CMOS - Transient electrical response

CMOS image sensor pixels are time-varying devices, whose current state depends strongly on their history of operation. To characterize the optoelectronic performance of an image sensor, the transient response can be used to accurately set the initial conditions for the device and measure its response to a variety of optical exposures both in terms of intensity and in terms of duration. In this topic, we discuss the simulation techniques required for the transient simulation of the CMOS image sensor pixel electrical response under varying illumination conditions.

Simulation Setup

Optical Simulation

For the optical simulation, the setup mirrors that of the angular response calculations. Only the normal angle of incidence will be necessary (at both polarizations): do not run the angular sweep. The generation rate can be calculated from the analysis group for blue sub-pixel or from the analysis group for blue/green sub-pixel pair. In the electrical simulation, the generation rate from the pair of sub-pixels is used. These objects are already included in the CHARGE files and do not need to be recalculated here.

Electrical Simulation

To perform the electrical simulation, CHARGE must be set to transient simulation mode, which can be done from the properties editor for the CHARGE solver. The duration of the transient simulation is determined by the sample points for the definitions of the contact biases and from the optical shutter. For example, if the only time-varying input is the voltage source attached to a terminal, and it is defined by

(i.e. a step with a 0.1us rise time and a 4.9us hold time), then the transient simulation will run for 5us. CHARGE uses an adaptive time-stepping algorithm that automatically adjusts the time step interval to ensure that the specified tolerance is maintained on the local truncation error. The limits on the time step size (minimum and maximum) and on the error tolerance can be set in the Transient tab of the CHARGE region properties. For transient simulations, the Newton solver should be enabled (see the Advanced tab of the CHARGE region settings).

An example of the transient settings is shown in the adjacent figure. In addition to setting the time step controls as described above, downsampling can be enabled by interval or by the number of steps. Many simulations may be required to accurately capture rapidly changing inputs (such as switched source voltages), which can impact memory requirements. By enabling downsampling, and choosing a limited set of results to record (see the Results tab of the CHARGE settings), the memory requirements can be managed.

To control the optical stimulus (generation rate) in the electrical simulation, the Global Optical Shutter properties can be set in the Transient tab of the CHARGE region properties (see above). The shutter can be set in one of five modes:

• step on
• step off
• pulse on
• pulse off
• always on

For each mode (as appropriate) the on and off time can be specified. For the transient simulation of the image sensor pixel, the illumination will be set to "pulse on", starting at 0.4us (after the floating diffusion has been isolated) and switching off at 200us. The slew rate (linear) can also be specified. The source intensity can also be scaled by adjusting the "illumination power scaling". This property will be used to sweep over a range of illumination power without requiring additional analysis in FDTD.

Three electrical contacts are specified for the operation of the image sensor. The substrate contact is maintained a fixed reference potential (0V). The transfer gate (TX) voltage is initialized to 3.3V and is then immediately switched off, isolating the n-well. After the end of the illumination period, a pulse is applied to TX starting at 240us and lasting for 10us. The contact model for the floating diffusion (sense) requires a capacitor to model the effect of the amplifier gate, and a switched series resistance to model the effect of the RST transistor impedance. The source voltage for the sense contact is maintained at 3.3V. The table below shows the values of the active components in the sense contact model at various times.

The following screenshot illustrates the circuit model associated with the sense contact

Run and results

To run the simulation, open the file cis-pulse-1fF-200us.ldev. In the Optimizations and Sweeps toolbox, choose the sweep titled "illumination" and run the sweep. Please see the note above regarding the run time.

When the simulations are complete, run the script cis_transient_analysis.lsf to perform the analysis. The analysis script will load the files from the sweep, and extract the voltage measured at the floating diffusion. Because a variable time-step is used, the number of simulations will vary for the different illuminations used in the sweep. The analysis script will interpolate those results on to a uniform array of time sample points for visualization. The result is plotted in the figure below. Note that the illumination is switched off at 200us, and the pixel is held for 40us before a 10us pulse is applied to the transfer gate (TX). For an individual simulation, the voltage on the sense contact can be plotted by loading the file and choosing "visualize > sense" from the CHARGE region context menu. Select the "Vc" (contact voltage) from the list of attributes.

Charge Integration

To calculate the total charge collected by the image sensor, the relationship between capacitance and voltage can be used: ΔQ = ΔV*C. In the simulations, the capacitance on the sense node was chosen to be 1fF. During the illumination period, a photocurrent is generated by the intrinsic photodiode formed between the sense n-well and the p-type substrate, resulting in an initial accumulation of charge on the capacitor. This is measured at the end of the illumination period (t = 200us). When the pulse is applied to the transfer gate, the charge stored in the buried n-well of the photo-detector is transferred to the floating diffusion (t = 240us). The total accumulation of charge can be calculated at the end of the simulation (t = 260us). Both the charge before the transfer pulse and after the transfer pulse are plotted in the figure adjacent.

Full Well Capacity

The capacity of the buried n-well can be estimated from the difference in the integrated charge count before and after the transfer gate pulse is applied. In the adjacent figure, we can see that (before the onset of saturation), the well capacity is approximately 1500e-.

Signal to Noise Ratio (SNR)

To calculate the SNR for the image sensor, only temporal noise sources are considered. In addition, the reset thermal noise and 1/f noise in the amplifier will be neglected. These sources of noise can be added to the SNR calculation if desired using an appropriate model. The SNR is calculated with respect to the total accumulated charge count and includes contributions from the dark current and the photon shot noise. The dark current, obtained previously, was found to be approximately 1e5e-/s, for a total dark count of 20e- during the simulation time (200us). The photon shot noise can be estimated from the total absorbed photon count, as calculated from the illumination intensity \(P_{in}\) \((\frac{w}{m^2})\) and the optical efficiency.

$$ N_{ph} = P_{in}A (\dfrac {OE}{OE_{max}})\dfrac{\lambda}{hc}T_{exp} $$

Both the dark current and photon shot noise contributions obey Poisson statistics. Therefore, the SNR is calculated as

$$ S N R=20 \log _{10} N_{s i g} - 20 ( \log _{10} \sqrt{N_{d a r k}} + \log _{10} \sqrt{N_{p h}}) $$

and the result is plotted in the figure below.

Related publications

1. F. Hirigoyen, A. Crocherie, J. M. Vaillant, and Y. Cazaux, “FDTD-based optical simulations methodology for CMOS image sensors pixels architecture and process optimization” Proc. SPIE 6816, 681609 (2008)
2. Wang, Xinyang, "Noise in Sub-Micron CMOS Image Sensors", Ph.D. Thesis, Delft University of Technology