# 7.5. AlGaAs/GaAs THz QCL¶

Input file:

• THz_QCL_Fathololoumi_OpticsExpress2012.xml (old format)

• THz_QCL_Fathololoumi_OpticsExpress2012.negf (since 2022-04)

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.

The input file in the XML format (old) uses constants (e.g. Barrier for the aluminum content of the barriers) and iterators for temperature sweep. In this case, single program execution simulates all the cases.

The input file in the .negf format (new) uses nextnano++-style variables starting with dollar sign (see Syntax definition). Then, the nextnanomat feature Template or nextnanopy Sweep can be used to sweep the variables before execution. This simply generates multiple input files, which can be run in parallel (see Options: Simulation).

Furthermore, in these input files 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 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 Al0.15Ga0.85As 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{
Thickness = 5.0                                 # Unit = nm
Material{
Base = GaAs
}

Probes = 1.0
Doping = 6e16                             # Unit = 1/cm^3
}


An alloy like Al0.15Ga0.85As is specifed as follows:

Material{
Base = "Al(x)Ga(1-x)As"
AlloyX = 0.15
}


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

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 = Center                                    # Comment = Specfiy the cluster where optical gain should be calculated.
PhotonEnergyInitial = 1e-3            # Unit = eV             # Comment = Min. photon energy for gain calculation.
PhotonEnergyFinal = 30e-3             # Unit = eV             # Comment = Max. photon energy for gain claculation.
PhotonEnergySteps = 117                       # Unit = #              # Comment = Number of photon energies for gain calculation.
}


The term Center refers to the Center entries in

BeginCluster = "Center, QCL"


and

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.

1. Specify Center

 Lead{
Name = Drain
Voltage{
Cluster = Center
}
}

1. or QCL.

 Lead{
Name = Drain
Voltage{
Cluster = QCL
}
}


Both are 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 variable with the name BarrierProbes which we set to 1.0.

$BarrierProbes = 1.0 # Enable/disable scattering within barriers. This can reduce computational time with minor influence on overall results.  Consequently, for each AlGaAs barrier layer we have included the constant BarrierProbes. Layer{ ... Material{ Base = "Al(x)Ga(1-x)As" AlloyX =$Barrier
}
Probes = \$BarrierProbes
...
}


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.