# kdotpy material definitions

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## HgTe, mercury telluride
[HgTe]
compound    = HgTe
composition = 1, 1     
P           = sqrt(18800. * hbarm0)
Ev          = 0.0
Ec          = -303.0 + 0.495 * T ** 2 / (11.0 + T)  # Eg of HgCdTe for x = 0
gamma1      = 4.1
gamma2      = 0.5
gamma3      = 1.3
F           = 0.0
kappa       = -0.4
ge          = 2.0
q           = 0.0
a           = 0.6462
strain_C1   = -3.83e3
strain_Dd   = 0e3
strain_Du   = 2.25e3
strain_Duprime = sqrt(0.75) * 2.08e3
exch_yNalpha   = 0.0
exch_yNbeta    = 0.0
diel_epsilon   = 20.8
delta_so    = 1.08e3
piezo_e14   = 0.035 * 1e18 * e_el  # from [Fortran]
bia_c       = -7.4
bia_b8p     = -106.46
bia_b8m     = -13.77
bia_b7      = -100.0

# On piezo_e14:
# [Fortran] A. Pfeuffer-Jeschke, E. G. Novik et al.
# See also:
# [Adachi] S. Adachi, "Properties of Semiconductor Alloys: Group-IV, III-V
# and II-VI Semiconductors" (book). This Ref. lists 0.029 C / m^2 for HgTe and
# 0.0335 C / m^2 for CdTe

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## CdTe, cadmium telluride
[CdTe]
compound    = CdTe
composition = 1, 1   
P           = sqrt(18800. * hbarm0)
Eg          = 1606.0 - 0.325 * T ** 2 / (78.7 + T)  # Eg of HgCdTe for x = 1
Eg0         = -303.0 + 0.495 * T ** 2 / (11.0 + T)  # Eg of HgCdTe for x = 0
Evoff       = -570. * (Eg - Eg0) / (1606 - -303)
Ev          = Evoff
Ec          = Evoff + Eg
gamma1      = 1.47
gamma2      = -0.28
gamma3      = 0.03
F           = -0.09
kappa       = -1.31
ge          = 2.0
q           = 0.0
a           = 0.6482
strain_C1   = -4.06e3
strain_Dd   = -0.7e3
strain_Du   = 1.755e3
strain_Duprime = sqrt(0.75) * 3.2e3
exch_yNalpha   = 0.0
exch_yNbeta    = 0.0
diel_epsilon   = 10.2
delta_so    = 0.91e3
piezo_e14   = 0.035 * 1e18 * e_el
bia_c       = -2.34
bia_b8p     = -224.1
bia_b8m     = -6.347
bia_b7      = -204.7

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## HgCdTe (Hg_{1-x} Cd_x Te), mercury cadmium telluride
[HgCdTe]
compound    = HgCdTe
linearmix   = HgTe,CdTe,x 
composition = 1 - x, x, 1  # is also set automatically by linearmix 
P           = sqrt(18800. * hbarm0)
Eg          = -303 * (1 - x) + 1606 * x - 132. * x * (1 - x) + \
              (0.495 * (1 - x) - 0.325 * x - 0.393 * x * (1 - x)) * T ** 2 / (11.0 * (1 - x) + 78.7 * x + T)  # identical to Ref. [HgCdTe2]
Eg0         = -303.0 + 0.495 * T ** 2 / (11.0 + T)
Evoff       = -570. * (Eg - Eg0) / (1606 - -303)
Ev          = Evoff
Ec          = Evoff + Eg
gamma1      = poly( 4.1, -2.8801,  0.3159, -0.0658, x)
gamma2      = poly( 0.5, -0.7175, -0.0790,  0.0165, x) 
gamma3      = poly( 1.3, -1.3325,  0.0790, -0.0165, x)
kappa       = poly(-0.4, -0.8475, -0.0790,  0.0165, x)
a           = 0.6462 + 0.0009 * x + 0.0017 * x**2 - 0.0006 * x**3

# The special parameter 'linearmix' defines all further material parameters (not
# specified explicitly here) by linear interpolation between HgTe and CdTe.

