Spectral Response
R(λ) = η(λ) · q · λ / (h·c). Responsivity and quantum efficiency of a silicon photodiode as a function of wavelength, and the quantum efficiency a datasheet value implies.
Silicon photodiode model
Peak responsivity
0.616 A/W
at 850 nm, QE 89.8%
Half-response band
402–1011 nm
ℛ ≥ ℛ_peak/2
Responsivity @ 650 nm
0.498 A/W
QE 95.0%
Check a datasheet value
Implied quantum efficiency
82.7%
η = 1 limit 0.726 A/W
ℛ(λ) = η(λ)·q·λ/(h·c), η(λ) = (1 − R)·[1 − e^(−α·W)/(1 + α·L)] (Gärtner), α(λ) of silicon at 300 K (Green 2008)
η = ℛ·h·c/(q·λ): a value above 100% means the datasheet number includes gain or is wrong.
The model has no dead layer or AR-coating spectrum, so it overstates the blue response of most commercial photodiodes; the long-wavelength edge follows from silicon's absorption and the collection depth W + L.
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 at 300 K: Green's absorption with Gärtner's depletion-plus-diffusion collection and a fixed surface reflectance, on a semi-infinite substrate (no back-surface recombination or reflection). No dead layer or AR-coating spectrum, so the blue response is an upper bound. The datasheet check is exact: η = ℛ·h·c/(q·λ), and η > 1 needs internal gain.
- 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
- Saleh B. E. A., Teich M. C. (1991). Fundamentals of Photonics. Wiley. §17.1 Quantum efficiency and responsivity, ℛ = η·λ₀/1.24 (λ₀ in µm). doi:10.1002/0471213748