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nextnano³ software

 

  NEGF

 

 

 
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==> Our new software nextnano.NEGF has a different website: ==> www.nextnano.com/nextnano.NEGF/

Quantum transport based on the Nonequilibrium Green's functions (NEGF) method

The method of calculating the carrier transport is defined as "fully self-consistent nonequilibrium Green's function (NEGF) approach for vertical quantum transport in open quantum devices with contacts".

It is suited for calculating quantum transport and gain in quantum cascade lasers.

 

This part of the nextnano³ code is based on the original code of Tillmann Kubis which is described in these publications:

 

There are several possibilities:

  • to include several scattering mechanisms (e.g. inelastic scattering, elastic scattering)
  • no scattering at all ("ballistic transport")

The electrons are described within a one-band model with a variable effective mass, i.e. a spatially dependent (= material dependent) effective electron mass me(z). Alternatively, it is possible to use an energy dependent effective mass (nonparabolicity). This nonparabolicity parameters are grid point dependent. The static and optical dielectric constants are also grid point dependent, i.e. material dependent.

This method is well suited to study resonant tunneling diodes and quantum cascade lasers.

 

Restrictions for green:

  • homogeneous grid
  • not too much grid points (~50-100)
  • for nextnano³: quantum cluster must extend over the whole device
  • for nextnano³: two contacts at the boundaries having 2 grid points at the left and 2 grid points at the right contact,
                          material at the contacts should be the same as the semiconductor material

For an example of the Green's function functionality, have a look at the RTD tutorial.

 

Global parameters for Green's function code

!--------------------------------------------------------------!
$global-parameters-NEGF                              optional  !
 grid_points_in_z                       integer      required  !
 grid_points_in_Ez                      integer      optional  !
 grid_points_in_E                       integer      optional  !
 contact_points                         integer      optional  !
 non_diagonal_range                     double       optional  ! [nm]
 max_energy_factor                      double       optional  !
 Ez_grid_power                          double       optional  !
 E_grid_power                           double       optional  !
 grid_exponent                          double       optional  !

 zero-drift-vector-in-contacts          character    optional  !
 use-maximum-drift-vector               character    optional  !
 drift-vector-maximum                   double       optional  ! [nm-1]
 off_drift                              double       optional  !
                                                               !
 fix-electric-field-at-contact          character    optional  !
 electric-field-at-contact              double       optional  ! [V/m]
                                                               !
 rescaling_green                        character    optional  !
test!
                                                               !
 grid_limit                             double       optional  !
 Poisson-damping-threshold              double       optional  !
 scatter_limit                          double       optional  !
 limit-for-density-convergence          double       optional  !
 grid_critical                          double       optional  !
                                                               !
 gain                                   character    optional  !
 gain-output-every-nth-iteration        integer      optional  !
 gain-integrate-device-from-to          double_array optional  ! [nm]
 min_photon                             double       optional  ! [eV]
 max_photon                             double       optional  ! [eV]
 photon_number                          integer      optional  !
                                                               !
 first-order-Born-approximation         character    optional  !
                                                               !
 solve-Poisson-equation                 character    optional  !
 Poisson-Newton-method                  character    optional  !
 Schroedinger-Poisson-Predictor         character    optional  !
 Schroedinger-Poisson-Predictor-lambda  double       optional  !
 built-in-potential                     double       optional  !
 calculate-transmission                 character    optional  !
 output-correlation-functions           character    optional  !
 output-quasi-Fermi-level               character    optional  !
 output-k-resolved                      character    optional  !
                                                               !
 read-inputfile-during-calculation      character    optional  !
 include-original-NEGF-output           character    optional  !
                                                               !
 get-cb-from-nextnano                   character    optional  !
 get-potential-from-nextnano            character    optional  !
 get-cb-masses-from-nextnano            character    optional  !
 get-nonparabolicity-from-nextnano      character    optional  !
 get-dielectric-from-nextnano           character    optional  !
 get-alloy-from-nextnano                character    optional  !
 get-doping-from-nextnano               character    optional  !
                                                               !
 directory-NEGF                         character    optional  !
 directory-contact                      character    optional  !
 directory-scattering-rates             character    optional  !
 directory-test-debug                   character    optional  !
 directory-stop                         character    optional  !
 save-every-nth-iteration               integer      optional  !
 number-of-MKL-threads                  integer      optional  !
 MKL-set-dynamic                        character    optional  !
                                                               !
$end_global-parameters-NEGF                          optional  !
!--------------------------------------------------------------!

 

 

!----------------------------------------------------------!
$global-parameters-NEGF                                    !

 grid_points_in_z                  = 40                    ! number of grid points in real space along z direction
                                                           !
It must hold:  nextnano³ grid points - 1 = grid_points_in_z
 grid_points_in_E                  = 110                   ! E =
total energy
 grid_points_in_Ez                 = 110                   !
k|| resolution, Ez = E - hbar2 * k||2 / [2m(1,E)]
                                                           ! 1 =
1st grid point, the mass m could depend on energy E
                                                           !
The in-plane momentum k|| is represented as an energy Ez.
!non_diagonal_range                = 1d0                   ! [nm]
for ballistic and to make calculation faster
 non_diagonal_range                = 3d0                   ! [nm]
for ballistic and to make calculation faster
!non_diagonal_range                = 8d0                   ! [nm] 8d0
is a useful value to treat the physics correctly. The default value is 6d0.
                                                           !
It has to be increased if the Debye screening length is large (at least in doped structures).
                                                           !
Specifies scattering correlations. Scattering range relevant for polar optical phonon scattering and charged impurity scattering.
                                                           !
Internally, non_diagonal_range is converted to the corresponding number of grid points that are involved. This depends on the grid spacing, obviously.
                                                           ! Nr_dself = nondiagonal_range /
grid_spacing  (It always holds: Nr_dself >= 1)
                                                           ! Nr_dself =
number of nondiagonal (z,z') bands of the self-energies, (i.e. 0 = diagonal, 1 = tridiagonal ... Nr_dself <= grid_points_in_z)
                                                           !
number of nonvanishing diagonals in the inverse retarded Green's function = 2*Nr_dself + 1
                                                           !
If the distance between z3 and z4 (nonlocal range) is longer than non_diagonal_range, the self-energies for the LO and TO phonon scattering
                                                           ! and impurity scattering (described by eq. (3.5.6) and eq. (3.5.52) of T. Kubis' PhD thesis) are set to zero.
                                                           !
See also Section "4.3.4 Scattering correlations" in PhD thesis of T. Kubis, p. 137f for a detailed discussion (Fig. 4.3.6 and Fig. 4.3.7).
                                                           !
 contact_points                    = 27                    ! 27
contact grid points for the left lead, and 27 contact grid points for the right lead, i.e. in total 54 lead grid points (default = 5).
                                                           !
The number of contact_points must be larger than (non_diagonal_range / grid_spacing) + 1 = Nr_dself + 1.

!-----------------------------------------------------------
!
Boundary condition for the electrostatic potential of the Poisson equation:
!-----------------------------------------------------------
 fix-electric-field-at-contact     = yes                   !
Use a finite electric field at the contacts, i.e. the derivative of the electrostatic potential d phi / d z = constant.
                                                           !
The electric field at the left boundary is fixed at the value specified at electric-field-at-contact.
                                                           ! The voltage drop will be achieved with drift vector.
                                   = no                    ! Determine the electric field at the contacts self-consistently.
 electric-field-at-contact         = 0d0                   ! [V/m]
(default: 0d0 = flat band, i.e. constant electrostatic potential at the left boundary = zero electric field)
                                                           ! electric-field-at-contact is only relevant if fix-electric-field-at-contact = yes.
                                                           ! electric-field-at-contact applies to left contact. The right contact is identical unless the dielectric constants of the left and right contacts are different.
!-----------------------------------------------------------
 zero-drift-vector-in-contacts     = yes                   !
semiconductor drift vector in the contacts, yes = equilibrium contacts
                                   = no                    ! no =
nonequilibrium contacts
 use-maximum-drift-vector          = no                    !
If zero-drift-vector-in-contacts = no, then use-maximum-drift-vector can be yes.
                                                           ! In this case, the drift vector is set to its maximum.
                                                           !
If zero-drift-vector-in-contacts = yes, then use-maximum-drift-vector is not used at all.
                                                           !
It is only used if both fix-electric-field-at-contact = no and entropicL = .FALSE..
                                                           !
(useful for extreme high current densities)
 drift-vector-maximum              = 5.0d0                 !
the maximum value of drift vector in the contacts in units of [nm-1]
 off_drift                         = 0d0                   !
should be zero
                                                           !
!Ez_grid_power                     = 2d0                   !
exponent n, i.e. xn - if present, static Ez grid
                                                           !
Ez grid: (grid point no.)^n + offset
                                                           !
if not present, a self-consistent multigrid for Ez is used
!E_grid_power                      = 1d0                   !
same as Ez_grid_power, but here for E grid
 grid_exponent                     = -0.3d0 !
default: -0.3d0 ! (/=0, a negative is preferred), controls the dynamical Ez grid, if approximately=0, then linear grid
                                                           !
determines the smoothness of the Ez-grid (the larger, the smoother), a small value (around 0.01d0) gives an almost linear grid

