本論文提出一個有系統的參數萃取方法來分析電流傳輸理論，以建立發光二極體電特性曲線之數值模型。為了考量發光二極體的非理想效應，此模型使用修正過的Shockley方程式，包含串聯電阻及非發光載子復合 (nonradiative recombination)，以建立擴散－復合模型。本論文使用兩步驟的迭代演算法結合非線性迴歸，以實現符合物理之電特性曲線模型。此數值方法可以有系統地分析多種發光二極體之電特性，有極高的準確性。所計算得到的復合電流可以量化Shockley-Read-Hall recombination，並提供發光二極體的磊晶品質給工程師參考。在本論文的分析過程中發現，分析區間須小心地選擇，以確保此模型是應用在適當的載子傳輸現象之中。由於GaN發光二極體具有較高的缺陷密度(dislocation)，其順向偏壓往往較AlGaAs及AlGaInP系列的發光二極體較高。而這些不同系列的載子陷阱 (trap) 具有不同的載子陷阱填補行為，反映在電特性曲線上。因此，我們可以從電特性曲線藉由擴散－復合模型，來估計陷阱填補過程。

本模型所萃取的參數包含zero-bias recombination current, reverse-bias saturation current, 及 series resistance。本論文提出簡易演算法，利用這些物理參數，計算復合－擴散電流之交會點；此交會點理論上代表兩項電流值相等，並可指出內部量子效率為50%之電壓值。本論文利用此復合－擴散交會點來驗證分析發光二極體之正確性，以偵測分析區間中的其他電流傳輸現象。此模型所計算之復合－擴散交會點與實驗值吻合，驗證了此模型之正確性。其後，此復合－擴散交會點可指出發光二極體之發光效率：當復合－擴散交會電壓值愈低，表示載子陷阱填補過程愈短，則順向偏壓值愈低。

In this dissertation, a systematic technique for numerical modeling of the current-voltage characteristics (I-V) for light-emitting diodes (LEDs) based on current transport mechanisms is proposed. The revised Shockley equation is employed under the consideration of nonideal effects, inclusive of series resistance and nonradiative recombination, leading to the diffusion-recombination model. The two-step iteration combined with the nonlinear regression technique to extract physical parameters for diodes, using a simple physical-based current-voltage model is demonstrated. The method has been applied to a wide variety of LEDs, and found to be an accurate and systematic technique for extracting diode parameters. The calculated recombination currents quantify the Shockley-Read-Hall recombination involving with localized states in LEDs, which can reveal the epitaxial quality for engineers. It has been found that the analyzing regime should be carefully chosen, for the adequate carrier transport phenomena. Frequently, the GaN-based LEDs bears higher forward voltage than the AlGaAs or AlGaInP-related LEDs, due to the high dislocation density in the epilayers. The various sets of traps have different trap-filling behaviors, which reflect on the I-V characteristics. Conversely, one can speculate the trap-filling process from the I-V plot.

The extracted parameters are zero-bias recombination current, reverse-bias saturation current, and series resistance. These parameters consists of the particular parameter for recombination-diffusion crossover, at which the recombination and diffusion currents have the same magnitude, indicating the theoretical internal quantum efficiency of 50%. In this dissertation, the recombination-diffusion crossover is proposed to examine the validity of the LED analyses by excluding the currents except for diffusion and recombination. The numerical recombination-diffusion crossover is in good accordance with the experiment at the adequate analyzing regime, which demonstrates the accuracy for the diffusion-recombination model. Consequently, the derived crossover reveals the optical efficiency for LEDs: The lower value for the crossover voltage, the shorter the trap-filling process and hence the lower value for forward voltage (operating voltage at 20 mA).

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