The rapid evolution of modern photonic devices in digital photographic and detection systems creates a need for physically-based simulation of charge collection and transfer. In this article we show the linearity, spatial sensitivity, and spectral response of a generalized silicon pixel structure using the Luminous module of the ATLAS device simulator. The Luminous module is used to simulate net charge generation due to incident light energy, and the S-Pisces module is used to simulate charge transport and generation-recombination mechanisms using the standard drift-diffusion transport equations coupled with Shockley-Read-Hall, Auger, and optical generation-recombination models.

Pixel Structure

The charge collection structure modeled here is typical of imaging applications, where charge is formed by electron-hole pair generation due to light incident on the silicon substrate. The charge is kept confined laterally by a transfer channel stop, shown in Figure 1 as a thick field oxide outside the active charge transfer region, and a lower concentration of phosphorus under the gate region. Generally, the charge transfer in pixel and charge-coupled devices is due to diffusion, drift due to the electric field, and fringing electric field effects. Free charge-transfer is used to simulate these mechanisms by modeling only the free electrons in the conduction band.

Figure 1 shows a generalized phosphorus-doped, polysilicon-gated pixel structure that is used to model linearity, spatial sensitivity, and spectral response of charge collection and transfer mechanisms. The structure was created in the ATHENA process module, and the solution grid was then modified for device simulation using the DevEdit device editor. The n-well pixel on the left side of the structure is coupled to the n-well drain on the right side by the polysilcon reset gate. The aluminum drain contact is isolated from the reset gate contact by silicon dioxide. As shown in Figure 1, the oxide retains charge from the implant process. Oxide charge is not modeled in this simulation, however, trapped and mobile oxide charge can be simulated using the ORCHID module.

Figure 1. The n-well charge collection and transfer structure.

To set up the charge collection and transport condition, the drain contact is biased to the 5V steady-state condition with the gate and substrate contacts grounded, as shown in Figure 2. This bias condition drops the drain well potential while keeping the drain isolated from the pixel. The reset gate is then biased to 5V, which lowers the potential under the gate and creates a region of high electron concentration in the n-well, as shown in Figure 3. The gate is then reset to 0V and the structure solution is immediately saved before illumination, as shown in Figure 4.

Figure 2. The pixel structure with the drain biased at 5V, showing
the metallurgical junction and depletion region edges.

Figure 3. The pixel structure with the reset gate biased at 5V.

Figure 4. The pixel structure with the gate contact reset to 0V, ready for illumination.

Transient Simulation Under Illumination

From the setup condition in Figure 4, the transient electrical behavior of the structure is simulated under a sequence of spot powers and frequencies for a duration of 10 ms (ramped from zero to peak intensity over 1ns), to model the linearity, spatial, and spectral response of the pixel. Response curves are extracted from the voltage change just under the surface of the pixel center.

For the transient response of the n-well, consider that as the free electron charge density in the pixel region increases due to irradiated energy, the surface and bulk potential decrease. This change is associated with the filling of the potential well with electrons. For a fixed gate voltage, the surface potential decreases linearly to first order as electron concentration increases. Thus we expect a linear potential and charge collection response in a constant-flux irradiation condition.

Figure 5 shows the linearity of device response with beam intensity at 500nm, corrected for dark current during the transient. Saturation occurs near 60 mW/cm, and the sensitivity of potential and charge is nearly linear at lower intensities, as expected from the discussion above.

Figure 6 shows the spatial response across the entire test structure at 500nm and 10 mW/cm spot power calculated as the change in potential under the pixel surface center after 10 ms, corrected for leakage current during the transient.

Figure 6. Spatial response across the entire structure under 500nm
illumination for 10 ms at 10 mW/cm spot power.

Figure 5. Linearity repsonse of the pixel structure
under 500nm illumination for 10ms

The spectral response of the pixel structure is shown in Figure 7 for wavelengths of 200-1200 nm at 10 mW/cm² spot power during the 10 ms transient, corrected for leakage current. The peak sensitivity occurs near 500 nm, and drops to 50% of the peak sensitivity near 600nm and 350 nm.

Figure 7. Spectral response of the pixel structure
under illumination at 10mW/cm² spot
power at 500 nm illumination for 10 ms.

It is important to consider the effect of dark current in the characterization of charge transport for this test structure. Dark current is a result of carrier generation in the depletion region, diffusion current at the depletion region edge, and the surface generation current. All these mechanisms are primarily dependent on the minority carrier lifetime, the diffusion constant, the diffusion length, and the surface recombination rate. For the structure considered here, the surface recombination rate is a negligible term compared to lifetimes and diffusion parameters, since the larger area of the pixel storage surface is free of charge coupling effects with a surface oxide or electrode which may cause nearly equal electron and hole concentrations, resulting in a large surface recombination rate and surface generation-recombination current. The other components of dark current, depletion region generation and diffusion current, are normalized in this analysis by subtracting the change in potential due to dark current (to first order) by extracting a dark 10 ms transient potential change.

Summary

The step illumination response of a biased pixel structure is modeled using drift diffusion, generation-recombination, and optical models in ATLAS and Luminous, in the free charge-transfer model, which considers only free electrons in the conduction band. The transition of conduction band electrons to bound states and midgap states, such as interface traps, is typically considered at medium to low frequencies in surface and buried CCDs. Also, trapped and mobile oxide charge under steady-state and transient bias conditions may be optionally modeled in ORCHID for devices which exhibit surface effects typically associated with oxide charge.

Spatial sensitivity and spectral response are simulated in the linear range of potential sensitivity to illumination intensity at 10 mW/cm2. The peak frequency sensitivity occurs near 500nm, and the n-well charge collection region is the most sensitive part of the structure, as expected. We also note that charge integration in the n-well pixel (calculations from the TonyPlot 'Extract' statement, not shown) gives nearly the same results as change in potential, which is the expected result.

References

S.M. Sze, Physics of Semiconductor Devices, 2nd Ed., John Wiley & Sons, New York, 1981.

B.G. Streetman, Solid State Electronic Devices, 3rd Ed, Pretice Hall, New Jersey, 1990