JPH03189548A - Method for evaluating characteristic of semiconductor device - Google Patents

Abstract

PURPOSE:To simulate element characteristics with high accuracy by finding the mobility of carriers when only impurities of a 1st or 2nd conduction type are admitted individually and finding the carrier mobility in an area where impurities of both the 1st and 2nd conduction types are present by using said found mobility. CONSTITUTION:The 1st mobility values of electrons and positive holes when only impurities of the 1st conduction type are injected into a semiconductor is found according to the concn. of the injected impurities. Further, the 2nd mobility values of electrons and positive holes when only impurities of the 2nd conduction type are injected into the semiconductor is found according to the concn. of the injected impurities. The 1st and 2nd found mobility values of electrons are used to find the total mobility of electrons in a semiconductor area where the impurities of the 1st and 2nd conduction type are present together. The 1st and 2nd found mobility values of the positive holes are used to find the total mobility of the positive holes in a semiconductor area where the impurities of the 1st and 2nd conduction types are present. Then the characteristics of the semiconductor device are evaluated by using the found total mobility values of the electrons and positive holes.

Description

[Detailed Description of the Invention] [Objective of the Invention] (Industrial Application Field) This invention evaluates with high precision the dependence of carrier mobility on impurity concentration and impurity conductivity type in semiconductors to determine device characteristics. This invention relates to a method for evaluating characteristics of semiconductor devices that enables highly accurate simulation.

(Prior art) 1. In a conductor element, a high concentration region where the concentration of impurities contained in a semiconductor is extremely high, for example, in silicon, 10
The behavior of carriers transported in a region larger than 11. cm has a large effect on device characteristics. Therefore, in order to accurately design devices, impurities must be introduced at high concentrations. The effect of high concentration of impurities on carriers must be evaluated with high precision in this region.

This high concentration effect of impurities includes various effects such as a decrease in carrier activation rate, narrowing of the band gap, and a decrease in carrier mobility. Among these, the decrease in carrier mobility is a phenomenon in which the mobility of both majority carriers and minority carriers decreases as the concentration of impurities introduced into a semiconductor increases, and this has a large effect on device characteristics. Therefore, in order to accurately understand this decrease in carrier mobility when developing and designing a semiconductor device, it is necessary to evaluate this decrease in carrier mobility with high accuracy.

The decrease in carrier mobility due to the introduction of impurities into semiconductors is
Even when N-type and P-type impurities coexist in a semiconductor, conventional evaluation methods do not distinguish between N-type and P-type impurities and calculate the total impurity concentration pJ (= N O + N
It was evaluated as a function of A). Here, No, N
A is the impurity concentration of the donor and acceptor, respectively.

For example, as a function for evaluating carrier mobility, the literature ■ rMawettl at al, I[21E T
Ran.

[Elcctron Devices, vol, I
Some are described in ED-30, PP, 764-769°1983 J. The solid line shown in FIG. 6 shows this function as the mobility of holes as majority carriers with respect to impurity concentration.

As shown in FIG. 7, the conventional evaluation procedure for device characteristics is that after manually determining the N-type and P-type impurity concentrations NT)%NA (step 100), the total impurity concentration N is reduced to N-
As a function of the total impurity concentration N, the mobilities μn (N), μ, (N) of electrons and holes are determined using the function of the above-mentioned document (■) (step 300). ), Poisson's equation, electron and II-hole current continuity equations were solved by numerical calculation using the obtained mobility, and the device and characteristics were evaluated (step 400).

In the past, the total amount of introduced impurities was calculated without considering the conductivity type of the introduced impurities, whether it was in terms of hole mobility or electron mobility. It was determined as the mobility of majority carriers relative to concentration. Therefore, when determining the mobility of holes in an N-type semiconductor, for example, the majority carrier function shown by the solid line in FIG. 6 has been used, even though holes are minority carriers.

However, recently, it has been found that the mobility of minority carriers is different from that of majority carriers, as shown by the dotted line in FIG. 6, for example, in the literature ■rs, t';

5vlrbunet et al., IEEE Tr.
an, Electron Device Letter
s, vol, EDL-7, PP, 168-171
．． 1986 J and literature ■ “S, 1shi, 5w1rhu
n et al,, IEDM TechDIg,,P
P24-27.1988 J.

