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nextnano3 - Tutorial

next generation 3D nano device simulator

1D Tutorial

Intersubband transitions in InGaAs/AlInAs multiple quantum well systems

Authors: Stefan Birner

-> 1DSirtoriPRB1994_OneWell_sg_self-consistent_nn3.in           / *_nnp.in  -  (single-band effective mass approximation)
-> 1DSirtoriPRB1994_OneWell_sg_quantum-only_nn3.in              / *_nnp.in  - 
(single-band effective mass approximation)
-> 1DSirtoriPRB1994_OneWell_kp_quantum-only_nn3.in              / *_nnp.in  - 
(8-band k.p)
-> 1DSirtoriPRB1994_TwoCoupledWells_sg_self-consistent_nn3.in   / *_nnp.in  - 
(single-band effective mass approximation)
-> 1DSirtoriPRB1994_TwoCoupledWells_sg_quantum-only_nn3.in      / *_nnp.in  - 
(single-band effective mass approximation)
-> 1DSirtoriPRB1994_TwoCoupledWells_kp_quantum-only_nn3.in      / *_nnp.in  - 
(8-band k.p)
-> 1DSirtoriPRB1994_ThreeCoupledWells_sg_self-consistent_nn3.in / *_nnp.in  - 
(single-band effective mass approximation)
-> 1DSirtoriPRB1994_ThreeCoupledWells_sg_quantum-only_nn3.in    / *_nnp.in  - 
(single-band effective mass approximation)
-> 1DSirtoriPRB1994_ThreeCoupledWells_kp_quantum-only_nn3.in    / *_nnp.in  - 
(8-band k.p)

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Intersubband transitions in InGaAs/AlInAs multiple quantum well systems

This tutorial aims to reproduce Figs. 4 and 5 of
    C. Sirtori, F. Capasso, J. Faist
    Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells
   
Physical Review B 50 (12), 8663 (1994)

This tutorial nicely demonstrates that for the ground state energy the single-band effective mass approximation is sufficient whereas for the higher lying states a nonparabolic model, like the 8-band k.p approximation, is necessary.
This is important for e.g. quantum cascade lasers where higher lying states have a dominant role.

 

Step1: Layer sequence

We investigate three structures:
  a) a single quantum well
  b) two coupled quantum wells
  c) three coupled quantum wells

 

Step 2: Material parameters

We use In0.53Ga0.47As as the quantum well material and Al0.48In0.52As 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 bound-to-bound and bound-to-continuum intersubband transitions in quantum wells
   
Physical Review B 50 (12), 8663 (1994)
lists the following material parameters:

conduction band offset Al0.48In0.52As/In0.53Ga0.47As 0.510 eV
conduction band effective mass (In0.53Ga0.47As) 0.043 m0
conduction band effective mass (Al0.48In0.52As) 0.072 m0

The temperature is set to 10 Kelvin.

 

Step 3: Method

Single-band effective mass approximation

Because our structure is doped, we have to solve the single-band Schrödinger-Poisson equation self-consistently.
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.

 $simulation-flow-control
  flow-scheme      = 2
  raw-potential-in = no

 $quantum-model-electrons
  ...
  model-name                     = effective-mass
 
number-of-eigenvalues-per-band = 3     !
Note: Single-band eigenstates are two-fold spin degenerate.

The Fermi level is always equal to 0 eV in our simulations and the band profile is shifted accordingly to meet this requirement.

 

8-band k.p approximation

Old version of this tutorial:

Becauce both, the single-band and the 8-band k.p ground state energy and the corresponding wave functions are almost identical, we can read in the self-consistently calculated electrostatic potential of the single-band approximation and calculate for this potential the 8-band k.p eigenstates and wave functions for k|| = 0.

 $simulation-flow-control
  flow-scheme      = 3
  raw-directory-in = raw_data/
  raw-potential-in = yes

 $quantum-model-electrons
  ...
  model-name                     = 8x8kp
 
number-of-eigenvalues-per-band = 6     !
Note: One k.p eigenstate for each spin component.

New version of this tutorial:

We provide input files for:
a) self-consistent single-band Schrödinger equation (because the structure is doped)
b) single-band Schrödinger equation (without self-consistency)
c) 8-band k.p single-band Schrödinger equation (without self-consistency)

For a), although the structure is doped, the band bending is very small. Thus we omit for the single-band / k.p comparison in b) and c) the self-consistent cycle.

 

 

Step 4: Results