JP2960465B2 - Device simulation method for semiconductor device - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for simulating the characteristics of a semiconductor device by numerical calculation and a technique for predicting the characteristics of a semiconductor device by a simulation system using the method.

[Conventional technology]

Conventional methods are discussed in Journal of Applied Physics 59 (1986) pp. 3175 to 3183 (J. Appl. Phys. 59 pp. 3175-3183 (1986)). The above paper is one-dimensional (MOS depth direction)
Is a simultaneous solution of the potential and the wave function. At present, it is limited to the comparison between the one-dimensional quantum calculation result and the classical calculation result.

[Problems to be solved by the invention]

In an MIS type semiconductor device in which a carrier is induced at a semiconductor-insulating film interface by an electric field, the carrier is localized near the interface, and thus exhibits a quantum mechanical behavior according to Fermi-Delack statistics. In order to predict the element characteristics by numerical calculation,
In order to accurately handle the above behavior, it is necessary to solve the particle density distribution by simultaneously combining the wave equation and the Poisson equation (referred to as a quantum method), but there is a problem that the amount of calculation is enormous. Therefore, conventionally, a device simulator that ignores the quantum mechanical behavior and treats the motion of the carrier as a classical fluid (referred to as a classical method) has been widely used. However, when the impurity concentration of the substrate is increased (10 ¹⁷ / cm ³
Above) There is a problem that the quantum mechanical behavior with respect to the carrier density in the inversion layer cannot be ignored and the device characteristics cannot be accurately predicted. That is, as shown in FIG. 3 showing the gate voltage dependency of the carrier density in the inversion layer,
The impurity concentration N _A is high comes to classical methods conspicuous difference classical methods (CL) and quantum method (QM) in two calculation methods is a problem that deviates from the experimental values.

SUMMARY OF THE INVENTION An object of the present invention is to provide a method for solving the above-described problem, which can obtain a result similar to that of the quantum calculation in a calculation time approximately equal to that of the classical calculation.

[Means for solving the problem]

The difference between the results of the quantum method and the classical method to achieve the above objective was considered as the shift of the carrier density distribution in the depth direction of the inversion layer, and was proportional to the shift of the carrier density distribution in the oxide film thickness and flat band voltage Perform the classical calculation by adding the quantities. FIG. 5 shows the difference in the average depth of the inversion layer charge density. The horizontal axis is the average gate electric field felt by the inversion layer and is called the gate effective electric field. Range of electric field (10 ^5-1
0 ⁶ V / cm) is equivalent to being 6V applied from 0.6V to the gate and the interface. Electric field of threshold voltage is substrate concentration 4 × 10
It is 10 ⁵ V / cm or more in a region of ¹⁶ / cm ³ or more. Further, a normal device operates at a gate voltage of 5 V or less with an oxide film thickness of 20 nm. On the other hand, at 10 ⁵ V / cm or less, the electric field is weak, so that the interval between quantum levels becomes narrow, and the average depth of the inversion layer becomes large. In an electric field of 10 ⁶ V / cm or more, a hot electric field in an oxide film causes a problem due to a strong electric field, so that it is rarely used as a normal device operation. Referring to FIG. 5, the difference in average depth of the inversion layer charge density is about 1.
From 6 nm to 1.0 nm, it has a gentle decreasing function with respect to the electric field. Also, there is little substrate concentration dependency. Therefore, the difference in the average depth is assumed to be a constant value (about 1.2 nm) or expressed as a function of the electric field and the substrate concentration. Then, add the length obtained by multiplying the difference in the average depth by the ratio of the dielectric constant to the thickness of the insulating film,
The flat band voltage is added to a voltage obtained by multiplying the average depth difference by a constant to obtain input data. With this method, it is possible to obtain a result that is as disastrous as the quantum calculation in the same calculation time as the conventional classical calculation.

[Action]

Since this method obtains an answer similar to that of the quantum method in the same calculation time as that of the classical method, it greatly contributes to high-speed and high-precision device design.

〔Example〕

Hereinafter, the present invention will be described in detail with reference to the following examples.