 max_energy_factor                 = 9.90d0                ! []
controls the maximum of considered total energy E (of total energy grid) by multiplying kBT with
                                                           ! max_energy_factor = - ln fmin
                                                           !
where fmin is the state occupancy which is typically considered to be empty,
                                                           !
i.e. fmin ~ 5 * 10^-5 ==> max_energy_factor ~ 9.90,
                                                           ! default: 0.9d0
                                                           !
see eq. (3.7.1), p. 100 in PhD thesis of T. Kubis.
                                                           !
If max_energy_factor * kBT is smaller than '2 ELO' than the energy value of two LO phonon energies ELO is taken instead.
                                                           !
In all cases, the value of the highest chemical potential of the two leads is added to this value.

 grid_limit                        = 0.05d0                ! []
controls multigrid convergence (default: -0.05d0)
!
The limit of the convergence parameter at which the energy grids E and Ez will not be changed any more.
 Poisson-damping-threshold         = 1d0                   !
default: 1d0
!
This value determines the criteria which of the Poisson-damping parameters is used. It is related to convergence of the density.
 scatter_limit                     = 1d0                   !
controls the limits of numbers of the scattering iterations (default: 1d0)
 limit-for-density-convergence     = 5d-5                  ! []
limit for convergence of density, default is 5d-5
 grid_critical                     = 1d-10                 !
used for determining resonances in the total device (default: 1d-10)
      !
It is used within subroutine find_hot_spots that is used for the self-adapting energy grid Ez.
      !
It is the difference of the derivative at adjacent positions when we have a hot spot.
      !
The "hot spots" (peaks in the density of states DOS(Ez)) will get a higher resolution in the energy grid Ez.)
      !
(This parameter is not important and can be omitted.)
                                                           !
                                                           !
 gain                              = yes                   !
                                   = no                    !
 gain-output-every-nth-iteration   = 10                    !
output gain every 10th iteration (default: 10)
 gain-integrate-device-from-to     = 5d0 65d0              ! [nm]
Integrate alpha(z,E) from zmin = 5 nm to zmax = 65 nm.
 min_photon                        = 1d-3                  ! [eV]
minimum  photon energy relevant for gain
 max_photon                        = 2d-2                  ! [eV]
maximum photon energy relevant for gain
 photon_number                     = 20                    !
number of energy grid steps between min_photon and max_photon
                                                           !
                                                           !
 get-cb-from-nextnano              = yes                   !
 get-potential-from-nextnano       = yes                   !
 get-cb-masses-from-nextnano       = yes                   !
 get-nonparabolicity-from-nextnano = yes                   !
 get-dielectric-from-nextnano      = yes                   !
 get-alloy-from-nextnano           = yes                   !

 get-doping-from-nextnano          = yes                   !
                                                           !
                                                           !
 directory-NEGF                    = NEGF/                 !
 directory-contact                 = contact/              ! ==> NEGF/contact/
 directory-scattering-rates        = scattering_rates/     ! ==> NEGF/scattering_rates/
 directory-test-debug              = test_debug/           !
 directory-stop                    = stop/                 ! ==> NEGF/stop/
 save-every-nth-iteration          = 3                     !
saves information in binary format that can be read in
                                                           ! later to restart a calculation (default: 20)
                                                           ! into the folder NEGF/stop/*.raw
                                                           !
(Note: These files are very large!)
 number-of-MKL-threads             = 8                     ! Note: Default is 0, then MKL can dynamically change the number of threads (recommended).
 MKL-set-dynamic                   = yes                   !
Note: Default is yes, then MKL can dynamically change the number of threads (recommended).
                                   = no                    !
Note: no does not guarantee that the user’s requested number of threads will be used. But it means that MKL will attempt to use that value.
                                                           !
Note: The number of parallel threads for OpenMP is specified under $global-settings.
$end_global-parameters-NEGF                                !
!----------------------------------------------------------!

 

 calculate-transmission            = yes   ! 'yes' / 'no' contact occupation (default: no)
 Flag to switch on/off calculation of transmission function T(E).

 first-order-Born-approximation    = no    ! 'yes' / 'nofirst order Born approximation (default: no)
 If 'yes', then greenLT4 will be calculated in lowest order Born approximation

 solve-Poisson-equation            = yes   ! 'yes' / 'no(default: yes, i.e solve Poisson equation)
 
Flag to switch on/off Poisson equation inside the NEGF algorithm.

 Poisson-Newton-method             = Newton-2             ! nextnano³'s Newton iterator
                                   = Newton-3             ! nextnano³'s Newton iterator
                                   = Newton-4             ! T. Kubis'     Newton iterator
                                   = Newton-5             ! T. Kubis'     Newton iterator with automatically determined residual
                                                          ! which must be larger than a minimum of 10-16
                                   = Newton-7             !
T. Kubis'     Newton iterator with automatically determined residual
                                                          !                  and original function/gradient
 Here one can chose several options for the Newton iterator that solves the Poisson equation.
 nonlinear-poisson-residual
can be used to vary the residual of Newton-2, Newton-3 and Newton-4 but not for Newton-5 and Newton-7. Additional adjustments can be made via nonlinear-poisson-iterations, newton-max-linesearch-steps, nonlinear-poisson-stepmax. (Check $numeric-control for more details.)

 Schroedinger-Poisson-Predictor        = exp    ! (default)
                                       = Fermi  !
                                       = none   !
 Schroedinger-Poisson-Predictor-lambda = 0.8d0  ! (default)
 
lambda used in predictor-corrector approach for Schrödinger-Poisson [damping parameter (actually 'lambda = 1 - damping')]
 

 built-in-potential                = 0.5d0 ! built-in potential in units of [V], default: 0 V
 
This optional flag introduces an additional built-in potential, e.g. necessary for pn junctions.
 First, the Poisson equation has to be solved in equilibrium to determine the built-in potential: Vbuilt-in = Vleft - Vright
 V is the electrostatic potential value at the left and right boundary.
 
This value is then taken and specified in the input file.
 The built-in potential affects the boundary condition (electric field) of the Poisson equation (electric-field-at-contact) only if it holds:
 IF (AppliedBias /= 0 .AND. .NOT. fix-electric-field-at-contact .AND. .NOT. entropicL)
 
This is useful for this option: Electric field at contact set constant - trying to achieve the voltage drop with drift vector.
 

 rescaling_green                   = yes                   ! switch for rescaling the lesser Green's function (greenL) (test!)
                                                           !
greenLT4 is rescaled, instead of occupied from the leads
                                   = no                    !
similar to A. Wacker (default: no)

 output-correlation-functions      = yes   ! 'yes' / 'no(default: no)
 
Flag to switch on/off plotting the correlation function(s).

 output-quasi-Fermi-level          = yes   ! 'yes' / 'no(default: no)
 
Flag to switch on/off the call to the subroutine that determines the quasi-Fermi level by dividing greenL with the spectral function.
  Output the quasi-Fermi level distributions.
  (correspond to Fig. 1 in IWCE-11 paper)

 output-k-resolved                 = yes   ! 'yes' / 'no(default: no)
 switch for k-resolved output (k distribution), the output folder is k_resolved/.

 

 gain                              = yes      ! 'yes' / 'no(default: no)
 
Flag to switch on/off the calculation of the gain.

 gain-output-every-nth-iteration   = 10       !
output gain every 10th iteration (default: 10)
 
When the whole calculation has converged, the gain will be printed out in any case.
 
