BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a prior art set up used for conventional charge pumping;
FIG. 2 is a trapezoidal wave pulse utilized in the charge pumping, in accordance with one aspect of the present invention;
FIG. 3A illustrates a trapezoidal charge pumping wave in accordance with yet another aspect of the present invention;
FIG. 3B illustrates yet another trapezoidal charge pumping wave at a different frequency than in FIG. 3A, in accordance with another aspect of the present invention;
FIG. 4 is a graphical representation of substrate current versus frequency according to another aspect of the present invention;
FIG. 5 illustrates an experimental result according to one aspect of the present invention;
FIG. 6 illustrates another experimental result according to one aspect of the present invention;
FIG. 7 illustrates measurements on various devices according to other aspects of the present invention;
FIG. 8 illustrates experimental results of tunneling current versus duty cycle according to yet another aspect of the present invention;
FIG. 9 shows substrate current versus duty cycle according to another aspect of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
The following description of the embodiment below is merely an example and is in no way intended to limit the invention or its application or uses. The present invention discloses a method for measuring interface traps in thin gate oxide MOSFET devices.
As semiconductor devices get smaller, hot carrier induced degradation of those devices is apt to occur. In order to make the MOSFET devices or Ultra-Large-Scale Integration (ULSI) components more reliable, it is critical to understand and quantify this degradation condition. The technique mentioned supra to accomplish this utilizes a charge pumping method, which is a measurement technique that can evaluate the substrate surface conditions at the Si—SiO2 interface, for example.
Turning now to the figures, FIG. 2 illustrates a trapezoidal wave pulse according to an aspect of the present invention. The interface traps between the Si and SiO2 layers that recombine with inversion or accumulation charges will constitute a net DC current. In other words, every time that the gate is pulsed from high voltage 202 (Vtop or Vhi) to low voltage 204 (Vlow or Vbase), an ultra short pulse of current will be obtained and can be measured. For example, by pulsing the gate at 100 kHz, or 100,000 times per second, a current is integrated to obtain a finite measured current. This technique is used widely throughout industry and academics to understand interface traps, and MOSFET characteristics, for example.
In FIG. 2 the pulse waveform is illustrated, showing at least one complete waveform 200. The waveform 200 begins at point 206 which represents the leading edge of the waveform 200, for example. The slope of the line continues traveling up and to the right from 206 until line reaches point 208 where the slope levels out, at the highest voltage 202 (Vtop or Vhi). The pulse rise time (tRISE) 210 is often defined as the time it takes to go from the low level voltage 204 to a high-level voltage 202. In this case the rise time is measured for the entire rise level, however, this value is often measured at 10% above the low voltage level, at point 212 and at 90% of the high voltage level, at point 214. The waveform continues along a horizontal path until it reaches point 216, wherein the line begins to slope downward until it reaches point 218.
The slope of the line travels downward and to the right from point 216 until the line reaches point 218 where the slope levels out at the base voltage 204 (Vbase). The fall time (tf) 220, for example, is often defined as the time the pulse takes to go from the high voltage level 202 to the low voltage level 204. In this case the pulse fall time is in measured for the entire fall distance; however this value can often be represented as the distance from 10% above the low voltage or point 212 to 90% of the high voltage at point 214. The pulse width is the amount of time a pulse remains at a specific (normally “true”) logic state. This can either be measured from the time between the leading edge at 50% amplitude to the trailing edge at 50% amplitude or as the time from the beginning of the leading edge 206 to the beginning of the trailing edge 216. The period is how long it takes the waveform measured in seconds to repeat and is also the inverse of the wave frequency.
FIG. 3A illustrates a trapezoidal charge pumping signal at 300, wherein the various regions of the wave form will be described in detail below. A first region, 302 is shown where the voltage is high and represents the region, where tunneling current occurs from the gate into the source/drain. A second region, 304 represents an area where the voltage goes from high to low. The second region 304 is dominated by the charge pumping current from the electron traps. The third region, 306, which goes from low to high voltage, is dominated by a charge pumping current created from hole traps. Finally, the fourth region, 308 is dominated by the gate tunneling current into the substrate. As clearly demonstrated in the illustration, utilizing only the traditional charge pumping technique, the tunneling current would totally obscure the charge pumping current.
