JP3431610B2 - Semiconductor element characteristic simulation method and characteristic simulation apparatus - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a semiconductor element characteristic simulation method and characteristic simulation apparatus, and is particularly suitable for application to measurement and evaluation of electrical characteristics of MOS transistors.

[0002]

2. Description of the Related Art Conventionally, in the circuit design of LSI,
Before actually manufacturing an LSI, it is necessary to confirm the operation of the circuit by circuit simulation using a circuit simulator.

For example, literature MOSFET Modeling & Bsim3 Us
er's Guide Y. Cheng and C. Hu, Kluwer Academic Publ
ishers 1999 describes an example of such a circuit simulation method.

When performing a circuit simulation, MOS transistor model parameters (see the above-mentioned document: pp409-420) extracted from the electrical characteristics of a MOS transistor manufactured in the target semiconductor process are required.

In the conventional extraction of MOS transistor model parameters, the gate voltage dependence of the drain current (ID-VD characteristics) and the gate voltage dependence of the drain current of the MOS transistor manufactured by the semiconductor process to be designed ( The measurement data of (ID-VG characteristics) is fitted to a MOS transistor model (see the above-mentioned document: pp421 to 448) by using the nonlinear least squares method and extracted.

[0006]

However, since the MOS transistor model used in the circuit simulator is very complicated and has a large number of parameters, a large amount of measurement data is required when fitting and extracting the MOS transistor model parameters. Become.

The measured data are the dimensions of the transistor,
Since the number of levels is individually required depending on the manufacturing process, the amount of data is enormous, which may exceed the allowable capacity of the database, or the processing capacity of the computer may be exceeded. In addition, long-time calculation is required to process a huge amount of data. Therefore, reducing the amount of measurement data and shortening the data measurement time have been major problems.

The present invention has been made to solve the above-mentioned problems, and by reproducing the electrical characteristics of a semiconductor element with high accuracy based on the minimum number of measurement points,
The purpose is to shorten the measurement time of electrical characteristics and to minimize the storage capacity of the digital database that stores the measurement results.

[0009]

A method of simulating characteristics of a semiconductor device according to the present invention is a method of simulating characteristics of drain current-drain voltage using MOS transistor model parameters, in which a specific gate voltage and substrate voltage are set. By using the measured data of the drain current for a plurality of drain voltages and the fitting using the nonlinear least squares method, it is possible to obtain a function form that reproduces the drain current-drain voltage characteristics for each of the specific gate voltage and the substrate voltage.

The actual measurement data of the drain current with respect to the plurality of drain voltages is the actual measurement data of at least three points.

The semiconductor element characteristic simulation method of the present invention is a drain current-gate voltage characteristic simulation method using a MOS transistor model parameter, in which a specific drain voltage and substrate voltage are set and a plurality of gates are set. By using the measured data of the drain current with respect to the voltage and the fitting using the nonlinear least squares method,
The drain current for each of the specific drain voltage and the substrate voltage −
A function form that reproduces the gate voltage characteristic is obtained.

The measured data of the drain current with respect to the plurality of gate voltages is the measured data of at least 7 points.

Further, the function form is obtained for each of the strong inversion region and the weak inversion region.

Further, the semiconductor element characteristic simulation apparatus of the present invention is a drain current-drain voltage characteristic simulation apparatus using MOS transistor model parameters, and is a data measurement for fetching measured data of drain current for a plurality of drain voltages. Means and
Fitting the acquired measured data to a dedicated function, a function fitting means for determining the form of the function, a characteristic calculating means for calculating the electrical characteristics of the drain current-drain voltage using the determined function, and the characteristic calculation Data output means for outputting the calculation result by the means, the function fitting means sets a specific gate voltage and substrate voltage, and performs the fitting by using the plurality of measured data and the nonlinear least squares method. The function for reproducing the drain current-drain voltage characteristic is determined for each specific gate voltage and substrate voltage.

Further, the measured data of the drain current with respect to the plurality of drain voltages is the measured data of at least three points.

The semiconductor device characteristic simulation device of the present invention is a drain current-gate voltage characteristic simulation device using MOS transistor model parameters, and is a data measurement for fetching measured data of drain current for a plurality of gate voltages. Means, fitting the measured data taken in to a dedicated function,
A function fitting means for determining the form of the function, a characteristic calculating means for calculating the electrical characteristics of the drain current-gate voltage using the determined function, and a data output means for outputting the calculation result by the characteristic calculating means. The function fitting means sets a specific drain voltage and a substrate voltage, and performs a combination using the plurality of actual measurement data and a nonlinear least squares method to obtain a drain current for each of the specific drain voltage and the substrate voltage. The function for reproducing the gate voltage characteristic is determined.