If one is interested in the gain, one also has to specify

 gain-integrate-device-from-to     = 5d0 65d0 ! [nm]
Integrate alpha(z,E) from zmin = 5 nm to zmax = 65 nm.
                                              !
This is important in order to exclude the absorption of the contacts.
                                              !
The affected output files are:
                                              ! gain_real_integrated_energy.dat     
alpha(E)
                                              ! gain_real_integrated_wavelength.dat 
alpha(lambda)
                                              !
If this flag is not present, by default, a 5 nm wide region is excluded on the left and right side.

 min_photon                        = 1d-3     ! [eV]
minimum  photon energy relevant for gain
 max_photon                        = 20d-3    ! [eV]
maximum photon energy relevant for gain
 photon_number                     = 20       !
number of energy grid steps between min_photon and  max_photon

 

 read-inputfile-during-calculation  = no    ! 'yes' / 'no'
                                            !
default: no
 
Flag for reading in the input file again and again during the calculation.
  This is useful in order to adjust e.g. the damping parameters during the calculation.
  (This feature is not recommended. Results of an input file cannot be reproduced if input parameters are modified during the calculation.)

 include-original-NEGF-output       = no    ! 'yes' / 'no' (default: no)
 
includes original NEGF output which is meanwhile redundant

 

 get-cb-from-nextnano              = yes   ! 'yes' / 'no'
 
Flag to read in conduction band edge profile (Gamma point) of nextnano³ calculation.

 get-potential-from-nextnano       = yes   ! 'yes' / 'no' / 'no-Kubis'
 
Flag to read in electrostatic potential of nextnano³ calculation.
 If no, a simple initial guess is used taking into account a linear potential drop (if any), and the chemical potentials (Fermi levels) of the contacts.
 If no-Kubis, another simple initial guess is used taking into account a linear potential drop (if any),
  and the chemical potential (Fermi level) of the right contact is assumed to be zero.
  At the left contact it is assumed to be 'zero + voltage', i.e. 'voltage'.

 get-cb-masses-from-nextnano       = yes   ! 'yes' / 'no'
 
Flag to read in conduction band effective masses profile (Gamma point) of nextnano³ calculation.

 get-nonparabolicity-from-nextnano = yes   ! 'yes' / 'no'
 
Flag to read in nonparabolicity parameter of conduction band effective mass (Gamma point) of nextnano³ calculation.

 get-dielectric-from-nextnano      = yes   ! 'yes' / 'no'
 
Flag to read in the static and optical dielectric constants of nextnano³ calculation.

 get-alloy-from-nextnano           = yes   ! 'yes' / 'no'
 Flag to read in alloy profile and alloy potential energy profile of nextnano³ calculation.
  The potential height due to alloy fluctuations, i.e. the alloy disorder scattering potential, enters quadratically into the equation.
  It is calculated internally from the conduction band offset of the two binary end points for each grid point, e.g. AlxGa1-xAs: CBO(AlAs) - CBO(GaAs).
  This information is needed for alloy scattering, i.e. for the computation of the lesser and retarded selfenergy for the elastic scattering on alloy disorder.
  For details, see Appendix A.2 in:
    Single and multiband modeling of quantum electron transport through layered semiconductor devices
    R. Lake, G. Klimeck, R. C. Bowen, D. Jovanovic
    J. Appl. Phys. 81, 7845 (1997)
 

 get-doping-from-nextnano          = yes   ! 'yes' / 'no'
 
Flag to read in n-type doping profile of nextnano³ calculation.
 Note: All donors are assumed to be ionized.

 

Specify directories for output files. If these specifiers are not present, the default values are taken.
Note that the directories must be present, as the nextnano³ code cannot create them.
Be sure to include the "/" (slash). On Windows systems, also the "\" (backslash) will work.

 directory-NEGF                    = NEGF/                 !
 directory-contact                 = contact/              ! ==> NEGF/contact/
 directory-scattering-rates        = scattering_rates/     ! ==> NEGF/scattering_rates/
 directory-test-debug              = test_debug/           !
 directory-stop                    = stop/                 ! ==> NEGF/stop/

 

 

Scattering mechanisms

!----------------------------------------------------------------------!
$scattering-mechanisms
                                       optional  !
 alloy-scattering                           character        optional  !
 acoustic-phonon-scattering                 character        optional  !
 artificial_acoustic                        double           optional  !
prefactor (for testing purposes)
 lattice-constants                          double_array     optional  ! [nm]
 mass-density                               double           optional  ! [kg/m3]
 sound-velocity                             double           optional  ! [m/s]
 acoustic-deformation-potential             double           optional  ! [eV]

 TO-phonon-scattering                       character        optional  !
only meaningful for wurtzite but not for zincblende
 TO-phonon-energy                           double_array     optional  !
only meaningful for wurtzite but not for zincblende
 LO-phonon-scattering                       character        optional  !
Note: The LO phonon energy has to be specified in the materials section.
 LO-phonon-energy-2nd                       double_array     optional  !
Here one can specify a 2nd LO phonon energy.
 LO-phonon-energy-3rd                       double_array     optional  !
Here one can specify a 3rd  LO phonon energy.
 LO-phonon-scattering-scale-selfenergy      double           optional  !
 LO-phonon-scattering-scale-selfenergy-2nd  double           optional  !
for 2nd LO phonon energy
 LO-phonon-scattering-scale-selfenergy-3rd  double           optional  !
for 3rd  LO phonon energy
 static-dielectric-constants-LO-phonon-2nd  double_array     optional  !
static dielectric constants for 2nd LO phonon energy
 static-dielectric-constants-LO-phonon-3rd  double_array     optional  !
static dielectric constants for 3rd LO phonon energy
 optical-dielectric-constants-LO-phonon-2nd double_array     optional  !
optical dielectric constants for 2nd LO phonon energy
 optical-dielectric-constants-LO-phonon-3rd double_array     optional  !
optical dielectric constants for 3rd LO phonon energy

 charged-impurity-scattering                character        optional  !

 interface-roughness-scattering             character        optional  !
interface roughness scattering
 correlation_length                         double           optional  !
for interface roughness scattering
 gaussian_correlationL                      character        optional  !
for interface roughness scattering
                                                                       !
 ballistic                                  character        optional  !

 pauli_principle                            double           optional  !

 electron-electron-scattering               character        optional  !
electron-electron scattering (Debye screening)

 contact-scattering-max-number-iterations   integer          optional  !
 contact-scattering-potential-broadening    double_array     optional  !
 
contact-scattering-potential-shift         double_array     optional  !

 max_cycle_counter                          integer          optional  !
maximum number of inner iterations
 max_cycle_counter1                         integer          optional  !
 max_cycle_counter2                         integer          optional  !
 max_cycle_counter3                         integer          optional  !
 scattering_boost                           character        optional  !
 scattering_boost_factor                    integer          optional  !
 scattering_boost_limit                     double           optional  !

 wacker_approximation                       character        optional  !
$end_scattering-mechanisms
                                   optional  !
!----------------------------------------------------------------------!

 

!-------------------------------------------------------------!
$scattering-mechanisms
                                        !

 alloy-scattering                  = no                       !
(default)
                                   = yes                      !
alloy scattering (elastic scattering on alloy disorder)

 acoustic-phonon-scattering        = no                       !    
no acoustic phonon scattering
                                   = elastic                  !
  elastic acoustic phonon scattering
                                   = inelastic                !
inelastic acoustic phonon scattering (default)
                                   = both                     !
both, elastic and inelastic acoustic phonon scattering (only for testing purposes!!!)
 
acoustic-piezoelectric-scattering = no                       !    
no acoustic piezoelectric scattering (default)
                                   = elastic                  !
  elastic acoustic piezoelectric scattering
                                   = inelastic                !
inelastic acoustic piezoelectric scattering
                                                              !
Only wurtzite. For zincblende, acoustic piezoelectric scattering does not make sense.
 artificial_acoustic               = 1d0      ! not relevant  !
artificial prefactor for inelastic acoustic phonon scattering (for testing purposes)

 lattice-constants                 = 0.56534d0 0.56534d0 0.56534d0 ! [nm]
a,a,c    default is GaAs lattice constant: 0.56534 [nm] used in acoustic phonon and alloy scattering

!--------------------------------------------------
The following variables are only relevant for acoustic phonon scattering.
 mass-density                   = 5.32d3                        ! [kg/m^3]
  default is GaAs mass density: 5.32d3 [kg/m^3]
 sound-velocity                 = 5.2d3                         ! [m/s]
        default is GaAs sound velocity: 5.2d3 [m/s]
 acoustic-deformation-potential = 10d0                          ! [eV]
          default is GaAs acoustic deformation potential: 10d0 [eV]
!--------------------------------------------------

 LO-phonon-scattering           = no                       !
                               
