connected to a measuring device 3 for measuring an object 2 to be measured. An example of the object 2 to be measured includes an integrated circuit with the long and short transistors Lo and Sh incorporated therein. For instance, an integrated circuit drawn from a lot which has been subjected to the fabrication steps is set into the measuring device 3 and then measured therein. The measuring device 3 is controlled by a control portion 4 in the characteristic evaluation device 1. An input portion 5 provides control information to the control portion 4, and comprises a keyboard, a mouse, and the like. Measurement data from the measuring device 3 and the control information are inputted from the control portion 4 to a calculation portion 6. The calculation portion 6 extracts the effective channel length Leff and the series resistance Rsd, based on the data inputted from the input portion 5. An output portion 7 outputs the extracted effective channel length Leff, the extracted series resistance Rsd, and the control information used during the extraction. The control information outputted from the output portion 7 is provided from the control portion 4 and the calculation portion 5.

[0134] The calculation portion 6 comprises a threshold voltage and hypothetical shift amount determination portion 11 for determining the threshold voltages VthLo and VthSh and hypothetical shift amounts δ; an extraction portion 12 for extracting the coordinates (DL*, Rsd*) of points of intersection which are the coordinates of the hypothetical points, and the slopes f of a characteristic curve at the points of intersection; a true shift amount determination portion 13 for determining the true shift amount δ0; and a channel length reduction determination portion 14 for determining the channel length reduction DL, the effective channel length Leff, and the series resistance Rsd. The coordinates of the points of intersection are used herein as the coordinates of the hypothetical points at which changes in the total drain-to-source resistance Rtot are estimated to be approximately zero if the gate overdrive Vgt is slightly changed based on the Lm−Rtot characteristic curve. However, the coordinates of the points of intersection may be determined by other than the method of determining the points of intersection. Otherwise, the coordinates of other points may be used as the coordinates of the hypothetical points as above described. The input portion 5 inputs to the threshold voltage and hypothetical shift amount determination portion lithe value of the variable K for determining the upper limit δsup and the lower limit δinf of the range over which the hypothetical shift amount δ is changed, the range of the region Ω of the gate overdrive Vgt to be measured, and the amount of change Ω in the hypothetical shift amount δ. The control portion 4 provides the measurement data about the source-drain current Ids and the gate-source voltage Vgs to the threshold voltage and hypothetical shift amount determination portion 11. Upon receipt of these data, the threshold voltage and hypothetical shift amount determination portion 11 provides to the extraction portion 12 the threshold voltage VthLo of the long transistor Lo and the hypothetical shift amount δ indicative of the difference between the threshold voltage VthLo of the long transistor Lo and the threshold voltage VthSh of the short transistor Sh. Using the mask channel length Lm from the input portion 5 and the measurement data about the source-drain current Ids and the gate-source voltage Vgs from the control portion 4, the extraction portion 12 extracts the rates of change dDL*/dVgt and dRsd*/dVgt in the coordinates (DL*, Rsd*) of the point of intersection and the slope f of the characteristic curve in the region Ω for each shift amount δ. Using the rate of change dDL*/dVgt in the Lm coordinate of the point of intersection, the rate of change dRsd*/dVgt in the Rtot coordinate of the point of intersection, and the slope f of the characteristic curve which are extracted by the extraction portion 12, the true shift amount determination portion 13 determines the hypothetical shift amount δ0 which minimizes the standard deviation of the function F given by one of Expressions (16), and (20) to (22) in the region Ω. After the true shift amount δ0 is determined, the extraction portion 12 outputs the true shift amount δ0, and the 1, coordinate DL* of a point of intersection, the total drain-to-source resistance Rtot and the slope f of the characteristic curve which are associated with the true shift amount δ0 to the channel length reduction determination portion 14. The channel length reduction determination portion 14 determines the channel length reduction DL, based on the Lm coordinate value DL* of the hypothetical point at the stationary point, and then performs the calculations given by Expressions (2) and (7) to determine the effective channel length Leff and the series resistance Rsd. The output portion 7 outputs the channel length reduction DL, the effective channel length Leff and the series resistance Rsd which are determined by the channel length reduction determination portion 14, the coordinates (DL*, Rtot) of the points of intersection and the slopes f of the characteristic curve at the points of intersection which are extracted by the extraction portion 12, and the true shift amount δ0 determined by the true shift amount determination portion 13.

