2.4.18. 1D - SiGe QW excitonic absorption

Attention

This tutorial is under construction.

Input files:

1D_Ge_GeSi_QCSE_Lever2010_8kp_nnp_exciton.in

Scope of the tutorial:

In this tutorial, we show an approach how to model absorption in a quantum well. This tutorial reproduces results from [LeverJLT2010].

The most relevant keywords:

• contacts

• optics{ quantum_region{} }

• quantum{excitons}

Solvers:

• strain

• poisson

• quantum

• quantum_optics

Relevant output files:

bias_xxxxx\Optics\absorption_quantum_region_TE_eV.dat

Introduction

This tutorial models an absorpiton inside a quantum well — an active region of electro-absorption modulator. The tutorial reproduces results from [LeverJLT2010] with 9 nm Ge well with 12 nm \(Si_{0.4} Ge_{0.6}\) barrier grown on \(Si_{0.3} Ge_{0.7}\) substrate. The Ge concentration profile is smoothend by interdifusion, which is modelled using analytic profile from [LeverJLT2010]. The Ge grown on the Si substrate is tensile strained, because the bulk thermal expansion coefficient of Ge is arger than of the Si substrate. In order to take in into account , 0.1% tensile residual strain is added to virtual substrate.

strain{
    residual_strain = 0.001
...
}

The figure Figure 2.4.18.1 shows the wavefunctions in conduction and valence bands.

Figure 2.4.18.1 The bandedges (colored) and the wavefunction probabilities (gray) in the quantum well under 0 bias.

The bias sweep from 0 V to 0.5 V is specified in the input file in the contacts

$left_bias_start = 0
$left_bias_finish = 0.27
...
contacts{
    ohmic{ name = "left" bias = [$left_bias_start, $left_bias_finish] steps = 3}
    ohmic{ name = "right" bias = 0}
}

For each bias the absorption in the device is calculated. Due to the quantum confinement, the excitonic absorption is still observable at room temperatures. The excitonic correction is added, more details are explained in tutorial “Optical interband absorption in a quantum well including excitonic effects”. The absorption at differnt biases is shows in the figure Figure 2.4.18.2.

Figure 2.4.18.2 Excitonic absorption in the device. Labels indicate electric field in the middle of the quantum well.

The redshift of exciton peak is observed when bias is applied to the structure. At a given wavelength, the absorption increase is significant allowing for electro-optic absorption modulation. The modelling can be used to optimize the parameters of the device and to choose the optimal wavelenght of the modulation for a given structure.

The position of exciton peaks are in a good agreement with simulation from [LeverJLT2010] — within \(1 meV\) error for each bias. While the relative change of absorption with applied bias also agrees with experimental data, the absolute value differs by a factor \(1.4-1.6\). The nextnano software is continiously improving to meet last criteria as well.

Acknowledgment

This tutorial is based on the nextnano GmbH collaboration in the scope of the SiPho-G Project aiming at development of ultrahigh-speed optical components for next-generation photonic integrated circuits, and it is funded by the European Union’s Horizon 2020 research and innovation program under grant agreement No 101017194.