= yes                      !
longitudinal polar-optical phonon scattering (polar LO phonon scattering) (inelastic and non-diagonal)
                                = isotropic                !
wurtzite anisotropy is not taken into account (meaningful for wurtzite only)
                                                           !
Note: The LO phonon energy has to be specified in the materials section.
                                                           !
Currently, an average value of all grid points is taken. In order to use
                                                           ! a constant LO phonon energy, each material should have the same value.
                                = two                      !
uses two LO phonon energies, i.e. a 2nd LO phonon scattering selfenergy is also taken into account.
                                = two-only                 !
uses only the 2nd LO phonon energy
                                = isotropic-two            !
uses two LO phonon energies, i.e. a 2nd LO phonon scattering selfenergy is also taken into account. (isotropic version)
                                = isotropic-two-only       !
uses only the 2nd LO phonon energy (isotropic version)
                                = three                    !
uses three LO phonon energies, i.e. a 2nd and 3rd LO phonon scattering selfenergy is also taken into account.
                                = three-only               !
uses only the 3rd LO phonon energy
                                = isotropic-three          !
uses three LO phonon energies, i.e. a 2nd and 3rd LO phonon scattering selfenergy is also taken into account. (isotropic version)
                                = isotropic-three-only     !
uses only the 3rd LO phonon energy (isotropic version)
 LO-phonon-energy-2nd           = 0.035d0 0.035d0 0.035d0  ! [eV]
For two  , two-only  , isotropic-two  , and isotropic-two-only  , a 2nd LO phonon energy has to be specified.
 LO-phonon-energy-3rd           = 0.035d0 0.035d0 0.035d0  ! [eV]
For three, three-only, isotropic-three, and isotropic-three-only, a 3rd  LO phonon energy has to be specified.
 LO-phonon-scattering-scale-selfenergy      = 1d0          !
This factor allows to scale the       LO-phonon-scattering selfenergy. 0 <= scale <= 1 (default: 1d0)
 LO-phonon-scattering-scale-selfenergy-2nd  = 1d0          !
This factor allows to scale the 2nd LO-phonon-scattering selfenergy. 0 <= scale <= 1 (default: 1d0)
 LO-phonon-scattering-scale-selfenergy-3rd  = 1d0          !
This factor allows to scale the 3rd  LO-phonon-scattering selfenergy. 0 <= scale <= 1 (default: 1d0)
                                                           !
                                                           !
The following dielectric constants for the 2nd and 3rd LO phonon energy are optional.
                                                           ! If only one value is specified, the dielectric tensor is isotropic, i.e. the perpendicular and parallel components are the same.
 static-dielectric-constants-LO-phonon-2nd  = 12.93d0 12.93d0 12.93d0 !
static dielectric constants  for 2nd LO phonon energy (epsr,perp, epsr,perp, epsr,par)
 static-dielectric-constants-LO-phonon-3rd  = 12.93d0 12.93d0 12.93d0 !
static dielectric constants  for 3rd  LO phonon energy (epsr,perp, epsr,perp, epsr,par)
 optical-dielectric-constants-LO-phonon-2nd = 10.10d0 10.10d0 10.10d0 !
optical dielectric constants for 2nd LO phonon energy (epsinfinity,perp, epsinfinity,perp, epsinfinity,par)
 optical-dielectric-constants-LO-phonon-3rd = 10.10d0 10.10d0 10.10d0 !
optical dielectric constants for 3rd  LO phonon energy (epsinfinity,perp, epsinfinity,perp, epsinfinity,par)

 TO-phonon-scattering           = no                       !
(default)
                               
= yes                      !
transverse polar-optical phonon scattering (polar TO phonon scattering) (inelastic and non-diagonal)
                                = isotropic                !
wurtzite anisotropy is not taken into account (meaningful for wurtzite only)
                                                           !
only meaningful for wurtzite but not for zincblende
 TO-phonon-energy               = 0.06956d0 0.06956d0 0.06608d0  ! [eV]
only meaningful for wurtzite but not for zincblende (a a c)
                                                           !
 charged-impurity-scattering    = no                       !
do not include charged impurity scattering
                                = yes                      !
include charged impurity scattering, i.e. averaging over the charged impurity
                                                           !
density (with respect to propagation coordinates)
                                                           !
 electron-electron-scattering   = no                       !
do not include inelastic electron-electron scattering (Debye screening)
                                = yes                      !
include inelastic electron-electron scattering (Debye screening)

 interface-roughness-scattering = no                       ! interface roughness scattering
                                = yes                      !

 gaussian_correlationL          = yes  ! (default: yes)    ! assuming Gaussian    shaped in-plane roughness autocorrelation
                                = no                       !
assuming exponential shaped in-plane roughness autocorrelation
                                                           !
see also $roughness-profile
                                                           !
!pauli_principle       = 0.5d0                             !
Pauli principle (should not be changed, default is 0.5)
                                                           !
 ballistic-calculation           = no                      !
include scattering mechanisms
                                 = yes                     !
switch off scattering (ballistic calculation)
                                                           ! to make calculation faster
 contact-scattering-max-number-iterations = 7              !
contact scattering: maximum number of iterations for scattering events in the contacts (default: 100)
                                                           !
maximum number of scattering events in the contacts

 contact-scattering-potential-broadening = 0.001d0 0.001d0 ! [eV]
scattering potential height (i.e. strength, hbar/2tsc) in the contacts (only for periodic and real-periodic contacts)
                                                           ! (first entry corresponds to left contact, second entry corresponds to right contact)
                                                           ! imaginary part, see eq. (3.7.48), p. 115 in PhD thesis of T. Kubis), (default: 0.001 eV)
 
contact-scattering-potential-shift      = 0d0     0d0     ! [eV]
energy shift at the contacts
                                                           ! (first entry corresponds to left contact, second entry corresponds to right contact)
                                                           ! real part (default: 0 eV)

!direct_contact        = no                                !
direct contact (should not be changed, default is no)

                                                           !
using the approximation similar to A. Wacker
 wacker_approximation  = no            ! (default: no)     ! no:   including the momentum dependence - correct version
                       = yes                               ! yes: all momentum dependence of scattering potential is ignored (similar to A. Wacker)
                                                           !
                                                           !
maximum number of iterations of Green's functions and self-energies (manual version)
 max_cycle_counter       = 20                              !
maximum number of inner iterations (default: 20)
                                                           !
maximum number of iterations of Green's functions and self-energies (automated version)
 max_cycle_counter1      =                                 !
maximum number of inner iterations for by far not converged calculations (default: max_cycle_counter)
 max_cycle_counter2      =                                 !
maximum number of inner iterations for          not converged calculations (default: max_cycle_counter)
 max_cycle_counter3      =                                 ! maximum number of inner iterations for     almost converged calculations (default: max_cycle_counter)
                                                           !
 scattering_boost        = no                              !
accelerates the calculation of the scattering self energies (only far from convergence)
                         = yes                             !
 scattering_boost_factor = 5                               !
amount of acceleration
 scattering_boost_limit  = 0.3d0                           !
boost, if convergency > scattering_boost_limit
                                                           !
$end_scattering-mechanisms                                 !
!----------------------------------------------------------!

 

Note: lattice_constant (a) and sound_velocity (v) determine the dispersion relation of acoustic phonons: ELA = hbar v q
where q is from 0 to pi/a.

 ballistic                     = yes   ! 'yes' / 'no'
Flag to switch between ballistic and nonballistic calculation.
Ballistic does not include any scattering (and is thus a rather fast calculation). Its results do not really correspond to physical reality but still might give a reasonable insight into a physical problem as it represents an extreme case where scattering is absent (i.e. it should yield an upper boundary for the expected current).
Nonballistic includes scattering (and is thus a very time-consuming calculation). Its results correspond (or are at least close) to physical reality.

