Calculation of Electron concentration and Electrostatic potential profile for $Al_{x}Gal{-x}As/Ga_{x}In1$_{-x}$As/GaAs HEMT device by 2-Dimensional Quantum Mechanical analysis)

2차원 양자 역학적 해석에 의한 고속 통신용 $Al_{x}Gal{-x}As/Ga_{x}In1$_{-x}$As/GaAs HEMT 소자의 전자 농도 및 전위분포 계산

We present a self-consistent, 2-dimensional solution of the Poisson and Sch rodinger equation based on the finite difference method with a nonuniform mesh size for a AlGaAs/GaInAs/GaAs HEMT devide. During the interative self-consistent calculation, however, we calculate Schrodinger equation only a some region of device, not a fully region in order to save the moemory and the speed-up of computation, and then use the approximated data for the other region using by a interpolation method with a given values. Also we adopt the proper matrix transformation method that allows preservation of the symmetric, form of the discretized Schrodinger equation, even with the use of a nonumiform mesh size, therefor, can reduce the computation time. We calculate the wavefunction, eigenstates and the electron concentration uat channel layer nder the thermal equilibrium and the biased conditions, respectively. Also,these parameters are used to solve 2-dimensional tdistribution of potential in he entire region of device. It is proved that the method is very efficient in finding eigenstages extending over relatively large spatial area without loss of accuracy. So, it can be used rather easily in any sarbitrary modulation doped utucture.