# Selecting Parameter in Transient Simulation in DEVICE

#1

Hi,

I am simulating the transient response of a VPD to calculate its bandwidth.
I found that the calculated frequency response is very sensitive to the value of the “min time step (fs)”, “abs lte limit”, and “rel lte limit” especially for large bandwidth devices. so I get different values in bandwidth calculation. is this expected? I was wondering how we should choose these numbers, Should I reduce them up to the point that results are similar?

Thanks,

#2

Hi. The result of the transient simulation should not be dependent on the time step unless you are using a very large time step and therefore are ending up with too few points in the frequency domain plot. The key to getting consistent result here most likely lies in the accuracy setting (abs. tol.) of the solver. The transient solver often requires a larger accuracy setting than the steady state solver. The default values for the abs. tol. (absolute tolerance) for both the Poisson and drift-diffusion solver are 1e-4. You can try reducing this value to (say) 1e-6 to see if this affects your result. Once you see the result is consistent irrespective of the value of abs. tol., you should have accurate result that will give you accurate bandwidth.

Now regarding the parameters for the transient solver, here are some pointers:

min time step (fs): The minimum time step should be small enough so that you have enough points in your time domain response. This will ensure, (i) you have enough points in your frequency domain response and (ii) your frequency domain response has a large enough span. The limiting factor here is the electron relaxation time in the semiconductor which typically varies from 0.2 to 1 ps. So the minimum allowed value for “min time step” is around (say) 500 fs.

max time step (fs): This option can be used to speed up the simulation when solver gets close to reaching steady state. However, if you are thinking about doing fft then you may need to re-sample the result to get a uniform time grid.

abs lte limit / rel lte limit: These entries determine when the solver will increase the time step to speed up the simulation. If the absolute error (or relative error) is less than this value then the solver increases the size of the time step.

Transient Simulation - Relaxation Time
#3

Following up on the Transient simulation of VPDs, does DEVICE take into account the RC values of the PD diode in frequency response calculation? for example when the length of PD is changed from 50 um to 10 um, we expect the capacitance to decrease and BW to increase, however the frequency response does not change. the VPD frequency response is clearly RC limited and not transit time limited, so the change in capacitance should result in change in BW.

#4

The bandwidth of the (ideal) intrinsic diode (PD) will be independent of the length since decreasing the length decreases the capacitance and increases the diode resistance at the same time. However, when you include the extrinsic components such as the load resistance and the internal resistance of the driving voltage source, the overall resistance of the circuit no longer increases linearly with length and you will see the effect of length on RC and on bandwidth. For your PD simulation, you will need to include (series) resistances at the electrical contacts to observe the effect of length on bandwidth.

NOTE: The resistance values set at the contacts are for the total surface area of the contacts for the simulated structure. When modeling contact resistances, the data is often defined in terms of Ohm-cm^2. This value has to be used to calculate the total resistance value (in Ohm) for the simulated structure (e.g. by dividing the Ohm-cm^2 value with the area of the contact in cm^2).

Avalanche Photodetectors (Carrier multiplication simulation)