Therefore, as shown in Figure 6, although the mobility of majority carriers and the mobility of minority carriers are significantly different, the conventional method of calculating carrier mobility Since the mobility of majority carriers was determined as a function of N, a large error occurred in the calculated carrier mobility.

(Problems to be Solved by the Invention) As explained above, in the conventional evaluation method of carrier mobility, the dependence of carrier mobility on impurity concentration is determined based on the total impurity concentration N, regardless of the conductivity type of impurities. I was looking for it as a function. For this reason, it has not been possible to evaluate carrier mobility in a high concentration region of a semiconductor with high accuracy.

This has made it difficult to design a highly accurate device that can accurately simulate electrical characteristics such as current-voltage characteristics obtained by simulation using carrier mobility.

Therefore, this invention has been made in view of the above, and its "first objective is to accurately evaluate the dependence of carrier mobility on impurity concentration in semiconductors, thereby improving It is an object of the present invention to provide a method for evaluating the characteristics of a semiconductor device, which enables accurate determination of carrier mobility and highly accurate simulation of device characteristics.

[Structure of the Invention] (Means for Solving the Problems) In order to achieve the above object, the present invention provides a first method for semiconductors.
The first mobility of electrons and holes when only conductive type impurities are introduced is determined according to the concentration of the introduced impurities,
The second mobility of electrons and holes when only impurities of the second conductivity type are introduced into the semiconductor is determined according to the concentration of the introduced impurity, and the determined first and second mobilities of electrons are used. The total mobility of electrons in the semiconductor region where impurities of the first and second conductivity types coexist is determined using the method, and the total mobility of electrons in the semiconductor region where impurities of the first and second conductivity types coexist is determined using the determined first and second mobilities of holes. The purpose of this paper is to determine the total mobility of holes in a semiconductor region and evaluate the characteristics of a semiconductor device from the determined total mobility of electrons and holes.

(Function) This invention calculates carrier mobility when only impurities of the first conductivity type or the second conductivity type are individually introduced, depending on the impurity concentration, and using the mobility of the first and second
The carrier mobility in a region containing both conductive type impurities is determined, and the characteristics are evaluated using this carrier mobility.

(Example) Hereinafter, the present invention will be explained in detail using the drawings.

FIG. 1 relates to one embodiment of this invention? FIG. 1 is a block diagram showing the main part configuration of a device simulator that executes a method for evaluating characteristics of a 1' conductor device.

In the simulator of the example shown in the figure, carrier mobility when only N-type impurities are introduced into the semiconductor, and P
The carrier mobility when only the type impurity is introduced is determined independently, and from the obtained mobility, the carrier mobility in the region containing both conductivity type impurities (hereinafter referred to as "total mobility") is determined. ).

In FIG. 1, the device simulator of this embodiment includes a human power section 1, a donor mobility determination section 2, an acceptor mobility determination section 3, a total mobility determination section 4, and a numerical calculation execution section 5. .

The input unit 1 provides the simulator with the concentration of impurities introduced into the semiconductor as input data, and inputs the concentration ND of N-type impurities and the concentration NA of P-type impurities, respectively. As the N-type impurity, As, P, Sb, etc. can be set, and as the PU impurity, B etc. can be set. The human power department 1 calculates each given impurity concentration ND.
1NA, the N-type impurity concentration NO is given to the donor mobility determining section 2, and the P-type impurity concentration NA is given to the acceptor mobility determining section 3.

The donor mobility determination unit 2 calculates the electron mobility μ71. given by scattering by N-type impurities when only N-type impurities are introduced into the semiconductor. and the hole mobility μ,
From input section 1! It is determined as a function of the N-type impurity concentration ND.

Specifically, when determining the electron mobility, the donor mobility determination unit 2 first determines the majority carrier mobility μn□ with respect to the concentration of the N-type impurity.

The mobility μn of electrons as majority carriers is the sixth
As shown in the figure, the experimental results of electron mobility with respect to impurity concentration are expressed by a formula, and calculated using the empirical formula described in the above-mentioned document ①. The mobility μnJ of electrons as majority carriers calculated in this way is the mobility given by scattering other than impurities such as phonon scattering. Then, it is expressed by the following equation.

