三五族合金之侷限效應與二硫化鉬鎢隨機合金之能帶計算

Abstract

三五族半導體擁有直接能隙與高電子遷移率，所以它們被廣泛的應用在不同的領域，例如發光二極體、雷射與高電子遷移率電晶體。三族氮化物合金具有較寬的能隙，因此它們能被應用在可見光與紫外光波段的發光二極體與高電壓電子元件。然而過去的文獻指出合金擾動會影響三族氮化物合金的電子特性，但對常見的三五族半導體合金影響卻不高，例如砷化銦鎵、砷化鋁鎵與磷化銦鎵。因此這個論文會探討為什麼合金擾動的影響在三族氮化物合金比常見的三五族半導體重要很多。為了去研究合金擾動在三五族半導體合金的影響，三維的隨機擾動合金地圖被採用在我們的模型中，並且使用了Localization landscape理論與薛丁格模型來探討載子在三五族半導體合金的行為。我們藉由了Localization landscape模型計算出載子實際看到的等效的量子位能分佈。等效的量子位能分佈在常見的三五族半導體合金中看起來非常平坦，而在三族氮化物合金位能的擾動卻很明顯。為了進一步研究合金擾動，我們挑選了氮化銦鎵與砷化銦鎵分別作為三族氮化物與三五族常見半導體合金的代表。為了量化位能擾動的程度，我們計算了不同銦比例的位能分佈標準差，其結果顯示導電帶、價電帶與等效量子位能分佈的標準差隨著銦比例變化都是非對稱的，且它們的峰值都落在約三十百分比的銦比例。這個結果是由兩個因素組合造成的。第一是氮化銦鎵的能隙斜率最大值在銦比例最小的時候。第二是合金比例的擾動分佈在銦比例為五十個百分比時，其標準差最大。為了探討由於合金擾動造成載子被束縛的程度，我們利用了薛丁格模型來計算波函數的分佈。電子與電洞基態的機率密度分佈顯示了在銦比例為三十個百分比的砷化銦鎵看起來分佈非常均勻，而在相同銦比例的氮化銦鎵則看起來被侷限在一些特定的區域。特別是氮化銦鎵的電洞基態被幾乎完全地束縛在一個小區域。為了量化束縛的程度，我們計算了氮化銦鎵的電洞的參與比例(participation ratio)與侷限長度(localization length)隨著銦比例不同的變化。其結果顯示當銦的比例靠近三十個百分比時，氮化銦鎵有更多的電洞被束縛，這個結果與位能分佈的標準差趨勢一致。再來我們定義當侷限長度小於一半的飽和侷限長度時為束縛態，並計算電子與電洞在氮化銦鎵的束縛態狀態密度。因此這個研究顯示出了合金為擾在氮化物合金中的重要性。

除此之外這個論文還使用了全s、p與d軌域的緊密束縛模型來計算單層與扶手椅邊緣的奈米帶的二硫化鉬鎢合金。使用全s、p與d軌域的緊密束縛模型可以精準地抓到能帶的特性。為了取出二硫化鉬鎢合金的緊密束縛模型參數，我們利用密度泛函理論計算了單層二硫化鉬、二硫化鎢與二硫化鉬鎢的條紋結構的能帶。並藉由這些密度泛函理論能帶結果取出所需的緊密束縛模型參數。此外我們採用了隨機合金地圖在緊密束縛模型中。因此我們探討了隨機合金地圖的大小與考慮的隨機地圖數目對結果影響。再者我們分析了二硫化鉬鎢合金單層與扶手椅邊緣的奈米帶的電子特性，例如狀態密度、軌域分佈、等效質量與能隙等等。

III-V semiconductor alloys have been widely used in various fields. Due to their wide bandgap range, III-nitride alloys have been used in visible and ultraviolet light-emitting diodes and high-power electronic devices. This thesis studied why the effects of alloy disorder are much more significant in III-nitrides than in conventional III-V semiconductor alloys. To study the effects of alloy disorder in III-V alloys, the three-dimensional random alloy map was utilized in simulation models in this work. The localization landscape theory and Schrodinger solver were used to investigate the carrier behavior in III-V alloys. First, the localization landscape theory was used to calculate the effective quantum potential, which is the actual potential seen by carriers. The two-dimensional cross-section maps of landscape potentials are much flatter in conventional III-V semiconductor alloys than in III-nitrides alloys. To further study the effects of alloy disorder in III-nitrides and conventional III-V semiconductor alloys, the InGaN and InGaAs were selected to be references for III-nitrides and conventional III-V semiconductor alloys, respectively. To quantify the scale of potential fluctuations, standard deviations of the conduction band, valence band, and landscape potentials were calculated. The standard deviations of potentials are asymmetric with Indium (In) composition variation. In addition, peaks of standard deviations for potentials of InxGa1-xN and InxGa1-xAs are around 30% In composition. This implies that the effects of alloy disorder would be significant for InGaN-based green and red light-emitting diodes. The combination of two factors leads to the peaks at 30% In compositions. The first is the maximum slope of the bandgap at low In composition. The other reason is that In composition fluctuation is largest at 50% In composition. To study the localization degree of electrons and holes in InGaN and InGaAs, the Schrodinger solver was used to calculate electron and hole wavefunctions for InGaN and InGaAs. The probability densities of electron and hole ground states are much more uniform in In0.3Ga0.7As than in In0.3Ga0.7N. In addition, the hole ground state of In0.3Ga0.7N is almost fully localized. To quantify the localization degree, the participation ratio and localization length was calculated. Participation ratios and localization lengths of hole for InxGa1-xN in the range of 3% to 97% In composition showed that the number of localization states increases when the In composition is close to 30%. Half of the saturated localization length was selected to distinguish the localized and delocalized states and count the density of states of localized states for electron and hole of InGaN. Thus, this study demonstrated the importance of considering the effects of alloy disorder in III-nitrides alloys compared to conventional III-V semiconductor alloys.

In addition, this thesis investigated the band structures of MoxW1-xS2 alloy monolayers and armchair nanoribbons using a full sp3d5 tight-binding model (TBM). A full sp3d5 TBM can catch features of band structures of MoxW1-xS2 alloy as much as possible and make the band structure more accurate. To extract TBM parameters required for MoxW1-xS2 alloy, density functional theory (DFT) was applied to calculate band structures of MoS2, WS2, and 2MoS2-2WS2 stripe structure monolayers. Then, TBM parameters required for MoxW1-xS2 alloy were extracted from the results of DFT calculations. Moreover, calculating an alloy system's band structure requires a large computational domain size and significant seeding numbers, which TBM can enable. However, simulated results for alloy systems are enormously dependent on the size of the computational domain and seeding number. This work did different sizes of the computational domain and seeding numbers to check if average results converge. Then, this work analyzed electronic properties by simulations, such as density of state effective mass, bandgap, and band structure.