JPH06216381A - Device parameter extractor - Google Patents

Abstract

PURPOSE:To accurately extract the length of a pinchoff region of a parameter of a MISFET model for a circuit simulation. CONSTITUTION:Data of gate voltage VG dependence of a drain current ID regarding a plurality of MISFETs having different gate lengths L is measured or input, a value (VG-VTH) obtained by subtracting a threshold value VTH from the gate voltage VG and a drain voltage VD are fixed, a regression line R = aL+b for relating mutual resistance R = (VG-VTH)ID and the length L of a plurality of (VG-VTH) are introduced, and coordinates (R0, L0) for converging the plurality of the lines to one point are decided.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a device parameter extracting device, and more particularly to a device parameter extracting device having a function of extracting the pinch-off region length of MISFET.

[0002]

2. Description of the Related Art In conducting circuit simulation, parameters are extracted so that a device model incorporated in a circuit simulator reproduces actual device characteristics. A normal parameter extraction method will be described below. The device model for giving the drain current I _{D of the} MISFET is a set of parameters (p ₁ , ..., P _N ) and three applied voltages (drain voltage V _D , gate voltage when the potential of the source terminal is taken as a reference point). It is represented by the following general formula including V ₀ and substrate voltage V _SUB ). I _D = f (p ₁ , ..., P _N ; V _D , V _G , V _SUB ) (1)

Parameters usually have physical meaning, and include mobility, saturation speed, gate length, and channel width. Of these, the device dimensions such as the gate length that can be directly measured are given in advance and are not subject to extraction. The number N of parameters is several tens in a high-precision model. on the other hand,
It is assumed that the measured device characteristics are represented by I _D = g (V _D , V _G , V _SUB ) (2). The general parameter extraction is to select p ₁ to p _N so that the above two equations substantially match in the entire applied voltage range of interest. In particular,
When the values of the above-mentioned two equations at the i-th applied voltage of the set of M applied voltages measured are respectively denoted by f _i and g _i ,
The parameters p ₁ to p _N are determined so that the squared error E = Σ (f _i −g _i ) ² is minimized. In the derivation, an iterative method using a computer program is generally used. This is a method of first giving a trial initial value of p ₁ to p _N , starting from that, repeatedly updating p ₁ to p _N, and repeating until the change becomes sufficiently small.

In the above parameter extraction, all parameters except a part such as the element size of the equation (1) are determined from the characteristics of a single element. However, if this method is simply applied, the parameters in the model often have physical meanings, but the extracted values often deviate from physical common sense. This is because even though the model represented by equation (1) does not completely match the actual characteristics, it is attempted to forcefully determine a large number of parameters based on the subtle deviation between equation (1) and actual measurement. This is because To compensate for this drawback, often physically important parameters are measured and determined separately before applying the above method. As an example, the mobility μ _EFF (which is a function of V _G −V _TH ) is calculated for an element having a relatively large gate length L and channel width W (which may be different from the element from which the parameter is extracted). the drain current I _D upon application of a small drain voltage V _D is measured, be calculated from _{I D = (W / L)} μ EFF C OX (V G -V TH) V D (3) the relationship it can. Here, C _ox is the capacitance of the gate oxide film per unit area and can be measured separately. Equation (3) is true only when V _D << V _G −V _TH , but μ _EFF is determined in advance independently of other parameters by performing measurement under the condition that this simple relationship holds. Can be kept. As another example, the deviation [Delta] L = L-L _EFF of the gate length L and the effective channel length L _EFF, and according to methods JP 54-26667 to derive the parasitic resistance R _EX of the source-drain terminal Has been done. This is to measure the above-mentioned value by measuring the resistance value between the source and the drain when the drain voltage V _D is very small for a plurality of elements having different gate lengths.

[0005]

In the model equation of MISFET described by the physically meaningful parameter group, it is difficult to extract the physically meaningful parameter only by the iterative method. This point can be improved by combining the iterative method with the conventional individual parameter extraction method. However, there is no conventional extraction method for the position of the pinch-off point, especially for the parameters that cannot be individually extracted. .

