Differences

This shows you the differences between two versions of the page.

--- qcl:tutorials:thz_qcl_-_fathololoumi_2012 [2017/02/17 17:22]
stefan.birner [Current density]
+++ qcl:tutorials:thz_qcl_-_fathololoumi_2012 [2018/03/20 11:14] (current)
thomas.grange [Device definition]
@@ Line 20: / Line 20: @@
 This ''*-FAST.xml'' file is only intended to show the user how to run a "quick" simulation.
 The results shown here correspond to the ''*-MEDIUM.xml'' file.
+''[Fathololoumi2012]'' designed the laser to operate at an electric field of -12.2 kV/cm.
-''[Fathololoumi2012]'' designed the laser to operate at an electric field of 12.2 kV/cm with a transition energy of 15.1 meV (or 11.5 meV?).
 ===== Simulation details =====
@@ Line 32: / Line 32: @@
 ==== Device definition ====
-First, the well (GaAs) and barrier materials (AlGaAs) have to be defined.
+First, the materials used in the structure (GaAs and AlGaAs) have to be defined. Each material is referred by an alias, which is here 'well' for GaAs and 'barrier' and AlGaAs.
 <code>
-  <Material_Well>
+  <Materials>
-   <name> GaAs </name>
-  </Material_Well>
-  <Material_Barrier>
+    <Material>
-   <name> Al(x)Ga(1-x)As </name>
+      <Name>GaAs</Name>
-   <Alloy_Composition> 0.15 </Alloy_Composition> <!-- x=0.15 (Al0.15Ga0.85As) -->
+      <Alias>well</Alias>
-  </Material_Barrier>
+      <Effective_mass_from_kp_parameters>yes</Effective_mass_from_kp_parameters>
+    </Material>
+    <Material>
+      <Name>Al(x)Ga(1-x)As</Name>
+      <Alloy_Composition>0.15</Alloy_Composition>
+      <Alias>barrier</Alias>
+      <Effective_mass_from_kp_parameters>yes</Effective_mass_from_kp_parameters>
+    </Material>
+    <!-- Model nonparabolicity -->
+    <NonParabolicity>yes</NonParabolicity>
+    <UseConductionBandOffset>yes</UseConductionBandOffset>
+  </Materials>
 </code>
+In addition, it is specified that the effective mass is calculated from the k.p parameters. Also, non
 Then, alternating layers consisting of barrier and well have to be specified, i.e. **4.1** / __16.0__ / **4.3** / 8.9 / **2.46** / 8.15, where AlGaAs is in bold fonts and the doping region is underlined, i.e. the wide GaAs quantum well is doped.
@@ Line 66: / Line 81: @@
 </code>
-The resulting conduction band edge profile can be found in the file called ''Band-Edge_vs_position.dat''.
+The resulting conduction band edge profile can be found in the file called ''BandEdge_conduction.dat''.
 This file includes the (small) band bending due to the electrostatic potential.
 At a bias voltage of 54 mV per period, it looks as follows.
@@ Line 72: / Line 87: @@
 <figure>
 ;#;
-<dataplot xlabel="Position (nm)" ylabel="Energy (eV)" ylegends="E_c">
+<dataplot xlabel="Position (nm)" ylabel="Energy (eV)" ylegends="E_c" title="Conduction band edge">
 -1.9959090909E-001	   7.4383341270E-002
 .0000000000E+000	   1.4844107543E-001
@@ Line 737: / Line 752: @@
 ;#;
-<caption>Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/cm</caption>
+<caption>Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/cm</caption>
 </figure>
@@ Line 755: / Line 770: @@
 </code>
 ==== Material parameters ====
-We set the conduction band offset between GaAs and Al<sub>0.15</sub>Ga<sub>0.85</sub>As to 0.120 eV, i.e. we overwrite the default material parameters that are contained in the [[qcl:material_database|material database]].
+We set the conduction band offset (CBO) between GaAs and Al<sub>0.15</sub>Ga<sub>0.85</sub>As to 0.120 eV, i.e. we overwrite the default material parameters that are contained in the [[qcl:material_database|material database]].
 <code>
  <Material_Parameters>
-  <Band_Offset            unit="meV"> 120 </Band_Offset>
+  <Overwrite_ConductionBandOffset>true</Overwrite_ConductionBandOffset>
+  <ConductionBandOffset unit="meV"> 120 </ConductionBandOffset>
  </Material_Parameters>
 </code>