 

 

Contacts

!----------------------------------------------------------!
$contact-type                                    optional  !
 type                            character       required  !
 contact_temperature             double          optional  ! [K]
 left_contact_temperature        double          optional  ! [K]
 right_contact_temperature       double          optional  ! [K]
 contact_sc_limit                double          optional  !
                                                           !
limits of (quasi-) periodicity averaging areas
 start_left                      integer         optional  !
the start point for the periodicity averaging on the left (not used for contact_occupation = no, contact_poisson = no)
 end_left                        integer         optional  !
the end  point for the periodicity averaging on the left
 start_right                     integer         optional  !
the start point for the periodicity averaging on the right
 end_right                       integer         optional  !
the end  point for the periodicity averaging on the right
                                                           !
These start and end grid points refer to the device grid points.

 contact_occupation              character       optional  !
 heated_part                     double          optional  !
 contact_poisson                 character       optional  !
 left_drift                      double          optional  !
 right_drift                     double          optional  !
 contact_den_diff                double          optional  !
only for entropic contacts
 electric-field-at-contact-limit double          optional  !
only for entropic contacts, default: 0.01d0 (The electric field at the contacts gets changed if density_convergence is smaller than electric-field-at-contact-limit.)
$end_contact-type                                optional  !
!----------------------------------------------------------!

 type = direct         ! direct contacts
      = indirect       !
indirect contacts
      = laser          !
laser contacts
      = periodic       !
periodic contacts
      = real-periodic  !
real periodic contacts
      = entropic       ! entropic contacts (a form of direct contact ==> contact_den_diff)

 contact_occupation = no       ! A Fermi distribution in the contacts is used (default).
                    = yes      !
using quasi periodic electron distribution in the contacts
                    = periodic !
using quasi periodic electron distribution in the contacts
                               ! Note: yes and periodic is equivalent.
                    = heated   ! heated electrons in the leads
In all other cases, a Fermi distribution in the contacts is used.
 

 heated_part        = ...d0    ! relative contribution of heated electrons
If contact_occupation = heated, this specifier is necessary.
If  heated_part is not specified, although contact_occupation = heated, then a Fermi distribution in the contacts is used.
 

 contact_poisson    = no       ! A flat conduction band in the contacts (except external potentials) is used.
                    = yes      !
using quasi periodic Poisson potential in the contacts
                    = periodic !
using quasi periodic Poisson potential in the contacts
                               ! Note: yes and periodic is equivalent.
In all other cases, a flat conduction band in the contacts (except external potentials) is used.
 

 

 

Instead of using bulk contacts, one can use quasi Stark ladder contacts.

!----------------------------------------------------------!
$left-contact-potential-profile                  optional  !
 left_potential_height            double         optional  ! [eV]
the external potential in the left contact, i.e. conduction band edge energy
 left_start_point                 integer        optional  !
 left_end_point                   integer        optional  !
$end_left-contact-potential-profile              optional !
!----------------------------------------------------------!


!----------------------------------------------------------!
$right-contact-potential-profile                 optional  !
 right_potential_height           double         optional  ! [eV]
the external potential in the right contact, i.e. conduction band edge energy
 right_start_point                integer        optional  !
 right_end_point                  integer        optional  !
$end_right-contact-potential-profile             optional  !
!----------------------------------------------------------!

These flags are relevant when using periodic leads.
$contact-type
 type = periodic       !
periodic contacts
Using these flags one defines a potential in the left and right lead section.
The size of these sections is defined via contact_points in the $global-parameters-NEGF section of the input file.
The potentials in the leads are chosen such that the lead barrier defines with the first barrier in the device close to the lead a quantum well that fits to the QCL periodicity.
In this way, each lead/device boundary cuts a quantum well into two segments. One segment is within the device, the other one is in the respective lead.
One can add more barriers in the leads but we have not seen a significant impact of them (except making the code slower).
Note: left_start_point, left_end_point, right_start_point, right_end_point refer to contact grid points and not to the device grid point numbering.
For details, see p. 92 "Multiquantum well and single period lead model" in section 3.6.2., and p. 114 "Multiquantum well leads" in section 3.7.4 in PhD thesis of T. Kubis.

Example

We have 'contact_points = 27', i.e. 27 contact grid points for the left lead and
27 contact grid points for the right lead.
The numbering of the lead grid points is from left to right, also for the right lead.

Left lead

In this example, lead grid points 1,...,8 have zero potential height,
lead grid points 9,10,11 have %CBO potential height.
For a 0.9 nm grid, 3 grid points correspond to a barrier width of 3 * 0.9 nm = 2.7 nm.
Then there are 16 (= 27 - 8 - 3) lead grid points left which have zero potential height (quantum well).
These 16 lead grid points, together with the first 5 device grid points inside the device represent
(for a 0.9 nm grid) the 18.9 nm (21 * 0.9 nm) quantum well left to the
leftmost barrier in the device region.

Right lead
In this example, lead grid points 1,...,5 have zero potential height (quantum well),
lead grid points 6,7 have %CBO potential height.
Then there are 20 (= 27 - 5 - 2) lead grid points left which have zero potential height.
The last 5 device grid points inside the device, together with the first 5 lead grid points, represent
(for a 0.9 nm grid) the 9.0 nm (10 * 0.9 nm) quantum well right to the
rightmost barrier in the device region.

!----------------------------------------!
$left-contact-potential-profile          !
 left_potential_height = %CBO            ! [eV]
 left_start_point      = 9               !
 left_end_point        = 11              !
$end_left-contact-potential-profile      !
!----------------------------------------!

!----------------------------------------!
$right-contact-potential-profile         !
 right_potential_height = %CBO           ! [eV]
 right_start_point      = 6              !
 right_end_point        = 7              !
$end_right-contact-potential-profile     !
!----------------------------------------!

This potential energy profile (conduction band edge) defined in the left and right contact regions is written to the following file:
- contact/contact_and_device_potential.dat -
This file also includes the conduction band edge profile of the device.

 

 

Interface roughness

Here, the user can specify
- the position dependent roughness width in growth direction (z direction) and
- the position dependent correlation length lambda(z) of the interface roughness in (x,y) direction.
Both entries are in units of [nm].
The selfenergy depends linearly on the roughness_width.

!----------------------------------------------------------!
$roughness-profile                               optional  !
 roughness_width                  double         required  ! [nm]
 correlation_length               double         optional  ! [nm]
 start_point                      integer        optional  !
 end_point                        integer        optional  !
$end_roughness-profile                           optional  !
!----------------------------------------------------------!

!----------------------------------------------------------!
$roughness-profile                                         !
 roughness_width                = 0.6d0                    ! [nm]
(default value: 0.6 nm)
 correlation_length             = 8d0                      ! [nm]
(default value: 8.0 nm)
 start_point                    = 1                        !
 end_point                      = 50                       !
$end_roughness-profile                                     !
!----------------------------------------------------------!

 

 

Damping parameters (used to influence the convergence of the equations)

!----------------------------------------------------------!
$damping-parameters                              optional  !
 Poisson-damping-1                   double      optional  !
 Poisson-damping-2                   double      optional  !
 Poisson-damping-3                   double      optional  !

 scattering-self-energies-damping-1  double      optional  !
 scattering-self-energies-damping-2  double      optional  !
 scattering-self-energies-damping-3  double      optional  !

 drift-vector-damping-1              double      optional  !
 drift-vector-damping-2              double      optional  !
 drift-vector-damping-3              double      optional  !

 electric-field-at-contact-damping-1 double      optional  !
 electric-field-at-contact-damping-2 double      optional  !
 electric-field-at-contact-damping-3 double      optional  !
$end_damping-parameters                          optional  !
!----------------------------------------------------------!

 

All values for the damping parameter should be between zero and 1: 0 <= x < 1

!----------------------------------------------------------!
$damping-parameters                                        !

!-------------------------------------------------------
!
damping parameters for the electrostatic potential of the Poisson equation
!-------------------------------------------------------
 Poisson-damping-1 = 0.2d0                                 !
 Poisson-damping-2 = 0.2d0                                 !
 Poisson-damping-3 = 0.2d0                                 !

!-------------------------------------------------------
!
damping parameters for the scattering self energies
!-------------------------------------------------------
 scattering-self-energies-damping-1 = 0d0                  !
for  1 <  cycle_counter <   5
 scattering-self-energies-damping-2 = 0d0                  !
for  5 <= cycle_counter <  10
 scattering-self-energies-damping-3 = 0d0                  !
for 10 <= cycle_counter < 100, else 0d0.