FIG. 1 is a flowchart of a device characteristic design support system according to an embodiment of the present invention. First, measurement data such as a capacitance value is obtained from a measuring device 1 (capacitance measuring device) from an actual device, and an element profile is numerically analyzed by an element profile calculating means 2 to obtain an element profile. The element profile can be stored in the element profile storage means 3 and read by the input data reading means 5 when necessary. Other necessary supplementary data can be input by the element structure input means 4. Further, the user can input the result of the artificial profile or process simulator or the analysis result such as SIMS by the element structure input means 4. The data read in step 5 is transferred to data extracting means 6 for taking in the quantum effect, and the oxide film thickness, flat band voltage, bias condition, and impurity distribution are selected. In 5, a lot of data including the above is stored. In 6, data necessary for the present invention is specified, and data is selected from the 5 data. Referring to the renormalization parameter table 7, the renormalization parameters are recalculated in the oxide film thickness and the flat band voltage by the oxide film thickness and flat band voltage rewriting means 8. The renormalization parameter table 7 is a table in which the difference in the average depth of the inversion layer between one-dimensional quantum calculation and classical calculation is tabled as a function of the bias condition and the impurity distribution. Do.

The average depth of the inversion layer used here is based on one-dimensional calculation, the amount of calculation is sufficiently small, and when analyzing a device in 2-3 dimensions, the calculation time is greatly saved.

Using the corrected oxide film thickness and the flat band voltage, which are the results, the current-voltage characteristic analyzing means 9 analyzes the result, and outputs the result by the analysis result output means 10. According to the present embodiment, it is possible to obtain a high-speed device characteristic design support system that can obtain the same result as the quantum calculation while treating the behavior of the carrier as a body.

Specifically, the renormalization is obtained by adding the difference between the average depth of the inversion layer to the oxide film thickness multiplied by the ratio of the dielectric constant between the semiconductor and the oxide film, and the flat band voltage also depends on the difference in the average depth of the inversion layer. In accordance with the table. That is,
As shown in FIG. 2, the inversion layer approximates a solution approaching zero near the surface, such as a solution based on a quantum calculation, to a form of a solution based on a classical calculation which is the largest on the surface. At the same time, the interface between the semiconductor and the oxide film is shifted so that the total amount of the inversion layer does not change. In this case, a potential shift occurs due to a difference in dielectric constant, so the flat band voltage is changed by an amount proportional to the shifted interface.

〔The invention's effect〕

According to the present invention, the quantum effect is incorporated into the device simulation, so that the accuracy is dramatically increased. Fig. 4 shows the results of quantum mechanical calculation (QM), the classical calculation (CL), the oxide film thickness and the flat band voltage corrected by the present invention (MD), and the experimental values. The comparison result is shown. The present invention agrees well with quantum mechanically calculated and experimental values.

[Brief description of the drawings]

FIG. 1 is a flow chart according to one embodiment of the present invention. FIG. 2 shows a method of incorporating a quantum solution according to one embodiment into a classical solution. FIG. 3 shows a comparison of the dependence of the inversion layer density on the gate voltage between the classical method and the quantum method. Fig. 4 shows the results of quantum mechanical calculation (QM), the classical calculation (CL), the oxide film thickness and the flat band voltage corrected by the present invention (MD), and the experimental values. The comparison result is shown. Fifth
The figure shows an example of the gate voltage dependence of the average depth of the inversion layer. The difference between the average depth of the quantum method and the classical method is shown on the vertical axis.

Claims (3)

(57) [Claims] 1. A device simulation method for analyzing current-voltage characteristics of an MIS type semiconductor device exhibiting quantum mechanical behavior due to localization of charges at an interface between a semiconductor and an insulating film, comprising: an inversion layer charge density at the interface. Adding a value corresponding to a difference between a quantum calculation result and a classical calculation result regarding the average depth of the insulating film to the thickness of the insulating film and the flat band voltage. 2. The method according to claim 1, further comprising: adding a product of a difference between the average depth and a ratio of a dielectric constant between the semiconductor and the insulating film to a thickness of the insulating film. 2. The device simulation method for a semiconductor device according to claim 1, further comprising a step of adding a product of the electric field in the depth direction and a constant representing the intensity of the electric field in the depth direction to the flat band voltage. 3. The product of the average depth difference and a constant representing the electric field strength in the depth direction is tabulated as a function of the average depth difference as a function of bias conditions and impurity distribution. Item 3. A device simulation method for a semiconductor device according to Item 2.