Quantum Efficiency
Detector QE from the absorption coefficient: silicon photodiode, back-illuminated and deep-depletion CCD and front-illuminated CMOS structures, and an InGaAs p-i-n, with reflection, dead-layer and fill-factor losses.
QE at probe λ
89.8%
ℛ = 0.616 A/W; R = 5.0%
Peak QE
95.0%
Optical fill 100.0%
Peak wavelength
250–695 nm (flat)
QE = (1 − R)·e^(−α·d)·[1 − e^(−α·W)/(1 + α·L)] × min(1, fill factor × microlens gain)
α(λ) is crystalline silicon at 300 K (Green 2008). Blue light is lost in the dead layer (α ≈ 10⁵ cm⁻¹ at 400 nm), near-infrared light passes through a thin collecting layer (α(900 nm) = 303 cm⁻¹, a 33 µm absorption length). The presets are illustrative structures, not a specific product; real sensors add AR-coating ripple, gate and colour-filter absorption, and etaloning in thin back-illuminated layers.
Silicon detector quantum efficiency
- Effective QE
- Internal QE (no reflection or fill loss)
- Probe
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Silicon or In₀.₅₃Ga₀.₄₇As at 300 K. A dead layer, a fully collecting layer W and diffusion from a semi-infinite substrate (Gärtner); L = 0 is a slab. Silicon α is Green's table; InGaAs α = A·√(E − E_g) with the Vurgaftman gap, fitted to Adachi within ±12 %, behind an InP cap taken as opaque short of 916 nm; InGaAs sits on a transparent InP substrate (L = 0). Reflection is a fixed R, or bare-silicon Fresnel for silicon; no AR-coating spectrum, etaloning, gate or colour-filter absorption. The presets are illustrative structures, not products.
- Green M. A. (2008). Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients. Sol. Energy Mater. Sol. Cells 92, 1305–1310. Table 1, n and k at 250–1450 nm (α = 4πk/λ). doi:10.1016/j.solmat.2008.06.009
- Gärtner W. W. (1959). Depletion-layer photoeffects in semiconductors. Phys. Rev. 116, 84–87. Collection efficiency 1 − e^(−αW)/(1 + αL). doi:10.1103/PhysRev.116.84
- Vurgaftman I., Meyer J. R., Ram-Mohan L. R. (2001). Band parameters for III–V compound semiconductors and their alloys. J. Appl. Phys. 89, 5815–5875. Ga₁₋ₓInₓAs gap with bowing 0.477 eV (Table XIII) and the InP Varshni set (Table VI). doi:10.1063/1.1368156
- Adachi S. (1989). Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlₓGa₁₋ₓAs, and In₁₋ₓGaₓAsᵧP₁₋ᵧ. J. Appl. Phys. 66, 6030–6040. In₀.₅₂Ga₀.₄₈As n, k as tabulated at refractiveindex.info; basis of the absorption fit. doi:10.1063/1.343580
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