# More avanced dependencies of gap value Eg and band offset Evoff:
# See:
# [HgCdTe1] Laurenti et al., J. Appl. Phys. 67, 6454 (1990)
# [HgCdTe2] Becker, Latussek, Pfeuffer-Jeschke, Landwehr, and Molenkamp, Phys. Rev. B 62, 10353 (2000)

# Nonlinear interpolation of gamma1, gamma2, gamma3, kappa:
# These are approximations to the results from the Pfeuffer-Jeschke program
# [Fortran], with deviations smaller than 0.0003; these errors are negligible in
# practice.
# Details may be found in his thesis [PJ]. However, it is not explained why the
# band parameters F, G, and H2 are linearly interpolated, while H1 is
# inverse-linearly interpolated (i.e., H1^-1 is linearly interpolated).

# Lattice constant a is adapted from [Berding] and [Ames]. Note that these Refs.
# contain a typo (factor of ten).

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## HgMnTe (Hg_{1-x} Mn_x Te),
[HgMnTe]
compound    = HgMnTe
copy        = HgTe
composition = 1 - x, x, 1
Ec          = -303.0 + (4726. * 1339. / 1909.) * x
Ev          = 0.0 + (4726. * -570. / 1909.) * x
exch_yNalpha = 0.4e3 * x  # y * 400 meV; questionable value
exch_yNbeta  = -0.6e3 * x  # y * -600 meV; questionable value
exch_g      = 2
exch_TK0    = 2.6
a           = 0.6462 - 0.0114 * x  # [Furdyna]

# The special parameter 'copy' copies all further material parameters (not
# specified explicitly here) from HgTe.

## Gap ansatz:
## (1) linear approximation to matHgCdTe(2 * y); a rather crude approximation
# Ec = -303.0 + 2678. * x
# Ev = 0.0 - 1140. * x
## (2) Cubic fit from data sheet and assumption of 'proportional scaling' of Ec
## and Ev as function of the gap, namely:
# Eg = -303 + 6229 * x - 34600 * x**2 + 122000 * x**3
# Ec = -303 + (1339/1909) * (6229 * x - 34600 * x**2 + 122000 * x**3)
# Ev =    0 -  (570/1909) * (6229 * x - 34600 * x**2 + 122000 * x**3)
## (3) Linear fit from data sheet and assumption of 'proportional scaling' of Ec
## and Ev as function of the gap, namely:
# Eg = -303 + 4726 * x
# Ec = -303 + (1339/1909) * 4726 * x
# Ev =    0 -  (570/1909) * 4726 * x
#
# These values for HgMnTe are accurate in the low-doping regime only

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## CdZnTe (Cd_{1-x} Zn_x Te), cadmium zinc telluride (substrate)
[CdZnTe]
compound    = CdZnTe
copy        = CdTe
composition = 1 - x, x, 1
a           = 0.6482 - 0.0378 * x  # similar to [Berding]
# very crudely approximated
# only the lattice constant is reliable
# band parameters are taken from CdTe, but there is no justification

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## Va, vacuum (use default parameters)
## Large k = 0 band edges for valence and conduction bands
## The (bulk) Hamiltonian is diagonal, with dispersions
## E(k=0) +/- (hbar k)^2/2m  [set by F = 0 and gamma1 = 1]
[Va]
compound    = Va
Ev          = -1e6
Ec          = 1e6


# References:
# [Fortran] A. Pfeuffer-Jeschke, E. G. Novik et al., Fortran program "bsqw"
# [Adachi]  S. Adachi, "Properties of Semiconductor Alloys: Group-IV, III-V and II-VI Semiconductors" (book).
# [HgCdTe1] Laurenti et al., J. Appl. Phys. 67, 6454 (1990)
# [HgCdTe2] Becker, Latussek, Pfeuffer-Jeschke, Landwehr, and Molenkamp, Phys. Rev. B 62, 10353 (2000)
# [PJ]      A. Pfeuffer-Jeschke, PhD thesis, University of Würzburg (1999)
# [Berding] Berding et al., J. El. Mater. 29, 676 (2000)
# [Ames]    C. Ames, PhD thesis, University of Würzburg (2015)
# [Furdyna] J. K. Furdyna, J. Appl. Phys. 84, R29 (1988)

