Patent Grant
7285963
The present invention relates to measurement techniques. In particular, this invention directs itself to a technique for highly localized measurements of dielectric constants of thin films using near field microwave probes.
More in particular, the present invention is directed to non-contact, non-destructive, and non-invasive measurements of the dielectric constant of low K films which can be used on both porous and non-porous dielectrics. The concept of the present invention is based on a balanced two conductor transmission line resonator which provides confinement of a probing field within a sharply defined sampling volume of the material under study to yield a localized determination of the material's dielectric constant.
The present invention is also directed to a technique for quantitative measurements of a material's dielectric constant based on the probe calibration permitting the construction of a linear calibration curve that substantially increases the preciseness of the dielectric constant measurement.
Rapid advancements are projected over the next decade to new materials for use in the interconnects: from aluminum to copper to reduce the resistance of the metal wires, and from SiO2 to dielectrics with lower dielectric constant k, commonly known as ‘low-k’ materials, for reduction of delay times on interconnect wires and minimization of crosstalk between wires. As stated in Semiconductor Industry Association, International Technology Roadmap for Semiconductors, Austin, Tex.: International SEMATECH, 2003, “The introduction of new low-k dielectrics . . . provide[s] significant process integration challenges”, and “ . . . will greatly challenge metrology for on-chip interconnect development and manufacture”. In addition, “design of interconnect structures requires measurement of the high frequency dielectric constant of low-k materials. High frequency testing of interconnect structures must characterize the effects of clock harmonics, skin effects, and crosstalk”. In general, such methodology should be non-destructive, non-contaminating, and provide real time/rapid data collection and analysis. (J. Iacoponi, Presented at the Characterization and Metrology for ULSI Technology conference, Austin, Tex., are performed on simplified structures or monitor wafers and are often destructive.
Currently, the two techniques most commonly used for dielectric constant measurements on blanket wafers are the Hg-probe and MIS-capacitor (D. K. Schroder, Semiconductor Material and Device Characterization, John Wiley & Sons, New York (1998)). Although widely employed, the Hg-probe contaminates the wafer, requires daily recalibration, is difficult to align, and cannot be used on production wafers. MIS-cap is considered more accurate than the Hg-probe, however it requires electrode patterning (e.g. destructive) and cannot be used on product wafers. The Corona discharge and Kelvin probe technique (D. K. Schroder, Meas. Sci. Technol. 12, R16 (2001)) which has traditionally been used to measure gate dielectrics is now being employed for low-k interconnect dielectrics, however, it is limited to blanket monitor wafers and there is some concern that the charging of the film surface may cause damage.
Near-field scanning microwave microscopy has proven to be a promising methodology for highly localized measurements.
One of the main goals of the near-field scanning microwave microscopy is to quantitatively measure a material's dielectric constant with high sensitivity of lateral and/or depth selectivity (i.e. to determine the material's property over a small volume while ignoring the contribution of the volume's surrounding environment). This is particularly important in measurements on complex structures, such as semiconductor devices or composite materials, where, for example, the permittivity of one line or layer must be determined without having knowledge of the properties of the neighboring lines or underlying layers.
In order to perform highly localized quantitative measurements of a material's complex permittivity at microwave frequencies by means of near-field microwave microscopy the near-field probe requires calibration. All calibration procedures currently in use for near-field microwave microscopy employ some information about the actual tip geometry which would include, for example, the tip curvature radius, etc., and further requires knowledge of the absolute tip-to-sample separation.
If there is no radiation from the tip of the probe, the response of the electrical near-field probe depends on the fringe impedance of the tip Zt=1/iωCt, where Ct is the static capacitance of the tip of the probe. This capacitance depends on the physical geometry of the tip, the tip-to-sample separation d, and the sample's dielectric constant k (assuming the sample is uniform in contour). Thus, in order to extract the sample's dielectric constant k from the impedance of the tip Zt, the tip geometry and absolute tip-to-sample separation must be known to a high degree of accuracy.
However, accurate determination of these parameters is difficult and often impractical, especially for small tips of less than or on the order of a few microns in size which are of great importance for near-field microwave microscopy. Further, analytical solutions to the problem of interaction between a near-field tip and a sample exist only for the most simple tip geometries, such as a sphere or a flush end of a coaxial line.
It is therefore highly desirable to perform quantitative measurement of a material's dielectric constant which does not require knowledge of either the actual tip geometry or the absolute tip-to-sample separation.
Accurate and precise novel measurement approach with the use of near-field microwave probe is needed to obtain a material's dielectric constant.
