Data processing: structural design – modeling – simulation – and em – Simulating electronic device or electrical system – Circuit simulation
Reexamination Certificate
1999-09-14
2003-04-22
Broda, Samuel (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Simulating electronic device or electrical system
Circuit simulation
C703S002000, C716S030000
Reexamination Certificate
active
06553339
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a semiconductor device simulation method, in particular, to a simulation method which evaluates the device characteristics of a MOSFET (Metal-Oxide Semiconductor Field-Effect-Transistor) with a higher degree of accuracy and at a higher speed by a numerical simulation.
2. Description of Related Art
In a simulation, distributions of electric potential, electron density, and hole density inside the device when a voltage is applied to the electrodes under a preset device configuration or impurity distribution are obtained numerically. Using these numerical values, the current, the distribution of the electric field, and the electrode current inside the device are obtained. In general, a system of simultaneous equations consisting of the following Poisson equation, equation of continuity of electrons, equation of continuity of holes, electron transport equation, and hole transport equation is solved for electric potential &psgr;, electron density n, and hole density p.
Poisson equation
div(−&egr;grad(&psgr;))=
q
(
p−n+Nd−Na
) (1)
Equation of continuity of electrons
div(
Jn
)=
q
(
R−G
) (2)
Equation of continuity of holes
div(
Jp
)=−
q
(
R−G
) (3)
Electron transport equation
Jn=−q
*(&mgr;
n*n
*grad(&psgr;)−
Dn
*grad(
n
)) (4)
Hole transport equation
Jp=−q
*(&mgr;
p*p
*grad(&psgr;)+
Dp
*grad(
p
)) (5)
where &egr;: permittivity of the medium, &psgr;: electric potential (potential), Nd: donor density, Na: acceptor density, R: carrier re-coupling amount, G: carrier generation amount, n: electron density, p: hole density, &mgr;n: electron mobility, &mgr;p: hole mobility, Dn: electron diffusion coefficient, Dp: hole diffusion coefficient, Jn: electron current density, Jp: hole current density, q: unit electric charge.
Moreover, the electron diffusion coefficient Dn and the hole diffusion coefficient Dp satisfy the following equations, respectively.
Dn=&mgr;n*k*T/q
Dp=&mgr;p*k*T/q
where k: Boltzmann constant, and T: temperature.
According to the conventional simulation method, a given MOS type semiconductor device is divided into many micro regions. Moreover, mesh points (or grid points) are placed on each of the micro regions. Next, the electric potential, a electron density, and hole density at each of the mesh points are calculated. It is interpreted that these electric potential, electron density, and hole density at each of the mesh points represent the electric potential, electron density, and hole density in the micro region. By connecting the electric potentials, electron densities, and hole densities in all the micro regions, the distributions of electric potential, electron density, and hole density throughout the MOS type semiconductor device are calculated.
Next, a MOSFET structure simulator according to the prior art will be explained.
This MOSFET structure simulator has an input means to which simulation conditions such as the shape of the semiconductor device, the distribution of impurities, temperature, input voltage, and the like are input, a characteristic calculation means which calculates the device characteristics of the semiconductor device by solving prescribed equations of device physics based on the distribution information provided from the input setting means, and a judging means which judges whether the characteristics value calculated by the characteristic calculation means has converged or not. In some cases, an output means which outputs information containing the calculation result produced by the characteristic calculation means in a prescribed form is installed in the apparatus, and the entire configuration including the output means is called a simulator. The expression “the characteristics value has converged” refers to a state in which the amount of change of the characteristic value that changes in accordance with the simulation process has reached below a prescribed level.
The following calculations are carried out in the above-described characteristics calculation means.
(1) Discretization of the semiconductor device into mesh points
(2) Setting the initial values of the electric potential &psgr;, electron density n, and hole density p
(3) Calculation of the vertical electric field Ev of the semiconductor device from the initial values of the electric potential &psgr;, electron density n, and hole density p
(4) Calculation of the carrier mobility &mgr; from the impurity concentration N, temperature T of the semiconductor device, and vertical electric field Ev
(5) Calculation of the electric potential &psgr;, electron density n, and hole density p at each mesh point from the vertical electric field Ev and the carrier mobility &mgr;
(6) Calculation of the electron current density Jn and hole current density Jp from the electric potential &psgr;, electron density n, hole density p, and carrier mobility &mgr; at each mesh point
(7) Calculation of the value of the electric current from the electron current density Jn and hole current density Jp
Next, the simulation method with the above-described MOSFET structure simulator will be explained with reference to the flow chart shown in FIG.
8
.
First, conditions required for the simulation such as the shape of the semiconductor, the distribution of impurities, temperature, and the like are input to the input means (step S
501
).
Next, prescribed calculations are carried out by the characteristic calculation means. First, the semiconductor device is divided into meshes (step S
502
). Next, the initial values of the electric potential &psgr;, electron density n, and hole density p are set based on the conditions defined in the simulation condition input process (step S
501
) (step S
503
). Using these values, the vertical electric field Ev of the semiconductor device is calculated (step S
504
).
Next, the carrier mobility &mgr; is calculated from the impurity concentration N, temperature T of the semiconductor device, and vertical electric field Ev obtained in the previous process (step S
505
). The electric potential &psgr;, electron density n, and hole density p at each mesh point are then calculated from the vertical electric field Ev and the carrier mobility &mgr; obtained in the previous process (step S
506
). Next, the electron current density Jn and hole current density Jp are calculated at each mesh point from the electric potential &psgr;, electron density n, hole density p, and carrier mobility &mgr; using equations (4) and (5) (step S
507
). Moreover, the value of the electric current that flows through each terminal is obtained from the electron current density in and hole current density Jp calculated in the previous process (step S
508
).
Next, the judging means judges whether the value of the electric current calculated in the previous process by the characteristic calculation means has converged or not. First, it is judged whether the difference between the amount of the incoming current and the amount of the outgoing current lies in a prescribed convergence condition range or not (step S
509
). If the difference does not lie in the prescribed convergence condition range, the characteristic value calculation is repeated re-starting from the vertical electric field calculation process (step S
504
) using the electric potential &psgr;, electron density n, and hole density p as the initial values obtained in the electric potential &psgr;, electron density n, and hole density p calculation process (step S
506
). If the difference lies in the prescribed convergence condition range, the device characteristic of the semiconductor device is evaluated using the electric current value.
The simulation information and the characteristic value of the semiconductor device obtained in the previous processes are output and displayed by an output device inside the simulator or another output device.
It should be noted that, in a MOS type semiconductor device,
Broda Samuel
Oki Electric Industry Co, Ltd.
Rabin & Berdo P.C.
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