半導體電激發光致冷元件與氮化鎵型發光二極體之理論模擬與分析

Abstract

在本篇論文中，我們以自洽求解的方式進行砷化鎵半導體電激發光致冷元件的可行性與致冷能力之相關研究；我們也使用簡便的模型化分析方式以了解氮化鎵型發光二極體之效率衰變成因與內部極化場所造成的影響。

針對半導體電激發光致冷元件，我們的研究指出漏電流是導致高偏壓下元件效率衰變的主要原因。藉由引入載子阻擋層，我們可以有效地避免少數載子直接到達對向電極，進而大幅提升元件的工作效率與冷卻能力。為了更進一步提高元件的冷卻功率，我們可以增加元件的主動層厚度以有效地提升元件內的總複合速率。我們發現，對砷化鎵電激發光致冷元件而言，最大冷卻功率發生在主動層厚度為5微米時，其可達97瓦每平方公分。進一步增加主動層的厚度將會使得主動區內的載子分佈不均，反而降低最大冷卻功率。另外，在主動區內進行摻雜並沒有帶來太多的好處，反之，若是主動層內的p型摻雜濃度太高反而會引發更強烈的歐傑複合，而不利於冷卻。我們也對電激發光致冷元件的可行性進行分析，我們發現欲使砷化鎵型致冷元件達到冷卻效果所需的外部量子效率高達82%，若是侷限在元件內部而無法逃脫的光子皆轉變成熱能，則所對應的光萃取效率為87%。如此高的效率需求，對現今的半導體工藝而言，仍是一大挑戰。幸運的是，我們可以藉由光子回收機制來大幅降低冷卻所需的光萃取效率。我們提供了一個簡單的模型來分析光子回收機制對外部量子效率所造成的增益關係。我們的模型指出，光子回收機制的作用就如同一個內建的光電池，它可以經由主動層吸收未能逃脫的光子，轉換成可利用的電子電洞對，進而降低外部的注入電流並提升元件的效率。在理想的光子回收效率下，達成冷卻所需要的光萃取效率可以大幅降至20%以下。而若是90%未能逃脫的光子可被回收利用，則所需的光萃取效率也僅需45%。我們的研究說明，有相當高的機會可以實現半導體電激發光致冷元件！

在另外一方面，我們也利用模型化的方式分析氮化鎵型發光二極體的效率表現。我們的穩態模型考量了各種複合機制、結構相關的漏電流、以及主動層內極化場所帶來的影響。在我們的模型中，我們以等效複合體積的概念來擬合極化場的效應。由於主動區內極化場的作用，導致量子井內的電子電洞對分離，並使得主動區的複合速率下降，造成過小的等效複合體積。我們發現，氮化鎵型發光二極體的等效複合體積僅約為實際體積的2%。這麼小的複合體積， 造成元件操作時的載子濃度偏高，導致歐傑效應主宰了整個非輻射複合機制，成為氮化鎵發光二極體效率衰變的主因。然而，我們也發現，若是等效複合體積再持續下降，則會導致元件的載子濃度更進一步提高並突破一臨界濃度(2.14×10^20 每立方公分)，進而誘發漏電流並劣化高偏壓下的量子效率。因此，提升元件的等效複合體積，可降低元件操作時的載子濃度，同時抑制歐傑複合和漏電流的發生，將有機會提高元件的效率並解決可見光發光二極體中“綠光斷層”的問題。我們也針對不同發光波長、不同長晶方向的元件進行擬合，我們也研究等效複合體積與外加偏壓的關係。如一般所預期，我們發現越短的發光波長、越窄的量子井寬度、以及長晶方向極化場越小的元件有著較大的等效複合體積。我們在成長於非極性平面、發光波長峰值為400奈米的元件上萃取到最大的等效複合體積為實際體積的235%倍，這意味著等效複合體積有機會大於1，而透過提高等效複合體積改善元件效率將會是一個有效的方法。

In this dissertation, we have performed a self-consistent calculation to investigate the cooling feasibility and capability of GaAs-based semiconductor electroluminescent (EL) refrigerators and also used a model to analyze the performance of GaN-based light-emitting diodes (LEDs).

For semiconductor EL refrigeration, our analysis indicates that the leakage current increases rapidly at high-bias condition, leading to the degradation of the injection efficiency. The low injection efficiency can be cured to a value of nearly unity by carrier blocking layers, which prevent the minority carriers from flowing directly to the opposite electrodes. The cooling power density generally increases with the active layer thickness due to an enhanced total recombination rate. The limiting cooling power density of 97 W/cm2 is obtained from the device of a 5-um GaAs active layer. Further increasing the active thickness causes the carriers to distribute non-uniformly in the active layer, and hence deteriorates the peak cooling power. Doping in the active layer does not remarkably improve the cooling power. Contrarily, an EL cooler of heavily p-doped active layer may have a small cooling power due to the enhanced Auger recombination. We also analyzed the cooling feasibility of GaAs-based EL coolers. The requirement of the external quantum efficiency for cooling is found to be 82%. This corresponds to a light extraction efficiency of 87% if the trapped photons are all parasitically absorbed. Such a high requirement can be alleviated by photon recycling, which behaves as an additional mean of generating electron-hole pairs in the active layer and hence reduces the injection current density and improves the external quantum efficiency. For a unity photon recycling efficiency, an EL cooler of high internal quantum efficiency can act in the cooling mode even if the light extraction efficiency is only 20%. For a practical value of 90% recycling efficiency, the required light extraction efficiency is 45%. Our results reveal that the realization of semiconductor EL refrigeration is achievable.

For GaN-based LEDs, we have built a model, with various recombination processes, the leak-age current, and the influence of the polarization field accounted, to investigate the origin of the efficiency droop and to understand the role of polarization field played in the performance of InGaN/GaN LEDs. The influence of the polarization field is interpreted as an effective volume for recombination, which is generally small (~2% of physical volume) for GaN-based LEDs grown on c-plane. The small effective volume results in a high carrier concentration for operation and hence makes the Auger recombination dominant in loss mechanisms, leading to the efficiency droop. An even smaller effective volume may cause the carrier density to surpass the “turn-on” concentration of 2.14×10^20 cm^(-3) for the leakage current, which further deteriorates the external quantum efficiency at high-bias condition. Increasing the effective volume is recommended for the improvement of the efficiency since it can reduce the carrier density at operation and hence eases the Auger recombination and the leakage current at the same time. The dependences of the effective volume on emission wavelength, growth orientations, and driving current are also analyzed. It is found that the effective volume is larger for a smaller emission wavelength, a narrower quantum width, and for devices of smaller polarization fields. A large effective volume of 235% is obtained from the device with an emission wavelength of 400 nm grown on m-plane. This indicates that an effective volume larger than unity is an achievable goal for the purpose of further improving the performance of InGaN/GaN LEDs.