If the model is given by physically meaningless parameters, the model characteristics when various parameters are changed are different from those when the actual device parameters are changed. A particular problem is that the gate length dependence of the characteristics is inconsistent. That is, in the parameters extracted by using the element having the gate length L ₁ , the model characteristics when L ₁ is changed to another value L ₂ are different from the actual element characteristics when the gate length is L _2. . This phenomenon is caused by the above-mentioned ΔL, which is the characteristic of the bias region (linear region) where the drain voltage V _D is small.
Although it can be greatly improved by correctly obtaining R _EX , the discrepancy is still large in the bias range (saturation region) where the drain voltage V _D is large. The biggest reason is that the pinch-off point directly related to the drain current in the saturation region cannot be extracted correctly.

The point at which the speed increases as the carriers run from the source to the drain and the speed finally saturates is called the pinch-off point, and from this point to the drain is called the pinch-off region. In the pinch-off region, carriers are attracted to a strong electric field and drain is extracted.
The substantial channel length that determines the FET saturation current is the length from the source to the pinch-off point. Therefore, to describe the saturated drain current correctly, it is necessary to know this length accurately.

In the conventional parameter extraction method, the position of the pinch-off point cannot be correctly described, so that the dependency of the saturation current on the gate length L cannot be accurately reproduced. That is,
If several L different elements were used, it was necessary to perform separate parameter extraction for all elements.
Furthermore, when evaluating the effect of variations in gate length, circuit simulation is performed by changing the gate length value of the model parameter by the expected variation, and changes in circuit characteristics are investigated. It had the drawback of being inaccurate.

An object of the present invention is to provide a device / parameter extraction device for accurately extracting the pinch-off region length which is a parameter of the MISFET model for circuit simulation.

[0010]

In order to achieve the above object, the device parameter extracting apparatus according to the present invention obtains the data of the gate voltage V _G dependency of the drain current I _D regarding a plurality of MISFETs having different gate lengths L. At least 1
Pieces a function of measured or inputted for applying the drain voltage V _D of, by fixing the gate voltage V value obtained by subtracting the threshold voltage V _TH from _G V _G -V _TH and the drain voltage V _D, a plurality of V _G for -V _TH, cross resistance _{R = (V G -V TH)} / I D
And a function of deriving a regression line R = aL + b that correlates the gate length L with the coordinate R at which the plurality of straight lines converge at one point.
₀ , L ₀ ).

The threshold voltage V _TH is extracted from the measured or input drain current I _D dependence on the gate voltage V _G.

[0012]

The data V _G -V obtained by subtracting the threshold voltage V _TH from the gate voltage V _G by measuring or inputting the data of the gate voltage V _G dependency of the drain current I _{D for} a plurality of MISFETs having different gate lengths L. _{With TH} and drain voltage V _D fixed, mutual resistance R = (V _G − for a plurality of V _G −V _TH
V _TH ) / I _D and regression line R = relating the gate length L =
Then, aL + b is derived, and the coordinates (R ₀ , L ₀ ) where these straight lines converge to one point are determined.

[0013]

Embodiments of the present invention will be described below with reference to the drawings.

(Embodiment 1) FIG. 1 is a block diagram showing a first embodiment of the present invention. The present embodiment includes an input device 1 such as a keyboard, a data processing device 2 that operates under program control, an output device 3 such as a display device, and an electrical measuring device 4.

The data processor 2 includes a measurement controller 21 and
A threshold voltage extraction unit 22, a regression line derivation unit 23, and a pinch-off region length calculation unit 24 are provided. Electric measuring device 4
Includes a measuring unit 41 and an element mounting unit 42.

Next, the operation of this embodiment will be described with reference to FIGS. First, the gate length L manufactured by the same process as the device for which the parameter extraction is performed
The device under test group 5 composed of a plurality of different MISFETs is prepared and attached to the device mounting portion 42 in advance.
The element mounting portion 42 is a probe (needle) for the element in the wafer state.
Is a prober when standing up, and a socket for mounting a package when measuring an element incorporated in a package. The element to be measured is electrically connected to the measuring section 41 via the element mounting section 42.

The measurement control unit 21 controls the measurement unit 41 to measure the drain current I _D vs. gate voltage V _G characteristics of the plurality of measurement target elements and fetches the data (step S1). In this measurement, the drain voltage V _D is fixed,
This is performed for at least one drain voltage value. For example, in the case of an n-channel element, V _D = 0.1,3.5V
In, the drain current I _D is measured by changing V _G = 0 to 5 V in 0.5 V steps. The normal measurement is performed while sequentially switching the plurality of measurement target elements. The switching is performed by switching a switch provided in the measuring unit 41, or when a prober is used as the element mounting unit 42, by moving a position where a probe (needle) of the element mounting unit 42 is set. The switching is controlled by the measurement control unit 21.

