nnp:1d_ingaas_laser_diode
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nnp:1d_ingaas_laser_diode [2020/03/11 11:06] takuma.sato [Input file] |
nnp:1d_ingaas_laser_diode [2024/01/03 15:17] stefan.birner removed |
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| ===== 1D InGaAs Multi-quantum well laser diode ===== | ===== 1D InGaAs Multi-quantum well laser diode ===== | ||
| Author: Takuma Sato, nextnano GmbH | Author: Takuma Sato, nextnano GmbH | ||
| + | |||
| + | **A newer version of this tutorial can be found here: | ||
| + | [[https://www.nextnano.com/manual/nextnanoplus_tutorials/1D/laser_diode.html|https://www.nextnano.com/manual/nextnanoplus_tutorials/1D/laser_diode.html]] | ||
| + | ** | ||
| In this tutorial, we simulate optical emission of a 1D InGaAs multi-quantum well laser diode grown on InP substrate. The blue region is the separate confinement heterostructure (SCH), which forms an optical waveguide in the transverse direction to confine the emitted light (red arrow). The multi-quantum wells and SCH are clad by InP on both sides. A voltage bias is applied to the gray edges. | In this tutorial, we simulate optical emission of a 1D InGaAs multi-quantum well laser diode grown on InP substrate. The blue region is the separate confinement heterostructure (SCH), which forms an optical waveguide in the transverse direction to confine the emitted light (red arrow). The multi-quantum wells and SCH are clad by InP on both sides. A voltage bias is applied to the gray edges. | ||
| Line 43: | Line 47: | ||
| **Radiative recombination** describes the recombination of electron-hole pairs at a position $\mathbf{x}$ by emitting a photon and is given by | **Radiative recombination** describes the recombination of electron-hole pairs at a position $\mathbf{x}$ by emitting a photon and is given by | ||
| $$ | $$ | ||
| - | R_{\mathrm{rad}}(\mathbf{x}) = C\left[n(\mathbf{x}) p(\mathbf{x}) – n_i^2\right], | + | R_{\mathrm{rad}}(\mathbf{x}) = C n(\mathbf{x}) p(\mathbf{x}), |
| $$ | $$ | ||
| - | where $n_i$ is the intrinsic density of the charge carriers. $C$ is a material dependent constant given in the database and has the unit of cm$^3$/s. $R_{\mathrm{rad}}(\mathbf{x})$ is written in ''emitted_photon_density.dat''. | + | where $C$ is a material dependent constant given in the database and has the unit of cm$^3$/s. |
| Since the radiative recombination process involves no phonons, this transition is vertical and therefore this contribution is only relevant for semiconductors with a direct band gap such as GaAs. | Since the radiative recombination process involves no phonons, this transition is vertical and therefore this contribution is only relevant for semiconductors with a direct band gap such as GaAs. | ||
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| </figure> | </figure> | ||
| - | In the input file ''LaserDiode_InGaAs_1D_qm_nnp.in'', the Schroedinger equation is coupled to the current-Poisson equation and solved self-consistently. The wave functions of electrons and holes are written in ''\Quantum\wf_probabilities_shift_quantum_region_Gamma_0000.dat''. | + | In the input file ''LaserDiode_InGaAs_1D_qm_nnp.in'', the single-band Schroedinger equation is coupled to the current-Poisson equation and solved self-consistently. The wave functions of electrons and holes along with eigenvalues are written in ''\Quantum\wf_probabilities_shift_quantum_region_Gamma_0000.dat'' and ''\Quantum\wf_probabilities_shift_quantum_region_HH_0000.dat'' (Figure {{ref>wf}} and {{ref>ev}}). The light hole and split-off states are out of the quantum wells and not of our interest here. |
| <figure wf> | <figure wf> | ||
| {{:nnp::laserdiode_tutorial_wf.png}} | {{:nnp::laserdiode_tutorial_wf.png}} | ||
| Line 142: | Line 147: | ||
| </figure> | </figure> | ||
| - | The charge density with- and without quantum calculation shows different features due to the discretization of energy levels in quantum calculation. In the output ''integrated_densities_vs_energy.dat'' we find the electron and hole densities as a function of energy (Figure {{ref>density}}). This quantity is integrated over the device. | + | <figure ev> |
| + | {{:nnp::laserdiode_ev.png}} | ||
| + | <caption>Eigenvalues of the Gamma-band and heavy-hole-band states in relation to bandedges. The Gamma band has single "miniband", whereas the heavy-hole band has three. </caption> | ||
| + | </figure> | ||
| + | |||