It is therefore an object of the present invention to provide low-k dielectric methodology based on a scanning near-field microwave probe which can achieve spatial resolution at the sub-micron scale. The subject invention is directed to an apparatus and a method for highly accurate determination of the dielectric constant of a sample under study which employs a probe capable of sharply localized measurements.
Another object of the present invention is to provide a technique for quantitative measurements of material's dielectric constant with near-field microwave probes which is independent of the actual geometry of the probe's tip and the absolute tip-to-sample separation.
It is a further object of the present invention to provide a method and apparatus for quantitative measurement of thin films' dielectric constant with near-field microwave probes which employ an independent distance control mechanism for maintaining the tip of the probe at possibly unknown but nominally equal distance from the sample surface during both the calibration procedure and the actual measurement.
It is still an object of the present invention to provide a unique calibration technique which permits construction of a linear calibration curve thereby attaining simplicity and preciseness of the dielectric constant measurements.
It is also an object of the present invention to provide a novel non-destructive non-invasive microwave near-field scanning probe technique for non-contact measurements of the dielectric constant of low-k films which can be used on both porous and non-porous dielectrics forming either single-layered or multi-layered micro-structures.
The present invention represents a method of measurement of dielectric constant of a sample under study which includes the steps of:
The calibration samples include calibration samples having dielectric constant k>>1, a calibration sample with the dielectric constant equal to dielectric constant of the substrate of the sample under test, and a set of thin films of a thickness ranging around the thickness of the sample under study. Each of these thin films has a dielectric constant that is close to the dielectric constant of the film under study. The thin films may include, for example, SiO2 films, thermal oxide (TOX) films, Teflon, sapphire, MgO, or other calibration materials.
The calibration curve is created as a result of interpolating the calibration data points either by a standard interpolation method, or by fitting calibration data points to a second or higher order polynomial function, or using the analytical function describing behavior of the tip of the near field microwave probe.
Although, the calibration curve may be the curve having a positive or negative second derivative, it is preferable that the calibration curve behave substantially in a linear fashion.
In order to obtain a linear calibration curve, in the method of the present invention, a tip-sample separation D* is determined at which the calibration curve is linear. The probe resonant frequency shift of the sample under study is further measured at the tip-sample separation D* which is determined by the following steps:
The present invention provides a system for measurement of dielectric constant of a sample under study which includes:
The processor includes a calibration unit for constructing a calibration curve based on calibration data points acquired as a result of calibrating of the near field microwave probe for the plurality of the calibration samples. Particularly, the calibration unit constructs the calibration curve based on measurements of the resonance frequency shift vs. tip-sample separation for the plurality of calibration samples. The processor further fits the resonance frequency shift measured vs. tip-sample separation for the sample into the calibration curve to extract the dielectric constant of the sample.
The near field microwave probe includes a balanced two conductor transmission line resonator which includes at least a pair of conductors extending in spaced relationship therebetween and spaced apart by a dielectric media.
Preferably, the calibration unit determines a tip-sample separation D* at which the calibration curve is substantially a linear calibration curve. The system measures the probe resonant frequency shift for the sample under study at the determined tip-sample separation D*.
Separation between the probe and the sample under study, as well as the separation between the probe and the calibration samples may be controlled by a shear force distance control mechanism in which the motion of the probe tip is detected by an optical beam deflection technique for a piezo element or alternatively by a phase-or-amplitude-locked loop for a quartz tuning-fork oscillator. A feedback loop maintains a constant motion of the probe tip at a value less than a predetermined threshold which permits precise distance control down to 1 nm. These and other features and advantages of the present invention will be fully understood and appreciated from the following detailed description of the accompanying Drawings.
Referring to
The probe 10 is primarily envisioned in two embodiments:
The probing end 20 of the resonator structure 28 is brought into proximity to the sample 12 (which may be ion-implanted silicon, metals, dielectric, metal films, or dielectric films on a wide variety of substrates) with the opposite end 22 of the transmission line resonator structure 28 being electrically shorted or opened. The resonator structure 28 is formed in order to measure the resonant frequency and the probe resonant frequency shift of the resonator structure 28 for determination of the dielectric constant (permittivity) of the sample 12.
The spacing between the two conductors 16, 18 and their cross-section must be properly chosen in order to maintain a resonator quality factor Q high enough for accurate measurements of the sample induced changes in the resonant frequency and the Q factor. As an example, the spacing between the conductors 16 and 18 may be on the order of or greater than 1 mm for Q>1000 at 10 GHz.
