Pixel Crosstalk & MTF

Charge diffusion and electrical crosstalk in a silicon image sensor: absorption depth, charge reaching the neighbouring pixels vs wavelength, and MTF at Nyquist.

Model: Textbook approximation

Pixel pitch p (µm)Depletion depth W (µm)Diffusion length L₀ below it (µm)Wavelength (nm)Kernel crosstalk X (both neighbours)

Absorption depth 1/α

1.56 µm

Si at 300 K (Green 2008)

Absorbed below the depletion layer

0.17 %

e^(−αW); 100.0 % of the absorbed charge is collected

Diffusion crosstalk

0.04 %

to the two neighbouring columns; 0.01 % lands farther out

Total neighbour crosstalk

3.03 %

diffusion followed by the kernel X

MTF at Nyquist

59.8 %

pixel 2/π × diffusion 0.999 × kernel 0.940

Seib diffusion MTF: η(f) = 1 − e^−αW/(1 + α L_f), 1/L_f² = 1/L₀² + (2π f)², MTF = η(f)/η(0).

Column shares for one uniformly lit column: C_n = 2∫ MTF(u/p) sinc²(π u) cos(2π n u) du; diffusion crosstalk = 2C₁.

Kernel [X/2, 1 − X, X/2]: MTF = 1 − X + X cos(2π f p), so 1 − 2X at f_N = 1/(2p).

Neighbour crosstalk vs wavelength

MTF at 550 nm

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

Seib's field-free diffusion for front illumination: light absorbed in the depletion depth W is collected in place, and below it carriers diffuse with length L₀ in a semi-infinite field-free region, so it overstates near-infrared crosstalk for thin-epitaxy sensors. No reflection or surface recombination. Diffusion crosstalk is the charge reaching the two adjacent columns when one column is lit uniformly (100 % fill), integrated from the line-spread MTF. The extra crosstalk X is a nearest-neighbour kernel [X/2, 1 − X, X/2].

Seib D. H. (1974). Carrier diffusion degradation of modulation transfer function in charge coupled imagers. IEEE Trans. Electron Devices 21, 210–217. Field-free diffusion MTF; the semi-infinite case η(f) = 1 − e^(−αW)/(1 + α L_f), 1/L_f² = 1/L₀² + (2π f)². doi:10.1109/T-ED.1974.17898
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. Absorption coefficient α(λ), Table 1. doi:10.1016/j.solmat.2008.06.009

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