JPH11204383A - Simulation apparatus, simulation method, and computer-readable recording medium storing simulation program - Google Patents

Abstract

[PROBLEMS] To provide a simulation technique capable of efficiently obtaining stable results while reducing computation time and consumption of computer resources such as storage media. SOLUTION: In determining the behavior of particles such as electrons in a semiconductor, and in determining electrical characteristics and element structure, one particle is divided into particles instead of determining the final state after a state transition by random numbers. Then, weights of transition probabilities are assigned to all states that can take the divided particles, and distribution is performed so as to satisfy the energy conservation law and the momentum conservation law. Next, by collecting the divided particles that have transitioned by state transition,
Reconstruct one particle. In this way, the final state of each particle after the state transition is determined.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technology for designing and examining the structure and electrical characteristics of a semiconductor device such as an LSI when developing the device, and more particularly to a device simulation and a process simulation of a semiconductor device using a Monte Carlo method. .

[0002]

[Prior Art] With the recent increase in integration density, the development cost of LSI has rapidly increased, and there is a demand for more efficient development. In designing and developing semiconductor devices, simulations with quantitative predictive capabilities are becoming increasingly common. It is becoming increasingly important. As a simulation in the design and development of such a semiconductor device, a process of simulating a manufacturing process of the semiconductor device and, as a result, obtaining a distribution of impurities and defects in the semiconductor device or a geometric shape of components of the semiconductor device. A simulator (process simulation apparatus) and a device simulator (device simulation apparatus) for simulating electrical characteristics of a semiconductor device are used.

As an actual work in the development of an LSI, first, an approximate device structure is selected and designed for a predetermined characteristic specification. Then, a process simulation for designing a process for realizing the general device structure is performed. In this process simulation, a raw material, a manufacturing procedure to be applied thereto, and individual process conditions in the manufacturing procedure are given as inputs, and an impurity distribution and other element structures formed in the manufacturing process are calculated. Next, a device simulation for obtaining the electrical characteristics of the element is performed using the element structure obtained in this way and the electrical conditions applied to the element from the outside as inputs. Whether or not the obtained characteristics are the desired characteristics to be produced is checked by device simulation, and if the characteristics are the desired characteristics, the actual semiconductor device manufacturing process is started. Here, when the desired characteristics are not obtained, the element desired to be produced cannot be produced in the conceived manufacturing process, so that the process simulation is changed again by changing the conditions of the manufacturing process or the procedure itself such as the order of the process. A device simulation is performed using the result of the process simulation as input data. By repeating the above operation until a manufacturing process of an element having desired characteristics is obtained,
A method of manufacturing a semiconductor device is determined, and a desired semiconductor device is actually manufactured.

In this device simulation, it is necessary to analyze and obtain the behavior of particles such as electrons and holes (holes) in a semiconductor region constituting a semiconductor device. Transport issues need to be dealt with. As one of methods for simulating the problem of transporting particles in a semiconductor, a Monte Carlo method is known. In this method, usually, tens of thousands of particles are prepared, and state changes of the particles due to scattering and an external field (an electric field or a magnetic field) are tracked by random numbers. However, the Monte Carlo method
There are two major problems. This problem will be described below by taking electrons as a representative of particles.

(A) One is that it takes a long calculation time to generate a random number. In particular, since the scattering angle distribution cannot be generally represented by an analytical function, it is necessary to generate further random numbers in selecting the final state by scattering, which consumes an enormous amount of calculation time. This will be described with reference to FIGS. 19 and 20. Assuming that the electron energy is ε, the probability that the carriers are scattered between the scattering angles π and θ is S (ε, COS θ).
Then, when a function representing the scattering angle distribution is F (ε, COS θ), S (ε, COS θ) is defined as follows.

[0006]

(Equation 1) F (ε, COS θ) has COS θ dependency as shown in FIG. 19, for example. When θ = 0, S (ε, COS θ) = λ (ε), and this is called the total scattering probability. When calculating the scattering angle θ,
Generate a random number rnd from 0 to 1. The following formula:

(Equation 2) Cos θ that satisfies is the cosine of the scattering angle. S (ε, cos
If θ) is expressed analytically with respect to cos θ, it is easy to find cos θ that satisfies this equation. On the other hand, the scattering angle distribution F
If (ε, cos θ) cannot be analytically expressed with respect to cos θ, it is necessary to generate further random numbers in order to obtain the scattering angle. A calculation procedure for determining a scattering angle by using random numbers will be described with reference to FIG.

First, in step 830, a random number rnd1 between 0 and 1 is generated, and the scattering angle is set to cos θ ₁ = 1-2 rnd1 (3). The scattering angle distribution at this time is defined as F ₁ = F (ε, cos θ ₁ ) (4). Next, at step 831, a random number rnd2 between 0 and 1 is generated again. This is set as the value of the scattering angle distribution, and F ₂ = Fmax × rnd2 (5) is set. Here, Fmax is the maximum value of the scattering angle distribution.
If F ₂ <F ₁ in step 832, cos θ ₁ is adopted as the scattering angle. If F ₂ > F ₁ , cos θ ₁ is not adopted as the scattering angle, and the process returns to step 830 again. Thus, the Monte Carlo method consumes an enormous amount of calculation time.

(B) On the other hand, another problem of the Monte Carlo method is that the distribution may be unstable because a finite number of electrons are tracked. In particular, a stable distribution cannot be obtained in a region with a low electron existence probability (a high-energy region of electrons when taking a device analysis of a semiconductor as an example).

As a method for solving such a problem of the Monte Carlo method, there is an "iterative method" (by Kazuya Matsuzawa,
"Analysis of carrier transport in semiconductors by Boltzmann transport equation", Keio University Master's thesis, 1986
Year). In this method, a space formed by energy and a scattering angle is first discretized into a predetermined size, thereby dividing the space into cells. Since the distribution function of electrons is distributed on each cell, the problem of unstable distribution in a low probability region does not occur. Hereinafter, the electron distribution in the cell is referred to as a cell distribution.
These cell distributions are repeatedly transitioned between cells according to state changes due to scattering and an external field. If such advantages of the iterative method are applied to the Monte Carlo method, it is possible to generate a particle distribution with high accuracy (Japanese Patent Laid-Open No. Hei 6-236).
354). Further, since a scattering angle is assigned to each cell, it is not necessary to generate a random number and determine the scattering angle in order to determine the final state after scattering. However, analyzing a low-probability high-energy state requires a wide range of wave numbers, and the number of cells becomes enormous. Therefore, the consumption of storage media such as a magnetic disk of a computer becomes enormous.