The measured data of the drain current with respect to the plurality of gate voltages is the measured data of at least 7 points.

The function fitting means obtains the function form for each of the strong inversion region and the weak inversion region.

[0019]

1 shows a characteristic simulation apparatus for semiconductor elements according to an embodiment of the present invention. This apparatus includes data measuring means 1 for incorporating the electrical characteristics of semiconductor elements into the apparatus. A function fitting means 2 for fitting the data to a dedicated function to determine the shape of the function, a characteristic calculation means 3 for calculating electrical characteristics using the determined function, and a data output means 4 for outputting the calculation result. It is configured.

The present invention fits measurement data that is as small as possible to a dedicated function and predicts bias data that has not been measured using the function. As the fitting function, a function newly conceived from the MOS transistor model (the above-mentioned document: pp421 to 448) was used, and the number of parameters to be fitted was set to a small number to realize highly accurate fitting from a small number of measurement points.

The fitting function and its derivation process will be described below. Derivation of the fitting function is
This is mainly performed in the function fitting unit 2 shown in FIG. MOS transistor model (above reference: pp42
1 to 448), the transistor model expressing all bias conditions is expressed by the following (Equation 1) to (Equation 4).

[0022]

[Equation 1]

Here, each variable, constant and the like are as follows. I _ds : drain current, W _eff : effective channel width,
n: n factor (model fitting parameter), e: electron elementary charge, μ: mobility, E: drain electric field, C _ox : gate oxide film capacitance,
_V gseff: effective gate _{voltage, V th:} threshold _{voltage, V} dseff: effective drain voltage, mu _0: intrinsic mobility, _{U A:} primary mobility degradation coefficient, _{U B:} Second mobility Degradation coefficient, U _C : Mobility degradation coefficient due to substrate effect, T _OX : Oxide film thickness, V _bseff : Effective substrate voltage, V _dsat : Drain saturation voltage, δ: Effective drain voltage parameter, ν _t : Thermal potential,
V _OFF: offset voltage of the sub-threshold region, _{L eff:} effective channel length, [psi _s: surface potential, q: electron elementary charge, epsilon _si: dielectric constant of silicon, _{N CH:} channel impurity concentration, _{V d s:} drain Voltage, V _gs : gate voltage, V _bs : substrate voltage.

However, if this model is fitted by the conventional method, a huge amount of measurement data is required as described above.

In this embodiment, the drain current (ID)-
To realize this method by paying attention to the method of individually fitting the VG dependency in the drain voltage (VD) characteristic and individually fitting the VD dependency in the drain current (ID) -gate voltage (VG) characteristic. It reduces the amount of measurement data. The procedure will be described in detail according to the following items (A) to (C).

(A) Combination of ID-VD characteristics Assuming a specific gate voltage and substrate voltage, (Equation 1) can be transformed into (Equation 5) below. (Equation 6) can be obtained by substituting as a parameter.

[0027]

[Equation 2]

Where α₁, Α_Two, Α_ThreeIs the present embodiment
The fitting parameters of And the real
Measured data is α₁By normalizing with (Equation 6)
Α _Two, Α_ThreeUsing the measured data and the nonlinear least squares method
Function form that reproduces the measured data
You can Generally, the nonlinear least squares method is
The solution stays at the local minimum depending on the period value and leads to an incorrect solution.
Since there is a possibility of issuing it, α_Two, Α_ThreeInitial value of global
With a certain level to reach the minimum point at
Ku.

In this fitting, α ₂ physically corresponds to the saturation voltage and its final solution must lie between 0 and the supply voltage. Also,
The final solution of α ₃ must exist between 0 and 1 because of its functional form. Therefore, the nonlinear least squares method is used as the initial value α.
_2. Divide the existence range of the solution of ₂ and α ₃ appropriately and search for the final stable point where the error is minimized in all regions.

In (Equation 6), the unknown variables are α ₁ , α
_Since there are three values of ₂ and α ₃ , it is possible to determine the value of the unknown variable by solving a simultaneous equation with 3 points of the measured data if the measured value is guaranteed to be expressed by (Equation 6). it can. In an actual case, it is assumed that the measured value is not guaranteed to satisfy (Equation 6). In this case,
The variable value closest to (Equation 6) is determined by the data of three or more points by the nonlinear least squares method.

