Optimizing well width for specific target transition energy in an infinite quantum well

Attention

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

Header

Relevant files

• 1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_sg_nnp.in (the same as here.)

• InfiniteWell_example.py (not public yet, provided on request)

Relevant output files:

• bias_00000/Quantum/energy_spectrum_quantum_region_Gamma_00000.dat

Scope

• design optimization

• quantum well

• transition energies

Important variables

• $QuantumWellWidth = thickness of the GaAs quantum well

Introduction

This tutorial demonstrates the use of nextnanoevo for optimization of a simple quantum well structure to achieve desired transition energy. The tutorial is based on the Intersubband absorption of an infinite quantum well tutorial.

Objective

The goal of this optimization is to determine the quantum well thickness that aligns the transition between the first and second electron states with a specified target energy.

Variables under optimization:

Name	Units	Initial value	Bounds
QuantumWellWidth	nm	10.0	–

Target output:

Name	Units	Initial value	Target
Transition energy	eV	0.1668	0.1

Scipy.optimize.root

In this example scipy.optimize.root root-solver is used. The algorithm searches for the root of the equation

\[f(x) - target = 0\]

where \(x\) represents the vector of input variables and \(f\) is the user-defined metric.

Optimization script

Initially, create a nextnanoevo.IO instance specifying the input file, optimization variables, and output files relevant for the metric.

from nextnanoevo.IO import IO
nn_io = NextnanoIO(input_file_path,
                 variable_names=['QuantumWellWidth'],
                 target_output_paths=[('bias_00000', 'Quantum', 'energy_spectrum_quantum_region_Gamma_00000.dat')])

Next, define the metric function to extract the transition energy from the energy_spectrum datafile.

def first_transition_extraction_function(df_list):
    df_energy_spectrum = df_list[0]  # df_list will be a list containing one datafile
    energy_spectrum = df_energy_spectrum.variables['Energy'].value
    transition_energy = energy_spectrum[1] - energy_spectrum[0]  # transition energy between the ground state and second state
    return np.array([transition_energy])

A nextnanoevo.Metric is created with the custom metric function. Extraction function takes single output file and converts it to single value, so both input length and output length equal 1.

from nextnanoevo.MetricExtractor import Metric
metric = Metric(input_length=1, output_length=1, extraction_function=first_transition_extraction_function)

Create the Optimizer, and set the initial value for quantum well thickness and target transition energy.

from nextnanoevo.OptimizerClass import Optimizer
optimizer = Optimizer(nextnanoio=nn_io, metric=metric, optimization_method='root')
# arguments of the optimization_method. For scipy optimize.root x0 is mandatory
optimizer.set_optimization_parameters(x0=np.array([10]))
# set target
optimizer.set_target(np.array([0.1]))

Run the optimization. The details are recorded in the Simulation*.log file, which tracks each input file execution.

result = optimizer.run_optimization()
print(f"The optimal quantum well thickness is {result.x} nm")

Output:

The optimal quantum well thickness is [12.80762256] nm

Conclusion

In summary, this tutorial has demonstrated an approach to optimize a quantum well structure to match a specific transition energy using nextnanoevo. The process involved setting up the NextnanoIO instance, defining a custom metric function, utilizing the NextnanoMetricExtractor, and finally employing the NextnanoOptimizer for the actual optimization task.