[0010]

As described above, in the particle simulation by the Monte Carlo method, since a finite number of particles are tracked, the distribution in the low probability region may become unstable. Further, since it is necessary to generate a random number to select the final state after scattering, the calculation time becomes enormous. Furthermore,
The iterative method solves the above-mentioned problems, but requires a great deal of computer resources such as a magnetic disk.

In view of the above problems, the present invention reduces the consumption of storage media such as a magnetic disk of a computer,
It is an object of the present invention to provide a semiconductor simulation device capable of efficiently obtaining a stable result.

It is another object of the present invention to provide a semiconductor simulation method capable of efficiently and stably obtaining a stable result in a short time while reducing the consumption of computer resources.

Still another object of the present invention is to provide a computer-readable recording medium storing a semiconductor simulation program for reducing computation time and obtaining efficient and stable results while reducing consumption of computer resources. It is.

[0014]

Means for Solving the Problems To achieve the above object, a first feature of the present invention is that each time a state transition of each particle in a semiconductor occurs, a finite number of possible states after this state transition is obtained. Means for dividing into state meshes, means for determining a "weight" from the transition probability to each state constituting the state mesh, and generation of a plurality of divided particles by dividing particles, weighting the state mesh And a step of collecting divided particles and reconstructing one particle after predetermined processing on the divided particles.

The particles in the semiconductor include electrons and holes in the semiconductor or ¹¹ B ⁺ ,
^It means impurity ions such as ³¹ P ⁺ and ⁷⁵ As ⁺ . For example, electrons in a semiconductor have a constant energy accelerated by an electric field, and impurities, defects, LO phonons, TO
The energy state changes due to scattering by phonons or the like, and the energy state is settled. The first feature of the present invention is that this process can be efficiently simulated in a short time. That is, according to the first aspect of the present invention, the final state of each particle after scattering can be determined without generating a random number, so that the calculation speed is improved as compared with the method of generating a random number. In addition, since the particles are divided and the transition probability is weighted and distributed for all states that can take the divided particles, a stable distribution can be obtained even in a region where the existence probability of the particles is low. Further, since the Monte Carlo method is applied to one particle configured for each state by adding the individual divided particles, consumption of a storage medium such as a magnetic disk of a computer can be reduced as compared with the iterative method.

The object of the simulation of the present invention is mainly a process simulation for obtaining a profile of an impurity distribution in a semiconductor, a geometric shape of a thin film, a trench, and the like, and a device simulation for obtaining electric characteristics of a semiconductor device. Here, the semiconductor device is a MOSFET,
Junction FET, MESFET, HEMT, bipolar transistor, static induction transistor (SIT), IGB
Discrete devices such as T and thyristor and integrated circuits including them. Furthermore, the behavior of high-energy particles (so-called "hot carriers" such as hot electrons) in avalanche photodiodes (APDs), impatt diodes, gun effect devices, and the like,
This is effective for determining the behavior of hot carrier injection into an insulating film used in an EEPROM or the like.
Process simulation is effective for describing the interaction between high-energy particles (ions and radicals) and a semiconductor substrate in ion implantation, ion etching, ion milling, plasma etching, and the like.

A second feature of the present invention is that each time a state transition of each particle in a semiconductor occurs, a state that can be taken after the state transition is divided into a finite number of state meshes; Determining a weight from the transition probability to each state, generating a plurality of divided particles by dividing the particles, weighting and distributing the state mesh, and after performing a predetermined process on the divided particles, Collecting at least one particle and reconstructing one particle.

According to the second feature of the present invention, the final state after scattering of each particle such as an electron, hole, or ion in a semiconductor can be determined without generating a random number. The calculation speed is improved as compared with. In addition, since the particles are divided and the transition probability is weighted and distributed for all states that can take the divided particles, a stable distribution can be obtained even in a region where the existence probability of the particles is low. Further, since the Monte Carlo method is applied to one particle configured for each state by adding the individual divided particles, the consumption of computer resources can be reduced as compared with the iterative method.

In particular, in the second aspect of the present invention, before the dividing step, there is a step of calculating a free flight time Δt by the Monte Carlo method, and after the distributing step, all the particles within this free flight time Δt are included. If it is determined whether the vehicle is traveling, and if all the particles are traveling, the step of collecting the divided particles is performed, so that Monte Carlo simulation can be performed more efficiently and with reduced computer resources. One electron can be reconstructed for each free flight time Δt, and the scattering table generated so far can be discarded, so that computer resources such as a data recording device can be saved. More specifically, it is preferable to set an analytic band structure represented by an analytic function, and determine the final state after scattering using a division model when the scattering probability is not represented by the analytic function. Here, the “division model” refers to a procedure of dividing the state into a finite number of state meshes, determining weights, assigning weights, and distributing the divided particles to the state mesh. Alternatively, a band structure calculated by band calculation may be set, and the final state after scattering may be determined using a division model.

Further, in the second aspect of the present invention, a threshold energy is set, and for a particle having an energy equal to or higher than the threshold energy, a band structure calculated by band calculation is used. For particles having the following energies, it is preferable to calculate a state transition by a division model using a band structure represented by an analytical function. In this way, the behavior of "hot electrons" having energy equal to or higher than the threshold energy injected into the floating gate (control gate) of the EEPROM can be obtained in a short time and accurately in consideration of the band structure of the semiconductor. Further, in the second feature of the present invention, a band structure obtained by self-consistently solving the Schrodinger equation and the Poisson equation is used for particles having energy equal to or higher than a certain threshold energy. Analytical bands are set for particles with energies less than or equal to the threshold energy.
It is preferable to calculate the state transition by The two methods can be selectively used according to the energy of the particles, and a highly accurate simulation can be performed while saving the calculation time.

A third feature of the present invention is that it is a computer-readable recording medium storing a program of the simulation method described in the second feature. That is, the program for implementing the semiconductor simulation method described in the second aspect is stored in a computer-readable recording medium, and the recording medium is read by a computer system, whereby the simulation of the present invention can be executed. . Here, the recording medium means, for example, a magnetic disk device, an optical disk device, a magnetic optical disk device, a magnetic tape, and the like. Specifically, a floppy disk, a CD-ROM, an MO disk, a cassette tape, and the like that can record these programs are included.

