Optical Transitions
The Optical Transitions 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.
Optical Transitions
Select a Frequency domain representation — Extra dimension (the default) or No extra dimension. 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 Transitions model — Direct band gap model (the default) or User defined.
Direct Band Gap Model
The Direct band gap model 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 Spontaneous emission check box to compute the recombination due to spontaneous emission. Select the Stimulated absorption and emission check box to add the stimulated emission generation or recombination terms. Both check boxes are selected by default.
User Defined
The User defined 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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Net generation rate from stimulated processes, Gstim (SI unit: 1/(m3·s)).
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Net generation rate from stimulated processes, reference material, 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.
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Spontaneous emission recombination rate, Rspon (SI unit: 1/(m3·s)).
Transition Matrix Element
This section is available when the Direct band gap model is selected as the Transitions model.
Select how to define the Matrix element — From spontaneous lifetime (the default), Momentum matrix element, Dipole matrix element, or Kane 4-band model.
Based on the options chosen enter:
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The spontaneous lifetime, τspon (SI unit: s). The default is 2 ns.
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The momentum matrix element, |M12av|2, (SI unit: kg2⋅m2/s2). The default is 0 kg2⋅m2/s2.
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The dipole matrix element, |μ12av|2, (SI unit: m2⋅s2⋅A2). The default is 0 m2⋅s2⋅A2.
For the Kane 4-band model enter the Kane 4-band model parameters:
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Electron effective mass: Select From band structure properties (the default, defined in the corresponding section), From density of states (converted from Nc, which is defined on the Semiconductor Material Model domain feature), or User defined. For User defined enter the ratio of the effective mass to the electron mass me*/me (dimensionless). The default is 0.053.
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Band gap: Select From band structure properties (defined in the corresponding section), From semiconductor material model (defined in the Semiconductor Material Model node), or User defined. For User defined enter the band gap Eg (SI unit: V). The default is 0.341 V.
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Valence band spin orbital splitting Δ (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).
Band Structure Properties
This section is available when the Direct band gap model is selected for the Transitions model.
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Select an Electron effective mass me* — From density of states (the default, which is converted from Nc, defined on the Semiconductor Material Model domain feature), or User defined. For User defined 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 Hole effective mass mh* — From density of states (the default, which is converted from Nv, defined on the Semiconductor Material Model domain feature), or User defined. For User defined 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 Band gap Eg — From semiconductor material model (defined in the material properties section of the Semiconductor Material Model domain feature) or User defined. For User defined enter the band gap Eg (SI unit: V). The default is 1.424 V.
Optical Excitation Frequency
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 Excitation frequency f0 — From study (the default), User-defined frequency, or User-defined wavelength.
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For User-defined frequency, enter the excitation frequency, f0 (SI unit: Hz). The default is 344 GHz.
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For User-defined wavelength, enter the wavelength, λ0 (SI unit: m). The default is 870 nm.
Optical Intensity
This section is available in the absence of a multiphysics coupling when the Direct band gap model is selected for the Transitions model and when the Stimulated absorption and emission check box is selected. It is used to define the intensity of the optical field that is driving the stimulated emission. Enter the Electric field norm, E0 (SI unit: V/m). The default is 500 V/m.
Optical Material Properties
Select the Electric displacement field model — Refractive index (the default) or Relative permittivity.
Refractive Index
For Refractive index the default Refractive index n and Refractive index, imaginary part k take values From material. For User defined select Isotropic (for Diagonal the average of the diagonal elements are taken). The material parameters Refractive index n and Refractive index, imaginary part k form the complex relative permittivity (n – jk)2.
The time-harmonic Sign Convention used in COMSOL Multiphysics requires that a lossy material to have a positive material parameter k.
Relative Permittivity
The default Relative permittivity (real part) ε' and Relative permittivity (imaginary part) ε'' take values From material. For User defined select Isotropic (for Diagonal the average of the diagonal elements are taken). The material parameters Relative permittivity ε' and Relative permittivity (imaginary part) ε'' form the complex relative permittivity εr = ε' – jε''.
The time-harmonic Sign Convention used in COMSOL requires that a lossy material has a positive material parameter ε''.
Optical Outputs
Select the Compute change in real part of susceptibility check box to compute the change in the real part of the susceptibility (or permittivity/refractive index) using a Kramers–Kronig integral.
Integral Properties
The settings in this section determine the range and resolution of the numerical scheme used to compute integrals over the frequency domain.
The Frequency domain integral discretization factor (dimensionless) is an integer related to the discretization 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 Frequency domain integral lower limit specifies the lower limit used in frequency domain integrals in units of (if Stimulated absorption and emission 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 Frequency domain integral upper limit specifies the upper limit used in frequency domain integrals in units of (if Stimulated absorption and emission 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 Kramers–Kronig integral pole region width specifies the total width of the pole region around the excitation frequency in units of (if Stimulated absorption and emission 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.