In the above equation, the mobility μ,. is considered to be the mobility of electrons as majority carriers μn when no impurities are included, so μ1. It is calculated from the empirical formula that calculated . From these, the electron mobility μnI) given by scattering only by N-type impurities is calculated.

On the other hand, when determining the mobility of the 1E hole in the donor mobility determination unit 2, first, the minority carrier mobility/l+++ with respect to the concentration of N-type impurity is determined.

The mobility μ, 1 of holes as minority carriers is the sixth
The experimental results shown by the dotted line in the figure are expressed by a formula, and calculated using the empirical formula described in the above-mentioned document (■). The mobility μ, 1 of holes as minority carriers calculated in this way is the mobility μ, which can be obtained by lj scattering other than impurities. Then, it is expressed by the following equation.

μp11′″μ, D 10μp o --(2
1 In the above equation, the mobility μ, 0 is defined as the minority carrier mobility μ, 1 when no impurities are included, and is calculated from the empirical formula used to calculate μ, 1. From these, the iE hole mobility μ, D given by scattering only by the N-type impurity is calculated.

In this way, the electron mobility μnD and the hole mobility μ, D calculated as a function of the N-type impurity concentration ND are provided to the total mobility calculation unit 4.

The acceptor mobility determining unit 3 determines the electron mobility μ7A and hole mobility μ given by scattering by P-type impurities when only P-type impurities are introduced into the semiconductor.
is determined as a function of the P-type impurity concentration NA given from the input section 1.

Specifically, when determining the electron mobility, the acceptor mobility determination unit 3 first determines the minority carrier mobility μn1 with respect to the concentration of the P-type impurity. The mobility μnI of electrons as minority carriers is calculated using the empirical formula described in Document (2). The mobility μn1 of electrons as minority carriers calculated in this way is
The mobility given by scattering other than impurities is μn. Then, it is expressed by the following equation.

μ. 1 − μ. ^ Ten μn.
......(3) In the above equation, the mobility μ
n. is defined as the mobility μn1 of electrons as minority carriers when no impurities are included, and is calculated from the empirical formula used to calculate μn1. From these, the electron mobility μn^ given by scattering only by P-type impurities is calculated.

On the other hand, when determining the mobility of the iIE hole in the acceptor mobility determination unit 3, first, the mobility μ of majority carriers with respect to the concentration of P-type impurities is determined. The mobility μm of holes as majority carriers is calculated by expressing the experimental results shown by the solid line in FIG. The mobility μpJ of holes as majority carriers calculated in this way is the mobility μ given by scattering other than impurities. Then, it is expressed by the following equation.

In the above equation, the mobility μ,. is the mobility of majority carriers μ2 when no impurities are included. It is defined as , and is calculated from the empirical formula used to calculate μn. From these, the hole mobility μ given by scattering only by P-type impurities is calculated.

In this way, the electron mobility μ7A and the hole mobility μ calculated as a function of the P-type impurity concentration NA are provided to the total mobility calculation unit 4.

The total mobility calculation unit 4 calculates the total electron mobility μn using the electron mobility μ7D given from the donor mobility determination unit 2 and the electron mobility μ0^ given from the acceptor mobility determination unit 3. do. A specific calculation method is performed according to the following formula.

In addition, the total mobility calculation unit 4 calculates the hole mobility μ, D given from the donor mobility determination unit 2, and the hole mobility μ9J − μ, 80 μPO, given from the acceptor mobility determination unit 3. ...(4) Using the mobility μ2^,
t[Calculate the total mobility μn of the hole. A specific calculation method is performed according to the following formula.

In this way, the total mobility μ of electrons and the total mobility μn of holes, respectively calculated assuming that the scattering by N-type impurities and P-type impurities in a region containing both N-type and P-type impurities are independent, are as follows: The information is input to the numerical calculation execution unit 5.

Using the total mobility of electrons and holes given from the total mobility p output unit 4, the numerical calculation execution unit 5 simultaneously calculates Poisson's equation, the electron current continuity equation, and the hole current continuity equation, and calculates the numerical value. Solve using old calculations and analyze element characteristics.

In such a device simulator, for example, the second
As shown in the figure, a P' type base region 7 is laminated relatively thinly on an N' type collector region 6, and a P' type base region 7 is formed by introducing N type impurities into this base region 7 at a high concentration. N
When simulating the current-voltage characteristics of an NPN bipolar transistor consisting of a °-shaped emitter region 8 and having an impurity concentration distribution in the cross section along the line ■-■ in FIG. 2 as shown in FIG. The results shown in FIG. 4 were obtained.