As described above, the computer simulation-readable recording medium storing the simulation program according to the third aspect of the present invention can realize the semiconductor simulation efficiently and in a short time while controlling the processing control unit of the computer. it can. That is, if a simulation is performed using the computer-readable recording medium according to the third aspect of the present invention, the final state after scattering of each particle can be determined without generating a random number. Calculation speed is improved compared to the method. In addition, since the particles are divided and the transition probability is weighted and distributed for all states that can take the divided particles, a stable distribution can be obtained even in a region where the existence probability of the particles is low. Further, since the Monte Carlo method is applied to one particle configured for each state by adding the individual divided particles, consumption of a storage medium such as a magnetic disk of a computer can be reduced as compared with the iterative method. As a result, it is possible to provide a simulation capable of improving the calculation speed and the calculation accuracy while consuming less computer resources than the conventional Monte Carlo method. In addition, the development efficiency of a fine device requiring a highly accurate simulation is improved.

[0023]

FIG. 1 is a block diagram showing a functional configuration of a process simulation apparatus according to the present invention. The process includes a deposition process such as CVD, an etching process such as RIE, and the like.
It has a function of simulating a semiconductor element manufacturing process such as an ion implantation step, an oxidation step, and a diffusion step, and a function of displaying, on an output device, an element shape and an impurity distribution in a semiconductor, which are the simulation results. That is, as shown in FIG. 1A, a process simulation apparatus 40 according to an embodiment of the present invention simulates a series of manufacturing processes with an input unit 31 that receives input of data and instructions from an operator. A processing control unit 41 having a function unit, an output unit 34 for outputting a simulation result, and a data storage unit 32 storing predetermined data required for a semiconductor device manufacturing process as input data.
And a program storage unit 33 storing a simulation program and the like.

Here, as functional means for simulating a series of manufacturing steps of the processing control section 41, ion implantation step processing means 42, oxidation step processing means 43, deposition step processing means 44, etching step processing means 45, diffusion step processing At least means 46 are provided. For example, the deposition process means 44 includes low-temperature CVD, high-temperature CVD, epitaxial growth, vacuum deposition, sputtering, and the like. Further, as the etching step processing means 45, RI
E, of course, includes wet etching in addition to dry etching such as ECR ion etching and light excitation etching. The input unit 31 includes a keyboard, a mouse, a light pen, a floppy disk device, and the like. The processing control unit 41, the data storage unit 32, and the program storage unit 33 include a CPU and an R connected to the CPU.
It is configured with a normal computer system including a storage device such as an OM, a RAM, and a magnetic disk. The output unit 34
Is composed of a display device, a printer device, and the like.

As shown in FIG. 1B, the ion implantation step processing means 42 in the processing control section 41 shown in FIG. 1A includes a state mesh dividing means 51, a weight determining means 52, a distribution means 53,
And at least a collecting means 54. The state mesh dividing means divides the possible states after the state transition into a finite number of state meshes every time a state transition occurs between the implanted ions and the atoms of the substrate with which the ions collide. The weight determination means 52 determines the weight of the dislocation energy for each scattering angle from the transition probability to each state constituting the state mesh. The distribution means 53 distributes the energy of the implanted ions so as to satisfy the energy conservation law and the momentum conservation law by weighting the dislocation energy for each scattering angle. The collecting means 54 calculates a change in energy due to elastic / inelastic scattering with the atoms of the substrate for each of the divided ions, reconstructs one ion for each of the changed energies, and calculates the energy of the ions after the state transition. Determine the final state. Thus, the distribution of the implanted ions after implantation, the projected range R _P , the standard deviation ΔR _P of the projected range, and the like can be obtained.

Input data for each process executed by the process control unit 41 is stored in the data storage unit 32, and program instructions are stored in the program storage unit 33. These input data and program instructions are sent to the CPU as needed.
And the arithmetic processing is executed, and data such as numerical information generated in each step is stored in a data storage unit 32 such as a RAM or a magnetic disk. Note that a program for implementing the process simulation method such as the ion implantation step may be stored in a computer-readable recording medium. This recording medium can be read by a computer system, stored in the program storage unit 33, and the program can be executed by the processing control unit 41 to realize the process simulation method. Here, the recording medium includes a device capable of recording a program such as a magnetic disk device, an optical disk device, a magneto-optical disk device, and a magnetic tape device. The external memory device of the computer
It is included in the recording medium mentioned here.

On the other hand, the device simulation apparatus
It has a function to input the results of the device structure and impurity distribution obtained by the process simulation, and sets the electrical boundary conditions such as applied voltage and current for the input structure to improve the electrical characteristics of the device. The simulation function and the resulting potential, electric field, and current distribution in the semiconductor device, carrier distribution of electrons and holes, or current-
It has a function of displaying voltage characteristics and the like on an output device. That is, as shown in FIG. 2A, a device simulation apparatus 70 of the present invention includes an input unit 61 for receiving an input of data, a command, or the like from an operator, and a processing control unit 71 for simulating electrical characteristics of a semiconductor device. And an output unit 64 for outputting a simulation result, a data storage unit 62 storing predetermined data necessary for analyzing characteristics of the semiconductor device, and a program storage unit 63 storing a device simulation program and the like. ing. The processing control unit 71 has at least a voltage / current setting unit 72 for setting a terminal voltage or current condition and an element characteristic calculation unit 73.

As shown in FIG. 2B, the element characteristic calculating means 73 includes the state mesh dividing means 51 and the weight determining means 5.
2, at least a distributing means 53 and a collecting means 54. The behavior of particles such as electrons and holes in a semiconductor device such as an FET, a bipolar transistor, and an electrostatic induction transistor (SIT) can be calculated by the element characteristic calculation means 73 using the Monte Carlo method. In particular, scattering of particles such as electrons and holes due to impurities and defects in the semiconductor or lattice vibrations such as LO phonons and TO phonons can be efficiently calculated in a short time. For example, nMOSFET
When the behavior of the electrons in the channel is calculated, the state mesh dividing means 51 creates a cell separated by the energy and the scattering angle, and divides the electrons. Weight determining means 52
Creates a scattering table according to the electron scattering and determines the weight of the scattering probability. The distribution means 53 divides the electrons according to the weight of the scattering probability, distributes the electrons to predetermined cells so as to satisfy the energy conservation law and the momentum conservation law, and creates a distribution electron distribution table. After it is confirmed that all the divided electrons have traveled within the predetermined time interval Δt, the collecting means 54 collects the divided electrons and reconfigures one electron to determine the final state of the electrons after the state transition. Such splitting of electrons
Set it to calculate the electron behavior which runs in the channel of the nMOSFET is repeated until the predetermined time t _{en d} elapses a predetermined time interval Delta] t. One electron can be reconstructed at every predetermined time interval Δt, and the scattering table generated so far can be discarded, so that computer resources can be saved and device simulation can be performed in a short time.