!-------------------------------------------------------
!
damping parameters for the drift vector for the shifted Fermi distribution in the contacts
!-------------------------------------------------------
 drift-vector-damping-1   = 0d0                            !
for nonequilibrium contacts, not used if zero-drift-vector-in-contacts = yes
 drift-vector-damping-2   = 0d0                            !
for nonequilibrium contacts, not used if zero-drift-vector-in-contacts = yes
 drift-vector-damping-3   = 0d0                            !
for nonequilibrium contacts, not used if zero-drift-vector-in-contacts = yes

!-------------------------------------------------------
!
damping parameter for the electric field at the boundary (Neumann boundary condition)
!
These parameters are only used when determining the boundary conditions for the Poisson equation.
!-------------------------------------------------------
 electric-field-at-contact-damping-1 = 0d0                 !
 electric-field-at-contact-damping-2 = 0d0                 !
 electric-field-at-contact-damping-3 = 0d0                 !
$end_damping-parameters                                    !
!----------------------------------------------------------!

The damping of the electrostatic potential (i.e. solution of Poisson equation) works as follows:
 !---------------------------------------------------------------
 ! phiVi-1: potential of previous iteration
 ! phiVi:   potential of current  iteration
 ! phiVi+1: potential of next     iteration
 !---------------------------------------------------------------
phiVi+1 = Poisson-damping * phiVi-1 + (1 - Poisson-damping) phiVi   CHECK: DOES THIS STATEMENT MAKES SENSE???

If strong damping is required, e.g. when the electrostatic potential is oscillating between two solutions, use a large value < 1d0. (Using 1d0 does not make sense at all.)
If no damping is required, e.g. when convergence is very good, use a small value > 0d0, or 0d0.
The idea is the following:
  1) The algorithm starts with Poisson-damping-1.
  2) It uses Poisson-damping-2 if the density does not change too much, i.e. some convergence of the density has been achieved.
  3) It uses Poisson-damping-3 if the convergence of the density is very good.
The degree of these convergence limits, .i.e. 2), 3), can be altered by Poisson-damping-threshold.

To be precise:
  !------------------------------
  !
Determine damping constants.
  !------------------------------
  IF      (density_convergence > 0.100d0 * Poisson-damping-threshold) THEN
     ==> Use Poisson-damping-1
     ==> Use electric-field-at-contact-damping-1
  ELSE IF (density_convergence > 0.010d0 * Poisson-damping-threshold) THEN
     ==> Use Poisson-damping-2
     ==> Use electric-field-at-contact-damping-3
  ELSE
     ==> Use Poisson-damping-3
     ==> Use electric-field-at-contact-damping-3
  END IF

This means that one can use different dampings, e.g. a high damping if the solution is far away from the converged solution, and a small damping if the solution is close to convergence (or vice versa).
density_convergence is the convergence parameter for the density.

 

 

Output

All output files will be written to the folder "NEGF/".

 

Files describing the structure (input parameters)

They are written to the folder NEGF/structure/.

  • Conduction band edge
    conduction_band_edge_input.dat  
    grid point in [nm]       conduction band edge Ec in [eV] (without electrostatic potential)
    conduction band edge (without electrostatic potential) in units of [eV]
     
  • Doping
    doping_concentration.dat        
    grid point in [nm]       doping concentration in [1018 cm-3]
     
  • Effective masses / nonparabolicity of effective masses
    effective_mass.dat              
    grid point in [nm]       Gamma conduction band effective mass in [m0]
    nonparabolicity.dat              grid point in [nm]       nonparabolicity parameter for Gamma conduction band effective mass in [1/eV]
     
  • Dielectric constants
    epsilon_infinity.dat            
    grid point in [nm]       optical dielectric constant epsiloninfinity in []
    epsilon_static.dat               grid point in [nm]       static dielectric constant epsilon0 in []
     
  • Interface roughness scattering
    interface_roughness_width.dat   
    grid point in [nm]       roughness width   in [nm]
    interface_correlation_length.dat grid point in [nm]       correlation length in [nm]

    interface_potential.dat         
    grid point in [nm]       interface potential
    For each grid point it holds: interface_potentialV(i) = 2 * Ec(i) - Ec(i+1) - Ec(i-1) where Ec is the conduction band edge
  • Alloy profile
    alloy_profile.dat               
    grid point in [nm]       alloy concentration in []    alloy conduction band edge energy difference in [eV]
     
  • Electrostatic potential
    potential_electrostatic_nextnano3.dat
    grid point in [nm]       electrostatic potential in [V]
    (Only relevant if the calculated electrostatic potential of a preceding nextnano³ calculation is passed over to the NEGF algorithm as an initial guess.)
     

 

 

 

Calculated data

  • Conduction band edge (incl. electrostatic potential)
    conduction_band_edge.dat                   
    grid point in [nm]    Gamma conduction band edge in [eV] (incl. electrostatic potential)
    conduction_band_edge_avs.dat/*.coord/*.fld  AVS output files that can be used to plot the conduction band edge (incl. electrostatic
                                                potential) in units of [eV] with AVS/Express visualization software
     
  • Electron density
    density.dat -
    grid point in [nm]       electron density in units of [1018 cm-3]
     
  • Electrostatic potential
    potential_electrostatic.dat: electrostatic potential (will be updated for each Poisson iteration) including grid points in [nm]
    ==> The feature "solving the Poisson equation" can be switched off:
     solve-Poisson-equation = no   ! 'yes' / 'no'

    Electric field
    electric_field.dat
    : electric field in units of [kV/cm] (will be updated for each Poisson iteration) including grid points in [nm]
     
  • mapping_E.dat:   energy resolution (total energy grid)                          in units of [eV]
  • mapping_Ez.dat: energy resolution in growth direction (z) (energy grid) in units of [eV]
  • current.dat:       grid point dependent current density in units of [A/cm^2]
  • dissipated_power.dat           ! in units of [Watts/cm2]
    The dissipated power will be printed out for each grid point.
  • averaged_dissipated_power.dat  ! in units of [Watts/cm2]
    The average dissipated power is the average of the dissipated power at each grid point.
    This quantity is very interesting to study the heating of the device during operation.
  • electric_field_at_contact.dat: value of the electric field at the left contact in units of [V/m]
    The new electric field at the left contact is written to this file.
    (written out each time when solving Poisson equation)
    Tune the electric field at the left contact, so that the difference in the potential at the boundaries equals the difference in the chemical potentials.
    (Use only with drifted Fermi distributions in the contacts.)
    The electric field at the right contact is proportional to the electric field at the left contact because the electric displacement vectors at the left and right boundaries must be equal:
    F(right) = - F(left) * epsilon(left) / epsilon(right)
    where F is the electric field (i.e. electric-field-at-contact) and epsilon is the dielectric constant.
     

 

AVS files

Note: AVS files can be opened conveniently by "double-clicking" on the *.v files.

  • density_energy_resolved_avs.fld, *.coord, *.dat
    energy resolved density "density(z,E)": z, energy, density in units of [eV-1 * 1018 cm-3].

    density_energy_resolved.dat:                        energy resolved density "density(z,E)": z, energy, density in units of [eV-1 * 1018 cm-3].
    density_energy_resolved_0.mtx
    :                    energy resolved density: matrix z x E (contains density for each matrix element (z,E))

    density_energy_resolved_averaged.dat: energy resolved density "density(E)" divided by device length:  energy, density in units of [eV-1 * 1018 cm-3].
    This is the average of n(z,E) in the total device, see eq. (3.7.2.) in PhD thesis of T. Kubis.
    This is only necessary to discretize the energy E accordingly in the total device (E_mappingV), i.e. for the adaptive grid of the total energy.

    density_Ez_energy_resolved_avs.fld, *.coord, *.dat
    energy resolved density "density(z,Ez)": z, energy Ez, density in units of [eV-1 * 1018 cm-3].
     
  • energy_current_energy_resolved_avs.v
    energy_current_energy_resolved_avs.fld, *.coord, *.dat
    energy resolved current density "current density(z,E)": z, energy, current density in units of [Ampere/(cm^2 eV)].
    current_energy_resolved.dat    -
    current_energy_resolved_ij.dat - x,y,f(x,y)
    format
    Note: current_energy_resolved_avs_interpolation.v.
     
