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qcl:software_documentation [2017/03/16 09:51]
thomas.grange [Working principle]
qcl:software_documentation [2017/07/24 12:51]
thomas.grange
Line 33: Line 33:
 If you have further questions, see the [[qcl:​faq|FAQ]] or contact <​support@nextnano.com>​. If you have further questions, see the [[qcl:​faq|FAQ]] or contact <​support@nextnano.com>​.
  
-===== Working principle ===== 
  
-The code is based on the non-equilibrium Green'​s functions (NEGF) formalism (also known as the Keldysh, or Kadanoff-Baym formalism). This formalism allows to account for both quantum transport effects (i.e. coherent transport effects, such as resonant tunneling), as well as scattering mechanisms. 
- 
-In the NEGF formalism, scattering processes are described in terms of self-energies. Self-energies and Green'​s functions are calculated in a self-consistent way, as both elastic and inelastic scattering processes are accounted within the the self-consistent Born approximation. 
- 
-The code uses **field-periodic boundary condition**. 
-In this way the simulation accounts for an infinite periodic structure, with a periodic electric field. 
-Coherent transport between periods is accounted on a length set by ''<​Coherence_length_in_Periods>''​. 
- 
-=== Program flow === 
- 
-{{ :​qcl:​flowchart.jpg?​400 |}} 
- 
-In the beginning of the calculation,​ the single-band effective mass Schrödinger equation is solved in real space. 
-The calculated energy levels and wave functions are then used as input to the NEGF algorithm. 
-The wave functions are termed **modes** and the NEGF algorithm is written in terms of **mode space** and not **real space** to make it computationally more efficient. 
-The number of QCL periods that are input to this Schrödinger equation are specified in ''<​Number_of_lateral_periods_for_band_structure>''​. 
-In general, the core of the NEGF algorithm should be rather independent of this number, e.g. 
-<​code>​ 
- <​Number_of_lateral_periods_for_band_structure>​ 4  
- </​Number_of_lateral_periods_for_band_structure>​ 
-</​code>​ 
-should lead to very similar results compared to a value of ''​5''​ but the numerical values might differ slightly. 
- 
-{{ :​qcl:​ldos_emin_emax_okay.jpg?​200 |}} 
- 
-As a second step, the scattering coupling terms are calculated for each of the accounted mechanism (optical and acoustic phonons, charged impurities, interface roughness, alloy disorder). 
- 
-Then, the main part of the calculation consists in the self-consistent NEGF solver. Starting from an initial guess of the Green'​s functions, the self-energies are calculated. The Green'​s functions are then calculated iteratively. 
-Simultaneously,​ the mean-field electrostatic potential is calculted self-consistenly (Poisson'​s equation). Such iterations are made until convergence is reached for the Green'​s functions as well as for the calculated current. 
- 
-From the Green'​s functions solution, the gain is then calculated (if requested in the input file). 
  
qcl/software_documentation.txt · Last modified: 2017/07/24 12:51 by thomas.grange