Trap analysis Validity of Hurkx trapassisted tunneling Student

Trap analysis Validity of Hurkx trap-assisted tunneling Student : Ying-Lun Kao Advisor : Dr. Hao-Hsiung Lin Date : 108. 09. 25

Abstract

Outline • • SRH recombination model Field-enhanced thermal emission rate model Curve fitting method Fitting results

SRH recombination model 1. Approximation of SRH recombination rate 2. SRH recombination current equation

Pure SRH recombination rate

SRH recombination current equation

Field-enhanced thermal emission rate model 1. Hurkx model: Effective-mass approximation 2. Korol model: Green’s function approach

Effective-Mass Approximation (EMA) Without periodic potential In periodic & external potential Classical E. O. M. : Semi-classical E. O. M. : Schrödinger’s equation : Effective-mass equation : General Hamiltonian equation in periodic lattice potential :

Two complete sets of orthogonal The Bloch functions The Wannier function

Expansion in Wannier functions normalized wave function

Differential equation for the amplitude function Re-ordering index j

Differential equation for the amplitude function But how? The dispersion relation of perfect crystal:

Hurkx TAT model: Linearly varying potential

General SRH+TAT expression:

Is it plausible?

General SRH+TAT expression:

In sum,

Validity of Hurkx trap-assisted tunneling model Single-band approximation Spherical & parabolic band approximation

In. Ga. As EMA confident interval

Band structure In. Ga. As: # of valleys 4 3 0. 4 0. 5 longitudinal 0. 95 0. 9 transverse 0. 32 0. 3 Valley separation 0. 54 0. 78 Nonparabolicity 1. 0 Effective mass In. P 1 0. 08

Curve fitting method Setting TCAD Doping Profile • Zn diffusion • Charge layer Distribution • In. P maximum field • In. Ga. As maximum field • Depletion width Least square method • Find best trap level, effective mass and lifetime

Fitting results •

游朝政論文內容截圖 2 e 17 7. 8 e 16 5 e 16 2 e 15 Multiplication layer: 0. 42 μm Charge layer: 0. 2 μm Grading layer: 0. 12 μm Absorption layer: 3 μm 7. 5 e 14

0917/IV_fitting. py

0917/IV_ABthick 1. py

0917/IV_fitting. py

0917/IV_ABthick 1_beta. py

0917/IV_fitting. py

0917/IV_fitting. py

0917/IV_ABthick 1. py

0917/IV_ABthick 1_beta. py

0917/IV_fitting. py

0917/IV_fitting. py

0917/IV_ABthick 1. py

0917/IV_ABthick 1_beta. py