Authors: Stefan Birner
> 1DSirtoriPRB1994_OneWell_sg_selfconsistent_nn3.in
/ *_nnp.in 
(singleband effective mass approximation)
(singleband effective mass approximation)
> 1DSirtoriPRB1994_OneWell_sg_quantumonly_nn3.in
/ *_nnp.in 
(8band k.p)
> 1DSirtoriPRB1994_OneWell_kp_quantumonly_nn3.in
/ *_nnp.in 
(singleband
effective mass approximation)
> 1DSirtoriPRB1994_TwoCoupledWells_sg_selfconsistent_nn3.in /
*_nnp.in 
(singleband
effective mass approximation)
> 1DSirtoriPRB1994_TwoCoupledWells_sg_quantumonly_nn3.in
/ *_nnp.in 
(8band k.p)
> 1DSirtoriPRB1994_TwoCoupledWells_kp_quantumonly_nn3.in
/ *_nnp.in 
(singleband effective
mass approximation)
> 1DSirtoriPRB1994_ThreeCoupledWells_sg_selfconsistent_nn3.in / *_nnp.in

(singleband effective
mass approximation)
> 1DSirtoriPRB1994_ThreeCoupledWells_sg_quantumonly_nn3.in /
*_nnp.in 
(8band k.p)
> 1DSirtoriPRB1994_ThreeCoupledWells_kp_quantumonly_nn3.in
/ *_nnp.in 
==>
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This tutorial aims to reproduce Figs. 4 and 5 of
C. Sirtori, F. Capasso, J. Faist
Nonparabolicity and a sum rule associated with boundtobound
and boundtocontinuum intersubband transitions in quantum wells
Physical Review B 50 (12), 8663
(1994)
This tutorial nicely demonstrates that for the ground state energy the
singleband effective mass approximation is sufficient whereas for the higher
lying states a nonparabolic model, like the 8band k.p approximation, is
necessary.
This is important for e.g. quantum cascade lasers where higher lying
states have a dominant role.
We investigate three structures:
a) a single quantum well
b) two coupled quantum wells
c) three coupled quantum wells
We use In_{0.53}Ga_{0.47}As as the quantum well material and Al_{0.48}In_{0.52}As as the barrier material. Both materials are lattice matched to the substrate material InP. Thus we assume that the InGaAs and AlInAs layers are unstrained with respect to the InP substrate.
The paper
C. Sirtori, F. Capasso, J. Faist
Nonparabolicity and a sum rule associated with boundtobound
and boundtocontinuum intersubband transitions in quantum wells
Physical Review B 50 (12), 8663
(1994)
lists the following material parameters:
conduction band offset  Al_{0.48}In_{0.52}As/In_{0.53}Ga_{0.47}As  0.510 eV 
conduction band effective mass  (In_{0.53}Ga_{0.47}As)  0.043 m _{0} 
conduction band effective mass  (Al_{0.48}In_{0.52}As)  0.072 m _{0} 
The temperature is set to 10 Kelvin.
Singleband effective mass approximation
Because our structure is doped, we have to solve the singleband
SchrödingerPoisson equation selfconsistently.
The doping is such that the electron ground state is below the Fermi level and
all other states are far away from the Fermi level, i.e. only the ground state
is occupied and contributes to the charge density.
$simulationflowcontrol
Note: Singleband eigenstates are twofold spin
degenerate.
flowscheme = 2
rawpotentialin = no
$quantummodelelectrons
...
modelname
= effectivemass
numberofeigenvaluesperband = 3
!
The Fermi level is always equal to 0 eV in our simulations and the band profile is shifted accordingly to meet this requirement.
8band k.p approximation
Old version of this tutorial:
Becauce both, the singleband and the 8band k.p ground state energy and the corresponding wave functions are almost identical, we can read in the selfconsistently calculated electrostatic potential of the singleband approximation and calculate for this potential the 8band k.p eigenstates and wave functions for k_{} = 0.
$simulationflowcontrol
Note: One k.p eigenstate for each spin component.
flowscheme = 3
rawdirectoryin = raw_data/
rawpotentialin = yes
$quantummodelelectrons
...
modelname = 8x8kp
numberofeigenvaluesperband = 6 !
New version of this tutorial:
We provide input files for:
a) selfconsistent singleband Schrödinger equation (because the structure is doped)
b) singleband Schrödinger equation (without selfconsistency)
c) 8band k.p singleband Schrödinger equation (without selfconsistency)For a), although the structure is doped, the band bending is very small. Thus we omit for the singleband / k.p comparison in b) and c) the selfconsistent cycle.
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