AlGaAs/GaAs THz QCL¶

The tutorial is based on this paper: [FathololoumiOE2012]

This paper describes a THz quantum cascade laser (QCL) with a performance up to 199.5 K. The QCL layout is based on a resonant phonon three well design. This example input file demonstrates the usage of constants (e.g. Barrier for the aluminum content of the barriers) and so-called iterators. These iterators can be used to sweep a variable (here T for temperature). The whole input file is run for every iterator combination.

Furthermore, in this input file the usage of so-called clusters is demonstrated. A cluster is a set of layers which is specified via BeginCluster and EndCluster, where the last layer is inclusive. The clusters are used to specify a certain voltage which is extended to the whole device and to define the region in which the optical gain is calculated. This is especially useful if more than one period is calculated.

The input file is called: THz_QCL_Fathololoumi_OpticsExpress2012.xml

This XML file can be edited by the users to input the structure of a device and some further necessary input parameters. The details of the syntax of the input files is explained in the input file documentation.

Our structure consists of GaAs wells and Al_0.15Ga_0.85As barriers of width

4.0 nm | 4.3 nm | 8.9 nm | 2.46 nm | 8.15 | 4.1 nm | 5.5 nm + 5.0 nm + 5.5 nm = 16.0 nm | 4.3 nm | 4.0 nm

where the barrier material is indicated in bold and the doped region in italics. The doping concentration is 6 \(\cdot\) 10¹⁶ cm^-3.

The QCL structure consists of the actual QCL period which is embedded between two 4.0 nm wide GaAs regions that serve as the leads at the left and right boundary. These lead layers are also doped. The concentration is 1 \(\cdot\) 10¹⁶ cm^-3.

The QCL design consists of three quantum wells (GaAs) and three barriers (AlGaAs). On the right, just before the lead, we have to add an additional barrier arising from the next QCL period. The total length of the structure as specified above is 56.21 nm. As we are using a 0.5 nm grid, our simulated structure essentially has a length of 56.5 nm. The QCL is designed with respect to an electric field of -12.2 kV/cm. This corresponds to a bias voltage of 68.93 mV for our 56.5 nm structure.

Each layer of the structure is defined within the keyword <Layer> where the material name is given, its width and a doping concentration if applicable.

<Layer>

 <Width    Unit="nm"    > 5.0  </Width>
 <Material Base="GaAs"/>
 <Doping   Unit="1/cm^3"> 6e16 </Doping>

</Layer>

An alloy like Al_0.15Ga_0.85As is specifed as follows:

<Material Base="AlGaAs" AlloyX=0.15 />

The following figure shows the conduction band profile at -12.2 kV/cm.

Add figure here.

The gain has been calculated between 3 and 30 meV in the cluster called Center. The photon energy interval includes of 100 photon energies.

<Gain>
 <Cluster                       Comment="Specfiy the cluster where optical gain should be calculated."> Center </Cluster>
 <PhotonEnergyInitial Unit="eV" Comment="Min. photon energy for gain calculation."       >   3e-3 </PhotonEnergyInitial>
 <PhotonEnergyFinal   Unit="eV" Comment="Max. photon energy for gain claculation."       >  30e-3 </PhotonEnergyFinal>
 <PhotonEnergySteps   Unit=""   Comment="Number of photon energies for gain calculation."> 100    </PhotonEnergySteps>
</Gain>

The term Center refers to the Center entries in

<Layer BeginCluster="Center, QCL">

and

<Layer   EndCluster="Center, QCL">.

There is also a Center entry in the Lead called Drain. Here, the applied voltage drops over the layers that are inside the Center region.

Specify Center

<Lead Name="Drain">
 <Voltage>
 <Cluster> Center </Cluster>

or QCL.

<Lead Name="Drain">
 <Voltage>
 <Cluster> QCL    </Cluster>

Both is possible because BeginCluster and EndCluster contain both labels.

In this tutorial, we have enabled, i.e. 1.0, the scattering within the AlGaAs barriers. For each layer we have defined a <Constant> with the <Name> BarrierProbes which we set to 1.0.

<Constant>
 <Name  Comment="Enable/disable scattering within barriers. This can reduce computational time with minor influence on overall results.">BarrierProbes</Name>
 <Value Unit="[0..1]">1.0</Value>
</Constant>

Consequently, for each AlGaAs barrier layer we have included the constant BarrierProbes.

<Layer>
 ...
 <Material Base="AlGaAs" AlloyX=0.15 />
 <Probes> BarrierProbes </Probes>
 ...
</Layer>

The simulation took

Duration in days, hours, minutes, seconds: 5h 50'34''

on an Intel Core i5-3470S (2.9 GHz) for a 0.5 nm grid spacing.