Optimization of Mid-IR Quantum Cascade Laser Gain

Note

The nextnanoevo Python package is under development. Its release is planned for 2024.

Header

Relevant files

• MidIR_QCL_InGaAs_InAlAs_Bai_NaturePhot2010_nextnanoevo.negf

• MIdIR_QCL_example.py (not available public yet)

Relevant output files:

• 330mV/Gain/SemiClassical_vs_Energy_[0.0,0.0,1.0].dat

Scope

• design optimization

• QCL

• NEGF

• laser gain

Important variables

• $thickness_scaling_factor (scaling factor for all wells and barries in QCL heterostructure)

Intoroduction

This tutorial shows how to optimize the gain of a 1D Mid-IR Quantum Cascade Laser (QCL) using the The nextnanoevo Python package. The goal is to maximize the gain of the QCL by varying the thickness of the quantum wells and barriers. The gain is calculated using the nextnano.NEGF.

Starting point

The starting point is the design of a Mid-IR QCL with a peak gain at photon energy of 275 meV. The design consists of sequence of InGaAs wells and AlInAs barriers with applied 330 mV bias ([Bai2010].)

The bandedges are shown in the figure below

Figure 7.3.4 The band edges of the MidIR QCL following [Bai2010] design.

The simulated gain with the peak at 275 meV is shown in the figure below

Figure 7.3.5 The gain of the MidIR QCL following [Bai2010] design.

Optimization objective

The goal is to maximize the gain of the QCL at 270 meV by varying the thickness of the quantum wells and barriers. All the wells and barriers will be scaled by the same factor.

Variables under optimization:

Name	Units	Initial value	Bounds
$thickness_scaling_factor	–	10.0	0.9-1.1

Target output:

Name	Units	Initial value	Target
Gain at 270 meV	\(cm^{-1}\)	199.49	max

Optimization script

At first, specify input file, variables, and relevant output files in the IO instance:

from nextnanoevo.IO import IO
output_files = [("330mV", "Gain", "SemiClassical_vs_Energy_[0.0,0.0,1.0].dat")]

nn_io = IO(
    input_file_path,
    variable_names=["thickness_scaling_factor"],
    target_output_paths=output_files,
)

Next, define the metric to get the gain at 270 meV.

def get_gain_at_270mev(df_list):
  df = df_list[0]
  energy = df.coords["Photon Energy"].value
  gain = df.variables["Gain"].value
  # get gain exactly at 270 meV
  mask = np.isclose(energy, 270, atol=0.001)
  gain_at_270mev = gain[mask]
  # minus sign to transform maximization to minimization
  return -gain_at_270mev

Define the Metric Metric class

from nextnanoevo import Metric
metric = Metric(input_length=1, output_length=1, extraction_function=get_gain_at_270mev)

Create and run evolution

from nextnanoevo import Evolution
evolution = Evolution(nextnanoio=nn_io, metric=metric, bounds=([1.0], [1.1]), size=5)

evolution.run(gen=4, algorithm_kwargs={"m": 0.4, "cr": 0.95, "seed": 2023}, seed=12345)

And print the final solution and fitness

for index, (sol, fit) in enumerate(
    zip(evolution.pareto_solutions, evolution.pareto_fits)
):
    print(f"{index}. Solution {sol}: {fit}")

This example is created to showcase how to use nextnanoevo to optimize the devices with nextnano.NEGF. To decrease the time of the simulations, the bounds are set to 0.9-1.1, and the number of generations is set to 3.

Result of optimization:

$thickness_scaling_factor	Gain at 270 meV (\(cm^{-1}\))
1.0662883	324.4952

The resulting gain in the optimized QCL is shown in the figure below

Figure 7.3.6 The gain of the MidIR QCL using optimized design.

Conclusion

This tutorial shows how to use the nextnanoevo to optimize the gain at the given photon energy of QCL. The optimized sttructure has a peak gain at the target wavelength after 5 generations of optimization.