When the probe 10 of the present invention is operated as the resonator, the odd and even modes of operation in general result in two different resonant frequencies due to dispersion of the signal and may therefore be separated in the frequency domain in a powered mode as well as being monitored independently. The dielectric medium 30 sandwiched between the conductors 16 and 18 serves to enhance such dispersion.
The coupling to the resonator 28 is accomplished by a coupling loop 32 positioned close to the resonator 28 and internal to an optional conducting sheath 34. A second coupling loop 36 may be used for the measurement electronics 24 schematically shown in
All calculations are carried out by data processor 42 based on predetermined formulas applied to the measured data. The processor 42 additionally controls the overall performance and operation of the measurement electronics 24 as well as the distance control mechanism 44.
The resonator structure 28 forms a (2n+1)λ/4 or (n+1)λ/2 resonator (n=0, 1, 2, . . . ), and its length is determined by the frequency of the lowest mode, e.g., about 7.5 mm for the λ/2 mode operating at 10 GHz.
The resonator structure 28 may be enclosed in a cylindrical or other shaped sheath 34 formed of a highly conductive material (such as Cu, Au, Ag, Al). The sheath 34 eliminates both radiation from the resonator 28 and the effect of the probe environment on the resonator characteristics. In particular, the variation influence of moving parts in the proximity of the resonator 28 is eliminated. The sheath 34 has an opening 46 near the sample area that permits efficient coupling of the sample 12 to the resonator 28 and thus permits the resonant frequency and Q factor to be dependent on the sample microwave permittivity. In situations where the spacing between the conductors 16 and 18 is small in comparison to the inner diameter of the sheath, the resonator properties are substantially unaffected by the sheath presence. The upper part of the sheath 34 makes electrical contact with the terminating plate 26. The bottom part of the sheath may have a conical shape in order to provide clear physical and visual access to the sampling area.
As discussed in previous paragraphs, the probing end 20 of the resonator structure 28, specifically tip 48 thereof, is brought into close proximity to the sample 12 for measurement purposes. The geometry of the tip 48, as well as the separation between the tip 48 and the sample 12 present information vital to calibration procedures used for near-field microwave microscopy for quantitative measurements of a material's dielectric constant (permittivity). Since the accurate determination of these parameters is difficult and often impractical, especially for the very small tips of less than, or on the order of a few microns in size of the transmission line 14 shown in
The distance control measurement 44 of the present invention may be one of many distance control mechanisms known to those skilled in the art, but it is envisioned as a shear-force based distance control mechanism by means of which the tip 48 of the resonant structure 28 is maintained at an unknown, but nominally the same or equal distance from the sample surface during both the calibration procedure and the actual measurement process. Combined with the appropriate theory describing the probe-to-sample interaction in terms of solely the geometry, the distance control mechanism 44 of the present invention has been found to yield accurate quantitative results.
In order to perform quantitative measurements with near-field microwave probes, shown in
Shear force based distance control mechanism 44 is a distance control mechanism applicable for use in near-field scanning optical microscopy (NSOM). The basic concept of the shear force distance control mechanism is that a probe, specifically the tip 48, is flexible and is mounted onto and dithered by a piezoelectric element or a quartz tuning-fork oscillator (TFO) with an amplitude from a few nanometers down to a few angstroms. As the tip 48 of such a probe is brought into close proximity to the sample surface 12, the amplitude of the tip oscillations is damped by interactions between the tip 48 and the sample surface 12. The motion of the tip is detected by an optical beam deflection technique for the piezo element or by a phase-or-amplitude-locked loop for the tuning fork oscillator (TFO).
In the measuring technique of the present invention, as shown in
The motion of the tip 48 is detected by an optical beam deflection unit which includes a laser 54 generating a laser beam 56 directed via the oscillating tip 48 to a photodetector (PD) 58. As the tip 48 is brought into close proximity to the sample surface 12, the amplitude of the tip oscillations is changed, i.e., damped, by interactions between the tip 48 and the sample surface 12 which is detected by the photodetector 58.
Responsive to the change of the amplitude of the tip oscillations, the photodetector 58 generates an output signal 60 indicative of the change in tip-to-sample separation. The signal 60 of the photodetector 56 is supplied to an input of a lock-in amplifier 62, which responsively generates an output control signal 64 indicative of unwanted changes in the separation between the tip 48 and the sample 12. Another generated signal from an oscillator output of the lock-in amplifier 62 is fed to the dithering element for maintaining the generation of oscillations thereat. The control signal 64 is fed from the output of the lock-in amplifier 62 to a PID (Proportional Integral Derivative) controller 66 which generates in response thereto a control signal 68 which is fed to the fine piezo Z-stage 52 for changing the position thereof along the section shown by the arrow 70 so that the probe attached to the fine piezo Z-stage 52, through the dithering element, will adjust its position with respect to the sample 12 in order to reach a predetermined separation between the tip 48 and the sample 12.