[0135] The above described arrangement provides the insulated gate transistor characteristic evaluation device which extracts the effective channel length Leff and the series resistance Rsd with increased accuracy.

[0136] It is needless to say that the insulated gate transistor characteristic evaluation described in the first preferred embodiment may be implemented using a computer in such a manner that the computer reads a characteristic evaluation program 30 for causing the computer to evaluate the insulated gate transistor according to the procedure shown in FIG. 3 which is described in the first preferred embodiment from a recording medium which stores the characteristic evaluation program 30 therein as shown in FIG. 10. The characteristic evaluation program 30 may be executed to extract measurement data 33 including the data pertaining to the effective channel length Leff and the series resistance Rsd, for example, based on measurement data 31 from the measuring device 3 of FIG. 9 and control information 32 from the input portion 5 as described in the first preferred embodiment.

[0137] A method of fabricating an insulated gate transistor according to the first preferred embodiment will be described hereinafter with reference to FIG. 11. First, the short transistor Sh serving as a target and the long transistor Lo serving as a reference are prototyped (step ST50). Then, the electrical characteristics of the short transistor Sh and the long transistor Lo are measured (step ST51). In this step of measurement are measured the Ids−Vds characteristic, an off leak current Ioff, and a drain current Idmax of each of the transistors. The off leak current off is a source-drain current flowing when Vds=VDD and Vgs=Vbs=0 V, for example. The current Idmax is a source-drain current flowing when Vds=Vgs=VDD and Vbs=0 V. The reference character VDD designates a power supply voltage herein.

[0138] Next, the threshold voltage VthSh and the effective channel length LeffSh of the short transistor Sh are extracted from the Ids−Vds characteristic and the like by using the method of evaluating the characteristic of the insulated gate transistor described in the first preferred embodiment. Then, whether or not the threshold voltage VthSh, the effective channel length IeffSh and the currents Idmax and Ioff of the short transistor Sh satisfy specifications is judged (step ST53). If the specifications are not satisfied, the flow returns to the step ST50, and prototypes are again produced using a new mask.

[0139] The method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment may determine the threshold voltage based on the known mask channel length and the electrical characteristics with high accuracy, thereby to reduce the time required for fabrication as compared with the method which involves the observation of the cross-section of the insulated gate transistor. Additionally, the method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment may accurately determine the range of the effective channel length Leff for the desired mask channel length Lm in accordance with the gate overdrive Vgt. Further, the method of evaluating the characteristic of the insulated gate transistor according to the first preferred embodiment may accurately determine the range of changes in the threshold voltage Vth in corresponding relation to the range of changes in the effective channel length Leff at the same time (See FIG. 13), thereby facilitating quality control for the threshold voltage Vth in the fabrication steps.

[0140] Second Preferred Embodiment

[0141] The outline of the method of evaluating the characteristic of the insulated gate transistor according to a second preferred embodiment of the present invention will now be described with reference to FIG. 14. FIG. 14 is a graph showing changes in the Lm coordinate value DL* versus the gate overdrive Vgt determined by the method of evaluating the characteristic of the insulated gate transistor of the first preferred embodiment. The graph of FIG. 14 depicts the changes in the Lm coordinate value DL* for five short transistors Sh having different mask channel length LmSh when the true threshold voltage is used. The mask channel length LmLo of the long transistor Lo serving as a reference for extraction of the Lm coordinate value DL* is commonly 21.6 μm. It will be understood from the comparison between the graphs of FIGS. 14 and 16 that, when the true threshold voltage is used, the changes in the Lm coordinate value DL* versus the gate overdrive Vgt are substantially similar independently of the mask channel length LmSh of the short transistor Sh. Thus, if the value of the gate overdrive Vgt which conforms to the characteristic curves of this graph, for example, in a range from 0.3 to 1.2 V is found, the true threshold voltage of the short transistors Sh may be extracted. It should be noted that the first and second insulated gate transistors, the first and second overdrives and the first and second estimated values of the second preferred embodiment are similar in definition to those of the first preferred embodiment.

