鍺 PIN 光偵測器之溫度相依光學與電性分析

Abstract

由於鍺（Germanium）具備與 CMOS 製程兼容的特性，且在通訊波段具有強大的吸收能力，因此鍺 PIN 光電偵測器被廣泛應用於矽光子平台的近紅外光學互連。然而，在高效能運算系統（HPC）與高密度光子積體電路（PIC）等實際環境中，光電偵測器經常在變動的溫度條件下運作。由於鍺的材料特性與載子傳輸機制具有高度的溫度依賴性，因此深入了解由溫度引起的性能權衡（Trade-offs），對於設計可靠的高速光電偵測器至關重要。

本論文針對傳統側向 PIN 型鍺光電偵測器（Lateral Ge PIN Photodetector）在 1310 nm 波段下的光學與電學行為，進行了系統性的物理基礎研究。研究中採用了光電耦合模擬框架：首先利用 ANSYS Lumerical FDTD 獲取光吸收與載子產生分布圖（Carrier generation profiles），隨後將其匯入 ANSYS Lumerical CHARGE 進行電學傳輸分析。透過此工作流程，本研究在寬溫度範圍內評估了多項關鍵性能指標，包括：暗電流、響應度、量子效率、瞬態響應、電容以及 3-dB 頻寬。

我們設計了一款長度為 15 μm 的鍺PIN 光電偵測器。研究結果顯示，暗電流隨著溫度的升高而顯著增加，這主要是由於能隙減小（Bandgap narrowing）以及更強的熱激發（Thermal excitation） 導致本身的載子濃度提升所致。相較之下，偵測器在高溫下表現出更佳的光吸收能力。在 −1 V 偏壓下，其響應度從 250 K 時的 0.265 A/W 增加到 350 K 時的 0.30 A/W 。這種性能是由於於溫度引起的鍺消光係數（Extinction coefficient） 與吸收係數（Absorption coefficient） 的增加，進而導致更強的光子吸收與載子產生率。

然而，元件的性能會隨溫度升高而退化。在 −1 V 偏壓下，所得到的 3-dB 頻寬從 250 K 時的 50 GHz 單調下降至 350 K 時的 44.4 GHz，這展現了明顯的響應度與頻寬之間的權衡關係（Responsivity–bandwidth trade-off）。這種頻寬減小主要是由溫度依賴的載子傳輸退化所主導：隨著溫度升高，聲子散射（Phonon scattering） 變得劇烈，進而降低了載子的遷移率（Mobility）與飽和速度（Saturation velocity）。這導致載子穿越時間（Transit time）增加，最終降低了受限於穿越時間的頻寬。

瞬態光電流（Transient photocurrent） 模擬進一步證實了此現象：在較高溫度下，光電流的幅值（Magnitude） 較高，但響應動態（Response dynamics） 卻因此變慢。最後，透過將總頻寬分解為 RC 受限頻寬（RC-limited） 與穿越時間受限頻寬（Transit-time-limited） 兩個分量，我們利用解析計算（Analytical calculations）驗證了模擬出的頻寬趨勢，結果顯示計算值與模擬值高度吻合。總體而言，本論文建立了關於溫度如何影響鍺 PIN 光電偵測器性能的清晰認知，並強調了在設計可靠的高速矽光子接收器時，進行溫度感知建模（Temperature-aware modeling）與優化的重要性。

Germanium PIN photodetectors are widely used in silicon photonics platforms for near-infrared optical interconnect applications due to their CMOS compatibility and strong absorption at telecommunication wavelengths. However, in practical environments such as high-performance computing systems and dense photonic integrated circuits, photodetectors often operate under varying thermal conditions. Since germanium material properties and carrier transport mechanisms are highly temperature dependent, understanding the temperature-induced performance trade-offs is essential for reliable high-speed photodetector design.

This thesis presents a systematic physics-based investigation of the temperature-dependent optical and electrical behavior of a conventional lateral Ge PIN photodetector at 1310 nm. A coupled optical–electrical simulation framework was employed, in which the optical absorption and carrier generation profiles were first obtained using ANSYS Lumerical FDTD, and then imported into ANSYS Lumerical CHARGE for electrical transport analysis. Using this workflow, key performance metrics—including dark current, responsivity, quantum efficiency, transient response, capacitance, and 3-dB bandwidth—were evaluated over a wide temperature range.

We demonstrate a 15 μm-long Ge PIN photodetector where the results show that dark current increases significantly with temperature, mainly due to enhanced intrinsic carrier concentration caused by bandgap narrowing and stronger thermal excitation. In contrast, the detector exhibits an improved optical absorption at elevated temperature as the responsivity increases from 0.265 A/W at 250 K to 0.30 A/W at 350 K under −1 V bias. This enhancement is attributed to temperature-induced increases in the extinction coefficient and absorption coefficient of Ge, leading to stronger photon absorption and improved carrier generation.

However, the high-speed performance degrades with temperature. The extracted 3-dB bandwidth decreases monotonically from 50 GHz at 250 K to 44.4 GHz at 350 K at −1 V, demonstrating a clear responsivity–bandwidth trade-off. This bandwidth reduction is dominated by temperature-dependent carrier transport degradation, where phonon scattering reduces mobility and saturation velocity, increasing carrier transit time and reducing the transit-time-limited bandwidth.

Transient photocurrent simulations further confirm this behavior, showing higher photocurrent magnitude at elevated temperature but slower response dynamics. Finally, the simulated bandwidth trends were validated through analytical calculations by decomposing the overall bandwidth into RC-limited and transit-time-limited components, showing close agreement between calculated and simulated values. Overall, this thesis establishes a clear understanding of how temperature affects the performance of Ge PIN photodetectors, highlighting the importance of temperature-aware modeling and optimization for reliable high-speed silicon photonic receiver design.