Optical Transitions

The feature adds stimulated and spontaneous emission generation/recombination rates to the semiconductor and computes the corresponding changes in the complex refractive index or relative permittivity.

Select a — (the default) or . This setting determines whether an extra dimension is added to represent the frequency domain. The use of an extra dimension typically makes the problem faster to solve, but it means that additional memory is required. An extra dimension also allows quantities such as the stimulated emission power to be visualized as a function of frequency.

Select a — (the default) or .

The uses a two-band model to represent a direct band gap semiconductor, as described in Optical Transitions in the Theory for the Semiconductor Interface.

Select the check box to compute the recombination due to spontaneous emission. Select the check box to add the stimulated emission generation or recombination terms. Both check boxes are selected by default.

The transitions model allows arbitrary specification of the recombination and generation rates due to spontaneous and stimulated emission, and can also be used to compute the Kramers-Kronig integral for the stimulated emission contribution to the change in the real part of the dielectric constant or the refractive index.

For this model enter the:

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, Grefstim (SI unit: 1/(m3·s)). This rate is used when performing the Kramers–Kronig integral to compute the change in the real part of the dielectric constant or refractive index.

This section is available when the is selected as the .

Select how to define the — (the default), , , or .

Based on the options chosen enter:

For the enter the :

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: Select (the default, defined in the corresponding section), (converted from Nc, which is defined on the Semiconductor Material Model domain feature), or . For enter the ratio of the effective mass to the electron mass me*/me (dimensionless). The default is 0.053.

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: Select (defined in the corresponding section), (defined in the Semiconductor Material Model node), or . For enter the band gap Eg (SI unit: V). The default is 0.341 V.

	The matrix element can be dependent on the excitation angular frequency if desired. Any function of the angular frequency can be used, but the angular frequency should take the form: semi.ot1.omega (for interface tag semi and feature tag ot1).

This section is available when the is selected for the .

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Select an me* — (the default, which is converted from Nc, defined on the Semiconductor Material Model domain feature), or . For enter the ratio of the electron effective mass to the electron mass me*/me (dimensionless). The default is 0.063.

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Select a mh* — (the default, which is converted from Nv, defined on the Semiconductor Material Model domain feature), or . For enter the ratio of the hole effective mass to the electron mass mh*/me (dimensionless). The default is 0.51.

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Select a Eg — (defined in the material properties section of the Semiconductor Material Model domain feature) or . For enter the band gap Eg (SI unit: V). The default is 1.424 V.

This section is available when the excitation frequency is needed to calculate the stimulated emission rate or the matrix element and when the feature is not coupled to an Electromagnetic Waves interface.

Select an f0 — (the default), , or .

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For , enter the excitation frequency, f0 (SI unit: Hz). The default is 344 GHz.

This section is available in the absence of a multiphysics coupling when the is selected for the and when the check box is selected. It is used to define the intensity of the optical field that is driving the stimulated emission. Enter the , E0 (SI unit: V/m). The default is 500 V/m.

Select the — (the default) or .

For the default n and k take values . For select (for the average of the diagonal elements are taken).

	The time-harmonic sign convention used in COMSOL Multiphysics requires that a lossy material has a negative imaginary part of the refractive index.

The default ε′ and ε″ take values . For select (for the average of the diagonal elements are taken).

	The time-harmonic sign convention used in COMSOL requires that a lossy material has a negative imaginary part of the relative permittivity.

Select the check box to compute the change in the real part of the susceptibility (or permittivity/refractive index) using a Kramers–Kronig integral.

The settings in this section determine the range and resolution of the numerical scheme used to compute integrals over the frequency domain.

The (dimensionless) is an integer related to the discretization of the of the frequency domain. A higher number indicates a finer mesh in the extra dimension (if present) or smaller steps in the numerical integration (if no extra dimension is used). The default is 6.

The specifies the lower limit used in frequency domain integrals in units of ħω0 (if is enabled, or user defined is chosen — ω0 is the excitation angular frequency) or in units of the band gap (if only spontaneous emission is chosen). The lower limit should be less than the band gap. The default is 0.5.

The specifies the upper limit used in frequency domain integrals in units of ħω0 (if is enabled, or user defined is chosen — ω0 is the excitation angular frequency) or in units of the band gap (if only spontaneous emission is chosen). The upper limit should be chosen so that the processes of interest are negligible above it. The default is 3.

The specifies the total width of the pole region around the excitation frequency in units of ħω0 (if is enabled, or user defined is chosen — ω0 is the excitation angular frequency) or in units of the band gap (if only spontaneous emission is chosen). It should be chosen so that the change in the susceptibility or the change in the absorption coefficient is linear to a good accuracy across the region. The default is 0.01.