The photodetector 58, the lock-in amplifier 62, the PID controller 66, and the fine piezo Z stage 52, in combination with the laser 54 form a feedback loop which maintains the amplitude of the oscillations of the tip 48 of the probe 10 fixed at a value less than a predetermined maximum amplitude of oscillations, and thus, permits precise distance control down to approximately 1 nm.
The height of the tip 48 over the samples 12, at which the distance control may be performed, is a function of the amplitude of the tip oscillation whereby the smaller the amplitude of oscillations, the smaller the distance attained.
In the apparatus of the present invention, the successful integration of the shear force distance control mechanism 44 with both coaxial probes (on the order of 100 microns) and with dielectric wire-based probes (with apertures down to 1 micron) are attainable with an achieved precision down to 2 nm. Such a precise distance control between the tip 48 and the sample 12 during the measurements of the dielectric constant of the material of the sample 12 is an important part of the measurement process of the present invention since the distance between the tip 48 and the sample 12 is to be maintained at substantially the same during the measurement and calibration routines.
The dielectric support member may be in the form of any of the following embodiments:
To fabricate the near-field microwave probe shown in
Numerical simulations using Ansoft's High Frequency Structure Simulator (HFSS™), a 3D finite element package, show that the fringe E-field at the end of such a tip forms a “bubble” with diameter on the order of the tip size. Unlike the “apertureless” schemes that have been previously employed, this “apertured” approach permits quantitative measurements on a few-micron length scale where the result is insensitive to the material property outside the probing area. The balanced line geometry virtually eliminates the parasitic stray fields and reduces the amount of microwave power radiated from the tip 48 by a few orders of magnitude when compared to unbalanced coaxial probes.
When the probe tip 48 is placed in close proximity to the sample 12 under test, its fringe capacitance Ct is governed by the tip geometry, the sample permittivity, and the tip-sample distance. The complex reflection coefficient from the tip may be determined as follows:
Γ≅exp(−i2ωZ0Ct) (1)
where ω is the operating frequency, Z0 is the line characteristic impedance, and ωZ0Ct<<1. In the experimental set-up shown in
From Eq. (1) the relative shift in the probe resonant frequency F is found versus change in the tip capacitance Ct:
where L is the resonator length, ε0 is vacuum permittivity, μ0 is vacuum permeability, εeff is the transmission line effective dielectric constant, and Z0 is the line characteristic impedance. An estimate for the tip capacitance in air is Ct0˜ε0αt, where αt is the tip size; for αt˜1 μmCt0˜10 αF. For typical probe parameters (L˜25 mm, Z0˜100Ω, εeff˜2.5) and a 100 Hz precision in ΔF, Eq. (2) yields sensitivity to changes in the tip capacitance on the order of 3×10−20F=30 zF.
The shear-force method was used in experiments to actively control the tip-sample separation with precision down to a few nanometers. The tapered quartz bar forms a mechanical resonator with the fundamental transverse mode frequency on the order of a few kHz. The probe package is dithered at this frequency with sub-nm amplitude using a piezo tube, and the tapered portion of the tip is illuminated with a laser beam projecting onto the photodetector. The ac portion of the photo-detector output is proportional to the tip vibration amplitude, which is a strong function of the tip-sample distance d for d<100 nm. The photo-detector output is fed into a lock-in amplifier and then into a PID controller which in turn controls the amplifier for the piezo z-stage and thereby the tip-sample separation. From experimental data and theoretical estimates, the typical operating tip-sample separation is found to be on the order of 50 nm. The shear-force distance control provides typical MTBF of a tip ˜103 hours.
The probe enclosure and the microwave and the shear-force circuits are installed into a measurement head that is mounted onto a highly accurate piezo-driven z-stage 52. The piezo stage is attached to a mechanical coarse z-stage, which is mounted onto a gantry bridge. A 100-300 mm wafer under test is placed onto a vacuum chuck that is scanned by the 350-mm-travel xy-stage 74. The whole setup is mounted onto a vibration-isolation platform and placed inside an enclosure to improve acoustic isolation and thermal stability.
