| 摘要: | 本論文針對基於金屬內部光輻射效應(internal photoemission)為主要運作機制之太陽能光電轉換元件進行其光電轉換效率與相關之物理機制之理論探討。透過虛位勢法(pseudopotential method)求得鋁、銅、銀之真實能帶結構(band structure)並藉此分析於考慮光激發過程中電子動量守恆條件與否下，光激發電子於能量軸上之分布；同時將入射電磁波於一維及三維空間位置之分布、受激發電子於傳遞過程之能量損耗與其於金屬與半導體(氧化物)介面之有限出射機率(emission probability)等因素納入考慮，分別對n型與p型平面蕭基元件(planar Schottky device)以及本實驗室團隊所設計之具二維金屬光柵之鋁-二氧化鈦-銀元件進行分析。
於計算中發現鋁、銅、銀之受激發電子於能量軸上之分布情形迥異。忽略動量守恆條件下，電子能態密度(density of states, DOS)之連續分布導致3種材料之受激發電子能譜於標準AM1.5G之太陽光譜內呈較平緩且連續之分布。考慮動量守恆條件並不使鋁之結果有明顯之差異，但對於銅與銀，由於d能帶(d-bands)結構之分布導致須以大於特定能量(銅: 2.2 eV；銀: 3.5 eV)之光子入射才能產生有效之光激發。此外，對於鋁而言，在太陽光譜範圍內將各躍遷組合所對應之動量矩陣元素(momentum matrix element)設為常數為相對合理之假設；然而對於銅，該假設會低估由其s能帶(s-band)與d能帶頂部所產生之向上躍遷機率。
透過對n型蕭基元件之分析得知，於考慮動量守恆條件下，由於沒有光激發所需之最小入射光子能量的限制，鋁之功率轉換效率(power conversion efficiency, PCE)極值為0.5530%，發生於當能障高度(barrier height)及金屬厚度分別為0.95 eV與13.0 nm時，於3種材料中最高；其量子產率(quantum yield)於能障較低時遠高於其他兩種材料，然而其值隨著能障高度上升而快速下降。銅之d能帶與s能帶於能量軸上之位置差異導致銅之量子產率隨能障高度增加呈兩段式變化。由於源自d能帶之受激發電子其額外能量(excess energy)較低而僅有部分能通過能障，因此銅之功率轉換效率極值僅為0.0022%(於能障高度: 0.9 eV，金屬厚度: 17.0 nm)。於太陽光譜內，銀之受激發電子主要源自於s能帶，其較高之額外能量導致銀之量子效率對能障高度之相依性較弱，但亦使其生命週期(lifetime)較短而導致其量子產率與功率轉換效率隨金屬厚度增加而快速下降。銀之光電轉換效率極值為0.0162%(於能障高度: 2.2 eV，金屬厚度: 5.0 nm)，其主要受限於絕大部分太陽光譜內之光子無法產生有效之光激發。在忽略動量守恆條件下，於3種材料中仍以鋁擁有最大之功率轉換效率極值，銀次之，銅則同樣d能帶之受激發電子其能量較低而對應最小之值。
對於p型蕭基元件，以鋁為材料下所得之光電流隨能障高度與金屬厚度之變化形式與n型相比並無顯著變化，唯因相同額外能量下電洞之生命週期較電子為短，因而所產生之光電流隨之減小。於考慮動量守恆條件下，將躍遷相對係數納入計算下所得之功率轉換效率極值為0.2673%(於能障高度: 0.95 eV，金屬厚度: 11.0 nm)；相較之下，n型元件於同樣計算方式下所得之值為0.2799%(於能障高度: 0.95 eV，金屬厚度: 13.0 nm)。對於銅而言，其p型與n型元件之結果恰好相反。由於d能帶電子之躍遷所產生之電洞其額外能量較高但生命週期過短，導致p型元件之量子產率對能障高度之相依性較弱，但隨金屬厚度增加而快速遞減。以標準AM1.5G太陽光譜內之整體表現而言，對於鋁與銅n型元件之光電轉換效率優於p型元件。
最後，由具二維金屬光柵之鋁-二氧化鈦-銀元件之相關分析顯示，於標準AM1.5G太陽光譜範圍內，該元件於考慮動量守恆條件下所得之淨量子產率為7.9293%；相較之下，相同材料與尺寸之平板結構之淨量子產率則為5.8515%。若於波長為612.61 nm之入射光照射下，該二維光柵元件之淨量子產率更可達14.0073%。就分析中發現該元件之淨量子產率之主要限制來自於上層鋁光柵結構內激發之電子，能傳遞至中間層鋁與與二氧化鈦介面並有效射出之比例僅約20%。若受激發電子之傳遞損失與其於介面之出射角度限制可被完全克服(即考慮彈道傳遞情形下)，則該元件之理論淨量子產率於標準AM1.5G太陽光譜範圍內可大於38%。;In this research, solar energy conversion based on internal photoemission in metals are theoretically investigated. The pseudopotential method is applied to first obtain the actual band structures of aluminum (Al), copper (Cu), and silver (Ag). The energy distributions of the photoexcited electrons within metals are quantified under the assumption of direct or fully nondirect transition. With the incorporation of the spatial distributions of incident electromagnetic wave, the propagation loss, and finite emission probabilities of photoexcited electrons, the theoretical limits of the quantum yield (QY) and the power conversion efficiency (PCE) of n- and p-type planar Schottky devices as a function of the barrier height Phi_B and metallic film thickness t_m are evaluated. Moreover, the photocurrent and the corresponding net quantum yield generated within one period of a two-dimensional (2D) metallic grating in Al-TiO_2-Ag configuration are estimated.