FIG. 4 shows base current IB and collector current ■ with respect to base-emitter voltage vn8. In Fig. 4, when the simulation values of the present invention shown by the solid line and the conventional example shown by the dotted line are compared, there is a difference of more than twice for the base current 11'l. Can be seen.

FIG. 5 shows the carrier mobility and N
Simulation of current-voltage characteristics using the amount of change in band gap in a region where both type and P type impurities are mixed, determined from the amount of sandwiching of each band gap when +11-type and P-type impurities are introduced respectively. Value and reality 7N-1
It is a figure showing a value.

As is clear from FIG. 5, the simulated values of the base current and collector current are both extremely close to the actual i'1?1 value. This means that the amount of change in the bandgap is evaluated with high precision, and the carrier mobility determined by the present invention shown in Figure 4 is evaluated with high precision compared to when determined using the conventional method. This is due to the presence of

Note that the present invention is not limited to the above embodiments, and for example, the total mobility of electrons and holes, μnμ, can be calculated using the equations (1) and (2) described above, and the equation (3) described above.
) and (4) may be calculated using the relational expression shown in .

[Effects of the Invention] As explained above, according to the present invention, the carrier mobility when only first conductivity type or second conductivity type impurities are individually introduced can be independently adjusted according to the impurity concentration. Since the carrier mobility in the region containing both the first and second conductivity type impurities is calculated using the carrier mobility determined independently, it is possible to calculate the carrier mobility in the region where both the first and second conductivity type impurities are included. It becomes possible to determine carrier mobility in a mixed region with high precision, and it becomes possible to simulate device characteristics with high precision.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the configuration of a device simulator that performs simulation using a characteristic evaluation method according to an embodiment of the present invention, FIG. 2 is a cross-sectional view showing the structure of a Vibora transistor that is a simulation model, and FIG. is a diagram showing the impurity concentration distribution of the transistor shown in Figure 2, Figures 4 and 5 are diagrams showing the simulation results of current-voltage characteristics, and Figure 6 is a diagram showing the movement of holes as majority carriers and minority carriers. FIG. 7 is a diagram showing a conventional analysis procedure for element characteristics. DESCRIPTION OF SYMBOLS 1... Input unit, 2... Donor mobility determination unit, 3... Acceptor mobility determination unit, 4... Total mobility calculation unit, 5... Numerical calculation execution unit.

Claims (2)

[Claims] (1) The first mobility of electrons and holes when only impurities of the first conductivity type are introduced into the semiconductor is determined according to the concentration of the introduced impurities, and when only impurities of the second conductivity type are introduced into the semiconductor. The second mobilities of electrons and holes when introduced are determined according to the concentration of the introduced impurity, and the first and second mobilities of electrons are determined using the determined first and second mobilities of electrons.
Determine the total mobility of electrons in a semiconductor region where conductivity type impurities are mixed, and use the determined first and second mobilities of holes to determine the first and second mobilities.
1. A method for evaluating characteristics of a semiconductor device, comprising determining the total mobility of holes in a semiconductor region in which conductive type impurities are mixed, and evaluating characteristics of the semiconductor device from the determined total mobility of electrons and holes. (2) The electron mobility given by the scattering of impurities of the first conductivity type is μ_n_1, the electron mobility given by the scattering of the second conductivity type impurities is μ_n_2, and the electron mobility given by scattering by substances other than impurities is degree μ_
Let n_0, μ_n^-^1=μ_n_1^-^1+μ_n_2^-
The total electron mobility μ_n is determined from the relational expression ^1+μ_n_0^-^1, the hole mobility given by scattering of impurities of the first conductivity type is μ_p_1, and the mobility of holes given by scattering of impurities of the second conductivity type is calculated as μ_p_1. Let the mobility of holes given be μ_p_2, and the mobility of holes given by scattering other than impurities be μ_
Let p_0, μ_p^-^1=μ_p_1^-^1+μ_p_2^-
2. The method for evaluating characteristics of a semiconductor device according to claim 1, wherein the total mobility μ_p of the holes is determined from a relational expression expressed as ^1+μ_p_0^-^1.