In FIG. 2A, the input unit 61 is constituted by a keyboard, a mouse, a light pen, a floppy disk device or the like. Processing control unit 71, data storage unit 6
2 and the program storage unit 63 are a CPU and this CP
It is configured with a normal computer system including a storage device such as a ROM, a RAM, and a magnetic disk connected to U. The output unit 64 is configured by a display device, a printer device, or the like. Note that a program for realizing the device simulation method as in the process simulation may be stored in a computer-readable recording medium. This recording medium is read by a computer system, and the program storage unit 63
And the program may be executed by the processing control unit 71 to implement the device simulation method. Here, the recording medium includes, for example, an apparatus capable of recording a program such as an external memory device of a computer, a magnetic disk device, an optical disk device, a magneto-optical disk device, a magnetic tape device, and the like.

The semiconductor simulation apparatus of the present invention is composed of the entire process simulation apparatus 40 of the present invention shown in FIG. 1 and the device simulation apparatus 70 of the present invention shown in FIG. Actually, the process simulation apparatus 40 of FIG. 1 and the device simulation apparatus of FIG. 2 may be configured by independent hardware, or may be configured by sharing the same hardware. That is, the input unit 31 shown in FIG. 1 and the input unit 61 shown in FIG. 2 may be the same, and the output unit 34 shown in FIG. 1 and the output unit 64 shown in FIG. It doesn't matter. The other data storage units 32 and 62, the program storage units 33 and 63, etc. may be common hardware or independent hardware. The processing controllers 41 and 71 have the same structure as the hardware.
Of course, each function may be achieved by software.

FIG. 3 is a bird's-eye view showing the external appearance of a semiconductor simulation device in which a process simulation device and a device simulation device are realized by the same hardware. The main body of the semiconductor simulation device 80 includes a floppy disk device (floppy disk drive) 81 and an optical disk device (optical disk drive) 82. A floppy disk 83 is inserted into the floppy disk drive 81 and a CD-ROM 84 is inserted into the optical disk drive 82 from the insertion slot, and a predetermined read operation is performed. Can be installed in the system. Also, by connecting a predetermined drive device, for example, a ROM 85 as a memory device used for a game pack or the like,
A cassette tape 86 as a magnetic tape device can also be used.

The flow of manufacturing an actual semiconductor device such as an LSI is as follows. Data such as the distribution of impurities and defects in the semiconductor device obtained by the process simulation apparatus is input to the device simulation apparatus, and the current-
Obtain device characteristics such as voltage characteristics, impedance characteristics, and high frequency characteristics. When performing device simulation, input data for providing electrical boundary conditions such as applied voltage and current are added at the same time as the results of the element structure and impurity distribution obtained by the process simulation.
Further, if necessary, the device characteristics as a result of the device simulation may be input data of the circuit simulation to obtain the circuit characteristics. It is checked by device simulation or circuit simulation whether the obtained characteristics are the desired characteristics to be produced, and if the characteristics are the desired characteristics, the process of manufacturing an actual semiconductor device is started. If the desired characteristics are not attained, the element desired to be produced cannot be produced in the production process considered.Therefore, the conditions of the production process are changed, and the procedure itself, such as the order of the processes, is changed and the process simulation is performed again. Device simulation is performed using the result as input data. Further, the characteristics of the actual semiconductor device obtained as a result of the actual semiconductor device manufacturing process are measured, and the initial design is evaluated. If the characteristics of the actually manufactured semiconductor device do not satisfy the required specifications as a result of the evaluation, the design is changed and the process simulation is performed again. Then, a loop consisting of a series of procedures for performing a device simulation using the result of the process simulation as input data is repeated.

[0033] In the field of semiconductor devices such as LSIs, the competition from research (design) to development is short. In consideration of the reality of such competition in the semiconductor industry, the simulation period must be as short and accurate as possible. According to the present invention, the cycle of a loop from research (design) to development of a semiconductor device including a process simulation and a device simulation is drastically shortened, so that an industrial benefit and its importance are extremely high.

Each function processing means shown in the processing control unit 41 or 71 in FIG. 1A or 2A has the function of a normal simulation apparatus and the functions of each embodiment (as shown below). Each specific example) has a characteristic function and is realized.

(First Embodiment) FIG. 4 shows a first embodiment of the present invention.
FIG. 13 is a cross-sectional view showing a schematic structure of an nMOSFET targeted for device simulation according to the embodiment. In the nMOSFET shown in FIG. 4, a channel region is formed near the upper interface of p-type semiconductor region 5 sandwiched between n ⁺ source region 3 and n ⁺ drain region 4. A gate electrode is formed above the channel region via a gate oxide film 2.

Hereinafter, the device simulation of the present invention will be described with reference to FIG. That is, FIG. 5 is a flowchart in the case where the behavior of the electrons 21 in the channel region 5 of the nMOSFET shown in FIG. 4 is obtained by Monte Carlo device simulation.

First, in step 101, physical parameters used in the Monte Carlo simulation and the initial state of electrons are set. In step 102, the free flight time by the Monte Carlo method is calculated. In step 103, a cell as shown in FIG. 6 is created by dividing by energy and scattering angle. The vertical axis is energy, the horizontal axis is the cosine of the scattering angle, and the horizontal axis is divided for each cosine of a constant scattering angle. As shown in FIG. 7, the energy of the cell may be expressed in a wave number space of k _x -k _y and may be divided by a certain wave number region. In this case, an energy value is assigned to each grid point of the cell according to the band structure. In the actual calculation, there is a wave number component k _z in the z direction, but it is omitted in FIG. 7 for simplicity.

Next, at step 104, a scattering table is created. The scattering table is created according to the type of scattering. As the type of scattering, for example, nM shown in FIG.
Various types of scattering such as impurity scattering in the channel region 5 of the OSFET, scattering due to surface defects, and phonon scattering can be cited.
Hereinafter, scattering refers to such scattering. In step 105, the electrons are divided according to the weight of the scattering probability in the channel region 5, and distributed to predetermined cells to create a distribution table of the divided electrons. Hereafter, Step 1
The process 400 from 03 to step 105 is called a “split model”. The process of determining the electron distribution by the division model will be described by taking impurity scattering as an example. In the impurity scattering, it is assumed that the scattering angle distribution has a shape shown in FIG. At this time, in the device simulation according to the first embodiment of the present invention, electrons are divided by weighting the scattering angle distribution shown in FIG. 8A, and cells are distributed as shown in FIG. 8B. I do. According to this division model, the distribution of electrons can be obtained without generating random numbers.
The calculation speed improves. Further, even when the scattering probability is low, the divided electrons are distributed with the weight of the scattering probability, so that a stable particle distribution can be obtained.