One of the most challenging tasks in thin film methodology is to deconvolve the film 78 and substrate 76 contributions. An original approach was developed as a part of the present invention, which employs a set of variable-thickness thermal oxide (TOX) films with kTOX=3.92 on nominally the same substrate as the low-k films under test and thicknesses ranging around the known low-k film thickness tf. In this study, all the low-k samples and the TOX calibration films were fabricated on Si substrates with bulk resistivity ρ<0.01Ω·cm. Under the condition ωCtρ/αt<<1 the material appears as a perfect metal for the probe for ρ˜0.01Ω·cm and 200-nm-thick film with k=4ωCtρ/αt<10−3.
The probe calibration is performed as follows. Two measurements of the frequency shift are made on the bare Si sample with ρ 0.001Ω·cm (i.e. perfect metal): ΔFm1=Fe−Fm[d0] and ΔFm2=Fe−Fm[d0+tf] where Fe is the probe resonant frequency with no sample, Fm[d0] is the frequency measured at some tip-sample distance d0 held by the shear-force distance control unit 44, and Fm[d0+tf] is the frequency measured at the distance d0+tf. The ΔFTOX=Fe−FTOX[d0] is measured for all TOX films, where FTOX[d0] is the probe frequency for the TOX sample at nominally the same d0. The obvious artificial point ΔFTOX(tTOX=0)=ΔFm1 is added to the ΔFTOX vs. tTOX data set and the result is fit to the empirical function A(t)=a+b(1−tanh[c(t−t0)], shown in
ΔFf vs. γf shown in
The theory underlying the principles of the measurements method of the present invention is presented in further paragraphs.
Consider a single point charge placed in vacuum distance d away from the surface of a dielectric layer of thickness t with dielectric permittivity εrf backed by a semi-infinite dielectric with permittivity εrs. In practice, such a sample is usually a single-layer dielectric film laying on a dielectric or metallic substrate. Using a method of a Bessel functions series expansion [W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, N.Y., 1968] it can be shown that the potential in vacuum above the same due to such a charge in polar coordinates is:
γs=1 for the backing with |εrs|>>|εrf|. It's important to note that using the same method the solution can be generalized for the multiple dielectric layers as well.
As shown in
The charges +1 and −1 are placed on the tip's first and second conductor, respectively. The charges provide some surface charge density σ[x,y,z;d] that for a particular sample and a given tip geometry depends on the tip-to-sample separation d. The potential due to this surface charge density in vacuum without the sample present is p[x,y,z;d]. Based on Eq. 3 the potential V1 in the space above the sample due to such a tip is seen to be:
Eq. 4 in turn yields for the mutual fringe capacitance Ct between the two tip conductors in presence of the dielectric layer sample:
where
Δp[0]=p[x2, y2, z2]−p[x1, y1, z1]
Δp[2d]=p[x2, y2, (z2−2d)]−p[x1, y1, (z1−2d)]
Δp[2d+2t(n+1)]=p[x2, y2, z2−(2d+2t(n+1))]−p[x1, y1, z1−(2d+2t(n+1))]
and (x1,y1,z1) and (x2,y2,z2) are the two points located somewhere on the surface of the first and the second tip conductors, respectively. Eq. 5 is exact and has the structure of an infinite series where each term is a product of the two functions as described below. The first one is a known function of the film and the substrate dielectric constants only. The second one, Δp[], is some unknown function of the film thickness and the tip-to-sample separation only called a geometrical coefficient.
The magnitude of the geometrical coefficients can be found using a perturbation approach. If the charges are placed on the tip conductors in the absence of the sample, the surface charge density and potential in vacuum are σe[x,y,z] and pe[x,y,z], respectively. If the semi-infinite dielectric or metallic sample with γc=(εc−1)/(εc+1) is placed underneath the tip, the surface charge density on the tip conductors is σc. The potential Vc in the vacuum space above the bulk sample due to σc is given by W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, N.Y., 1968):
Vc=pc[x,y,z]−γspc[x,y,−(z−2dc]
where pc[x, y, z] is the potential in vacuum due to the surface charge density σc with no sample present. And for the tip fringe capacitance it is found
Cc−1=Δpc[0]−γyΔpc[2dc] (6)
Generally σ,σe, and σc are different. However in the framework of the first order perturbation approach it is assumed that all surface charge distributions are the same and therefore
p[x, y, z]=pe[x, y, z]=pc[x, y, z]
while the E-field depends on the sample dielectric properties and the tip-to-sample separation. Eqs. 5 and 6 can be rewritten as follows:
where d and dc are the tip-to-sample separations for the dielectric layer sample under study and the bulk sample, respectively. By letting
dc=d,d+t(n+1),n=0,1,2 (8)
and taking into account that change in the probe resonant frequency ΔF=Fe−F is proportional to the change in 1/Ct, e.g. ΔF∝Δ(1/Ct) equations (7) finally yield:
where ΔFef=Fe−Ff, ΔFec=Fe−Fc, Fe is the probe resonant frequency with the empty resonator, Ff is the probe resonant frequency for the dielectric layer sample at the tip-to-sample separation d, and Fc is the probe resonant frequency for the bulk sample at the tip-to-sample separation given by Eq. (8).
