Intersubband absorption of an infinite quantum well¶

Input files for nextnano³:

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_sg_nn3.in

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_kp_nn3.in

Input files for nextnano++:

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_sg_nnp.in

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_Gamma_nnp.in

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_kp_nnp.in

This tutorial presents calculation of intersubband absorption spectrum of a GaAs quantum well with infinite barriers.

Input files for both the nextnano++ and nextnano³ software are available.

The following input file was used:

1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_sg_nn3.in (single-band effective mass approximation)

This tutorial aims to reproduce the example discussed on p. 376f of Section 9.6.2 Intersubband Absorption Spectrum of [ChuangOpto1995].

Structure¶

Property	Symbol	unit	[ChuangOpto1995]	nextnano
quantum well width	L	nm	10.0	10.0
barrier height	E _b	eV	infinite quantum well model	1000
effective electron mass	m_e	m₀	0.0665	0.0665
refractive index	n_r		3.3	3.3
doping concentation (n-type)	N_D	cm^-3	1 $\cdot$ 10¹⁸	1 $\cdot$ 10¹⁸
linewidth (FWHM)	$\Gamma$	meV	30	30
temperature	T	K	300	300

[ChuangOpto1995] models the infinite quantum well using the analytical solution while we are using a numerical model with a barrier height of 1000 eV.

Results¶

[ChuangOpto1995] uses the analytical infinite quantum well model and calculates the energy levels, and the intersubband dipole moment exactly. Our calculated transition energies differ by 3 meV which is acceptable as we use a finite grid spacing of 0.05 nm. Our calculated dipole moment is also reasonable. More difficult are the densities. In our calculation we solve the Schrödinger-Poisson equation self-consistently. For that reason, the quantum well bottom is not entirely flat but slightly bent. At T = 300 K, the second subband shows a small density which is larger than in the model of [ChuangOpto1995]. The difference in subband densities leads to a slight deviation for the peak of the absorption spectrum because the occupation of the second level N₂ reduces absorption. Nevertheless, the agreement is reasonable.

Property	Symbol	unit	[ChuangOpto1995]	nextnano
energy level	E₁	meV	56.5 (exact)
energy level	E₂	meV	226 (exact)
transition energy	E₂₁	meV	169.5 (exact)	166.5
dipole moment	x₂₁	nm	-1.8 (exact)	-1.82
E_F - E₁		eV	78	28.2
subband density	N₁	cm^-2	7.19 $\cdot$ 10¹¹	9.92 $\cdot$ 10¹¹
subband density	N₂	cm^-2		3 $\cdot$ 10⁹
peak in absorption	$\alpha$_peak	cm^-1	1.015 $\cdot$ 10⁴	0.986 $\cdot$ 10⁴

The following figures show the

lowest eigenstates (probability densities) of the infinite quantum well
absorption spectra $\alpha(\omega)$ in units of cm^-1
position dependent absorption spectra $\alpha(\omega ,x)$ in units of cm^-1

The peak in the absorption spectra occurs at the transition energy E₂₁.

Then we perform two parameter sweeps:

We vary the quantum well width (Variable: $QuantumWellWidth).
We vary the doping concentration (Variable: $DopingConcentration).

Results and explanations for the sweeps can be found further below.

— Begin —

Automatic documentation: Running simulations, generating figures and reStructured Text (*.rst) using nextnanopy

The following documentation and figures were generated automatically using nextnanopy.

The following Python script was used: intersubband_InfiniteQW_nextnano3.py

The following figures have been generated using the nextnano³ software. Self-consistent Schrödinger-Poisson calculations have been performed for an infinite quantum well.

A single-band effective mass approach has been used, i.e. not $\mathbf{k} \cdot \mathbf{p}$.

The absorption spectra have been calculated assuming a parabolic energy dispersion $E(k)$.

Infinite Quantum Well (QuantumWellWidth = 10 nm)

Infinite Quantum Well (QuantumWellWidth = 13 nm)

Infinite Quantum Well (QuantumWellWidth = 16 nm)

Infinite Quantum Well (QuantumWellWidth = 19 nm)

Parameter sweep: Well width

Figure 2.5.12.37 shows the absorption spectra for different quantum well widths (Variable: $QuantumWellWidth). The larger the well, the closer the energy level spacings. Therefore the peak occurs at smaller energies. The larger wells show absorption also for transitions other than E₂₁.

Parameter sweep: Doping concentration

Figure 2.5.12.38 shows the absorption spectra for different doping concentrations (Variable: $DopingConcentration). The peak absorption coefficient increases with the doping concentration N_D.

Last update: nn/nn/nnnn