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Database for wurtzite materials (hexagonal crystal system)

=> ../Syntax/database_nnp.in

Group IV, III-V, II-VI, I-VII materials

binary_wz {
 name    = GaN                 #
material name, e.g. GaN, AlN, InN, ...
 valence = III_V               # IV_IV
for group IV materials (like SiC, ...)
                               # III_V for III-V materials (like GaN, AlN, ...)
                               # II_VI for II-VI materials (like ZnO, ...)
                               # I_VII for I-VII materials (like CuCl, ...)

 lattice_consts{
  a           = 3.189          # [Angstrom]  
lattice constant at 300 K (perpendicular to hexagonal c axis)
                               #
In a hexagonal crystal system, the two lattice constants perpendicular to the hexagonal c axis are equal.
  a_expansion = 5.59e-5        # [Angstrom/K] The lattice constants are temperature dependent => a(T).

  c           = 5.185          # [Angstrom]  
lattice constant at 300 K (along hexagonal c axis)
  c_expansion = 3.17e-5        # [Angstrom/K]
The lattice constants are temperature dependent => c(T).
                               # The lattice constants a and c in the database should be given for 300 K.
                               # For all other temperatures, the lattice constants are calculated by the following formula
                               # where T is the temperatue in units of [K]:
                               # a(T) = a(300 K) + a_expansion * (T - 300 K)
                               # c(T) = c(300 K) + c_expansion * (T - 300 K)
                               #
The lattice constants are needed for the calculation of the strain.
 }

 dielectric_consts{
  static_a  =  9.28            # [-]
static or low frequency (epsilon(omega=0)) dielectric constant (perpendicular to hexagonal c axis)
  static_c  = 10.01            # [-]
static or low frequency (epsilon(omega=0)) dielectric constant (along hexagonal c axis)
  optical_a =  5.29            # [-]
The optical dielectric constant (perpendicular to hexagonal c axis) is currently not in use but maybe it is necessary in the future for laser calculations.
  optical_c =  5.29            # [-]
The optical dielectric constant (along hexagonal c axis) is currently not in use but maybe it is necessary in the future for laser calculations.
                               #
In a hexagonal crystal system the two dielectric constants perpendicular to the hexagonal c axis are equal.
                               # The static dielectric constants enter the Poisson equation.
                               # They are also needed to calculate the optical absorption and enter the equation for the exciton correction.
 }

 elastic_consts{
  c11 = 390                    # [GPa]
elastic constants
  c12 = 145                    #
1 * 1011 dyn/cm2 = 10 GPa  ->  39.0 * 1011 dyn/cm2 = 390 GPa
  c13 = 106                    #

  c33 = 398                    #
  c44 = 105                    # The elastic constants are needed for the calculation of the strain in heterostructures.
 }

 piezoelectric_consts{
  e31 = -0.35                  # [C/m2]
piezoelectric constants
  e33 =  1.27                  #
  e15 = -0.30                  #
If strain is present, then generally piezoelectric charges and thus piezoelectric fields arise.

  B311 = 0.0                   # [C/m2]
2nd order piezoelectric constant (optional)
  B312 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B313 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B333 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B115 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B125 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B135 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
  B344 = 0.0                   # [C/m2] 2nd order piezoelectric constant (optional)
 }

 pyroelectric_consts{ p1 = -0.034 }  # [C/m2] pyroelectric constant (spontaneous polarization)
                               #
The pyroelectric field is directed along the hexagonal c axis ([0 0 0 1] direction).

 conduction_bands{
  Gamma{                       #
material parameters for the conduction band valley at the Gamma point of the Brillouin zone
   mass_t          = 0.202     # [m0]  
electron effective mass perpendicular to hexagonal c axis (parabolic)
   mass_l          = 0.206     # [m0]  
electron effective mass along hexagonal c axis                (parabolic)
                               #
This mass is used for the single-band Schrödinger equation and for the calculation of the densities.

   bandgap         = 3.510     # [eV]  
band gap energy at 0 K
   bandgap_alpha   = 0.909e-3  # [eV/K]
Varshni parameter alpha for temperature dependent band gap
   bandgap_beta    = 830       # [K]   
Varshni parameter beta  for temperature dependent band gap