Based on the presented theory, the method to quantitatively measure the dielectric constant of a dielectric layer backed by the metallic substrate is suggested using a semi-infinite dielectric or metallic sample with known dielectric constant as a calibration sample.
The Algorithm for measurements of dielectric constant of thin films on a metallic or arbitrary substrate is provided as follows:
Step 1. Adjust the tip-sample distance control unit 44 in a manner that it holds the probe tip 48 at some fixed distance d0 above the sample 12 surface. Typically d0 is in the range from 10 to 200 nm. Generally, the absolute value of this tip-sample separation is unknown. However, it is estimated, by measuring the distance control signal by the distance control mechanism 44 as a function of the tip-to-sample separation by means of the tip approaching the sample in the open feedback loop as described and as shown in
Step 2. Perform calibration of the probe on a metallic-like film with |k|>>1, e.g., γ=(k−1)/(k+1)=1. A bulk calibration sample with very large dielectric constant |km|>>1 and γm=1 is used. It may be some high-k dielectric (such as TiO2 with k˜100), metal (Al, Cu, W, etc.), or low resistivity silicon wafer. The probe frequency shift ΔFm=Fe−Fm as a function of the tip-to-sample separation d for this sample is measured in the measurements electronics 24, shown in
Step 3. Perform calibration on air film with k=1. A bulk calibration sample with nominally the same dielectric permittivity as the substrate of the film under test can be used for this step. If the film under test is on metallic or highly conductive substrate, the same calibration sample as in Step 2 can be used. The probe frequency shift ΔFea=Fe−Fa is measured as a function of the tip-to-sample separation d for this calibration sample d varying from d0 to >3αt.
Step 4. Calibration on SiO2 films with k˜4. Additionally, other dielectrics with known dielectric constants may be used. In fact, any film with a well-known dielectric constant that is close to the dielectric constant of the film under study may be used. The calibration materials may include (but not limited to) SiO2, Teflon, sapphire, MgO, and other materials. However, as an example only, and not to limit the scope of the present invention, the calibration on SiO2 films is described herein. A set of SiO2 thin films are used with variable thickness ranging around the thickness of the film under test on nominally the same substrate as the film under test. If the film under test is on a highly conductive or metallic substrate then, preferably, SiO2 should be thermally grown on highly conductive Si, since the k-value of such a thermal oxide (TOX) is well known: kTOX=3.93±0.01. However, alternatively, SiO2 may be deposited by a CVD process (on a wide variety of substrates). The probe frequency shift ΔFTOX is measured as a function of the tip-sample separation d for each of these samples for d varying from d0 to >3αt. Steps 2-4 result in the diagram shown in in
Step 5. For the thin film sample under study the probe frequency shift ΔFef=Fe−Ff is measured vs. the tip-sample separation varying from d0 to 3αt.
Step 6. Interpolate all of the above ΔF vs. d data using some standard interpolation method to construct a calibration curve shown in
There are several calibration approaches envisioned in the scope of the present invention.
I. Non-Linear Calibration Curve, Theoretical Form
Step 7(I): After the Step 6, from Eq. (7) and the calibration analytical function Fm(z) for the metallic calibration sample, the apparatus function is constructed for the probe frequency shift as follows:
where N can be cut off at ˜3αt/2t due to the near-field nature of the probing E-field.
Step 8(I): Fit the function Ff to the experimental data ΔFef using γf as the fit free parameter. The substrate's γ, is known; for highly conductive substrate γs=1.
Step 9(I): For each of the calibration thin films fit the apparatus function Ff[d] to the experimental data ΔF using γfc as the fit free parameter, similar to the Step 8(I). Generally, the resulting values γfc≠γfc0. If more than one calibration thin film is used, construct the array from the pairs {tci, γfci} and add the pair {0m λfco} to it. Interpolate the result to find Γ[t].
Step 10(I): If more than one calibration thin film is used construct the following array: {0, ΔFes},{tc1, ΔFec[d0, tc1]},{tc2, ΔFec[tc2]} . . . , where ΔFes is the total frequency shift for the bulk sample with γs (e.g. for tc=0). From interpolation ΔF[tf] is found.
Step 11(I): Construct the following array {{0, ΔFea└tf┘},{Γ[t], ΔF└tf┘}, {1, ΔFem}}, ΔFem which is the total frequency shift for the metallic sample. Fit it to the second order polynomial.
