Si vs InGaAs Detectors
Compare silicon and InGaAs p-i-n photodiodes: QE spectra from absorption data, responsivity, generation dark current and SNR vs wavelength.
Si QE
0.0%
beyond the cutoff
InGaAs QE
81.8%
ℛ = 1.023 A/W
Si SNR
0.0
dark 3.09e-11 A
InGaAs SNR
100.6
dark 3.03e-9 A
SNR = I_s/√((2q·(I_s + I_dark) + i_amp²)·B), I_s = ℛ·P, I_dark = q·n_i·W·A/τ_g (reverse bias)
Si:Green's 300 K absorption, W = 20 µm, L = 100 µm, R = 5 %, τ_g = 1 ms; the absorption edge does not move with temperature.
InGaAs: In₀.₅₃Ga₀.₄₇As, d = 3 µm fully depleted, R = 2 %, τ_g = 100 µs; the cutoff follows the band gap (1682 nm at 300 K). Ideal collection: real devices lose part of the light short of 1.1 µm in the contact layers. The InP cap is taken as opaque above its band gap.
Dark current is generation in the depletion region only. InGaAs has n_i 65.3× that of Si at 300 K, so its dark current is higher per unit volume; above room temperature diffusion current, left out here, often dominates.
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
Two reference p-i-n devices, not products. Si: Green's 300 K absorption with Gärtner collection (W = 20 µm, L = 100 µm, R = 5 %); its edge does not move with temperature. InGaAs: x = 0.53, Vurgaftman gap, α = A·√(E − E_g) fitted to Adachi within ±12 %, a 3 µm fully depleted absorber, R = 2 %, behind an InP cap taken as opaque above its 1.353 eV gap (916 nm at 300 K). Collection is ideal. Dark current is depletion generation q·n_i·W·A/τ_g only (τ_g 1 ms Si, 100 µs InGaAs); diffusion and surface leakage are left out. SNR adds signal and dark shot noise to a white amplifier noise.
- 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
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- Sze S. M., Ng K. K. (2007). Physics of Semiconductor Devices, 3rd ed. Wiley, ch. 2. Space-charge generation current q·n_i·W/τ_g. doi:10.1002/0470068329
- Saleh B. E. A., Teich M. C. (1991). Fundamentals of Photonics. Wiley. §17.5 Noise in photodetectors: shot noise 2qīB and circuit noise. doi:10.1002/0471213748
- Altermatt P. P., Schenk A., Geelhaar F., Heiser G. (2003). Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing. J. Appl. Phys. 93, 1598–1604. n_i = 9.65e9 cm⁻³ at 300 K. doi:10.1063/1.1529297