The energy distributions of photoexcited electrons are found to be disparate markedly among Al, Cu, and Ag. Under the fully nondirect approximation, the continuous distributions of the electron density of states results in a relatively smooth and continuous energy distributions of photoexcited electrons in each metal considered here.The condition of direct transition (i.e. momentum conservation) only has little influence on the energy distributions of photoexcited electrons in Al. However, such transition criteria leads to the threshold energies in Cu and Ag for the incident photons at which vertical transitions can occur. Within the solar spectrum range, the assumption of constant optical matrix element is applicable for Al. However, such an assumption may underestimate the upward transition rates from the s-band and the top of d-bands in Cu.
For planar n-type Schottky devices under the assumption of direct transition approximation, the absence of the threshold incident photon energy gives rise to the maximum PCE up to 0.5530% in Al at Phi_B=0.95 eV and t_m=13.0 nm, the highest one among the 3 metallic materials. The QY of Al-based devices is much higher than the other two metals at small barrier heights but drops rapidly as the barrier height increases. For Cu-based devices, the slope of the QY versus Phi_B plot shows 2 distinct phases owing to the energy differences of the s-band and d-bands in Cu with respect to the Fermi level. Since electrons excited from the d-bands carry smaller excess energies and only part of them have sufficient energies to overcome or tunnel through the barrier, the maximum PCE in Cu is merely 0.0022% (at Phi_B=0.9 eV and t_m=17.0 nm). For Ag, excitations are restricted from the s-band within the solar spectrum range. The relatively high excess energies possessed by electrons form the s-band cause a weak dependence of the QY of Ag-based devices on the barrier height but a strong dependence on the metallic film thickness because of their shorter lifetimes. The maximum PCE in Ag is 0.0162% (at Phi_B=2.2 eV and t_m=5.0 nm). It is mainly limited by photon energies within a large part of the solar spectrum. When the momentum conservation condition is ignored, Al has the highest maximum PCE while Cu has the lowest value as a consequence of the low excess energies carried by electrons excited from the d-bands.
For Al-based p-type Schottky devices, the behaviors of the photocurrent as a function of the barrier height and metallic film thickness are similar to their n-type counterparts. The major difference originates form a shorter hole lifetime compared to that of electrons at the same excess energy, leading to a slightly smaller photocurrent. With nonconstant optical matrix elements considered, the maximum PCE of Al-based p-type devices is 0.2673% (at Phi_B=0.95 eV and t_m=11.0 nm), while that of its n-type counterpart is 0.2799% (at Phi_B=0.95 eV and t_m=13.0 nm) using the same calculation method. In contrast to n-type devices, holes generated by electrons excitations from the d-bands in Cu carry relatively high excess energies and thus shorter lifetimes. As a result, the QY of Cu-based p-type devices is a strong function of the metallic film thickness but is dependent weakly on the barrier height. $n$-type Schottky devices are therefore superior to p-type Schottky devices for Al and Cu in terms of their overall performances within the solar spectrum range.
Finally, the analysis on the 2D grating in Al-TiO_2-Ag configuration shows that when the momentum conservation condition is considered, the net QY within solar spectrum is found to be 7.9293%,%, while that of a planar Si_3N_4- Al-TiO_2-Ag device with identical dimension is 5.8515%. At a free-space wavelength of 612.61 nm, its net QY can reach up to 14.0073%. The major limiting factor of the present device is that, only around 15% of those electrons excited within the top metallic structure can reach and emit through the Al-TiO_2 interface. If the losses during the electron transport and finite emission angles at the Al-TiO_2 interface are ignored, theoretically the net QY of the present device with 2D gratings can exceed 38% under standard AM1.5G solar illumination. |