Step 12(I): Find the corrected γfcorr and calculate the film dielectric constant εrf as follows:
It is readily apparent to those skilled in the art that the material's dielectric constant can be identified as ε or k. In the present application, ε and k are used for the identification of the dielectric constant of the samples and are used intermittently throughout the text.
II. Non-Linear Calibration Curve
Steps 1-6 are the same as in the Method I. In the Method II the probe is still calibrated by measuring resonant frequency shift ΔF=Fe−F for three “standard” calibration films of nominally the same thickness and on nominally the same substrate as the low-k film under test: ΔFea└tf┘ for an air film with dielectric constant k=1; ΔFTOX└tf┘ for a thermal oxide film (TOX) with well-known dielectric constant kTOX=3.92; and ΔFsi for a low-resistivity silicon wafer which effectively exhibits infinitely large dielectric constant k>>1 for the probe (Steps 1-6 above). Fe is the probe resonant frequency with no sample, and F is the frequency measured at some distance d0 above the film surface. The following step 7(II) is however distinct from steps 7(I)-12(I).
Step 7(II): In order to create a calibration curve ΔF vs. γ=(k−1)/(k+1) of
In order to determine the dielectric constant of the low-k film under test, the probe resonant frequency shift Flow-k is measured and then converted into the k-value using the calibration fit function.
III. Linear Calibration Curve
Steps 1-6 are the same as in the methods (I) and (II). The following steps 7(III) -9(III) differ from the previous methods.
Step 7(III): Again, in order to create a calibration curve ΔF vs. γ=(k−1)/(k+1) of
Specifically, in the Step 7(III), in order to determine the distance D*, the probe resonant frequency shift Δec vs. tip-sample separation is measured for a plurality of calibration films of different thicknesses,
The calibration films are the films with a well-known dielectric constant that ranges around the dielectric constant of the film under study. The calibration material may include SiO2, thermal oxide, Teflon, sapphire, MgO, and others.
Step 8(III): Further, D* for the film thickness tf of the sample under study is determined; and the probe resonance frequency shift ΔFef of the sample under study is measured at the tip-sample separation Ds*.
Step 9(III): The calibration curve ΔF vs. (k−1)/(k+1) at D* shown in
The data corresponding to the probe resonance frequency shift ΔFef of the sample under study measured at the tip-sample separation Ds* are fitted into the linear calibration curve B of
It is readily apparent to those skilled in the art that the linear calibration curve ΔFec vs. γ=(k−1)/(k+1) of
Using the instrument and technique of the present invention, the dielectric constant of 13 low-k films on Si substrates with ρ<0.01Ω·cm are quantitatively measured. These samples are both SOD and CVD films with thicknesses ranging from 0.35 μm to 1.4 μm and dielectric constants ranging roughly from 2.1 to 3.1. For each film, the average dielectric constant across the wafer as measured by the new technique is compared to the values obtained by the conventional mercury probe. The correlation plot between the two data sets is shown in
In
The sample-to-sample repeatability of these measurements Δk/k is currently ˜2%. It is controlled primarily by the repeatability of the tip-sample separation. Estimates show that the practical limit can be as low as 0.1%. The accuracy of the measurements is currently ˜5% and depends mainly on the accuracy of the empirical fit P(γ) for the frequency shift vs. γ.
The system 10 operates in accordance with a novel software run by the data processor 42.
Further, the procedure flows to block 102, “Calibrate NMP (Near Field Microwave Probe) on Metallic-Like Films by Measuring ΔFem=Fe−Fm vs. d0”. In this block, a calibration bulk sample with a very large dielectric contant km>>1 and γm=1 is measured.
From block 102, the procedure flows to block 104 “Calibrate NMP on Air Film by Measuring ΔFea=Fe−Fa vs. d0”, where a bulk sample with nominally the same dielectric permittivity as the substrate of the film under test is measured. If the film under the test is a metallic or highly conductive substrate, the same calibration sample as in block 102, can be used.
The process further flows to box 106 “Calibrate NMP on SiO2 Films by Measuring ΔFTOX=Fe−FTOX vs. d0”, where a set of SiO2 thin films with variable thickness ranging around the thickness of the film under test on nominally the same substrate as the film under the test are measured. Instead of SiO2, alternative materials such as TOX, Teflon, sapphire, MgO, and others may also be used.