[0142] An example of the method of evaluating the characteristic of the insulated gate transistor according to the second preferred embodiment of the present invention is described below with reference to FIGS. 15 and 16. In the method shown in FIG. 15, the characteristic curves shown in FIG. 14 are extracted by using the small standard deviation of the characteristic curves in the range from 0.3 to 1.2 V, for example. The method of evaluating the characteristic of the insulated gate transistor of the second preferred embodiment determines the true threshold voltage of the short transistor by utilizing the dependence of the Lm coordinate value DL* upon the gate overdrive Vgt. Therefore, the second preferred embodiment is similar to the first preferred embodiment in the procedure of the determination of the true threshold voltage. The method of evaluating the characteristic of the insulated gate transistor of the second preferred embodiment differs from that of the first preferred embodiment in the step ST1 of the procedure shown in FIG. 1 but is similar thereto in the step ST2.

[0143] FIG. 15 shows an example of the procedure of the extraction of the effective channel length Leff in the step ST1 according to the second preferred embodiment. The procedure of the extraction of the effective channel length Leff in the method of evaluating the characteristic of the insulated gate transistor of the second preferred embodiment differs from that of the first preferred embodiment in that the steps ST1.12, the step ST1.13 and the steps ST1.14 to ST1.16 of FIG. 15 are used in place of the steps ST1.6, the step ST1.7, and the steps ST1.9 to ST1.11 of FIG. 3, respectively.

[0144] The graph of FIG. 16 plots the extracted L, coordinate values DL* of hypothetical points determined in the step ST1.12 of FIG. 15 on the Y-axis versus the gate overdrive Vgt on the X-axis. The Lm coordinate value DL* of the hypothetical point and the gate overdrive Vgt also outside the region Ω are plotted in FIG. 16 for ease of illustration of the relationship between the Lm coordinate value DL* of the hypothetical point and the gate overdrive Vgt. In the step ST1.13, the average value of the Lm coordinate value DL* of the hypothetical point and the standard deviation σ[DL*] are calculated for the shift amount δ.

[0145] If it is judged that the calculation in the step ST1.13 for the shift amount 6 in the predetermined range from δinf to δsup has been completed, (step ST1.4), the shift amount δ0 which gives the true channel length reduction DL is estimated in the step ST1.14. The shift amount δ0 estimated herein is the shift amount δ0 which minimizes the standard deviation σ[DL*]. In the step ST1.15, the true channel length reduction DL is provided by the average value of the Lm coordinate value DL* of the hypothetical point for the shift amount δ0. In the step ST1.16, the effective channel length Leff is determined by the difference between the mask channel length Lm and the true channel length reduction DL, and the series resistance Rsd is determined by Expression (7).

[0146] The device for evaluating the characteristic of the insulated gate transistor according to the second preferred embodiment will be described below with reference to FIG. 17. An insulated gate transistor characteristic evaluation device 1A, similar to the insulated gate transistor characteristic evaluation device 1 of the first preferred embodiment, is connected to the measuring device 3 for measuring the object 2 to be measured. The elements of the insulated gate transistor characteristic evaluation device 1A which are designated by the reference characters identical with those of the characteristic evaluation device 1 of FIG. 9 are elements corresponding to those of FIG. 9. More specifically, the characteristic evaluation device 1A is similar to the characteristic evaluation device 1 except an extraction portion 12A, a true shift amount determination portion 13A and a channel length reduction determination portion 14A which are included in a calculation portion 6A. The extraction portion 12A of the characteristic evaluation device 1A determines the coordinates (DL*, Rsd*) of points of intersection, with the gate overdrive Vgt changed in the region Ω. The true shift amount determination portion 13A finds the hypothetical shift amount δ0 which minimizes the standard deviation a [DL*] of the Lm coordinate value DL* of a point of intersection in this region Ω to determine the true shift amount δ0. The extraction portion 12A outputs the true shift amount δ0 and its associated Lm coordinate value DL* of the point of intersection to the channel length reduction determination portion 14A. The channel length reduction determination portion 14A determines the channel length reduction DL, based on the average of the Lm coordinate value DL* of the hypothetical points extending over the region Ω for the true shift amount δ0.

[0147] The method of fabricating the insulated gate transistor according to the second preferred embodiment may be provided by replacing the KY method in the step ST52 of FIG. 11 with the method of evaluating the characteristic of the insulated gate transistor of the second preferred embodiment, thereby providing effects similar to those of the first preferred embodiment.

