In this unit, we will perform a simple transient simulation using the CHARGE solver to simulate
the bandwidth of a pin diode.
The germanium slab and aluminum contacts of the diode are already setup in the simulation
For germanium, the monotonic model for high field mobility has been enabled since it is
known that photogenerated carriers move under a strong electric field in the reverse biased
pin diode and velocity saturation plays an important role in limiting their velocities
at large reverse bias and therefore limits the bandwidth.
It is important to make sure that the CHARGE solver mode has been set to “transient”
and under the transient tab, the transient simulation controls have been set correctly.
To obtain the step response of the photodiode to illumination, an step pulse has been applied
in global source shutter settings.
This means that the transient simulation starts without any illumination and then the device
is exposed to illumination at a particular moment in time allowing us to capture the
transit time of the photogenerated electrons and holes which is the main contributor to
the bandwidth limit of this device.
Lets switch to partitioned volume mode to see how our simulation boundary conditions
and doping profiles are assigned.
The emitter contact has been assigned to the top aluminum layer and the base is applied
to the bottom one.
This has been done by selecting the “solid” surface type in the geometry tab for each
boundary condition and choosing the corresponding contact from the list of solids.
In addition, two diffusion doping profiles are added.
The n-type doping has been applied to an area just above the base contact and the p-type
is located right below the emitter contact.
For this example, to apply a reverse bias to the diode, the emitter contact is biased
at -2V by choosing the “transient” bc mode for the emitter voltage boundary condition
and adding entries to the voltage time table.
The first one specifies the contact voltage at the start of the simulation, and the second
one determines the voltage at the end of the simulation.
Since both entries have the same voltage value, this means that this contact remains at the
same voltage for the entire duration of simulation.
The end time of simulation should be large enough so that the system has reached its
steady state condition before the end of simulation.
The base contact will be kept at zero volt.
In addition, a constant optical generation source is added as a simple way to model the
carrier generation inside the photodiode due to illumination by light.
For a more realistic simulation, the generation rate should come from an optical simulation
(done for example using Lumerical’s FDTD Solutions).
Lets run the simulation.
Once the simulation is run, right-click on the CHARGE solver and select visualize>base.
Remove all the attributes except “I” which is the current at the base contact.
The current is plotted as a function of time since we performed a transient simulation.
You will notice that the system’s response has reached the steady-state before the end
of simulation which indicates correct setting for the end time of simulation.
To obtain the bandwidth value for the device, we need to obtain its impulse response which
can be easily calculated by taking a derivative of its step response.
Then the bandwidth can be calculated by taking a Fourier transform of the impulse response
to calculate the frequency response.
All of this can be done using Lumerical’s scripting language and we have prepared a
script file which can be run to perform the necessary calculations.
The script file can be downloaded from the link provided above this video.
To learn more about Lumerical’s scripting language, please check out the scripting 100
course available in Lumerical University.
Lets open the script file in script file editor and click run script.
The script will gather the necessary data, perform calculations and return the frequency
response results as a plot.
From the plot, it is obvious that the diode has a bandwidth of around 12 GHz.
To observe the effect of carriers velocity saturation on bandwidth, you can disable the
high field mobility model in germanium material properties and run the simulation again.
You will notice that this time the bandwidth is much higher since the effect of velocity
saturation is not considered in the simulation.