 

   # absolute deformation potentials of Gamma conduction band minima ac,a=a2 (a axis), ac,a=a2 (a axis), ac,c=a1 (c axis)

   defpot_absolute_t = -11.3   # [eV]   absolute deformation potential of the Gamma conduction band perpendicular to hexagonal c axis ac,a=a2
   defpot_absolute_l = -4.9    # [eV]  
absolute deformation potential of the Gamma conduction band along hexagonal c axis ac,c=a1
   #
Note that I. Vurgaftman et al., JAP 94, 3675 (2003) lists a1 and a2 parameters.
   # They refer to the interband deformation potentials, i.e. to the deformation of the band gaps.
   # Thus we have to add the deformation potentials of the valence bands to get the deformation potentials for the conduction band edge.
   # ac,a = a2 = a2 + D2
   # ac,c = a1 = a1 + D1

   g_t             = 0         # []     g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)
   g_l             = 0         # []    
g factor along hexagonal c axis                (for Zeeman splitting in magnetic fields)
  }
 }

 valence_bands{                # material parameters for the valence band valley at the Gamma point of the Brillouin zone
  bandoffset = -0.726          #
valence band offset (VBO) with respect to the "average" of the three valence band edges as defined below.
                               # Note: This energy determines the valence band offset (VBO) between two materials
                               #          VBOv,av = bandoffset(material1) - bandoffset(material2)
                               # The average of the three holes in wurtzite is defined as: bandoffset = Ev,av = (Ehh + Elh + Ech ) / 3 - 2/3 Deltacr
                               # For comparison, in zinc blende this reads:           bandoffset = Ev,av = (Ehh + Elh + Eso ) / 3
                               # The "average" valence band edge energy in wurtzite is according to Ev in:
                               #    S.L. Chuang, C.S. Chang
                               #    k.p method for strained wurtzite semiconductors
                               #    Phys. Rev. B 54 (4), 2491 (1996)
                               #
The valence band energies for heavy hole (HH), light hole (LH) and crystal-field split-hole (CH) are calculated by
                               # defining an "average" valence band energy Ev (=Ev,av) for all three bands and adding the spin-orbit-splitting and
                               #
crystal-field splitting energies afterwards.
                               # The "average" valence band energy Ev (=Ev,av) is defined on an absolute energy scale and must take into accout the
                               # valence band offsets which are "averaged" over the three holes.

  HH{ mass_t = 1.6             # [m0]
heavy hole effective mass perpendicular to hexagonal c axis (parabolic !)
      mass_l = 1.1             # [m0]
heavy hole effective mass along hexagonal c axis                (parabolic !)
      g_t    = 0               # []  
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)
      g_l    = 0               # []  
g factor along hexagonal c axis                (for Zeeman splitting in magnetic fields)
  LH{ mass_t = 0.15            # [m0]
light   hole effective mass perpendicular to hexagonal c axis (parabolic !)
      mass_l = 1.1             # [m0]
light   hole effective mass along hexagonal c axis                (parabolic !)
      g_t    = 0               # []  
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)
      g_l    = 0               # []  
g factor along hexagonal c axis                (for Zeeman splitting in magnetic fields)
  SO{ mass_t = 1.1             # [m0]
crystal-field split-off hole effective mass perpendicular to hexagonal c axis (parabolic !)
      mass_l = 0.15            # [m0]
crystal-field split-off hole effective mass along hexagonal c axis                (parabolic !)
      g_t    = 0               # []  
g factor perpendicular to hexagonal c axis (for Zeeman splitting in magnetic fields)
      g_l    = 0               # []  
g factor along hexagonal c axis                (for Zeeman splitting in magnetic fields)
                               #
These masses are used for the single-band Schrödinger equation and for the calculation of the densities.

  defpotentials = [ -3.7 ,     # [eV]
deformation potential of the valence bands: D1
                     4.5 ,     # [eV] D2
                     8.2 ,     # [eV] D3
                    -4.1 ,     # [eV] D4
                    -4.0 ,     # [eV] D5
                    -5.5 ]     # [eV] D6

  delta         = [ 0.010   ,  # [eV]
crystal-field splitting energy Deltacr = Delta1
                    0.00567 ,  # [eV]
spin-orbit splitting energy parameter Delta2
                    0.00567 ]  # [eV]
spin-orbit splitting energy parameter Delta3
 }                             #
Very often one assumes Delta2 = Delta3 = 1/3 Deltaso.

