Single Particle Transport in GaAs Using Monte Carlo

This page is best viewed by Mozilla Firefox 21.0 at a screen resolution of 1024 x 768 pixels.

The program of electron transport in bulk GaAs using Monte Carlo method consists of main program and some subroutines named param, initia, smc, and out. Inside smc subroutine, there are also subroutines named drift(tau) and scat. The parameters involved here are tem (lattice temperature), cimp (impurity concentration), tmax (total simulation time), and fx (applied electric field). The flowchart of main program is shown in Fig 1.

Fig 1. Main Program

The Gamma and L valleys are engaged here. The scattering mechanisms taken into account are those to acoustic acoustic phonons, non-polar optical phonons and impurities. The non-parabolicity of bands are included except for the scattering by polar optical phonon, for which the parabolic  band model is assumed. The other parameters such as q (magnitude of electronic charge), h (Plank’s constant), bk (Boltzmann’s constant) , ep0(permittivity of free space), and am0 (electron mass in vacuum) are declared in param subroutine. This subroutine output are gm (gamma), and swk (scattering rate). The flowchart of param subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method is shown in Fig 2.

Fig 2. The param Subroutine

The initia subroutine provides initial condition for particles and also some outputs such as: iv (valley index) for Gamma and L valleys; kx, ky, and kz, i.e., the component of wave vector in x, y, and z direction. This subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method is shown in Fig 3.

Fig 3. The initia Subprogram

Then, the particle motion during simulation time is calculated in smc subroutine. Here, tau (the flight time) is generated by random number generator. After the free flight, the electron will be scattered again by one of the scattering mechanisms, including self-scattering. Figure 4 shows the smc subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method.

Fig 4. The smc subroutine

If we assume that only the  electric field in x-component is non zero, then the drift(tau) subroutine will produce the carrier velocity and energy by monitoring each electron flight and then taking an average over all flights. The calculation is processed in drift(tau) subroutine. The drift(tau) subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method is shown in Fig 5.

Fig 5. The drift(tau) subroutine

For isotropic scattering, (i.e., if the scattered electron has the same probability of being in any direction after scattering), the components k’x, k’y and k’z can be found in scat subroutine. Figure 6 shows the scat subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method.

Fig 6. The scat subroutine

Figure 7 shows the rnd subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method that generates random number generator.

Fig 7. The rnd subroutine

Figure 8 shows the out subroutine as part of program of electron transport in bulk GaAs using Monte Carlo method that displays the output paramaters such as ve (mean velocity), en (mean energy).

Fig 8. The out subroutine

If you want to learn more about Monte Carlo method, you can read “Numerical Simulation Of Submicron Semiconductor Devices” by Kazutaka Tomizawa.

Acknowledgment

I want to acknowledge Assoc. Prof. Dr.  Ah Heng You (Multimedia University, Malaysia) who giving me discussions on many topics of Monte Carlo Method.

By Anak Agung Ngurah Gde Sapteka, University of Indonesia.

One Response to Single Particle Transport in GaAs Using Monte Carlo

  1. gung dwi says:

    great job, gung!

Leave a Reply

Your email address will not be published. Required fields are marked *

*

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>