Dark Noise vs Temperature
Temperature dependence of photodiode dark current and its shot noise.
E_g(25 °C) = 1.1250 eV, E_g(−40 °C) = 1.1404 eV
Dark @ 25 °C
500 pA
Shot noise @ 25 °C
12.7 fA rms
in 1 Hz
Dark @ −40 °C
526 fA
Ratio (80 / −40 °C)
×4.7e+4
n_i ∝ T^(3/2) · exp(−E_g(T) / 2k_BT); I_dark ∝ n_i (generation) or n_i² (diffusion)
E_g(T) = E_g(0) − αT² / (T + β) (Varshni)
i_n = √(2q · I_dark · Δf)
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
Dark current ∝ n_i (generation) or n_i² (diffusion) with a fixed band gap or Varshni E_g(T) for Si and Ge, and shot noise √(2q·I·Δf) at reverse bias |V| ≫ k_BT/q (at zero bias a diffusion diode gives √2 more). One mechanism over the whole range, although diffusion overtakes generation in hot Si. Surface leakage, tunnelling and 1/f noise are left out.
- Sze S. M., Ng K. K. (2007). Physics of Semiconductor Devices, 3rd ed. Wiley. n_i(T), generation (∝ n_i) and diffusion (∝ n_i²) currents. doi:10.1002/0470068329
- Varshni Y. P. (1967). Temperature dependence of the energy gap in semiconductors. Physica 34, 149–154. Coefficients (Si 1.17 eV, 4.73e-4 eV/K, 636 K; Ge 0.7437 eV, 4.774e-4 eV/K, 235 K) as in Sze, 2nd ed. (1981). doi:10.1016/0031-8914(67)90062-6