 kp_6_bands{                   #
Rashba-Sheka-Pikus parameters
   A1 = -7.21                  # [-]
6-band k.p hole effective mass parameter A1
 
 A2 = -0.44                  # [-]
6-band k.p hole effective mass parameter A2
 
 A3 =  6.68                  # [-]
6-band k.p hole effective mass parameter A3
   A4 = -3.46                  # [-]
6-band k.p hole effective mass parameter A4
 
 A5 = -3.40                  # [-]
6-band k.p hole effective mass parameter A5
 
 A6 = -4.90                  # [-]
6-band k.p hole effective mass parameter A6
 }

 kp_8_bands{
   S1   = 0.866  S2   = 0.962  # [-]          
electron effective mass parameter S1=Sparallel and S2=Sperp. for 8-band k.p
   E_P1 = 14.0   E_P2 = 14.0   # [eV]         
Kane's momentum matrix elements Ep1=Ep,parallel, Ep2=Ep,perp.
                               #
Note: The momentum matrix element parameter P is related to Ep: P2 = hbar2/(2m0) Ep
                              
#    
 The units of P are [eV Angstrom].
   B1 = 0.0937   B2 = 0.0937   # [hbar2/(2m0)]  bulk inversion symmetry parameters B1, B2, B3 (sometimes also called A7)
   B3 = 0.0937                 #
   A1 = -3.221                 # [-]
8-band k.p hole effective mass parameter A1' (Rashba-Sheka-Pikus parameter)
 
 A2 = -0.44                  # [-] 8-band k.p hole effective mass parameter A2' (Rashba-Sheka-Pikus parameter)
 
 A3 =  2.691                 # [-]
8-band k.p hole effective mass parameter A3' (Rashba-Sheka-Pikus parameter)
   A4 = -1.466                 # [-]
8-band k.p hole effective mass parameter A4' (Rashba-Sheka-Pikus parameter)
 
 A5 = -1.406                 # [-]
8-band k.p hole effective mass parameter A5' (Rashba-Sheka-Pikus parameter)
 
 A6 = -2.080                 # [-]
8-band k.p hole effective mass parameter A6' (Rashba-Sheka-Pikus parameter)
 }

Mobility models
 mobility_constant{...}        #
constant mobility model (required)

 mobility_masetti{...}         #
Masetti mobility model (optional)

 mobility_arora{...}           #
Arora mobility model (optional)

 mobility_minimos{...}         #
MINIMOS mobility model (optional)

 mobility_simba{...}           #
SIMBA mobility model (optional)




 recombination{
   SRH      {...}              #
Shockley-Read-Hall recombination
   Auger    {...}              #
Auger recombination
   radiative{...}              #
direct recombination
 }
} : {
name = galliumn_nitride        #
It is possible to define a synonym or several synonyms for this material. Here: "GaN" and "galliumn_nitride" are synonyms for the same set of material parameters.
valence = III_V
}

} : {
name = "galliumn nitride"      #
It is possible to define a synonym or several synonyms for this material. Here: "GaN" and "galliumn nitride" are synonyms for the same set of material parameters.
valence = III_V
}

 

 

The deformation potentials are only used if strain is present. They enter the k.p equations. If the single-band approximation is used, the deformation potentials are used to shift and split the conduction and valence band edges.

The g factors (g_t, g_l) are optional. If the g factors are specified in the input file, the database value for the g factors are overwritten with the value in the input file. If no g factors are present in the input file or in the database, a g factor of 2 is assumed by default.

 

ternary_wz{
   ...
  
Analogously to the zincblende case. Please check the appropriate secion there.
}

ternary2_wz{
   ...
  
Analogously to the zincblende case. Please check the appropriate secion there.
}

 

########################### QUINTERNARY WURTZITE ##########################

 is analogous with _wz instead of _zb ...