[0148] In the extraction of the channel length reduction DL according to the first and second preferred embodiments, the true channel length reduction DL of the short transistor Sh may be determined with little influence of the difference between the mask channel length LmLo and a gate finished length LgLo of the long transistor Lo exerted upon the determination of the Lm coordinate value DL* of the hypothetical points, if the mask channel length LmSh of the short transistor Sh is sufficiently small relative to the mask channel length LmLo of the long transistor Lo (LmSh<<LmLo). For instance, the evaluation of device/circuit performance with a pattern width of not greater than 0.35 μm requires the extraction of the channel length reduction DL of each transistor. For the extraction of the channel length reduction DL for each transistor, two transistors are used: one short transistor Sh and one long transistor Lo serving as a reference. In such extraction of the channel length reduction DL, an error occurs which results from the difference between a gate finished length Lg and the mask channel length Lm depending on transistors, which will be described below. The Lm coordinate value DL* of the hypothetical point when the mask channel length Lm is used is given by 18$\begin{array}{cc}{\mathrm{DL}}^{*}\left(V_{\mathrm{gt}}\right)=\left(L_{\mathrm{mSh}}-\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}·L_{\mathrm{mLo}}\right)·{\left(1-\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}\right)}^{-1}& \left(24\right)\end{array}$

[0149] The Lg coordinate of a point of intersection in a gate finished length versus total drain-to-source resistance plane (Lg−Rtot plane) is designated by DL* *. 19$\begin{array}{cc}{\mathrm{DL}}^{**}\left(V_{\mathrm{gt}}\right)=\left(L_{\mathrm{gSh}}-\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}·L_{\mathrm{gLo}}\right)·{\left(1-\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}\right)}^{-1}& \left(25\right)\end{array}$

[0150] The difference between the gate finished length LgLo and the mask channel length LmLo of the long transistor Lo is designated by ΔLLo, and the difference between the gate finished length LgSh and the mask channel length LmSh of the short transistor Sh is designated by ΔLSh. Then, the relationships expressed by

L gLo =L mLo +ΔL Lo   (26)

L gSh =L mSh +ΔL Sh   (27)

[0151] hold. Using Expression (27) based on Expression (24), the difference between the Lm coordinate value DL* of the point of intersection and the Lg coordinate value DL* * of the point of intersection is 20$\begin{array}{cc}\begin{array}{c}{\mathrm{DL}}^{*}-{\mathrm{DL}}^{**}=-\Delta L_{\mathrm{Sh}}+\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}·{\left(1-\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}\right)}^{-1}·\Delta L\\ \approx -\Delta L_{\mathrm{Sh}}+\frac{R_{\mathrm{totSh}}^{\prime }}{R_{\mathrm{totLo}}^{\prime }}·\Delta L\left(\mathrm{for}{L}_{\mathrm{mSh}}⪡L_{\mathrm{mLo}}\right)\\ \approx -\Delta L_{\mathrm{Sh}}+\frac{L_{\mathrm{effSh}}}{L_{\mathrm{effLo}}}·\Delta L\end{array}& \left(28\right)\end{array}$

[0152] where ΔL is defined as

ΔL≡ΔL Lo −ΔL Sh   (29)

[0153] Expressions (27) and (28) show that the effective channel length Leff of the short transistor Sh is extracted when the relationship LmSh<<LmLo holds. The second term of the last expression (rightmost side) of Expression (28) represents an error. 21$\begin{array}{cc}\frac{L_{\mathrm{effSh}}}{L_{\mathrm{effLo}}}·\&LeftBracketingBar;\Delta L\&RightBracketingBar;<r·L_{\mathrm{effSh}}& \left(30\right)\end{array}$

[0154] where r is a relative error. Assuming that LLo≈LmLo, Expression (30) is transformed into 22$\begin{array}{cc}{L}_{\mathrm{mL}o}>\frac{\&LeftBracketingBar;\Delta L\&RightBracketingBar;}{r}& \left(31\right)\end{array}$

[0155] Expression (31) limits the size of the long transistor Lo. For example, when ΔL=0.1 μm and r=0.02, the mask channel length LmLo of the long transistor Lo is required to be greater than 5 μm for accurate extraction of the effective channel length LeffSh of the short transistor Sh.

