Electro-absorption modulation in SiGe quantum well structure

In this example, we demonstrate the workflow for simulating a Quantum Confined Stark Effect (QCSE) Electro Absorption Modulator (EAM) based on a SiGe quantum well structure. The simulated absorption vs electric field will be compared with the measurements given in a reference [1].

The simulation is enabled by the following features of our CHARGE and MQW solvers.

• 8x8 k.p method
• variational algorithm for excitonic modes
• graded alloy feature in CHARGE-MQW coupled simulation workflow

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Overview

Understand the simulation workflow and key results

The Quantum-Confined Stark Effect (QCSE) serves as a crucial mechanism in electro-absorption modulators, enabling the modulation of optical absorption through the application of an electric field. In the absence of an external electric field, the wave functions of ground-state electrons and holes are symmetrically distributed inside the well and only a discrete set of frequencies of light may be absorbed or emitted by the system. When an external electric field is applied, the electron states shift to lower energies, while the hole states shift to higher energies. This reduces the allowed frequencies for light absorption. The external electric field also shifts the electrons and holes to the opposite sides of the well, resulting in a decrease in the overlap between electron and holes wavefunctions. As a result, the initial excitonic peak in the absorption spectrum of a QCSE modulator experiences both a redshift and a decrease in magnitude proportional to the strength of an applied electric field.

Run and Results

Instructions for running the model and discussion of key results

Step 1: CHARGE-MQW simulations

To start, we need to set a command line option in the CHARGE solver. To do so, open CHARGE IDE File \(\rightarrow\) Resources \(\rightarrow\) CHARGE \(\rightarrow\) Edit. In the “Resource advanced options” window, find “extra command line options” and enter the following string (without quotation marks) “-wf-location-filter-cutoff 1”. Click OK and save. This setting ensures the quality of our absorption spectrum result by admitting some more delocalized wavefunctions into the calculation.

1. Open SiGe_QW.ldev . All the material, geometry, and solver options are already set in this file. Simply run the simulation.
2. Run SiGe_QW_analysis .lsf to extract plots for the absorption spectrum under different voltages, wavefunction (probability distribution), band diagram, and bandstructure.

We assume a 0.8 V built-in potential, which drops principally across a region consisting of 10 quantum wells, a top spacer (100 nm), and a shortened bottom spacer (25 nm). The thickness of the well and barrier are assumed to be 10 nm and 16 nm, respectively, with a reduced thickness of 8 nm for the first and last barrier. At zero external bias, the built-in electric field is 0.8 V / 385 nm.

To accelerate our simulation, we use a simplified version of the actual device by including only one QW. This leads to a significant reduction of simulation time, and it is justified since the barriers between QWs are thick, leading to decoupled QWs. Our simulated device spans over only 242 nm. In order to match the electric field values, we set the first bias voltage for our device to (0.8 V / 385 nm) * 242 nm = 0.503 V. Similarly, when the original device is put under 4.0 V (external bias), the actual potential across the intrinsic region is approximately 4.8 V. Correspondingly, for our simulated device, we set (4.8V / 385nm) * 242 nm = 3.017 V.

CHARGE simulation is coupled with the MQW solver to incorporate quantum effects in optical absorption, especially the enhancement due to excitons. The simulation calculates the optical absorption spectrum of a SiGe quantum well with depleted carrier concentration under a few different bias voltages.

The spectrum clearly shows the excitonic peak at room temperature, which is a characteristic of a quantum well unlike in the case of bulk, where the exitonic peak can only be observed at low temperatures. Due to Quantum Confined Stark Effect (QCSE), the initial excitonic peak experiences both a redshift and a decrease in magnitude proportional to the strength of an applied electric field. We also observe a shift of the absorption edge to lower photon energies as a function of applied electric field.

Here, we compare the experimental results of Kuo et al. [1] with our simulation results. The position of the first excitonic peak and its shift as a function of applied voltage demonstrates a good match to the measurements. The simulated magnitude is smaller, which is the usual discrepancy observed in publications, due to the possibility of additional sources of losses in experiments other than exciton absorption.

The band diagram shows how it varies as a function of applied voltage. A smooth transition between well and barrier is due to the graded alloy composition along the thickness. The external electric field shifts the electrons and holes to the opposite sides of the well leading to a decrease in the overlap between electron and holes wavefunctions. Probability distribution of single particle eigen-states at band edges \((k=0)\) clearly shows an increase in the offset between the valance and conduction band as a function of applied electric field. The reduction in the overlap between the probability distribution of the valance and conduction band leads to a decrease in the magnitude of absorption as a function of applied voltage.

Here the non-parabolic nature of band structure is captured by 8x8 k.p method. The energy levels for electrons and holes are quantized due to the confinement in the well. When an external electric field is applied perpendicular to the plane of the quantum well, it interacts with the confined charge carriers, leading to a shift in their energy levels. This shift in energy levels is known as the Stark shift, and results in a decrease in the effective quantum band gap in the presence of external electric field which can be calculated using the band structure. As a result of this decrease in the effective quantum band gap, the shift in the energy corresponding to the absorption edge or the excitonic peak is observed.

Important Model Settings

Description of important objects and settings used in this model

Strain : a tensile strain of 0.1% is assumed in the substrate made of Si0.1Ge0.9, according to the literature.

MQW material diffusion length : A diffusion length of 1nm is chosen and the resulting diffusion profile of alloy contents is set in the Material property of geometric objects.

Valence band offset (VBO) : In CHARGE/MQW coupled mode, to set the VBO for both CHARGE and MQW, set the work function of base electric materials for each alloy such that the desired VBO is reached.

Hard wall cutoff : adequately increase the cutoff parameter in the boundary conditions setting of MQW when a high electric field is applied. Also set -wf-location-filter-cutoff 1 command line option in the Resource configuration window.

Doping diffusion: for built-in voltage, we assume doping diffusion such that the intrinsic region is shorter by 75 nm.

Taking the Model Further

Information and tips for users that want to further customize the model

The actual device fabricated in the experiment consists of ten quantum wells, spacers, and doped buffers. To fully simulate such a device, it is necessary to build the whole device model and run again the CHARGE/MQW coupled simulation.

Here we show the band diagram calculated with the uncoupled CHARGE simulation.

Additional Resources

Additional documentation, examples and training material

Related publications

1. Y. -H. Kuo et al. , "Quantum-Confined Stark Effect in Ge/SiGe Quantum Wells on Si for Optical Modulators," IEEE Journal of Selected Topics in Quantum Electronics, vol. 12, no. 6, pp. 1503-1513, 2006.

See also

• GaAs-AlGaAs Electro Absorption Modulator – Ansys Optics

Appendix

Additional background information and theory

Graded alloy definition

In order to modify the alloy composition along the thickness (z direction), we use the following expressions for the top barrier, well, and bottom barrier, respectively.

By incorporating such a graded behavior, the following distribution will be used by the three layers. These figures are plotted using Graded_x_distribution.lsf .