  • Energy resolved local density of states (LDOS) (see Fig. in ICPS poster) (z, Ez, LDOS(z,Ez)) in units of [1 / (eVAngstrom)]
     LocalDOS_avs.fld , *.coord, *.dat
    local density of states (LDOS), i.e. real part of spectral function divided by 2pi at k|| = 0.
          DOS_avs.dat                 
    density of states at k|| = 0.

    ==> LDOS.v
     spectral_real_avs.fld , *.coord, *.dat
    (spectral_aimag_avs.fld, *.coord, *.dat) -
    The imaginary part of the diagonal of the spectral function should be zero.
     spectral_real.dat
    :
     spectral_real2.dat:
     spectral_aimag.dat:
     spectral_aimag2.dat:
     spectral_real_old.dat:
     
  • spectrum_ana.mtx: matrix representation of spectral_real.dat
  • spectrum_ana2.mtx: matrix representation of
  • spectrum_aver.dat:

 

  • Optical gain within linear response theory
    These files contain the gain (and the absorption alpha which is -gain)
      gain(z,E) where z is the spatial coordinate and E is the photon energy.
    Note that positive values correspond to gain, negative values to absorption.
    The output units for the gain (i.e. -absorption) are [1/m].

    - gain_Re.v
      gain_Re.fld, *.coord, *.dat
     (gain_Im.fld, *.coord, *.dat  ==>
    This file, i.e. the imaginary part of the gain, only shows zero entries.)
      -
    The x axis is the distance in units of [nm].
      - The y axis is the photon energy in units of [eV].
        The y axis is from
          - 'min_photon' (minimum  photon energy relevant for gain) to
          - 'max_photon' (maximum photon energy relevant for gain) as specified in the input file.
          - 'photon_number' (e.g. = 20, = 100) is the number of energy grid steps between 'min_photon' and 'max_photon'.

    - gain_integrated_energy.dat
     
    contains the integrated gain over spatial coordinate divided by interval used for integration:
                        gain(E)      where E         is in units of [eV], gain is in units [1/cm]
      gain_integrated_wavelength.dat
     
    contains the integrated gain over spatial coordinate divided by interval used for integration:
                        gain(lambda) where lambda is in units of [µm], gain is in units [1/cm]
        Note: The interval that is used for integration is specified via the optional flag:
                gain-integrate-device-from-to     = 5d0 65d0 ! [nm]

    complex optical conductance sigma
      optical_conductance_Re.fld, *.coord, *.dat:  Re(sigma)
      optical_conductance_Im.fld, *.coord, *.dat:  Im(sigma)
      -
    The x axis is the distance in units of [nm].
      - The y axis is the photon energy in units of [eV].
        The y axis is from
          - 'min_photon' (minimum  photon energy relevant for gain) to
          - 'max_photon' (maximum photon energy relevant for gain) as specified in the input file.
          - 'photon_number' (e.g. = 20, = 100) is the number of energy grid steps between 'min_photon' and 'max_photon'.
      The optical conductance is obtained from the quotient of the perturbation of the current density delta j(z,w) and the electric field of the photon Ez(w).
      sigma(z,w) = delta j(z,w) / Ez(w)

    complex permittivity epsilon: epsilon(z,w) = epsilon0 epsilonr(z) + i sigma(z,w)/w
     
    dielectric function epsilon in units of [epsilon0]
      dielectric_function_Re.fld, *.coord, *.dat:  Re(epsilon)
      dielectric_function_Im.fld, *.coord, *.dat:  Im(epsilon)
      -
    The x axis is the distance in units of [nm].
      - The y axis is the photon energy in units of [eV].
        The y axis is from
          - 'min_photon' (minimum  photon energy relevant for gain) to
          - 'max_photon' (maximum photon energy relevant for gain) as specified in the input file.
          - 'photon_number' (e.g. = 20, = 100) is the number of energy grid steps between 'min_photon' and 'max_photon'.
    Note: If the imaginary part of the dielectric function epsilon(z,w) is negative, i.e. Im(epsilon) < 0, the medium delivers energy to the wave, and thus amplifies the wave which corresponds to positive gain. If Im(epsilon) < 0, absorption is present.

     

 

Current (I-V characteristics)

  • IV_characteristics1D_NEGF.dat:         current-voltage characteristics (I-V characteristics)
    There are three columns:
      voltage[V]    j_average[A/cm^2]    Deta_phi_electrostatic[V]
    - applied bias: voltage in units of [V] - The meaning of 'applied bias' is voltage difference between left and right contact: applied_bias = Vleft - Vright = -(EF,left - EF,right) / |e|.
    - current density (averaged value over all grid points (N-2)) in units of [A/cm2]
    - difference in electrostatic potential of left and right boundaries in units of [V]: Delta_phi = phi(1) - phi(Nz) = phileft - phiright
    The applied bias and Delta_phi have the same sign.
    Here, one can check if the applied bias also drops in terms of electrostatic potential drop.

    An additional nonzero built-in potential (built-in-potential = ... in units of [V]) has to be taken into account when comparing the electrostatic potential drop to the applied bias.


    Comments: If the conduction band edge at the left side is higher than at the right side, then the electric field is negative.

     

 

Convergence files

During the calculation, one can check the status of the convergence.

  • minimum_ConductionBandEdge.dat: minimum of conduction band edge during iterations ==> if converged, this value should be converged
    Returns the lowest value (minimum) of the conduction band edge in units of [eV], i.e. of the file ConductionBandEdge_ind000.dat.
    Note: min_potV is currently used only in FUNCTION get_drift_momentum.
  • convergence_density.dat:           contains convergence parameter for the density: relative change of density with respect to previous iteration
    These values are written out with respect to the Poisson self-consistency cycle.
    See also specifier limit-for-density-convergence.
  • convergence_density_temp.dat: contains convergence parameter for the density: relative change of density with respect to previous iteration
    These values are written out in both the Poisson self-consistency cycle and in the scattering self-consistency cycle.
  • iterations_current.mtx: electron current density [A/Angstrom2] - each line corresponds to an iteration
    - current density at each grid point (should be the same for all grid points if converged)
  • iterations_density.mtx: electron density               [1018 cm-3] - each line corresponds to an iteration
  • screening_length_Debye.dat    - electrostatic Debye    screening length in units of [nm]
    screening_length_Lindhard.dat - electrostatic Lindhard screening length in units of [nm]   (The Lindhard screening length is only an output quantity. It is not used inside the code.)
    Both are written out in subroutine get_density.
    The screening length is input for the computation of the
    - lesser selfenergy due to inelastic scattering with LO-phonons.
    - retarded and lesser selfenergy for elastic scattering on charged impurities.
    - retarded and lesser self-energies for the inelastic electron-electron scattering. Here, the simplest approach for the screening is used: Debye screening length

    The Debye screening length is defined as
         LD = SQRT ( epsilon0 * epsilonr * kB T / (e2 n) )
    where n is the averaged density in the device, i.e. a constant Debye screening length is used.
    See eq. (3.4.21), p. 54 in PhD thesis of T. Kubis.

 

 

Other files

  • tau.dat -
  • test_greenL.dat -
  • second_div_low.dat -
  • LOS.dat - SUBROUTINE get_density
    contains real part of the spectral function for k|| = 0.
  • mass_nonparabolicity_avs.fld - energy and position dependent effective mass in units of [m0], i.e. m(z,E) where E is the total energy. alpha is the nonparabolicity parameter.
                                   m(z,E) = m(z) ( 1 + ( E - E_c(z) ) * alpha(z) )
  • contact/contact_ElectrostaticPotential_left.dat  -  -electrostatic potential at left contact, i.e. at leftmost grid point in units of [V]
    contact/contact_ElectrostaticPotential_right.dat -  -
    electrostatic potential at left contact, i.e. at rightmost grid point in units of [V]

 

 

Further output for debugging

 $global-settings
  ...
  debug-level = 2  !
Choose a number higher than 0 for additional output useful for debugging.
 

If the debug level is larger than 1, the following output is available:

  • debug/Greens_function_lesser(z,Ez,E).fld    lesser    Green's function G<(z,z,Ez,E), i.e. G<(z,Ez,E)
  • debug/Greens_function_retarded(z,Ez,E).fld  retarded Green's function GR(z,z,Ez,E), i.e. GR(z,Ez,E)

 

 

How to restart a calculation

If you used

 save-every-nth-iteration = ! saves information in binary format that can be read in
                               ! later to restart a calculation (default: 10)

then you can restart a calculation by reading in previously saved data. This feature is useful if you had a system crash or system shut down, for instance. The calculations are then restarted from the point where the NEGF/stop/*.raw files have been written.