[0156] The influence of unequal channel widths due to field isolation variations will now be contemplated. The total drain-to-source resistance Rtot is expressed by 23$\begin{array}{cc}{R}_{\mathrm{totSh}}=\frac{L_{\mathrm{effSh}}}{W_{\mathrm{effSh}}}·g+R_{\mathrm{sd}}& \left(32\right)\end{array}$

[0157] where g is a sheet resistance of a channel.

[0158] Using ΔW (=WeffSh−WeffLo) as the difference in channel width W between the short transistor Sh and the long transistor Lo, Expression (32) is transformed into 24$\begin{array}{cc}\begin{array}{c}{R}_{\mathrm{totSh}}=\frac{L_{\mathrm{effSh}}}{W_{\mathrm{effLo}}+\Delta W}·g+R_{\mathrm{sd}}\\ \approx \frac{L_{\mathrm{effSh}}·\left(1-\frac{\Delta W}{W_{\mathrm{effLo}}}\right)}{W_{\mathrm{effLo}}}·g+R_{\mathrm{sd}}\end{array}& \left(33\right)\end{array}$

[0159] Expression (33) shows that the effective channel length LeffSh appears to be multiplied by (1−ΔW/WeffLo) if it is assumed that the sheet resistance g is not dependent upon the effective channel width Weff. For an error Δr, 25$\begin{array}{cc}{L}_{\mathrm{effSh}}·\frac{\&LeftBracketingBar;\Delta W\&RightBracketingBar;}{W_{\mathrm{effLo}}}<r·L_{\mathrm{effSh}}& \left(34\right)\end{array}$

[0160] is given where r is the relative error.

[0161] Assuming that the effective channel width WeffLo is approximately equal to the mask channel width WmLo, Expression (34) is transformed into 26$\begin{array}{cc}{W}_{\mathrm{mL}o}>\frac{\&LeftBracketingBar;\Delta W\&RightBracketingBar;}{r}& \left(35\right)\end{array}$

[0162] Expression (35) limits the mask channel width WmLo of the long transistor Lo used for the extraction. For example, when the effective channel width difference ΔW between the two transistors Lo and Sh is 0.1 μm and the relative error r is 0.02, the mask channel length LmLo of the long transistor Lo is required to be greater than 5 μm for accurate extraction of the effective channel length LeffSh of the short transistor Sh.

[0163] The influence of the difference in series resistance Rsd between transistors used for the extraction will be contemplated. Assuming that the dependence of the series resistance Rsd upon the gate overdrive Vgt is negligible, an error ΔRsdSh is expressed by 27$\begin{array}{cc}\begin{array}{c}\Delta R_{\mathrm{sdSh}}\equiv R_{\mathrm{sd}}^{*}-R_{\mathrm{sd}}^{**}\approx \frac{L_{\mathrm{effSh}}}{L_{\mathrm{effLo}}-L_{\mathrm{effSh}}}\\ \approx \frac{L_{\mathrm{effSh}}}{L_{\mathrm{effLo}}}·\Delta R_{\mathrm{sd}}\le \frac{L_{\mathrm{mSh}}}{L_{\mathrm{mL}o}}·\Delta R_{\mathrm{sd}}\end{array}& \left(36\right)\end{array}$

[0164] where A Rsd is given by

ΔR sd =R sdSh −R sdLo   (37)

[0165] Rsd*−Rsd** is defined in FIG. 34.

[0166] Using the relative error r, 28$\begin{array}{cc}\frac{L_{\mathrm{mSh}}}{L_{\mathrm{mL}o}}·\&LeftBracketingBar;\Delta R_{\mathrm{sd}}\&RightBracketingBar;<r·R_{\mathrm{sdSh}}& \left(38\right)\end{array}$

[0167] is given. Expression (38) is transformed into 29$\begin{array}{cc}{L}_{\mathrm{mL}o}>\frac{1}{r}·\frac{\&LeftBracketingBar;\Delta R_{\mathrm{sd}}\&RightBracketingBar;}{R_{\mathrm{sdSh}}}·L_{\mathrm{mSh}}& \left(39\right)\end{array}$

[0168] Expression (39) limits the size of the long transistor Lo. For example, when |ΔRsd|/RsdSh=1, r=0.05 and LmSh=0.2 μm, the mask channel length LmLo of the long transistor Lo is required to be greater than 4 μm for accurate extraction of the effective channel length LeffSh of the short transistor Sh.