One aspect of the invention is a method where the gate tunneling current is subtracted out of the summation of the current. The tunneling current has an exponential dependence on the gate to source voltage. Therefore a small error in the estimation of the gate voltage will cause a large error in the tunneling current. What ends up happening is that two large numbers are subtracted in order to wind up with a small number which typically results in a large error (e.g., 100-200%). Ultimately this requires a prior knowledge of the device operation, which is normally not known to a great extent. However, this problem is solved in the present invention by looking at two aspects of the current, the tunneling current and the charge pumping current and understanding what controls or influences each of the two currents. The charge pumping current, as illustrated in FIG. 3A, only occurs at the edge transitions of the pulse, 304 and 306, and the tunneling current occurs when the pulse is not in transition, 302 and 308. Looking at the pulse from a signal standpoint, the tunneling current is controlled by the duty cycle of the pulse and the charge pumping current is determined or influenced by the frequency of the pulse or how many times the pulse cycles from high to low or low to high (transitions).
FIG. 3B illustrates an additional trapezoidal charge pumping signal at 350, where the frequency of the signal 300 in FIG. 3B is greater than the frequency of the signal 350 shown in FIG. 3A. As FIG. 3B clearly demonstrates, the charge pumping current regions 324 and 326, represent a larger percentage of the total current obtained. As seen in FIG. 3B the tunneling current regions 322 and 328, are much smaller than the tunnel current regions, 302 and 308 in FIG. 3B. This aspect of the present invention indicates that as the frequency of the charge pumping signal increases the charge pumping current increases.
Accordingly, there are two different mechanisms to vary the charge pumping current and vary the tunneling current and the two mechanisms are uncoupled from each other, as one mechanism is varied the other does not vary to the first order. Therefore, turning to FIG. 4, is a graphical representation 400 of substrate current or ISUB (Amps) plotted on the vertical or y-axis 402 versus frequency in cycles/sec (Hz) plotted on the horizontal or x-axis 404. The slope of the curve 406 provides the total interface trapped charge, in this example, 5.08 E-15 Coulombs. The y-intercept provides the average tunneling current from the gate to the substrate, for example, 2.56 E-10 amps from EQ. 1. The equations for the linear curve 406 are shown below as EQS. 1 and 2. The parameter R2, called the correlation coefficient, is a measure of how closely the variables are correlated together. The closer R2 approximates a value of 1, the “better the fit”. The R2 value is actually a property of the data set and not of the line that is drawn by the least squares criterion, for example. In this case, the R2 value is approximately 1 and there is a very good fit to the data. Consequently, FIG. 4 shows that the charge pumping current is a function of the frequency of the pulse applied to the device.