Next, at step 106, it is determined whether all the divided electrons have traveled within the predetermined time interval Δt. If there are any split electrons that are not running, the process returns to step 102 again. If all the divided electrons have traveled, the process proceeds to step 107, where the divided electrons included in the state mesh obtained by dividing all the states of the analysis space prepared in advance into a finite number are collected to reconstruct one electron. By reconstructing one electron, the scattering table generated so far is discarded, and computer resources can be saved. Next, at step 108, a time for the next calculation is set, and at step 1
At 09, it is determined whether a predetermined time t _end has elapsed. If not, the process proceeds to step 102.

In the case of a pMOSFET, Monte Carlo device simulation can be performed in exactly the same procedure by applying the above-described division model for holes instead of electrons.

(Second Embodiment) FIG. 9 shows a second embodiment of the present invention.
FIG. 3 is a cross-sectional view showing a schematic structure of an EEPROM targeted for device simulation according to the embodiment.
p sandwiched between n ⁺ source region 3 and n ⁺ drain region 4
A floating gate electrode (floating gate electrode) 7 is formed above the type semiconductor region 5 via a gate oxide film (first gate insulating film) 6. On the floating gate electrode 7, a control gate electrode (control gate electrode) 9 is formed via a second gate insulating film. As the first gate insulating film 6, for example, a silicon oxide film (SiO ₂ film) formed by a thermal oxidation method is used. The floating gate electrode 5 has
For example, a polycrystalline silicon (doped polysilicon) film doped with an impurity for ensuring high conductivity is used.
As the second gate insulating film 8, an ONO (SiO ₂ / Si ₃ N ₄ / SiO ₂ ) film in which a silicon oxide film and a silicon nitride film each having a high capacitance value and excellent insulation resistance are sequentially laminated is used. . The control gate electrode 9 has a doped polysilicon film,
Either a silicide film that is a compound of doped polysilicon and a refractory metal, a single-layer film of a refractory metal film, or a composite film in which a silicide film or a refractory metal film is laminated on a doped polysilicon film Is done. In order to increase the operation speed of the EEPROM, for example, the information reading operation speed, it is preferable to use a single layer film of a silicide film or a high melting point metal film, or a composite film. The control gate electrode 9 is connected to a word line or is formed integrally with the word line.

The write operation of the EEPROM is realized by applying a high voltage to the control gate (control gate) 9 and injecting channel hot electrons into the floating gate (control gate) 7. In order to be injected into the floating gate 7, the hot electrons in the channel need to have a higher energy than the potential barrier E _{C at} the interface between the gate oxide film 6 and the p-type semiconductor region 5 as shown in FIG. is there. When the energy of the electron is more than E _C ,
Electron conduction reflects high energy bands in semiconductor regions, eg, silicon (Si). Therefore, in order to accurately calculate the current injected into the floating gate 7, an accurate band structure of silicon (Si) as shown in FIG. 11 is required. The value of E _C is 3.1 eV in the case of hot electron writing in the EEPROM. The band structure in the p-type semiconductor region 5 is considered by band calculation.

FIG. 12 is a flowchart in the case of performing a device simulation of the EEPROM shown in FIG. 9 using the Monte Carlo method.

First, in step 201, physical parameters used in the Monte Carlo method and initial states of electrons are set. In step 202, the free flight time by the Monte Carlo method is calculated.

Next, in step 203, it is determined whether or not the energy of the electrons is equal to or higher than the potential barrier E _C shown in FIG. That is, (a) Step 20
In step 3, if the electron energy is equal to or higher than E _C , the process proceeds to step 204. That is, since energy is the behavior of the more hot electrons E _C reflects the higher energy band of the silicon, as shown in FIG. 11, consider the band calculation the band structure in a step 204. When a band structure obtained by band calculation is used, it is necessary not only to generate random numbers but also to search the band structure to select a final state that satisfies the band structure after scattering, which further increases the calculation time. . Therefore, in step 205, calculation is performed using the division model described in the first embodiment. That is, the first
In this embodiment, cells similar to those described with reference to FIGS. 6 and 7 are created, and a scattering table is created. Then, a process of a division model including a series of steps of dividing the electrons according to the weight of the scattering probability in the channel region 5 and distributing the divided electrons to predetermined cells to create a table of the distribution of the divided electrons is performed. Next, the process proceeds to a step 210.

[0046] (b) the energy of the particles in step 203 proceeds to step 206 when the following threshold energy E _C, the setting of the analytical band. That is, step 2
At 06, the relationship between energy and wavenumber is analytically given. In the case of electrons in a semiconductor, for example, the following relationship exists between the energy ε and the wave number.

[0047]

(Equation 3) Next, in step 207, it is determined whether or not the scattering probability is represented by an analytic function to determine the scattering angle. If the scattering probability is represented by an analytical function, the Monte Carlo method is used in step 208. On the other hand, as described above, when the scattering probability cannot be represented analytically, it is necessary to generate a larger number of random numbers than in the case where the scattering probability is represented analytically. Therefore, in such a case, the division model described in FIG. In the split model, the split particles are allocated to all reachable states. Therefore, the scattering angle of each split particle is determined without generating a random number, and the calculation time is significantly reduced. Then
The process moves to step 210.

Next, at step 210, it is determined whether all the divided electrons have traveled within the predetermined time interval Δt. If there are any split electrons that are not running, the process returns to step 202 again. If all the divided electrons have traveled, the process shifts to step 211 to collect the divided electrons included in the state mesh obtained by dividing all the states of the analysis space prepared in advance into a finite number to reconstruct one electron. By reconstructing one electron, the scattering table generated so far is discarded,
Save computer resources. Then, step 21
2 to set the time for the next calculation, it determines whether elapsed predetermined time t _{en d} in step 213. If it has not elapsed, the process proceeds to step 202.

(Third Embodiment) A third embodiment of the present invention relates to device simulation of a miniaturized MOSFET. Here, the nMOSFET will be described.

As the miniaturization of the gate length (channel length) of the nMOSFET as shown in FIG.
In the vicinity of the channel region of T, a strong electric field F in a direction perpendicular to the interface
Confine electrons in a potential well as shown in FIG. As a result, as shown in FIG. 13, the motion of the electrons near the channel region of the nMOSFET becomes two-dimensional, and the energy is quantized. The potential shown in FIG. 13 is given, for example, by the following equation.

