Enhanced Quantum Dot Emission in Fibonacci Photonic Crystal Cavities Optimized for PECVD-Compatible Porous Silicon: A Computational Study

This computational study investigates the optical properties of a sixth-order Fibonacci quasi-periodic photonic crystal cavity designed for the infiltration of near-infrared colloidal quantum dots (QDs, e.g., InAs/ZnSe or PbS) and fully compatible with plasma-enhanced chemical vapor deposition (PECVD) using porous silicon layers. Using the transfer matrix method (TMM), we simulate transmission (T), reflection, absorption, electric field distributions and Purcell factors (F) for both TE and TM polarizations, incorporating the wavelength-dependent absorption of porous silicon. A multi-objective figure-of-merit is defined to simultaneously maximize transmission (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>></mo><mn>95</mn><mo>%</mo></mrow></semantics></math></inline-formula> at 800 nm) and the one-dimensional Purcell factor. The optimized structure (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>H</mi></msub><mo>=</mo><mn>0416</mn></mrow></semantics></math></inline-formula>) yields a quality factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mo>≈</mo><mn>4300</mn></mrow></semantics></math></inline-formula>, a 1D Purcell factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi><mrow><mn>1</mn><mi>D</mi></mrow></msub><mo>≈</mo><mn>3.6</mn></mrow></semantics></math></inline-formula> and a realistic 3D Purcell enhancement estimated between 4 and 8 (under lateral confinement assumptions). This conservative estimate, derived via the effective index method to account for 3D effects, aligns with the detailed discussion within the article and is lower than the ideal upper bound of the 1D model. The integrated emission enhancement is approximately 3.0-fold. Monte Carlo simulations demonstrate remarkable robustness to fabrication tolerances (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>10</mn></mrow></semantics></math></inline-formula> nm thickness variations result in a <5% reduction in transmission), highlighting the structure’s scalability for PECVD-based processing. Comparison with periodic Bragg structures reveals superior angular stability and disorder tolerance in the Fibonacci design, positioning it as a promising platform for robust QD-based light sources and integrated refractive index sensors.