Band-to-band tunneling at low temperature

quantumex17.in : Band-to-band tunneling at low temperature

Requires: Blaze
Minimum Versions: Atlas 5.28.1.R

This gives an example of using the BBT.NONLOCAL model to study the forward tunneling current in a degenerately-doped Germanium diode at 4.2K.

The deck uses the dbinternal interface to consider 6 values of doping and to obtain the results in a format suitable for use with TonyPlot. The auxiliary file quantumex17_aux.in is run for the 6 values of doping specified in quantumex17.in.

The auxiliary file sets up a simple p-n diode in Germanium, with a fine mesh being specified near the actual junction. Both the donor and acceptor concentration are set to be the same value, as specified by the $doping parameter supplied by the main deck. The actual tunneling junction is set up by the QTREGION statement. Its limits in the y-direction (-0.2 microns to 0.2 microns) are sufficient to ensure that the tunneling slices start and end outside the depletion region under the biasing conditions considered.

There are 6 tunneling slices which are parallel and regularly spaced, with 151 points each on which to do the tunnel current calculation.

The parameters on the MATERIAL statement

me.tunnel and mh.tunnel

have the major influence on the tunneling current and can be used as fitting parameters. ni.min is specified to avoid underflow at these low temperatures.

The model BBT.NONLOCAL is specified on the MODELS statement, along with BBT.NLDERIVS which includes fully non-local coupling into the jacobian matrix.

If you wish to save out a structure point at a given value of bias, you can see the internal quantum tunnel current as a generation rate. This is optional.

The bias is ramped up to 0.15 V of forward bias and the I-V curves saved in logfiles. The extract statement is used to find the peak value of the current, and the value of bias at which it occurs. The I-V curves are plotted.

The other plots are of the logarithm of the peak current versus the reciprocal of the square root of the doping level. This curve is approximately a straight line as is observed experimentally. Also shown is the bias at which the tunnel current is a maximum. This increases with the doping level, reflecting the more favourable band lineup for tunneling under more degenerate doping.

To load and run this example, select the Load button in DeckBuild > Examples. This will copy the input file and any support files to your current working directory. Select the Run button in DeckBuild to execute the example.