Ψ (z) = Fz, z> 0 (7) = ∞, z <0 (8) In this region, it is necessary to consider the subband structure of the quantized two-dimensional electron. Therefore, it is necessary to obtain the energy level and the wave function of each subband and calculate the scattering probability. By the way, there are two methods for calculating the subband structure of a quantized two-dimensional electron. One is FIG.
Assuming a triangular potential like this, this method is to solve the Schrodinger equation to analytically determine the wave function and energy (first method). The electron energy obtained by this method is given by the following equation, for example.

[0052]

(Equation 4) In this case, there is no need to solve the Poisson equation. The other is a method for solving Poisson's equation and Schrodinger's equation in a self-consistent manner (second method). In this method, since the wave function and the energy cannot be obtained analytically, it is necessary to store both as numerical data.

In the first method, since the wave function and the energy are analytically represented, there is no need to store them as numerical data, so that computer resources can be saved and the calculation speed can be improved. However, since the potential is simplified by approximating it with a triangle, there is a problem in accuracy. On the other hand, in the second method, the quantized subband is obtained while determining the effective potential felt by the electrons by solving the Poisson equation, so that the accuracy is high. However, since the Schrodinger equation and Poisson equation must be solved for each time step in a self-consistent manner,
The calculation time becomes enormous. By the way, the physical review magazine B48 (1993), pp. 2244 to 2274 (Physic
al Review B48 (1993) pp2244-2274 (hereinafter referred to as Document A)) shows a subband structure as shown in FIG. According to FIG. 14, in the low energy region, it can be seen that the analytical subband structure is sufficiently accurate. However, at a certain energy E _C or more, the accuracy of the analytical sub-band structure deteriorates, and it can be seen that the accuracy is better when the sub-band structure is provided by solving the Schrodinger equation and the Poisson equation in a self-consistent manner.

The third embodiment of the present invention provides a method for obtaining the subband structure of the two-dimensional electrons quantized in a miniaturized nMOSFET in a short time and with high accuracy. FIG. 15 shows the flowchart.

First, in step 301, physical parameters used in the Monte Carlo simulation and the initial state of electrons are set. Next, in step 302, the free flight time by the Monte Carlo method is calculated.

Next, at step 303, it is determined whether or not the electron energy is larger than a certain threshold energy E _C. In order to obtain a two-dimensional electron subband structure of the nMOSFET, E _C = 0.5 eV. As shown in FIG. 14, this threshold energy E _C 0.5 eV
Is an energy at which the accuracy of the subband structure obtained analytically becomes worse at an energy higher than this. Therefore, the third Schrodinger equation and Poisson's equation by the threshold energy E _C = 0.5 eV or more in the embodiment of the present invention provides a sub-band structure as a numerical value by solving self-consistently data, below E _C Gives an analytical subband structure. However, this threshold energy does not necessarily need to be fixed to 0.5 eV, and may be changed as needed. For example, to increase the calculation accuracy, the threshold energy may be reduced. With this method, it is possible to perform a highly accurate simulation while saving the calculation time.

Therefore, as shown in FIG. 15, the calculation is divided into two types in step 303. That is, (a)
When the energy of the particles is equal to or _smaller than the threshold energy Ec in step 303, the process proceeds to step 304, and an analytical band is set in step 304. Step 3
At 05, it is determined whether the scattering probability is represented by an analytical function. If the scattering probability cannot be represented by the analytic function, the Monte Carlo method needs to generate extra random numbers as compared to the case where the scatter function is represented by the analytic function. If the scattering probability is represented by an analytic function, the scattering angle can be determined analytically. Next, the process proceeds to step 310.

(B) In step 303, when the electron energy is equal to or higher than the threshold energy E _C , the process proceeds to step 308. In step 308, the band structure is calculated by solving the Schrodinger equation and the Poisson equation in a self-consistent manner. Next, as described in step 205 of the second embodiment, the division model is used in step 309. Next, the process proceeds to step 310.

Then, in step 310, it is determined whether all the divided electrons have traveled within the predetermined time interval Δt. If there are any split electrons that are not running, the process returns to step 302 again. If all the divided electrons have traveled, the process shifts to step 311 to collect the divided electrons included in the state mesh obtained by dividing all the states of the analysis space prepared in advance into a finite number to reconstruct one electron. By reconstructing one electron, the scattering table generated so far is discarded, and computer resources can be saved. Next, at step 312, a time for the next calculation is set, and at step 312,
It is determined whether the processing time t _end has elapsed in 02. If not, the process moves to step 302.

As described above, in the third embodiment of the present invention, the method of solving the Schrodinger equation to obtain the wave function and the energy analytically, and the method of making the Poisson equation and the Schrodinger equation self-consistent. By appropriately combining the solving methods, a highly accurate simulation can be performed while saving the calculation time.

(Fourth Embodiment) The above first to third embodiments
Although the device simulation has been described in the fourth embodiment, the process simulation will be described in the fourth embodiment. As an example of this process simulation, ion implantation in a manufacturing process of an nMOSFET will be described. NMOSFE as shown in FIG.
The manufacturing process of T will be briefly described as follows.

(A) First, a Si ₃ N ₄ film is CVD-formed on an n-type silicon substrate doped with phosphorus (P), and is patterned so as to leave the Si ₃ N ₄ film in a device region. Then, an oxidation (LOCOS) step for forming an isolation insulating film is performed using the Si ₃ N ₄ film as an oxidation-resistant film. Prior to oxidation for element isolation (LOCOS), the portion where the Si ₃ N ₄ film is removed has boron ( ¹¹ B) as a p-type impurity for preventing inversion.
⁺ ) Is ion-implanted. A thick oxide film is formed in the element isolation region where the Si ₃ N ₄ film is removed, and p-type impurity boron ( ¹¹ B ⁺ ) is introduced under the oxide film to prevent inversion. Thereafter, the Si ₃ N ₄ film used for LOCOS is peeled off.

(B) Next, boron ( ¹¹ B ⁺ ) is ion-implanted and thermally diffused to form a p-type well region 5 to be a p-type semiconductor region shown in FIG. 4 in a portion to be an element region. Get the desired depth and concentration.

(C) Next, a thin oxide film serving as a dummy oxide film is formed on the surface of the p-type well region 5. The boron gate threshold voltage Vth control the ⁽¹¹ B ⁺⁾ is ion-implanted into the dummy oxide film over.

(D) Further, boron ( ¹¹ B ⁺ ) for preventing punch-through is ion-implanted at an increased acceleration energy so that a high-concentration p-type region is located below the channel region.