Next, the matching of the ID-VG characteristics will be described. (B) Considering the current characteristics in the strong inversion region under specific drain voltage and substrate voltage conditions in the combination of the ID-VG characteristics in the strong inversion region (Equation 1), the following (Equation 7) is obtained. It can be transformed, and by replacing a common item as a parameter, it can be rewritten as in (Equation 8).

[0032]

[Equation 3]

Here, β ₁ , β ₂ , and β ₃ represent the fitting parameters of this embodiment. And
By combining β ₀ , β ₁ , β ₂ , and β ₃ in (Equation 8) with the actual measurement data using the nonlinear least squares method, it is possible to obtain a functional form that reproduces the actual measurement data. Further, in general, the nonlinear least squares method has a possibility that the solution stays at the local minimum depending on the initial value and leads to an erroneous solution.
The initial values of ₀ and β ₁ are given levels within a certain range so as to reach the global minimum point.

In this fitting, β₀Thing
Theoretically it corresponds to the threshold voltage, and the final
The solution usually exists between 0 (V) and the power supply voltage. Well
, Β ₁Is the slope of the straight line of the current characteristic, which is usually 0 to the current
Within the range of about 5 times the maximum value of divided by the power supply voltage.
It Therefore, the nonlinear least squares method is used as the initial value β.₀, Β₁Solution of
Appropriately divide the existence range of
To find the final stable point where the error is minimized. Where β
_Two, Β_ThreeFor, the position of the deterioration correction of the inclination from the straight line
In addition, the final solution is stable regardless of the initial value.

(C) Incorporation of ID-VG characteristics in weak inversion region To perform fitting in the weak inversion region, V _gs in (Equation 8) is replaced with V _gseff as in (Equation 9) below.

[0036]

[Equation 4]

Here, for β ₀ , β ₁ , β ₂ , and β ₃ , the parameters obtained by the strong inversion of item (B) are used. Also V
_{As for gseff} , the common item in (Equation 4) is replaced as a parameter and rewritten as in (Equation 10) is used.

[0038]

[Equation 5]

Here, γ ₁ , γ ₂ , and γ ₃ represent the fitting parameters of this embodiment. And
By combining γ ₁ , γ ₂ , and γ ₃ in (Equation 10) with the actual measurement data using the nonlinear least squares method, it is possible to obtain a functional form that reproduces the actual measurement data. The unknown variable (β ₀ , which is used in (Equation 8), (Equation 9), or (Equation 10),
Since the number of β ₁ , β ₂ , β ₃ , γ ₁ , γ ₂ , γ ₃ ) is 7, it is possible to obtain a functional form that reproduces the measured data by using the measured data of at least 7 points. Become.

2 to 7 are characteristic diagrams showing the characteristic obtained from the function form obtained by the above-mentioned method and the result of verifying its validity. FIG. 2 shows the result of function fitting of the drain voltage dependence of the drain current described in the item (A). FIG. 2 shows the characteristics standardized (Arb.Unit) with an ID of 1.0 when VD = 5V. In FIG. 2, two measurement points are the actual measurement data used at the time of fitting. ID calculated by the determined function by performing the operation shown in FIG. 2 under other gate voltage conditions
FIG. 3 shows a comparison between the −VD characteristic (function value) and the actual measurement data used as a sample. The function determined by fitting is exactly the same as the actual measurement in all areas,
This method proved to be valid.

Similarly, the result of function fitting the gate voltage dependence of the drain current in the strong inversion region according to the above item (B) is shown in FIG. 4, and the gate voltage dependence of the drain current in the weak inversion region as a function according to the above item (C). The results of fitting are shown in FIG. 6 and 7 show the results of comparison with the actual measurement data using the functions determined in the above items (B) and (C). These characteristic diagrams are also standardized with an ID of 1.0 when VG = 5V, and FIG. 5 is a logarithmic representation of the standardized characteristics. 6 and 7 show the same data linearly and logarithmically.
The determined function is in good agreement with the measured data in the linear domain and the logarithmic domain, demonstrating that this method is valid.

FIG. 8 shows the result of confirming the effect of exploring the global minimum point by changing the level of the initial value. FIG. 8 shows contour lines of the error between the function value and the actual measurement value when β ₀ and β ₁ in item (B) have a level, and the portion marked with dots in FIG. 8 has the global error minimum point. It is a combination of initial values. Thus, by using this method, the function form at the global error minimum point can be effectively determined.

According to this embodiment, the number of data points of electrical characteristics to be measured is 1020 to 104, which is about 1/10.
Could be reduced to As a result, the time required for measurement and the required recording amount of digital data can be reduced to about 10
It can be reduced by a factor of 1.

