Dark Current & Temperature
Simulate thermally generated dark current in CMOS pixels and visualize its impact on image quality across operating temperatures.
Dark Current & Noise Simulator
Simulate temperature-dependent dark current, noise budget, and dark frame pattern for CMOS image sensor pixels.
Dark Current vs Temperature
Noise Budget vs Temperature
Dark Frame Visualization
Simulated dark frame image showing noise pattern at current temperature and integration time.
Model scope
Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.
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Thermal Generation and Dark Noise
Even in total darkness, silicon pixels slowly accumulate electrons just from heat — like a faint hiss on a turned-off radio. The hotter the sensor and the longer the exposure, the more of these dark electrons pile up, adding their own random noise on top of any real signal. This is especially painful for long-exposure or astrophotography use cases.
Dark current is thermally generated charge accumulated during exposure. It rises rapidly with temperature and contributes shot noise.
Assumptions
- Dark current follows an Arrhenius-like temperature dependence with a compact activation-energy parameter.
- The model treats average dark current and noise, not pixel-level hot pixels, RTS, or column offsets.
- Temperature, exposure time, and read noise are assumed stable over the simulated frame.
Outputs
- Dark charge, dark-current shot noise, total noise impact, temperature scaling, and low-light image-quality warning.
- A quick estimate of when cooling, shorter exposure, or read-noise reduction matters most.
Validation Example
- Increasing temperature should raise dark current rapidly, often much faster than a linear trend.
- Doubling exposure time should double accumulated dark charge and increase dark shot noise by roughly $\sqrt{2}$.
Core Equations
- \(I_{\text{dark}}\): Dark current generation rate
- \(E_a\): Activation energy
- \(k\): Boltzmann constant
Activation energy controls how steeply dark current rises with temperature.
- \(D\): Accumulated dark charge
- \(t_{\text{exp}}\): Integration time
Longer exposure accumulates more dark electrons.
- \(\sigma_{\text{dark}}\): RMS noise due to dark current
Thermal generation is a Poisson process in this simplified model.
Model Interpretation
- Cooling, pinned photodiodes, and better isolation reduce dark-current impact.
- Hot pixels are spatial outliers and are not captured by a single average current.
- Dark noise matters most in long exposure and low-light operation.
Temperature Scaling
- The Arrhenius term means small temperature changes can dominate long-exposure noise.
- Activation energy $E_a$ depends on the dominant generation mechanism, so one slope may not fit all temperatures.
- Cooling reduces both mean dark signal $D$ and dark shot noise $\sqrt{D}$.
Measurement Notes
- Measure dark frames at multiple exposure times to separate fixed offset from time-dependent dark current.
- Use temperature-stabilized acquisition because dark current can drift during a measurement run.
- Track hot pixels separately from median dark current; they drive image defects and calibration tables.
Known Missing Physics
- The compact model does not distinguish diffusion current, depletion current, surface generation, and trap-assisted tunneling.
- It does not model random telegraph signal, hot-pixel distributions, or radiation/aging effects.
- Dark-frame correction residuals depend on temperature matching and calibration cadence.