y=5.08 E-15x+2.56 E-10 (EQ. 1)
R2=9.98 E-01 (EQ. 2)
Where:
- tr=pulse rise time=100 nanoseconds (ns)
- tf=pulse fall time=100 nanoseconds (ns)
- Vtop=0.6 volts
- Vbase=−0.9 volts
- W/L=10/5 μm
In estimating Dit (the density of the interface traps)
ΔE=−2 kT Ln[σp σn tr tf)1/2 vth ni (Vt Vfb)Va] (EQ. 3)
(Vt−Vfb)/Va˜1 (EQ. 4)
Where:
- Nit=6.35 E+10/cm2 (number of interface traps)
- (σp σn)1/2˜10−15 cm2
- ni=1.45×1010 cm−3
- Vth=10−7 cm/s (thermal velocity of carriers in the semiconductor)
- tr=tf=10−7 seconds (pulse rise time and pulse fall time)
- ΔE˜0.58 eV (Electron Volts)
- Dit˜Nit/ΔE˜1.1 E+11/eV/cm2
- σp=hole-capture cross-section (cm2)
- σn=hole-capture cross-section (cm2)
- k=Boltzmann's constant (Joules/Kelvin)
- T=Absolute temperature (Kelvins)
- Va=Amplitude (Vhi−Vlo) of the gate pulse (Volts)
FIG. 5 illustrates graphical experiment results at 500 that was performed in order to further validate the present invention. QCP measured in Colombes is plotted on a y or vertical axis and voltage (Vbase) is plotted on the x or horizontal axis. One of the characteristics of charge pumping current is that if the amplitude of the pulse is varied, the charge pumping pulse will disappear or go to zero. The amplitude of the pulse was varied as illustrated in box 502, by adjusting Vbase 504, while the Vtop 506 was kept constant at 0.6 V (always greater than the threshold voltage (Vt)). The rise time (tr) 508 and the fall time (tf) 510 were both 100 ns. The charge pumping current started out relatively flat until the Vbase reached approximately −1.2 V, and then curve progressed downward until it disappears at about −0.5 V. This is typical behavior of what would be seen in traditional charge pumping technique, when plotting this type of curve. Therefore, what is being measuring here utilizing this aspect of the claimed invention, is charge pumping current, and is not an artifact of tunneling current, for example. If this were measuring tunneling current, the tunneling current would not vary at all or only slightly over a given range.
Another experimental result for the present invention is illustrated in FIG. 6, at 600, for example. In this experiment result, the base voltage (Vbase) 602 is kept constant, while the voltage (Vtop) 604, the voltage at the top of the pulse is adjusted or varied, for example. In this experiment it is expected that the QCP 606 will saturate when the voltage Vtop 604 is greater than a threshold voltage, Vt 608. In this test the voltage, Vbase 602 is kept at approximately −0.95 V, the rise time (tr) 610 and the fall time (tf) 612 are both set to 100 ns and the W/L ratio is 10/5 μm. Once the amplitude of the pulse (Vtop) 604 exceeds the threshold voltage (Vt) 608 it was anticipated that the charge pumping current would approximately flatten out and referring to the graph in FIG. 6, this is clearly the case.
FIG. 7 illustrates measurements for various devices (See index 702) and the number of interface traps (Nit) versus a base voltage (Vbase). The devices under test (DUT) range in size from 1 μm to 10 μm. As illustrated in this graph, the number of interface traps is fairly independent of the base voltage. The rise time and the fall time was set at 100 ns and the voltage at the top amplitude (Vtop) was set at a constant 0.6 V.
In another aspect of the invention, FIG. 8 shows experimental results of tunneling current (Itunneling) 802 plotted on the y-axis (vertical axis) vs. duty cycle 804 plotted on the x-axis (horizontal axis). The tunneling current 802 flowing into the substrate from the gate, for a given duty cycle, is estimated from the y-intercept of a line fitted to the tunneling current versus duty cycle plot at that duty cycle. It can be seen from the R2 value of approximately one that represents a good linear fit exists which is consistent with the current theory relating to charge pumping. The estimate of tunneling current for this graph is approximately the slope of the line on the left which is 862 pA, for example in this case.
y=−10x+8.62 E (EQ. 5)
R2=9.93 E-01 (EQ. 6)
Where:
- tr=pulse rise time=100 nanoseconds (ns)
- tf=pulse fall time=100 nanoseconds (ns)
- Vtop=0.6 volts
- Vbase=−0.9 volts
- W/L=10/5
Finally in FIG. 9, which illustrates charge pumping current versus duty cycle, experimental results are illustrated at 900 which demonstrate the effect of the duty cycle time charge pumping current. In this experiment the width to length ratio is equal to 10/5 (W=10 μm), the rise time and fall time are both set equal to 100 ns, Vtop was set equal to 0.6 V and Vbase was adjusted equal to −0.95 volts. At the very low duty cycles, less than 20%, the rise and fall times (tr and tf) are comparable to the pulse width, therefore the approximations break down at that level. As the duty cycle increases the graph flats out, as anticipated. The QCP remains substantially independent of the duty cycle, until the duty cycle exceeds 80%.