The measured I _D vs. V _G characteristic data is supplied to the threshold voltage extraction unit 22. Threshold voltage extraction unit 2
2 is the threshold voltage V _TH from the data of the I _D vs. V _G characteristics.
Is extracted (step S2). V _TH is MISFET
Is the gate voltage that is regarded as the boundary between the ON state and the OFF state. For V _TH , for example, V _D is sufficiently small (0.
Approximately 1 V or less), the tangent line at the point where the slope of the I _D vs. V _G plot is maximum is defined as V _G at the point where I _D = 0. In order to extract V _TH based on this definition, it is necessary to measure the I _D vs. V _G characteristics when V _D is very small in step S1, but the extraction of the pinch-off region length which is the object of the present invention. This method is desirable. In another definition, I _D is defined as a gate voltage at a certain value (1 μA in the example). In any case, V _TH can be derived from the input I _D vs. V _G characteristic. The threshold value V _TH may be extracted for one element to be measured when the gate length dependency is considered to be small. To be exact, it is individually calculated for all elements to be measured. Strictly speaking, since the threshold voltage has a drain voltage V _D dependency, each V _D that has been measured may be extracted.

The work described below is generally performed for a plurality of measured drain voltages V _D. Then, it may be performed in parallel the steps for all V _D, may be repeated to perform all the steps for each V _D, which is not related to the essence of the present invention. Therefore, only the operation for a single V _D will be described below.

The value of V _TH obtained by the threshold voltage extracting unit 22 is supplied to the regression line deriving unit 23 together with the data of the I _D vs. V _G characteristic. The regression line deriving unit 23 first calculates V
_G -V _TH certain values _{V 1, V 2, ...,} I D when the V _N
Is calculated for each gate length L. The V _{1 to} V _N are, for example, 1,1.5,2,2.5,3V. Since V _G corresponding to V _{1 to} V _N does not always match the measured V _G , I _D is determined by interpolation. However, when ignoring the L dependence of V _TH , V ₁ -V _N was measured as V
_It is assumed that V _TH is added to _G itself (that is, V _G −V _TH
Instead of V _G itself), the interpolation for I _D may be omitted. Then for each _{V 1 ~V N, R = (} V G
-V _TH ) / _ID Plot against gate length L,
The coefficients a and b of the regression line R = aL + b are derived by the least square method or the like (step S3). An example of an R vs. L plot is shown in FIG. This is data for an n-channel MOSFET having a channel width of 1 μm and a gate oxide film thickness of 10 nm. The plot is a measurement point, and the straight line group is a regression straight line group for the data at each V _G -V _TH . A plurality of straight lines corresponding to V _{1 to} V _N converge at almost one point.

Each V _G -V _TH = V _{1 to} V obtained as described above
The coefficients a and b of the regression line with respect to _N are supplied to the pinch-off area length extraction unit 24. Pinch-off area length extraction unit 24
Computes the values of a and b to obtain the coordinates where the straight line converges at one point (step S4). The coordinates are (L
₀ , R ₀ ), L−L ₀ corresponds to the distance between the source and the pinch-off point. That is, L ₀ is equal to the sum ΔL + L _P of the deviation ΔL between the gate length and the effective channel length and the pinch-off region super L _{P in} FIG. ΔL can be separately extracted as described above, and if its value is known, L _P can be found at the same time. L ₀ calculated as above
Alternatively, the value of L _P is output to the output device 4 (step S
5).

To calculate L ₀ , two lines out of the straight lines shown in FIG. 3 may be selected and the coordinates of their intersections may be obtained from a and b. L by going especially V _G -V _TH as V ₁ and V _2, V ₂ and V _3, ... for 2 straight lines V _G -V _TH is closer to the (L _0, R ₀₎ sequentially calculate ₀ V _G -V _TH
Dependency can be calculated. Also, multiple V _G -V _TH
An average L ₀ for may be calculated. As an example, the average of L ₀ obtained from a plurality of sets of two straight lines may be obtained. Further, as another example, in order to determine L ₀ so as to minimize the variance of R ₀ , L ₀ = −Cov (a, b) / Var (a) (4) may be calculated. Where Cov (a, b) and Var
(A) represents the covariance of a and b, and the variance of a, respectively.