| + | The charge density with- and without quantum calculation shows different features due to the discretization of energy levels in quantum wells. In the output ''integrated_densities_vs_energy.dat'' we find the electron and hole densities as a function of energy (Figure {{ref>density}} and {{ref>density_Eresolution}}). This quantity is integrated over the device and has the unit [cm$^{-2}$eV$^{-1}$]. We observe a good correspondence between the spectra and relevant energies of the present structure. | ||
| <figure density> | <figure density> | ||
| {{:nnp::laserdiode_density.png}} | {{:nnp::laserdiode_density.png}} | ||
| - | <caption>Electron (red) and hole (blue) densities integrated over the device as a function of energy. </caption> | + | <caption>Electron (red) and hole (blue) densities integrated over the device as a function of energy. This figure illustrates the population inversion in stationary (quasi-equilibrium) state of the device under bias. Solid and dashed lines are for quantum and classical calculations, respectively. The black arrows mark the relevant energies of the structure {{ref>wf}} at bias of $0.8$ V. The hole density is shown in Figure {{ref>density_Eresolution}} with higher resolution.</caption> |
| </figure> | </figure> | ||
| + | |||
| + | The hole density has been calculated with higher energy resolution in Figure {{ref>density_Eresolution}}. The ratchet-like shape within the wells results from the step-like density of states multiplied by (quasi) Fermi-Dirac distribution (cf. Figure 9.8 in [Chuang]). | ||
| <figure density_Eresolution> | <figure density_Eresolution> | ||
| {{:nnp::laserdiode_density_eresolution.png}} | {{:nnp::laserdiode_density_eresolution.png}} | ||
| - | <caption>Hole density integrated over the device from classical (dashed) and quantum (solid) calculation. </caption> | + | <caption>Hole density integrated over the device from classical (dashed) and quantum (solid) calculation. The energy resolution has been increased by a factor of 10 from Figure {{ref>density}}.</caption> |
| </figure> | </figure> | ||
| - | + | The spontaneous and stimulated emission spectra are written in ''\Optical\emission_spectrum_photons.dat'' and ''\Optical\stim_emission_spectrum_photons.dat'', respectively (Figure {{ref>emission}}). __**Please note that the stimulated emission calculation in nextnano++ assumes photon modes occupied by one photon each, i.e. takes into account neither energy-dependent photon density of states nor Bose-Einstein distribution. **__ | |
| - | The spontaneous and stimulated emission spectra are written in ''emitted_photon_spectrum.dat'' and ''stimulated_emission_spectrum.dat'', respectively. | + | |
| <figure emission> | <figure emission> | ||
| - | {{:nnp::laserdiode_tutorial_emission.png}} | + | {{:nnp::laserdiode_emission.png}} |
| - | <caption>Emission spectrum of the laser diode for the bias $0.8$ V.</caption> | + | <caption>Emission spectrum of the laser diode for the bias $0.8$ V. The peak is at around 0.7-0.8eV, which is consistent with the charge distribution in Figure {{ref>density}}. The stimulated emission does not occur above the quasi Fermi level separation, $E_{Fn}-E_{Fp}$.</caption> |
| </figure> | </figure> | ||
| + | |||
| + | The absorption coefficient $\alpha(E)$ and gain (coefficient) $g(E)$ are essentially the same quantity with opposite signs, | ||
| + | \begin{equation} | ||
| + | \alpha(E)=-g(E). | ||
| + | \end{equation} | ||
| + | These are by definition independent of the initial photon population. __**Please note that the gain spectrum in nextnano++ is cut off where it is negative.**__. For details, see [[https://www.nextnano.com/nextnanoplus/software_documentation/input_file/classical.htm|classical{} documentation]]. | ||
| + | |||
| + | The spectrum changes its sign at the energy $E_{Fn}-E_{Fp}$, that is, the separation of the quasi Fermi levels. According to the output ''bandedges.dat'', this value is -0.0001-(-0.7702)=0.7701eV. The following result has been calculated classically. We also get qualitatively consistent results from quantum mechanical simulation. | ||
| <figure cl_gain> | <figure cl_gain> | ||
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| <figure IV> | <figure IV> | ||
| - | {{:nnp::laserdiode_tutorial_IV.png}} | + | {{:nnp::laserdiode_IV.png}} |
| <caption>Charge current and photocurrent as a function of bias voltage (IV characteristics). This figure clearly shows the consequence of the difference in Figure {{ref>bandedge}} and {{ref>bandedge2}}.</caption> | <caption>Charge current and photocurrent as a function of bias voltage (IV characteristics). This figure clearly shows the consequence of the difference in Figure {{ref>bandedge}} and {{ref>bandedge2}}.</caption> | ||
| </figure> | </figure> | ||
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