The charge pumping current total charge equation is calculated as:
Q
CP
=D
it(2)(q)(k)(T)Ag Ln[(σp σn tr tf)1/2 vth ni|Vt−Vfb|/Va] (EQ. 7)
Where:
- Dit=Density of interface traps
- q=Electron charge
- k=Boltzmann's constant
- T=Absolute temperature (K)
- Ag=Gate area of the MOSFET
- Ln=Natural logarithm
- σp=Hole-capture cross-section
- σn=Electron-capture cross-section
- tr=Pulse rise time
- tf=Pulse fall time
- vth=Thermal velocity
- ni=The intrinsic carrier concentration at the temperature of measurement
- Vt=Threshold voltage
- Vfb=Flat-band voltage
- Va=Amplitude (Vhi−Vlo) of the gate pulse
The component of the gate tunneling current (Itunneling) that enters or goes into the substrate has a linear frequency dependence and can be a source of error in the QCP measurement, for example. The following can be used as an approximation of the tunneling current into the substrate:
I
tunnel, avg=(1/Tperiod)(1/Kf+1/Kr)∫(V)dV+{(1−DC)−(tr+tf)/2Tperiod}|(Vlo) (EQ. 8)
Where:
- f=1/Tperiod=frequency of the pulses (cycles/sec);
- Tperiod=period=the time for one complete cycle (sec);
- Kf=tf/(Vhi−-Vlo);
- Kr=tr/(Vhi−Vlo);
- DC=duty cycle=τ/T;
- τ is the duration a operation (e.g., pulse) is non-zero;
- I(V)=Isubstrate with gate voltage V and source/drain grounded (0 V);
- tr=pulse rise time;
- tf=pulse fall time;
- ∫ I(V) dV is the integral of the substrate current I(V), as function of gate voltage V, with, V ranging from V=Vhi to V=Vlo;
The contribution from I(Vhi) can be ignored, for example, as it is very small (In inversion, the bulk of the gate tunneling current goes to the source/drain terminals and not the substrate).
For example, the tunneling current has two frequency (f) dependent terms (term 1, [f (1/Kf+1/Kr)∫ I(V) dV] and term 2, [f l(Vlo) (tr+tf)/2]) and a duty cycle (DC) term. The DC term is the y-intercept of the substrate current (Isub) versus frequency (f) plot and one of the frequency (f) dependent tunneling current (Itunneling) terms, I(Vlo) (tr+tf)/2. Therefore, the duty cycle can be calculated using the y-intercept value and the rise and fall times of the trapezoidal pulse, for example. The second term, (1/Kf+1/Kr)∫I(V) dV, of EQ. 3, can be estimated from the DC Isub versus gate voltage sweep. In table 1 shown below, the percentage error in QCP, calculated utilizing the two Tperiod dependent tunneling current terms, can be calculated for a 5×10 um NMOS device employing 100 nS rise and fall times, a Vhi voltage set at 0.6V, a Vlo of −0.9V and an assumed 5e10/cm2 interface traps (Nit), for example. The measured DC Isub vs. Vgate data was used to compute ∫ I(V) dV. In this manner, both of the errors, mentioned supra, can be estimated and thus corrected for.
TABLE 1
|
|
Nit
q(Nit)(W)(L)
% Error (tr + tf)/2
% Error ∫ I(V) dV
|
|
5.00E+10
4.00E−15
−3.86
0.64
|
|
Although the invention has been shown and described with respect to one or more implementations, equivalent alterations and modifications will occur to others skilled in the art based upon a reading and understanding of this specification and the annexed drawings. The invention includes all such modifications and alterations and is limited only by the scope of the following claims. In particular regard to the various functions performed by the above described components (assemblies, devices, circuits, etc.), the terms (including a reference to a “means”) used to describe such components are intended to correspond, unless otherwise indicated, to any component which performs the specified function of the described component (i.e., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary implementations of the invention. In addition, while a particular feature of the invention may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms “includes”, “having”, “has”, “with”, or variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.”
Patent Application
20080096292