+(In fact, the figures shown in the tutorial were generated using a different CBO of 0.149 eV.)
 ==== Electric field ====
 The total length of one period is L = 43.91 nm.
-A bias of V = 54 mV per period then corresponds to an electric field of F = V/L = 12.3 kV/cm.
+A bias of V = 54 mV per period then corresponds to an electric field of F = V/L = -12.3 kV/cm.
-==== Eigenfunctions ====
+==== Wannier-Stark states ====
 <figure>
@@ Line 1433: / Line 1449: @@
 ;#;
-<caption>Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/cm and corresponding probability densities ($\left|\psi_i(x)\right|^2$).</caption>
+<caption>Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/cm and corresponding probability densities ($\left|\psi_i(x)\right|^2$) of the Wannier-Stark states.</caption>
 </figure>
-The following two figures show the Wannier-Stark states at an applied bias of 56 mV/period (12.8 kV/cm).
+The following two figures show the Wannier-Stark states at an applied bias of 56 mV/period (-12.8 kV/cm).
 They compare Fig. 1 of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.
 {{ :qcl:tutorials:fathololoumi:fig1_grangeprb2015.jpg |}}
 <figure>
-<caption>Wannier-Stark states at a bias of 56 mV/period (12.8 kV/cm) (Fig. 1 of T. Grange, PRB 92, 241306(R) (2015)).
+<caption>Wannier-Stark states at a bias of 56 mV/period (-12.8 kV/cm) (Fig. 1 of T. Grange, PRB 92, 241306(R) (2015)).
 The three-well design consists of one large well and two small wells.
 The optical photon transition is a diagonal transition (i.e. from the left thin well to the right thin well) and occurs between the states 2 (blue) and 3 (red).
@@ Line 1452: / Line 1468: @@
 {{ :qcl:tutorials:fathololoumi:fig1_grangeprb2015_nextnano.jpg |}}
 <figure>
-<caption>Wannier-Stark states at a bias of 56 mV/period (12.8 kV/cm) (Results of this input file)</caption>
+<caption>Wannier-Stark states at a bias of 56 mV/period (-12.8 kV/cm) (Results of this input file)</caption>
 </figure>
 ==== Local density of states ====
-The following figure shows the local density of states (LDOS) at a bias of 54 mV / period corresponding to 12.3 kV/cm).
+The following figure shows the local density of states (LDOS) at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 The LDOS tells us where and at which energy electronic states are available that the charge carriers can occupy.
 The LDOS is shown for $k_\parallel=0$, i.e. there are also electronic states available for $k_\parallel \ne 0$.
@@ Line 1466: / Line 1482: @@
 </figure>
 ==== Electron density ====
-The following figure shows the energy resolved electron density $n(x,E)$ at a bias of 54 mV / period corresponding to 12.3 kV/cm).
+The following figure shows the energy resolved electron density $n(x,E)$ at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 The electron density is obtained from occupying the LDOS (for both $k_\parallel=0$ and $k_\parallel \ne 0$) with charge carriers.
 The occupation is not described by a Fermi distribution (equilibrium).
@@ Line 1474: / Line 1490: @@
 <figure>
-<caption>Energy resolved electron density $n(x,E)$ and conduction band edge $E_{\rm c}$ at a bias of 54 mV / period (12.3 kV/cm)</caption>
+<caption>Energy resolved electron density $n(x,E)$ and conduction band edge $E_{\rm c}$ at a bias of 54 mV / period (-12.3 kV/cm)</caption>
 </figure>
@@ Line 1482: / Line 1498: @@
 <figure>
-<caption>Electron density $n(x)$ at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/cm</caption>
+<caption>Electron density $n(x)$ at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/cm</caption>
 </figure>
-The following two figures show the energy resolved electron density at an applied bias of 58 mV/period (13.2 kV/cm). They compare Fig. 3 (a) of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.