(E) Thereafter, the dummy oxide film is peeled off to form a gate oxide film 2 as shown in FIG. A polysilicon serving as a gate electrode is deposited thereon, and the gate is patterned to form a polysilicon gate electrode 1. Then, the surface of the patterned polysilicon gate electrode 1 is post-oxidized. Arsenic ⁷⁵ As ⁺ , which is an n-type impurity, is ion-implanted into p-type semiconductor region 5 to form n ⁺ source region 3 and n ⁺ drain region 4 using patterned polysilicon gate electrode 1 as a mask. At this time, ⁷⁵ As ⁺ is also ion-implanted into the polysilicon region 1 serving as the gate electrode. Subsequently, the upper surface in the CVD oxide film covered, ⁷⁵
A thermal step for activating As ⁺ is performed.

(F) Further, a contact hole is opened in the CVD oxide film to expose a part of the surface of n ⁺ source region 3 and n ⁺ drain region 4. Then, a metal such as Al is deposited by vacuum evaporation or sputtering, and the metal is patterned by RIE or the like to form a source electrode above the n ⁺ source region 3 and a drain electrode above the n ⁺ drain region 4. I do.

What is important in the simulation of the nMOSFET manufacturing process is the p-type well region 5, boron (B) for controlling the gate threshold voltage Vth, boron (B) for preventing punch-through, the n ⁺ source region 3, and The purpose is to determine the diffusion depth and impurity profile of each of the n ⁺ drain regions 4. In this case, boron (
^In addition to the ion implantation dose Q for each of ¹¹ B ⁺ ) and arsenic ( ⁷⁵ As ⁺ ), the projected range Rp of each of these ions, the standard deviation ΔRp of the projected range, x, perpendicular to Rp, It is necessary to find predetermined boundary conditions (initial conditions) such as standard deviations Δx and Δy in the y direction. Then, based on these boundary conditions (initial conditions), the diffusion of impurities is calculated in consideration of predetermined heat treatment conditions such as heat treatment temperature and heat treatment time.

The Monte Carlo method is used to calculate the projection range Rp and the like that give the initial conditions for impurity diffusion. In this method, a random number is generated for each collision process, the relative position with respect to the target atom (for example, silicon atom), that is, the collision parameter is determined, and the scattering of the implanted ions is calculated based on the value. It is. The scattering factors are nuclear stopping power and electron stopping power. Here, “nuclear stopping power” means the amount of energy loss of the implanted ions due to collision between the implanted ions and the nuclei constituting the substrate. On the other hand, "electron stopping power"
Means the energy loss of the implanted ions due to the collision between the implanted ions and the electrons in the substrate. With this method, not only can the ion implantation distribution through a complicated laminated film be accurately calculated, but also the damage amount at each position can be accurately estimated. However, in order to obtain a highly accurate distribution, it is necessary to calculate the trajectories of a large number of implanted ions, and the calculation by the conventional Monte Carlo method has a problem that the calculation time is enormous.

There are two types of scattering processes of the ions implanted into the semiconductor: scattering with atoms constituting the semiconductor substrate and scattering with electrons surrounding the atoms. The scattering with atoms will be described with reference to FIG. As shown in FIG. 16, the energy, mass, and atomic number of the implanted ions 11 are E and M, respectively.
Assuming that the mass and atomic number of the atom (atom of the substrate) 12 against which the implanted ions collide are M2 and Z2, respectively, the transfer energy T (E, θ) is

(Equation 5) The scattering angle θ is the Coulomb potential energy V (r) representing the interaction between the two particles 11 and 12 involved in the collision.
Using,

(Equation 6) Can be expressed as Here, p is a collision parameter shown in FIG. By solving the equation (12) for p, p is obtained from θ. Nuclear stopping power Sn (E) is obtained by integrating transfer energy T (E, θ) with respect to collision parameter p,
It is required as follows.

[0071]

(Equation 7) On the other hand, the electron stopping power is defined by the following equation.

S _e (E) = k _e ε ^0.5 (14) Here, ε is a normalized energy, and k _e is a constant determined by the type of ion.

In the process simulation according to the fourth embodiment of the present invention, the Monte Carlo method is applied as follows using a divided model. In this process simulation, the region is finely divided in the depth direction (z direction),
Consider ion implantation into a layered structure. First, as shown in FIG. 17, each of the implanted ions is divided by weighting the transfer energy for each scattering angle. When this operation is performed for each implanted ion, a classification table as shown in FIG. 18 is created. Now, if the division of the implanted ion energy is represented by a subscript i and the division of the scattering angle θ is represented by a subscript j, (i, j)
Can be represented by F _ij . This classification table is prepared for each depth (z to z + dz).

The implanted ions undergo elastic or inelastic collisions with the atoms of the substrate while traveling by the depth dz, and the traveling direction θ
(J) and the energy E (i) are changed. The probability of transition from (i, j) to (i ', j') is calculated using the nuclear stopping power and the electron stopping power described above. When all the split ions travel in dz, the distribution of ions in (i, j) is updated from F _ij to F ′ _ij . This updated ion distribution F '
One ion for each energy is reconstructed from _ij . This calculation is performed for each depth, and the calculation is performed until the implanted ions stop.

According to this method, the number of ions can be substantially increased by dividing the implanted ions, so that the distribution N of the implanted ions can be increased without increasing the actual number of implanted ions.
(Z ₀ ) can be determined accurately. When the distribution N (z) of the implanted ions after heat treatment is determined using the distribution N (z ₀ ) of the implanted ions as an initial condition and a predetermined diffusion coefficient, heat treatment temperature and heat treatment time, the p-type well region 5 of the nMOSFET can be obtained Determine the diffusion depth of boron (B) for controlling gate threshold voltage Vth, boron (B) for preventing punch-through, arsenic (As) in n ⁺ source region 3 and n ⁺ drain region 4, and the impurity profile thereof. can do.

(Other Embodiments) As described above, the present invention has been described with reference to the first to fourth embodiments.
The discussion and drawings that form part of this disclosure should not be understood as limiting the invention. From this disclosure, various alternative embodiments, examples, and operation techniques will be apparent to those skilled in the art.

In the above description, the MOS device has been mainly described, but the junction type FET, MESFET, H
Of course, the present invention may be applied to an EMT, a bipolar transistor, a static induction transistor (SIT), an IGBT, a thyristor, a GTO, and the like. Of course, the present invention is also effective for a simulation of a semiconductor device such as an avalanche photodiode (APD), an impatt diode, and a gun effect device in which hot electrons pose a problem. It is also possible to simulate a mixed mode diode of a tannet diode and an impatt diode with avalanche multiplication. Further, simulation of Brillouin laser or Raman laser involving interaction of electrons with LO phonons and TO phonons can be performed.

