LED是近年來發展快速的研究課題之一，許多文獻引用Shockley方程式來描述LED內部p-n junction處之電流-電壓變化，但由於Multiple Quantum Well結構之LED出現，導致Shockley方程式可能已經不再適用於當今之LED。
本文參考其他文獻之實驗數據與適用於具有多重量子井結構之LED的Diode方程式，並將其應用至LED模型內進行數值模擬。藉由數值模擬，可以得到LED內部之電位分佈與溫度分佈，溫度、電壓、總功率和發光效率之間的關係。
根據本文之研究，可以得到在不同電壓與冷卻裝置下對同一顆LED晶片的模擬結果，之後只要改變材料參數即可對大量商用的LED進行模擬，除了可以減少對LED測試的成本外，也可以經由分析出的答案找出最符合經濟價值的LED，在本文的研究中發現冷卻裝置的強弱，在一開始的時候其效果十分顯著，當其冷卻裝置越來越強，反而對整個LED的影響並不是非常劇烈，而輸入電壓的大小對功率和發光效率的變化比較劇烈。一般來說，如果在同一個電壓下想增加其發光效率，那就要設法加強LED的冷卻裝置，但是，總功率卻會隨著冷卻裝置的加強而變小，而且在較強的冷卻裝置下在加強其冷卻效果，其效果不彰，因此要在這裡面做選擇。

[1] Schubert EF. Light-Emitting Diodes, 2nd ed., Cambridge University Press, Cambridge, England; 2006.
[2] Lin JF, Wu MC, Jou MJ, Chang CM, Lee BJ, Tsai YT. Highly reliable operation of indium tin oxide AlGaInP orange light-emitting diodes. Electronics Lett 1994;30:1793-4.
[3] Chitnis A, Kumar A, Shatalov M, Adivarahan V, Lunev A, Yang JW, Simin G, Khan MA. High-quality p-n junction with quaternary AlInGaN/InGaN quantum wells. Appl Phys Lett 2000;77: 3800-2.
[4] Xi Y, Schubert EF. Junction-temperature measurement in GaN ultraviolet Light-emitting diodes using diode forward voltage method. Appl Phys Lett 2004;86:2163.
[5] Lee CC, Chen WV, Park J. A new I-V model for light-emitting devices with a quantum well. Microelectronics J 2006;37: 1335-8.
[6] Chen JC, Sheu GJ, Hwu FS, Chen HI, Sheu JK, Lee TX, Sun CC. Electrical-Optical Analysis of a GaN/Sapphire LED Chip by Considering the Resistivity of the Current-Spreading Layer. Opt Rev 2009;16:213-5.
[7] Hwu FS, Chen JC, Tu SH, Sheu GJ, Chen HI, Sheu JK. A Numerical Study of Thermal and Electrical Effects in a Vertical LED Chip. J Electrochem Soc 2010;157: H31-7.
[8] 徐岳,垂直式發光二極體電位降之數學模式研究, 國立清華大學碩士論文, 新竹, 台灣; 2011。
[9] Lee SL. A Strongly Implicit Solver for 2-Dimensional Elliptic Differential-Equations. Numer Heat Transfer 1989;16:161-78.
[10] Incropera FP, Dewitt DP, Bergman TL, Lavine AS. Fundamentals of Heat and Mass Transfer. New York: Wiley-Interscience; 2007.
[11] Eiting CJ, Grudowski PA, Dupuis RD. P- and N-Type of GaN and AlGaN Epitaxial Layers Grown by Metalorganic Chemical Vapor Deposition. J Electron Mater 1988;27:206-9.
[12] Tahar RBH, Ban T, Ohya Y, Takahashi Y. Tin doped indium thin films: Electrical properties. J Appl Phys 1998;83:2631-45.
[13] Kim DH, Park MR, Lee HJ, Lee GH. Thickness dependence of electrical properties of ITO film deposited on a plastic substrate by RF magnetron sputtering. Appl Surf Scie 2005;253:409-11.
[14] Kim H, Kim KK, Choi KK, Kim H, O Song JO, Cho J, Baik KH, Sone C, Park Y, Seong TY. Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry. Appl Phys Lett 2007;91:023510.
[15] Benoy MD, Mohammed EM, Suresh BM, Binu PJ, Pradeep B. Thickness dependence of the properties of indium tin oxide (ITO) FILMS prepared by activated reactive evaporation. Braz J Phys 2009;39:629-32.
[16] Kim DH, Kim HR, Lee SH, Byon E, Lee GH. Electrical and structural properties of multicomponent transparent conducting oxide films prepared by co-sputtering of AZO and ITO. J Non-Cryst Solids 2010;356:1779-83.