+The following two figures show the energy resolved electron density at an applied bias of 58 mV/period (-13.2 kV/cm). They compare Fig. 3 (a) of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.
 {{ :qcl:tutorials:fathololoumi:fig3_grangeprb2015.jpg |}}
@@ Line 1491: / Line 1507: @@
 <figure>
 <caption>
-Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (13.2 kV/cm) (Fig. 3(a) of T. Grange, PRB 92, 241306(R) (2015))
+Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (-13.2 kV/cm) (Fig. 3(a) of T. Grange, PRB 92, 241306(R) (2015))
 </caption>
 </figure>
@@ Line 1499: / Line 1515: @@
 <figure>
 <caption>
-Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (13.2 kV/cm) (Results of this input file)
+Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (-13.2 kV/cm) (Results of this input file)
 </caption>
 </figure>
@@ Line 1505: / Line 1521: @@
 ==== Current density ====
-The following figure shows the energy resolved current density $j(x,E)$ at a bias of 54 mV / period corresponding to 12.3 kV/cm).
+The following figure shows the energy resolved current density $j(x,E)$ at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 {{ :qcl:tutorials:fathololoumi:current_density_image.png |}}
@@ Line 1511: / Line 1527: @@
 <figure>
 <caption>Current density $j(x,E)$ and conduction band edge $E_{\rm c}$.
-One can clearly see that the current density inside the thick quantum well changes abruptly because the electrons lose energy.
+One can clearly see that the current density inside the thick quantum well changes abruptly because the electrons lose energy of order 35 meV.
-The reason is that the electrons scattering resonantly with LO phonons ($E_{\rm LO}=35 meV$)</caption>
+The reason is that the electrons scattering resonantly with LO phonons ($E_{\rm LO}=35{\rm~meV}$).</caption>
 </figure>
+== Longitudinal polar-optical phonon scattering ==
+The material parameter for the LO phonon energy is specified in the [[qcl:material_database|material database]].
+<code>
+   <LOPhononEnergy Unit="eV"> 36.75e-3 </LOPhononEnergy>
+</code>
 ==== Gain ====
-The following figure shows the energy resolved gain $g(x,E_{\rm ph})$ at a bias of 54 mV / period corresponding to 12.3 kV/cm).
+The following figure shows the energy resolved gain $g(x,E_{\rm ph})$ at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 Note that the energy axis corresponds to the photon energy $E_{\rm ph}$.
 The thin white lines indicate the barrier/well interfaces and are only a guide to the eye.
@@ Line 1580: / Line 1603: @@
 Time for electron to travel through one period = 8.90375389605566 ps
-Electric Field = 12.2978820314279 kV/cm
+Electric Field = -12.2978820314279 kV/cm
 Doping sheet density per period 30000000000 cm^-2
 Average 3D doping density  6.83215668412662E+15 cm^-3
@@ Line 1643: / Line 1666: @@
   </SweepParameters>
 </code>
+==== Interface roughness scattering ====
+For interface roughness we assume typical values of an amplitude of 0.1 nm and an exponential correlation length of 8 nm.
+<code>
+  <Roughness>
+    <Interface_Roughness>
+      <Amplitude_in_Z unit="nm"> 0.1 </Amplitude_in_Z>
+      <InterfaceAutoCorrelationType> 0 </InterfaceAutoCorrelationType>
+               <!-- Correlation type: 0=Exponential, 1=Gaussian -->
+      <Correlation_Length_in_XY unit="nm"> 8 </Correlation_Length_in_XY>
+      <Asymmetric_Interfaces> false </Asymmetric_Interfaces>
+      <Amplitude_in_Z_Left>  0.1 </Amplitude_in_Z_Left>
+      <Amplitude_in_Z_Right> 0.2 </Amplitude_in_Z_Right>
+    </Interface_Roughness>
+  </Roughness>
+</code>
+==== Computational resources ====
+The CPU time was about 5-6 hours and used about 9 GB RAM.
+==== Feedback ====
 If you have questions regarding this tutorial or if you have comments how we can improve it, please contact us at <support@nextnano.com>.

nextnano.NEGF - Software for Quantum Transport

User Tools

Site Tools

Differences

Page Tools

nextnano.NEGF - Software for
Quantum Transport