QCSE Simulations

With Harold’s modulator module, users can simulate the Quantum Confined Stark Effect used to simulate Electro Absorption Modulators (EAM) as well as Electro refractive Modulators (ERM),

Unlike other electro-absorption modulator models, Harold provides a rigorous first-principle physical model which relies on a rigorous modelling of the physics at a fundamental level.

The EAM model consists of four solvers that are run in sequence:

• Poisson-Drift-Diffusion Solver
• Schrödinger Solver
• Exciton Electrical
• Permittivity Solver  

In a multi-stage model like this, it is sometimes difficult to track the origin of problems but in Haorld, each step of the complex simulation can be controlled. Users can inspect the results of the intermediate solvers, obtain physical insight into specific trends of the device’s behaviour and spot problems at early stages.

Poisson-Drift-Diffusion Solver

For a defined range of reverse biases, Harold can produce the following physical values as functions of vertical position  

• conduction and valence band edges of the structure
• quasi-Fermi levels
• carrier and charge densities  

The Schrödinger Solver of Harold can produce  

• electron and hole wavefunctions and their energy levels in the QW structure
• number of electron-hole pairs with an overlap integral above a defined cutoff value  

This tool allows the user to observe the Quantum-Confined Stark Effect (QCSE) in a specific QW structure as a function of reverse bias. 

The final results, the absorption and index spectra, are produced for TE and TM polarizations and can be plotted in different units:  

• wavelength or photon energy in the x-axis
• absorption, real and imaginary parts of refractive index or electrical permittivity  

The user can chose the temperature, the bias and spectrum range. 

We used Harold's modulator module to model a AlGaAs electro-absorption modulator and a SiGe electro-absorption modulator. The results are shown below alongside published experimental data; as you can see the simulations are in good agreement with the experiments, with all main features reproduced. We expect that the differences in absolute absorption coefficients are due to scaling ambiguities in the experimental papers.

[1] S.-L. Chuang, S. Schmitt-Rink, D. A. B. Miller and D. S. Chemla, “Exciton Green’s function approach to optical absorption in a quantum well with an applied electric field”, Phys. Rev. B, 43, 2, pp. 1500-1509 (1991)

[2] Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Quantum-confined stark effect in Ge–SiGe quantum wells on Si for optical modulators”, IEEE J. Sel. Topics Quantum Electron., 12, pp. 1503–1513 (2006)