[0169] The influence of a saturation drift velocity upon the extraction of the channel length reduction DL will be contemplated. The drain current may be estimated as 30$\begin{array}{cc}{I}_{\mathrm{ds}}=\frac{\mu ·C_{\mathrm{OX}}·W_{\mathrm{eff}}}{L_{\mathrm{eff}}}·{\left(1+\frac{\mathrm{U1}·V_{\mathrm{ds}}}{L_{\mathrm{eff}}}\right)}^{-1}·\left(V_g-V_{\mathrm{ih}}-\frac{V_{\mathrm{ds}}}{2}\right)& \left(40\right)\end{array}$

[0170] where μ is a mobility, Cox is an oxide capacitance, and U1=μ/(2·Vsat) where Vsat is a saturation velocity. The term (1+U1·Vds/Leff)−1 expresses the effect of the saturation drift velocity. Assuming that the channel resistance per unit channel is not dependent upon the effective channel length Leff, the effective channel length LeffSh of the short transistor Sh effectively appears to be multiplied by (1+U1·Vds/Leff). As a result, the extracted channel length reduction DL is smaller by U1·Vds.

[0171] The saturation drift velocity limits the source-drain voltage Vds among the measurement bias conditions of the source-drain current versus source-drain voltage characteristic (Ids−Vds characteristic). FIGS. 18 and 19 show the dependence (Vds-dependence) of the extracted values of the channel length reduction DL upon the source-drain voltage Vds for 0.18 μm NMOS and PMOS transistors, respectively. The S&I method shown in FIGS. 18 and 19 is the method of evaluating the characteristic of the insulated gate transistor of the second preferred embodiment. For the PMOS transistor, U1 indicative of the slope of the characteristic line drawn in the graph is not greater than about 0.03 μm/V. Thus, when the source-drain voltage Vds is not greater than 0.1 V, the extracted values of the channel length reduction DL have a difference of only not greater than about 0.003. For the NMOS transistor, on the other hand, the slope U1 is about 0.15 μm/V. Thus, when the source-drain voltage Vds is 0.1 V, the extracted value of the channel length reduction is about 0.015 μm smaller. The value of the true effective channel length Leff is provided by the effective channel length Leff at the source-drain voltage Vds=0 by the extrapolation from the line indicative of the effective channel length versus source-drain voltage characteristic, for example, by using the value of the effective channel length for each drain voltage inputted from the calculation portion 6 shown in FIG. 9 to the output portion 7. However, the extracted value from data which indicates that the source-drain voltage Vds is 0.05 V is used for monitoring the effective channel length Leff in the fabrication steps. When the extrapolated value is used, the monitoring must be performed in consideration for the requirement of data which are at least twice greater and the variations which might be greater than actual variations.

[0172] The efficient and accurate extraction of a channel length reduction DLT defined by the difference between the gate finished length Lg and the effective channel length Leff is important for correction of the gate finished length Lg in parameter extraction associated with logic circuit simulation, for example, SPICE parameter extraction. For instance, in the SPICE parameter extraction, an electrical correction is made to the gate finished length Lg of transistors having a mask channel length Lm of not greater than about 0.5 μm. The non-linear relationship between the mask channel length Lm and the gate finished length Lg is not permitted to be neglected for transistors having a mask channel length Lm of not greater than 0.35 μm. Therefore, it is necessary to know the gate finished length Lg of each of the transistors. However, it is difficult to measure the gate finished length Lg of all transistors under an electron microscope. Then, the KY method of the first preferred embodiment or the S&I method of the second preferred embodiment may be used to make the electrical correction to the gate finished length Lg in a manner to be described below.

[0173] First, the gate finished length Lg of at least one transistor is measured under an electron microscope by using a conventional technique. The measured transistor serves as a reference. Next, the difference DLT between the gate finished length Lg and the effective channel length Leff of the at least one transistor serving as the reference is extracted by the KY method or the S&I method. Then, the effective channel length Leff of a transistor with the gate finished length Lg having not yet been measured under the electron microscope is extracted, and the gate finished length Lg of the transistor is given by the sum of the effective channel length Leff and the channel length reduction DLT. An interpolated value of the channel length reduction DLT is used if two or more transistors which differ in mask channel length Lm are used as a reference. It is assumed herein that the variations in the channel length reduction DLT are negligible relative to the variations in the gate finished length Lg. FIG. 20 shows the result of the correction of the gate finished length Lg of a PMOS transistor having a mask channel length Lm of 0.18 μm by using the KY method and the S&I method. FIGS. 21 to 23 show the Ids−Vds characteristic for measured values and simulation results using the values extracted by the KY method when the mask channel width Wm is 21.6 μm and the mask channel length Lm is 0.16 μm, 0.18 μm and 0.20 μm, respectively. The measured values and the simulation results shown in FIGS. 21 to 23 coincide with each other with such accuracy that an error is not greater than 2%.

