導模共振奈米光柵於光學感測之應用及其公差分析

Abstract

導模共振奈米光柵係近年來製造生物晶片的新興方法，開啟了新世代生醫感測發展的另一重要領域。為了確保其檢測之穩定性，可重複性，乃至量產重現性，在這篇論文中，我們的研究主要著眼於特定粗糙度對於導模共振奈米光柵分別在近紅外光及近紫外光波段操作下的影響。為此，本文所設計之導模共振奈米光柵不論是在近紅外光或近紫外光波段均擁有非常窄頻之反射式半高全寬光譜響應，以增強光柵表面感測的靈敏度；藉由待測生醫材料之被覆及粗糙度幾何分形之疊加，造成光柵結構折射率的微量變化，引起反射光譜共振峰值的飄移，達成生醫檢體濃度及粗糙度尺度的逆向推演與預測。 我們接著針對幾種特定光柵粗糙度（例如，隨機分佈，正弦分佈，矩形分佈，等效介質分佈等），以簡化之相關長度ξ及最大粗糙度之均方根值σ，從數學上具體描述粗糙度之功率譜密度函數，透過嚴格耦合波理論，量化導模共振奈米光柵因粗糙度所造成反射共振峰值的飄移量。 模擬結果令人驚訝的是，在近紅外光入射下，在某些特定ξ值中，垂直側壁粗糙度σ值即便高達 10 奈米，反射共振峰值依然不會飄移，因此在σ-ξ圖中所闡述之反射共振峰值產生帶隙狀條紋區域，我們把它類比於光子晶體中的能帶區域，並稱之為「類能隙」。換言之，若垂直側壁粗糙度之尺度，落在σ-ξ圖中之類能隙區域內，其副作用對於導模共振奈米光柵之檢測能力是微不足道的。因此，在奈米製程線寬邁向僅十幾奈米尺度的同時，如能將光柵之類能隙區域透過σ-ξ作有效控制，將使垂直側壁粗糙度公差具高度容忍範圍。惟獨表面粗糙度即便小於次奈米尺度，仍然對於導模共振奈米光柵造成顯著的共振峰值的飄移，甚至造成無效的光譜識別。 另外，為因應更短波長的近紫外光入射於更小線寬的光柵尺度，令其具有較大的檢測鑑別率，我們首先定義了製程窗口函數η，用於量化類能隙出現的概率。我們發現若要求η= 90％時，則σ的公差容忍範圍在近紫外光和近紅外光的情況下幾乎沒有太大差別。因此，在實務製程條件下，近紫外光入射毋須另外訂定更嚴格的製造公差極限。 未來，在奈米製程線寬邁向僅十幾奈米之尺度的同時，如能將光柵之類能隙區域作有效控制，將使垂直側壁粗糙度等製程公差，具有高度容忍範圍，以提昇元件製程良率。

Nano-grating of guided-mode resonance (GMR) is a promising method to fabricate biosensors. To guarantee its stability, repeatability, and reproducibility of biosensors, in this dissertation, we present our investigations mainly on the effects of roughness on the guided-mode resonance (GMR) filters made of subwavelength grating for applications to ultrasensitive biosensors operated under near-infrared (near-IR) and near-ultraviolet (near-UV) illumination. We design the spectral full width at half maximum (FWHM) of the grating filter to be as narrow as possible in order to emphasize the enhanced surface-to-bulk sensitivity and highlight the roughness effects. Several types of roughness (e.g., randomized, sinusoidal, rectangular, and effective medium) morphologies on the grating—in terms of the correlation length ξ and the root mean square of the maximum roughness deviation σ—cast in a power spectral density function were evaluated by rigorous coupled wave analysis (RCWA) to quantify the shifts in the reflective resonance peak wavelength value (PWV) of the grating filter. Our simulations show that for specific ξ values under near-IR radiation, the PWVs remain constant even if σ of the vertical sidewall roughness (VSR) becomes as large as 10 nm; this indicates dramatic bandgap-like stripes, which are similar to the bandgaps observed in the band diagrams of photonic crystals. In other words, the effects of VSR on the GMR biosensor performance are insignificant when ξ is located at certain bandgap-like stripes; therefore, this type of roughness is highly tolerable even if the line width of the filter is decreased to only a few tens of nanometers. Sub-nanometer surface roughness, none the less, caused significant PWV shifts, leading to invalid spectral recognition. Under near-UV radiation, the parameter η of process window is also proposed to quantify the probability of the bandgap-like peak-value stripes that appeared. When η = 90%, the process window is narrower and almost the same for near-UV and near-IR cases. Therefore, there is less need to calibrate the PWV shift at the expense of a more severe fabrication limit especially under near-UV illumination. Finally, as the line width in nanotechnology towards only a few tens of nanometers, the effective controlling of bandgap-like region will enable the larger tolerance limit of roughness, such as VSR to improve the production yield rate.