All of the above ΔF vs. d0 data are interpolated using some standard interpolation method. Further, the procedure passes to block 108 “Construct a Calibration Curve ΔF vs. γ=(k−1)/(k+1)”. In order to create a calibration curve, which is generally dependent on the probe geometry and the low-k film thickness, the three calibration data points for probe resonant frequency shift vs. γ are plotted and fitted to some functional form such as second order polynomial or analytical function describing the tip behavior if known. In order to determine the dielectric constant of the low-k film under test, the probe resonant frequency shift ΔFef is measured in block 110 “Measure ΔFef=Fe−Ff of the sample under study vs. d0”.
In order to extract the dielectric constant k of the sample under study, the algorithm passes to the block 112, “Fit ΔFef in the Calibration Curve”, and then in block 114, the procedure extracts the dielectric constant of the sample under study from the calibration fit function.
The procedure of measurement of dielectric constant of a sample under study, particularly the calibration of NMP portions thereof can create a calibration curve exhibiting a linear behavior. The flow chart diagram of the “linear” approach is shown in
As seen, blocks 120-124 of
This dependence is close to linear, as shown in
Further, a resonance frequency shift for the sample under study is measured at tip-sample separation D* determined in block 132.
The calibration curve ΔF vs. γ=(k−1)/(k+1) at D* for the film thickness tf under study is linear, as shown in
A novel technique of the present invention was developed for measuring the dielectric constant of low-k films on Si or metallic substrates. The advantages of this new technique are as follows: a) it is non-contact, non-invasive and non-contaminating; b) it has high spatial resolution (on the order of a few microns, but potentially can be scaled below one micron); and c) the measurement is made at microwave frequencies (4 GHz in this example, but can be scaled up), which is well matched to the operating frequencies of the devices in which these materials are used. The non-contact nature and high spatial resolution of this technique make it particularly well suited for measurements on patterned wafers, and the high-frequency measurement provides information about material properties at device frequencies. With the current probe geometries, inhomogeneities in dielectric constant can be quantitatively imaged on a few microns scale, and efforts are underway to scale the probing area down to sub-micron dimensions.
The novel low-k dielectric methodology is based on a scanning near-field microwave probe. The main feature of the near-field approach is that the spatial resolution is defined by the probe tip geometry rather than by the wavelength of the radiation used. Therefore, even for microwave frequencies with wavelengths of centimeters, a near-field probe can achieve spatial resolution down to the sub-micron scale. The quantitative dielectric constant measurements on a variety of low-k dielectric films show excellent correlation with mercury probe measurements on the same films.
Although this invention has been described in connection with specific forms and embodiments thereof, it will be appreciated that various modifications other than those discussed above may be resorted to without departing from the spirit or scope of the invention as defined in the appended Claims. For example, equivalent elements may be substituted for those specifically shown and described, certain features may be used independently of other features, and in certain cases, particular locations of elements may be reversed or interposed, all without departing from the spirit or scope of the invention as defined in the appended Claims.
This Utility Patent Application is based on Provisional Patent Application Ser. No. #60/560,590, filed 9 Apr. 2004.
| Number | Name | Date | Kind |
|---|---|---|---|
| 5256978 | Rose | Oct 1993 | A |
| 5397993 | Tews et al. | Mar 1995 | A |
| 5502392 | Arjavalingam et al. | Mar 1996 | A |
| 5508627 | Patterson | Apr 1996 | A |
| 5543386 | Findikoglu et al. | Aug 1996 | A |
| 5821410 | Xiang et al. | Oct 1998 | A |
| 5900618 | Anlage et al. | May 1999 | A |
| 5936237 | Van Der Weide | Aug 1999 | A |
| 6173604 | Xiang et al. | Jan 2001 | B1 |
| 6285811 | Aggarwal et al. | Sep 2001 | B1 |
| 6376836 | Anlage et al. | Apr 2002 | B1 |
| 6496018 | Nagata et al. | Dec 2002 | B1 |
| 6532806 | Xiang et al. | Mar 2003 | B1 |
| 6597185 | Talanov et al. | Jul 2003 | B1 |
| 6614227 | Ookubo | Sep 2003 | B2 |
| 6856140 | Talanov et al. | Feb 2005 | B2 |
| 20020153909 | Petersen et al. | Oct 2002 | A1 |
| 20050150278 | Troxler et al. | Jul 2005 | A1 |
| 20060087305 | Talanov et al. | Apr 2006 | A1 |
| 20060288782 | Sawamoto et al. | Dec 2006 | A1 |
| Number | Date | Country | |
|---|---|---|---|
| 20050230619 A1 | Oct 2005 | US |
| Number | Date | Country | |
|---|---|---|---|
| 60560590 | Apr 2004 | US |