(Embodiment 2) FIG. 5 is a block diagram showing a second embodiment of the present invention. This embodiment comprises an input device 1 such as a keyboard, a data processing device 2 which operates under program control, and an output device 3 such as a display device.

The data processing device 2 has a data input section 25.
, Threshold voltage extraction unit 22 and regression line extraction unit 23
And a pinch-off area length calculation unit 24.

Next, the operation of this embodiment will be described with reference to FIGS. The present embodiment removes the function of measuring the element characteristics in the first embodiment, and replaces it with I _D
The data of the V _G characteristic is input from the outside.

In the operation, first, the I _D vs. V _G characteristic data prepared by some method is input to the data input unit 25 (step S1). The data is supplied to the threshold voltage extractor, and the following operation is the same as that of the first embodiment.

In this embodiment, as the I _D vs. V _G characteristic data, data collected by a separate measuring device or device
Use the one calculated by simulation,
The data is supplied to the data input unit 25 via a keyboard or a portable auxiliary storage device (such as a floppy disk).

The saturation drain current I _D of the MISFET whose grounds for explaining that the intersection shown in FIG. 3 corresponds to the pinch-off point will approximately satisfy the following relational expression. _{R = (V G -V TH)} / I D = {2 / Wμ EFF C OX (V G -V TH)} (L-L 0) + (1 / WC OX v SAT) (5) where, L -L ₀ is the distance from the source to the pinch-off point, W is the channel width, μ _EFF is the effective mobility, C _OX is the capacitance of the gate oxide film per unit area, and v _SAT is the saturation velocity of carriers. L ₀ is the gate length L in the pinch-off region L _P
Is equal to the sum of the deviation ΔL of the effective channel length L _EFF , the magnitude thereof is substantially constant regardless of the gate length L, and the gate voltage V _G dependency is small. Further, the dependency of the second term on the rightmost side of the equation (5) on the gate voltage V _G is small. Thus, equation (5) corresponds to a straight line on the R vs. L plane, this straight line is V _G -V be a varied _TH, fixed point (L _0,
1 / WC _OX v _SAT ). Therefore, the pinch-off point can be known from the coordinates of such fixed points.

Although the gate length L is used as the element size in the above description, the designed gate length or the effective channel length L _EFF = L-ΔL may be used instead. Particularly when the effective channel length is used instead of L, the extracted L ₀ becomes equal to the pinch-off region length L _P.

[0030]

As described above, the device parameter extracting apparatus according to the present invention uses a plurality of MISFETs having different gate lengths L and uses the simple relational expression shown in Expression (5) to pinch off the MISFET. A parameter L ₀ indicating a point is extracted. Therefore, physically correct pinch-off points can be extracted with high accuracy, which was impossible with the conventional parameter extraction method that fits the characteristics of a single MISFET to a complicated model formula. Further, by using the parameters of this method, there is an effect that it is possible to improve the accuracy of circuit simulation, particularly the accuracy of simulation for an element having a gate length different from the extraction target element.

[Brief description of drawings]

FIG. 1 is a block diagram illustrating a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating first and second embodiments.

FIG. 3 is a diagram showing an example of a relationship between mutual resistance R and gate length L.

FIG. 4 is a diagram for explaining the relationship between L ₀ and the pinch-off region length L _P.

FIG. 5 is a block diagram illustrating a second embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 input device 2 data processing device 3 output device 4 electric measuring device 5 device to be measured 21 measurement control unit 22 threshold voltage extracting unit 23 regression line deriving unit 24 pinch-off region length extracting unit 25 data input unit 41 measuring unit 42 element Mounting part

Claims (2)

[Claims] 1. A plurality of MISFETs having different gate lengths L
Drain current I and a function of measuring or input for at least one of the applied drain voltage V _D of the gate voltage V _G data dependencies and _D, the value V _G of the gate voltage V _G minus the threshold voltage V _TH about
-V _TH and drain voltage V _D are fixed and a plurality of V _G -V is set.
For _TH, cross resistance _{R = (V G -V TH)} / I D and a and a function of deriving a regression line R = aL + b that relates the gate length L, the coordinates of the plurality of straight lines converge to one point (R _0, L ₀ ), and a device parameter extraction device having a function of determining L ₀ ). 2. The device parameter extracting apparatus according to claim 1, wherein the threshold voltage V _TH is extracted from data of the gate voltage V _G dependency of the measured or input drain current I _D. .