[0174] While the invention has been described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is understood that numerous other modifications and variations can be devised without departing from the scope of the invention.

Claims

1. An insulated gate transistor characteristic evaluation device using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, said insulated gate transistor characteristic evaluation device for evaluating a characteristic of said second insulated gate transistor using a characteristic of said first insulated gate transistor as a reference, said insulated gate transistor characteristic evaluation device comprising: threshold voltage estimation means for extracting a threshold voltage for said first insulated gate transistor to estimate a threshold voltage for said second insulated gate transistor to define the estimated value as a first estimated value; extraction means for extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when first and second gate overdrives are slightly changed, based on a characteristic curve drawn in an X-Y plane with said mask channel length measured on an X-axis and said total drain-to-source resistance measured on a Y-axis, said characteristic curve indicating the relationship between said mask channel length of said first and second insulated gate transistors and said total drain-to-source resistance, the value of said mask channel length and the value of said total drain-to-source resistance at said hypothetical point being defined as second and third estimated values, respectively, said extraction means also extracting the slope of said characteristic curve at said hypothetical points to define the value of the slope as a fourth estimated value, said first gate overdrive being defined as the difference between the gate voltage of said first insulated gate transistor and the extracted threshold voltage of said first insulated gate transistor, said second gate overdrive being defined as the difference between the gate voltage of said first and second insulated gate transistors and said first estimated value; threshold voltage determination means for determining optimum second to fourth estimated values that are respective ones of said second to fourth estimated values which satisfy that the amount of change in said third estimated value equals the product of the amount of change in said second estimated value and said fourth estimated value when said first and second gate overdrives are slightly changed, to determine an optimum first estimated value associated with said optimum second to fourth estimated values, thereby to determine a true threshold voltage of said second insulated gate transistor based on said optimum first estimated value; and channel length reduction determination means for determining the difference between said mask channel length and an effective channel length, and a series resistance, based on said true threshold voltage.

2. The insulated gate transistor characteristic evaluation device according to claim 1, wherein said extraction means approximates said characteristic curve using a first line drawn in said X-Y plane and passing through first and second points, said first point being given for said first insulated gate transistor when said first gate overdrive has a first value, said second point being given for said second insulated gate transistor when said second gate overdrive has said first value.

3. The insulated gate transistor characteristic evaluation device according to claim 2, wherein said threshold voltage determination means determines said optimum second to fourth estimated values which satisfy that the amount of change in said third estimated value equals the product of the amount of change in said second estimated value and said fourth estimated value when said first and second gate overdrives are slightly changed, using the relationship expressed by 31F⁡(δ,VgtLo)= ⁢dL*⁡(δ,VgtLo)+f⁡(δ,VgtLo)f′⁡(δ,VgtLo)· ⁢dL*′⁡(δ,VgtLo)-DL*⁡(δ,VgtLo)where d is the difference between the first estimated value of the threshold voltage of said second insulated gate transistor and the threshold voltage of said first insulated gate transistor, VgtLo is said first gate overdrive, dL* is an X-intercept provided by extrapolation from said characteristic curve, f is said slope of said characteristic curve at said hypothetical point, DL* is the X coordinate of said hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

4. The insulated gate transistor characteristic evaluation device according to claim 2, wherein said threshold voltage determination means determines said optimum second to fourth estimated values which satisfy that the amount of change in said third estimated value equals the product of the amount of change in said second estimated value and said fourth estimated value when said first and second gate overdrives are slightly changed, using the relationship expressed by 32F⁡(δ,VgtLo)=f2⁡(δ,VgtLo)f′⁡(δ,VgtLo)·d⁢ ⁢L*′⁡(δ,VgtLo)-Rsd*⁡(δ,VgtLo)where δ is the difference between the first estimated value of the threshold voltage of said second insulated gate transistor and the threshold voltage of said first insulated gate transistor, VgtLo , is said first gate overdrive, dL* is an X-intercept provided by extrapolation from said characteristic curve, f is said slope of said characteristic curve at said hypothetical point, Rsd* is the Y coordinate of said hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

