在三維泊松-擴散飄移、薛丁格、藍斯蓋特模型之下氮化銦鎵發光二極體中的載子傳輸之數值模擬探討

Abstract

由我們實驗室開發的三維有限元素帕松與漂移-擴散模型能夠與 各種方程解結合來模擬載子傳輸與元件特性，不過目前很難與薛丁 格方程式做結合，所以我們使用了三維有限元素帕松與漂移-擴散模 型結合藍斯蓋特理論。藍斯蓋特理論能夠考慮有效的量子位勢，並 解Hu(r) = (-Δ+Ec;v)u(r) = 1 類薛丁格方程式，這不只能夠避免直 接解需耗費大量時間的薛丁格方程式，還能夠在三維帕松與漂移-擴 散模型中考慮到有效量子位勢。在計算帕松與漂移-擴散模型前，我 們運用了隨機合金分佈擾動產生器得到原子分布以及解應變方程。 在第三章中，考慮藍斯蓋特理論之後的位勢較高且較為平滑導致較 平整的載子分佈。在平均銦含量為14、17與20百分比的發光二極體 中，考慮藍斯蓋特後所解出的極化位勢能夠導致啟動電壓降低。但 在銦含量為11百分比的發光二極體中，是否考慮藍斯蓋特的啟動電 壓差距並不大，因為壓電場極化較小且能帶較寬。在第四章中，我 們模擬了載子在波動量子井厚度的傳輸。在量子井厚度有波動的情 況下，極化電場下降導致在位勢屏障，在不考慮藍斯蓋特所解出來 的啟動電壓會隨著波動量子井厚度增加而降低。然而，啟動電壓在 考慮藍斯蓋特理論下，並不會隨著波動量子井厚度增加而降低，波 動量子井的厚度增加會導致量子井變小增加限制。

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.