The Simulation of Carrier Transport under 3D Poisson and Drift-Diffusion, Schr?dinger and Landscape Model in InGaN Light Emitting Diode

In the classical 3-D Poisson drift-diffusion self-consistent solver developed by our lab is versatile that we can combine it with other solvers and functions to simulate the carrier transport behavior and electric characteristic. However, it is hard to couple well with Schr odinger equation and solve them self-consistently under current injection conditions. Therefore, we apply the Poisson drift-diffusion with landscape theory. The landscape theory model is able to consider the quantum effective potential. It solvesHu(r) = (-Δ+Ec;v)u(r) = 1, which is a Schr odinger-like equation with uniform right-hand side and modifies the electron and hole density according to the obtained effective potential (1/u). Not only localized landscape theory avoids solving Schr odinger equation, which is a eigenvalues and eigenvectors problem and it costs much computation time, but also provides the effective quantum potential in the classical Poisson drift-diffusion model. In this thesis, we apply the random alloy generator and strain solver to construct the atom distribution and calculate the strain distribution before solving the Poisson drift-diffusion equations. Simulation results show that quantum well potential solved with landscape model is smoother and higher, which leads to the extended carrier distribution. It also lowering the quantum barrier''s potential due to the quantum tunnelling effects. The forward voltage is smaller as a result. When the random atom distribution is obtained by random number generator, the composition map is decided by a Gaussian weighting function with broadening factor sigma. When sigma increases, the potential and carrier density becomes smoother and forward the voltage declines because of lower potential. Different average indium compositions from 11%, 14%, 17% to 20% were studied. It appears that lower piezoelectric potential would be obtained with landscape model which leads to the decrease of forward voltage. But in the In0.11Ga0.89N case, the forward voltages solved with and without landscape are closed because peizo-polarization is smaller and the bandgap is higher. In chapter 4, we simulate the carrier transport behavior in the fluctuate quantum well(QW) thickness. With fluctuated thickness in a larger scale compared to local indium fluctuation, the polarization declines and provides a percolation path at the barrier. The forward voltages solved without landscape decline with increasing fluctuate thickness. However, fluctuated thickness may leads to the stronger confinement, larger effective bandgap and reduction of forward voltage.