[0044]

According to the present invention, the electrical characteristics of the semiconductor element can be reproduced with high accuracy based on the minimum number of measurement points, the measurement time of the electrical characteristics can be shortened, and the measurement result can be stored. The storage capacity of the digital database can be minimized.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a semiconductor element characteristic simulation device according to an embodiment of the present invention.

FIG. 2 is a characteristic diagram showing a fitting result of ID-VD characteristics.

FIG. 3 is a characteristic diagram showing a comparison between a function value of an ID-VD characteristic and an actually measured value.

FIG. 4 is a characteristic diagram showing a fitting result of ID-VG characteristics in a strong inversion region.

FIG. 5 is a characteristic diagram showing a fitting result of ID-VG characteristics in a weak inversion region.

FIG. 6 is a characteristic diagram in which a function value of an ID-VG characteristic and an actual measurement value are compared in a linear display.

FIG. 7 is a characteristic diagram in which a function value of an ID-VG characteristic and an actually measured value are compared in logarithmic display.

FIG. 8 is a schematic diagram showing an example in which the global minimum point is searched by changing the initial value.

[Explanation of symbols]

1 Data measurement means 2 Function fitting means 3 characteristics calculation means 4 Data output means

Claims (10)

(57) [Claims] 1. A drain current-drain voltage characteristic simulation method using a MOS transistor model parameter, wherein specific gate voltage and substrate voltage are set, and measured data of drain current for a plurality of drain voltages and a nonlinear minimum of 2. A method of simulating characteristics of a semiconductor device, characterized in that a function form reproducing a drain current-drain voltage characteristic for each of the specific gate voltage and substrate voltage is obtained by fitting using a multiplication method. 2. The method for simulating the characteristics of a semiconductor device according to claim 1, wherein the measured data of the drain current with respect to the plurality of drain voltages is measured data of at least three points. 3. A drain current-gate voltage characteristic simulation method using a MOS transistor model parameter, wherein specific drain voltage and substrate voltage are set, and drain current measurement data for a plurality of gate voltages and nonlinear minimum 2 are set. A method for simulating characteristics of a semiconductor device, characterized in that a function form reproducing a drain current-gate voltage characteristic for each of the specific drain voltage and substrate voltage is obtained by fitting using a multiplication method. 4. The characteristic simulation method for a semiconductor device according to claim 3, wherein the measured data of the drain current with respect to the plurality of gate voltages is measured data of at least 7 points. 5. The semiconductor device characteristic simulation method according to claim 3, wherein the functional form is obtained for each of the strong inversion region and the weak inversion region. 6. A drain current-drain voltage characteristic simulation device using a MOS transistor model parameter, comprising: data measuring means for taking measured data of drain current for a plurality of drain voltages; and a dedicated function for the taken measured data. Function fitting means for determining the shape of the function, characteristic calculation means for calculating electrical characteristics of drain current-drain voltage using the determined function, and data for outputting the calculation result by the characteristic calculation means Output means, the function fitting means sets a specific gate voltage and substrate voltage, and the plurality of measured data and the nonlinear minimum 2
A device for simulating characteristics of a semiconductor device, wherein a function for reproducing a drain current-drain voltage characteristic is determined for each of the specific gate voltage and substrate voltage by fitting using a multiplication method. 7. The semiconductor device characteristic simulation apparatus according to claim 6, wherein the measured data of the drain current with respect to the plurality of drain voltages is measured data of at least three points. 8. A device for simulating drain current-gate voltage characteristics using a MOS transistor model parameter, comprising: data measuring means for acquiring measured data of drain current for a plurality of gate voltages; and a dedicated function for the acquired measured data. Function fitting means for determining the shape of the function, characteristic calculation means for calculating electrical characteristics of drain current-gate voltage using the determined function, and data for outputting the calculation result by the characteristic calculation means Output means, the function fitting means sets a specific drain voltage and a substrate voltage, and performs a combination using the plurality of actual measurement data and a nonlinear least squares method to determine each of the specific drain voltage and the substrate voltage. To determine the function that reproduces the drain current-gate voltage characteristics. Characteristics simulation apparatus for a semiconductor device characterized. 9. The semiconductor device characteristic simulation device according to claim 8, wherein the measured data of the drain current with respect to the plurality of gate voltages is measured data of at least 7 points. 10. The characteristic simulation apparatus for a semiconductor element according to claim 8, wherein the function fitting means obtains the function form for each of the strong inversion region and the weak inversion region.