Further, the present invention is applicable not only to the simulation of particles in a semiconductor as described above, but also to the whole of transport simulation. For example, the present invention is also applicable to simulation of particles in a gas phase or plasma, or simulation of particles at a gas phase / solid phase interface. Therefore, although the ion implantation process has been described as an example of the process simulation, it is needless to say that the process may be applied to a deposition process such as CVD or an etching process such as RIE. Further, the present invention may be applied to simulation of general particle transport phenomena in fields other than semiconductor devices and semiconductor manufacturing technology.

As described above, it should be understood that the present invention includes various embodiments and the like not described herein. Therefore, the present invention is limited only by the matters specifying the invention described in the claims that are reasonable from this disclosure.

[0080]

As described above, according to the present invention,
It is possible to provide a semiconductor simulation device capable of improving calculation speed and calculation accuracy while reducing consumption of a storage medium such as a magnetic disk.

Further, according to the present invention, it is possible to provide a semiconductor simulation method capable of efficiently obtaining a stable result in a short time while reducing the consumption of computer resources.

Further, according to the present invention, it is possible to provide a computer-readable recording medium storing a semiconductor simulation program for shortening the calculation time and efficiently obtaining stable results while reducing the consumption of computer resources. it can.

Further, according to the present invention, the development efficiency of a fine device requiring a highly accurate simulation is improved.

[Brief description of the drawings]

FIG. 1 is a block diagram schematically showing a process simulation apparatus according to the present invention.

FIG. 2 is a block diagram schematically showing a device simulation apparatus according to the present invention.

FIG. 3 is a bird's-eye view showing the appearance of the semiconductor simulation device of the present invention.

FIG. 4 is a cross-sectional view illustrating a schematic structure of an nMOSFET to be subjected to device simulation according to the first embodiment of the present invention.

FIG. 5 is a flowchart illustrating a device simulation process according to the first embodiment of the present invention.

FIG. 6 is a diagram showing cells separated by cosine of energy and scattering angle.

FIG. 7 is a diagram showing cells separated by energy and wave number.

FIG. 8A is a diagram illustrating a scattering angle distribution of impurity scattering, and FIG. 8B is a diagram illustrating a split electron distribution in the first embodiment of the present invention.

FIG. 9 is a schematic cross-sectional view schematically showing an EEPROM to be subjected to device simulation according to a second embodiment of the present invention.

FIG. 10 is a diagram for explaining a phenomenon in which electrons cross a potential barrier of a gate oxide film of an EEPROM and are injected into a floating gate electrode.

FIG. 11 is a diagram illustrating a band structure of silicon.

FIG. 12 is a flowchart illustrating a device simulation process according to the second embodiment of the present invention.

FIG. 13 is a diagram showing a quantized energy level and its state density in a two-dimensional electronic potential well in a channel region of a short channel nMOSFET.

FIG. 14 is a diagram comparing the energy obtained analytically with the energy obtained by solving the Schrodinger equation and the Poisson equation simultaneously and self-consistently.

FIG. 15 is a flowchart illustrating a device simulation process according to the third embodiment of the present invention.

FIG. 16 is a diagram illustrating an interaction between implanted ions and atoms constituting a substrate in a process simulation according to a fourth embodiment of the present invention.

FIG. 17 is a diagram illustrating a distribution of divided ions.

FIG. 18 is a diagram showing a classification table of implanted ions.

FIG. 19 is a diagram showing a function F (ε, COS θ) representing a scattering angle distribution in the Monte Carlo method.

FIG. 20 is a flowchart showing a process of determining a scattering angle by random numbers from a scattering angle distribution in a conventional Monte Carlo simulation.

[Explanation of symbols]

Reference Signs List 1 gate electrode 2 gate oxide film 3 n ⁺ source region 4 n ⁺ drain region 5 p-type semiconductor region (P well region) 6 gate oxide film (first gate insulating film) 7 floating gate electrode (floating gate electrode) 8 ONO film (Second gate insulating film) 9 control gate electrode (control gate electrode) 10 depletion layer 11 implanted ions 12 atoms colliding with ions (atoms of substrate) 21 electrons 22 hot electrons 31 input unit 32 data storage unit 33 program storage Unit 34 output unit 40 process simulation apparatus 41, 71 processing control unit 42 ion implantation process processing unit 43 oxidation process processing unit 44 deposition process processing unit 45 etching process processing unit 46 diffusion process processing unit 51 state mesh division unit 52 weight determination unit 53 Distributing means 54 Collecting means 70 Vice simulation device 72 voltage / current setting unit 73 element characteristic calculation unit 80 semiconductor simulation apparatus 81 floppy disk drive 82 CD-ROM drive 83 Floppy disk 84 CD-ROM 85 ROM 86 Tape

──────────────────────────────────────────────────の Continued on the front page (51) Int.Cl. ⁶ Identification code FI H01L 21/82 G06F 15/353 27/115 H01L 21/82 C 29/00 27/10 434 29/78 29/78 301Z 21 / 336 371 21/8247 29/788 29/792

Claims (4)

[Claims] 1. Every time a state transition of each particle in a semiconductor occurs, means for dividing a possible state after the state transition into a finite number of state meshes, and a transition to each state constituting the state mesh Means for determining a weight from the probability, means for dividing the particle to generate a plurality of divided particles, means for assigning the weight to the state mesh and distributing the divided mesh, At least the step of collecting and reconstructing one particle. Each time a state transition of each particle in the semiconductor occurs, dividing a possible state after the state transition into a finite number of state meshes; and a transition to each state constituting the state mesh. Determining weights from the probabilities; generating a plurality of divided particles by dividing the particles; distributing the state mesh with the weights; after performing predetermined processing on the divided particles, At least a step of collecting and reconstructing one particle. 3. A step of calculating a free flight time Δt by a Monte Carlo method before the dividing step, and determining whether all particles travel within the free flight time Δt after the distributing step. 3. The simulation method according to claim 2, wherein the step of collecting the divided particles is performed when all the particles are traveling. 4. Each time a state transition of each particle in the semiconductor occurs, dividing a possible state after the state transition into a finite number of state meshes. Determining a weight from a transition probability to each of the states constituting the state mesh; generating a plurality of divided particles by dividing the particles; distributing the state mesh with the weight; Computer-readable recording medium storing a program including at least a step of collecting the divided particles and reconstructing one particle after predetermined processing on the divided particles.