Dark Current vs Temperature
Silicon detector dark current — exponential doubling model. I_dark(T) = I₀ · 2^((T−T₀)/T_d).
Dark @ -80 °C
5.39e-7 e⁻/s
Dark @ 40 °C
5.66e-1 e⁻/s
Ratio (40 / -80 °C)
×1.0e+6
Dark noise = read noise at
Outside range
Colder than this, read noise dominates
D(T) = D₂₅ · 2^((T − 25 °C) / T_d) σ_dark = √(D · t)
The doubling law is the local form of the n_i scaling. For silicon at 25 °C (Varshni E_g(T)) it gives T_d ≈ 8.3 K for depletion generation current and 4.2 K for diffusion current; CCD and CMOS data sheets usually quote 5–9 K.
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
Empirical doubling law about 25 °C with dark shot noise √(D·t) against a fixed read noise. It is the local form of the n_i scaling: for Si at 25 °C that gives T_d ≈ 8.3 K (generation) or 4.2 K (diffusion), and a single T_d drifts away from it over a wide range.
- Janesick J. R. (2001). Scientific Charge-Coupled Devices. SPIE Press. Dark current temperature dependence and dark shot noise. doi:10.1117/3.374903
- Varshni Y. P. (1967). Temperature dependence of the energy gap in semiconductors. Physica 34, 149–154. Si E_g(T) used for the equivalent doubling temperature. doi:10.1016/0031-8914(67)90062-6