  1. Generate a file named run.txt in the folder of the executable. The content of that file does not matter – it may be empty.
  2. Start the program with the same input file the NEGF/stop/*.raw files have been generated with.
  3. Wait until the following is written on the screen output, or in the output file in the case you pipe (> logfile.out) the screen output (may take some time, depending on the job):
    - reading the Green's functions
    - reading the self-energies on hard drive
    - reading the numerical constants
    - reading the physical constants
    - reading the remaining global variables
    - reading the global functions
    Then the reading of the former program process is done.
  4. Now you may delete the run.txt file. That might be safer, but it should not matter leaving the file as it is. (We have not seen any problems with that.)

Note: If save-every-nth-iteration = is chosen, then for each iteration the *.raw files are written. On modern architectures, this is usually fast. On older systems, this might take significant time.

 

For an example of the Green's function functionality, have a look at the RTD tutorial.

 

Parallelization of NEGF algorithm

The NEGF algorithm has been parallelized.
Two options for parallelization are available.

  • no parallelization

  • parallelization with OpenMP (executables compiled with Intel compiler, including parallel version of MKL)
    Very easy to use, i.e. specify number of threads via command line: nextnano3.exe -threads 4
    (uses four threads, e.g. on a quad-core CPU)

For further details, see also:
  $global-settings
   ...
   number-of-threads = 2     ! 2 =
for dual-core CPU

 

Necessary input files

The following input files are necessary for the NEGF algorithm. They are located in the folder input_files/NEGF/.

 

Recent changes

The following changes have been done for the 2012 version of nextnano³.

  • All output files related to the input structure like conduction band edge profile, effective mass profile, ... are now written to the folder NEGF/structure/.

  • All convergence files related to the calculation are now written to the folder NEGF/convergence/.
    convergence_density.dat was previously called long_convergency.dat.
    minimum_conduction_band_edge.dat was previously called min_pot.dat.

  • Output files mapping_E.dat and mapping_Ez.dat were previously called E_mappingV.dat and Ez_mappingV.dat.

  • The output of the gain/absorption has now the opposite sign, i.e. gain is positive, absorption is negative.
    The integrated gain is now in units of [1/cm].

  • The specifier roughness_width in the $scattering-mechanisms section has been deleted. Now the position dependent roughness width roughness_width should be specified instead.
    The specifier correlation_length in the $scattering-mechanisms section has been deleted. Now the position dependent roughness width correlation_length should be specified instead.
    Now the units are [nm] for both input and output. Previously they were [Angstrom].

  • The following keywords and specifiers changed slightly.
    !------------------------------------------!
    $nonparabolicity-profile                   !
     nonparabolicity = 1.5d0                   ! [1/eV]
     start-point     = 1                       !
     end-point       = 95                      !
    $end_nonparabolicity-profile               !
    !------------------------------------------!

  • The following specifiers are new:
     get-alloy-from-nextnano        = yes
     mass-density                   = ...
     acoustic-deformation-potential = ...

  • limit-for-density-convergence            was previously called long_conv_limit.
    Poisson-damping-threshold               
    was previously called poisson_limit.
    zero-drift-vector-in-contacts           
    was previously called zero_drift.
    use-maximum-drift-vector                
    was previously called max_drift.
    drift-vector-maximum [1/nm]             
    was previously called drift_length [1/Angstrom]. Note that the units have changed.
    output-correlation-functions            
    was previously called correlation.
    output-quasi-Fermi-level                 was previously called fermi.
    output-k-resolved                        was previously called k_resolved.
    first-order-Born-approximation           was previously called first_born.
    calculate-transmission                   was previously called transmission.
    Poisson-damping-1                        was previously called poisson_damping1.
    Poisson-damping-2                        was previously called poisson_damping2.
    Poisson-damping-3                        was previously called poisson_damping3.
    electric-field-at-contact-damping-1      was previously called slope_damping1.
    electric-field-at-contact-damping-2      was previously called slope_damping2.
    electric-field-at-contact-damping-3     
    was previously called slope_damping3.
    scattering-self-energies-damping-1      
    was previously called self_damping1.
    scattering-self-energies-damping-2       was previously called self_damping2.
    scattering-self-energies-damping-3       was previously called self_damping3.
    drift-vector-damping-1                   was previously called drift_damping1.
    drift-vector-damping-2                   was previously called drift_damping2.
    drift-vector-damping-3                   was previously called drift_damping3.
    alloy-scattering                         was previously called alloy_scattering.
    lattice-constant                         was previously called lattice_constant.
    acoustic-phonon-scattering               was previously called acoustic_phonons.
    LO-phonon-scattering                    
    was previously called optical_phonons.
    electron-electron-scattering            
    was previously called electron_electron.
    charged-impurity-scattering              was previously called charged_impurity.
    interface-roughness-scattering           was previously called interface_roughness.
    ballistic-calculation                   
    was previously called ballistic.
    contact-scattering-max-number-iterations was previously called contact_scat.
    contact-scattering-potential-broadening  was previously called contact_sc_pot.
    fix-electric-field-at-contact            was previously called given_slope.
    electric-field-at-contact                was previously called poisson_slope.
    electric-field-at-contact-limit          was previously called slope_limit.
    built-in-potential                      
    was previously called built_in_potential.

  • non_diagonal_range        is now in units of [nm].   Previously it was [Angstrom].
    lattice-constant          is now in units of [nm].   Previously it was [Angstrom].
    sound-velocity            is now in units of [m/s]. Previously it was [Angstrom/s].
    electric-field-at-contact is now in units of [V/m]. Previously it was called poisson_slope was in units of [V/Angstrom] and had the opposite sign.

  • read-inputfile-during-calculation  = no    ! default value is now: no
     

 

To do:

  • Output gain_real_integrated_frequency.dat  alpha(nu)

  • Implement temperature sweep.

  • Add alloy scattering documentation to online docu and source code based on Jirauschek/Kubis review article

 

This will become obsolete:

!--------------------------------------------------!
$doping-function-NEGF                      optional !
 doping_density             double         required ! [1/Angstrom^3]
 start_point                integer        optional !
 end_point                  integer        optional !
$end_doping-function-NEGF                  optional !
!--------------------------------------------------!

!--------------------------------------------------!
$potential-profile                         optional !
 potential_height           double         required ! [eV]
 start_point                integer        optional !
 end_point                  integer        optional !
$end_potential-profile                     optional !
!--------------------------------------------------!


!--------------------------------------------------!
$left-contact-potential-profile            optional !
 left_potential_height      double         optional ! [eV]
 left_start_point           integer        optional !
 left_end_point             integer        optional !
$end_left-contact-potential-profile        optional !
!--------------------------------------------------!


!--------------------------------------------------!
$right-contact-potential-profile           optional !
 right_potential_height     double         optional ! [eV]
 right_start_point          integer        optional !
 right_end_point            integer        optional !
$end_right-contact-potential-profile       optional !
!--------------------------------------------------!

!--------------------------------------------------!
$alloy-profile                             optional !
 alloy_concentration        double         required ! []
 alloy_pot_difference       double         optional ! [eV]
 start_point                integer        optional !
 end_point                  integer        optional !
$end_alloy-profile                         optional !
!--------------------------------------------------!

!--------------------------------------------------!
$roughness-profile                         optional !
 roughness_width            double         required ! [Angstrom]
 correlation_length         double         optional ! [Angstrom]
 start_point                integer        optional !
 end_point                  integer        optional !
$end_roughness-profile                     optional !
!--------------------------------------------------!

!--------------------------------------------------!
$mass-profile                             optional !
 effective_mass             double        required ! [m0]
 start_point                integer       optional !
 end_point                  integer       optional !
$end_mass-profile                         optional !
!--------------------------------------------------!

!--------------------------------------------------!
$nonparabolicity-profile                  optional !
 nonparabolicity            double        required ! [1/eV]
 start-point                integer       optional !
 end-point                  integer       optional !
$end_nonparabolicity-profile              optional !
!--------------------------------------------------!

!--------------------------------------------------!
$dielectric-profile                       optional !
 dielectric_const           double        required ! []
 dielectric_inf             double        required ! []
 start_point                integer       optional !
 end_point                  integer       optional !
$end_dielectric-profile                   optional !
!--------------------------------------------------!

 
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