5. The insulated gate transistor characteristic evaluation device according to claim 2, wherein said threshold voltage determination means determines said optimum second to fourth estimated values which satisfy that the amount of change in said third estimated value equals the product of the amount of change in said second estimated value and said fourth estimated value when said first and second gate overdrives are slightly changed, using the relationship expressed by 33F⁡(δ,VgtLo)= ⁢R*⁡(δ,VgtLo)-f⁡(δ,VgtLo)f′⁡(δ,VgtLo)· ⁢R*′⁡(δ,VgtLo)-Rsd*⁡(δ,VgtLo)where δ is the difference between the first estimated value of the threshold voltage of said second insulated gate transistor and the threshold voltage of said first insulated gate transistor, VgtLo is said first gate overdrive, R* is a Y-intercept provided by extrapolation from said characteristic curve, f is said slope of said characteristic curve at said hypothetical point, Rsd* is the Y coordinate of said hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

6. The insulated gate transistor characteristic evaluation device according to claim 2, wherein said threshold voltage determination means determines said optimum second to fourth estimated values which satisfy that the amount of change in said third estimated value equals the product of the amount of change in said second estimated value and said fourth estimated value when said first and second gate overdrives are slightly changed, using the relationship expressed by 34F⁡(δ,VgtLo)=R*′⁡(δ,VgtLo)f′⁡(δ,VgtLo)+DL*⁡(δ,VgtLo)where δ is the difference between the first estimated value of the threshold voltage of said second insulated gate transistor and the threshold voltage of said first insulated gate transistor, VgtLo is said first gate overdrive, R* is a Y-intercept provided by extrapolation from said characteristic curve, f is said slope of said characteristic curve at said hypothetical point, DL* is the X coordinate of said hypothetical point, and the prime denotes a first derivative with respect to VgtLo.

7. An insulated gate transistor characteristic evaluation device using at least two insulated gate transistors differing from each other only in mask channel length and including a first insulated gate transistor having a longer channel length and a second insulated gate transistor having a shorter channel length, said insulated gate transistor characteristic evaluation device for evaluating a characteristic of said second insulated gate transistor using a characteristic of said first insulated gate transistor as a reference, said insulated gate transistor characteristic evaluation device comprising: threshold voltage estimation means for extracting a threshold voltage for said first insulated gate transistor to estimate a threshold voltage for said second insulated gate transistor to define the estimated value as a first estimated value; extraction means for extracting a hypothetical point at which a change in a total drain-to-source resistance is estimated to be approximately zero when a first gate overdrive and a second gate overdrive are slightly changed, based on a characteristic curve drawn in an X-Y plane with said mask channel length measured on an X-axis and said total drain-to-source resistance measured on a Y-axis, said characteristic curve indicating the relationship between said mask channel length of said first and second insulated gate transistors and said total drain-to-source resistance, the values of said mask channel length at said hypothetical point being defined as a second estimated value, said first gate overdrive being defined as the difference between the gate voltage of said first insulated gate transistor and the extracted threshold voltage of said first insulated gate transistor, said second gate overdrive being defined as the difference between the gate voltage of said second insulated gate transistor and said first estimated value; threshold voltage determination means for determining a first estimated value by said second estimated value, said first estimated value satisfying that a characteristic curve indicating the relationship between said second gate overdrive measured on an X-axis and said second estimated values measured on a Y-axis has a predetermined configuration in a predetermined range of said second gate overdrive, to determine the determined first estimated value as a true threshold voltage of said second insulated gate transistor; and channel length reduction determination means for determining the difference between said mask channel length and an effective channel length, and a series resistance, based on said true threshold voltage.

8. The insulated gate transistor characteristic evaluation device according to claim 7, wherein said threshold voltage determination means determines a standard deviation of said second estimated value in said predetermined range to detect the characteristic curve having said predetermined configuration.

9. An insulated gate transistor characteristic evaluation device comprising: calculation means for extracting an effective channel length from each of at least two drain current versus gate voltage characteristics differing from each other in source-drain voltage, by using a resistance-based method; and output means for determining an effective channel length by extrapolation from the effective channel lengths extracted for different source-drain voltages.