Tight Binding program to compute the band structure of simple semiconductors.

Parameters taken from Vogl, Hjalmarson and Dow, A Semiempirical Tight-Binding Theory of the Electronic Structure of Semiconductors, J. Phys. Chem. Sol. 44 (5), pp 365-378 (1983).



In [1]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from numpy.linalg import eigvalsh
from collections import namedtuple

import TB



In [2]:

    
TB.band(TB.Si)



In [3]:

    
TB.band(TB.GaAs)



In [4]:

    
TB.band(TB.Ge)

Interpolated SiGe band structure

The band structure for Si(1-x)Ge(x) is supposedly well approximated by a linear interpolation of the Si and Ge band structures.



In [15]:

    
def SiGe_band(x=0.2):
    Si_data = TB.bandpts(TB.Si)
    Ge_data = TB.bandpts(TB.Ge)
    data = (1-x)*Si_data + x*Ge_data
    TB.bandplt("SiGe, %%Ge=%.2f" % x,data)
    return



In [16]:

    
SiGe_band(0)



In [9]:

    
SiGe_band(0.1)



In [10]:

    
SiGe_band(0.25)



In [11]:

    
SiGe_band(0.37)

Plotting misc parts of Brillouin zones

Compare Si and Ge CBs.



In [12]:

    
Ge_CB = TB.bandpts(TB.Ge)[:,4]
Si_CB = TB.bandpts(TB.Si)[:,4]

nk = len(Si_CB)
n = (nk-2)//3

plt.plot(Si_CB)
plt.plot(Ge_CB)
TB.band_labels(n)
plt.axis(xmax=3*n+1)









    Out[12]:





(0.0, 76, 0.5, 3.5)



In [13]:

    
plt.plot(Si_CB,label='Si')
plt.plot(Ge_CB,label='Ge')
plt.plot(0.9*Si_CB + 0.1*Ge_CB,label='Si_0.9 Ge_0.1')
TB.band_labels(n)
plt.axis(xmax=3*n+1)
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)









    Out[13]:





<matplotlib.legend.Legend at 0x10fd53b50>



In [14]:

    
min_Si = min(Si_CB)
min_Ge = min(Ge_CB)
print min_Si, min_Ge
# min_Si - min_Ge = 0.12
Si_CB_shifted = Si_CB - min_Si + min_Ge + 0.12









    



1.17218123643 0.764866886075



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