import pylab as pl from NL.CommonConcepts.Configurations.Utilities import fractional2cartesian #------------------------------------------------------------------------- # Model data #------------------------------------------------------------------------- # alpha parameter fitted to bulk InAs alpha_bulk = 2.869 # InAs bulk conduction band effective mass meff_bulk = 0.028*electron_mass # Effective widths of nanowire Dx = 30*Angstrom Dz = 30*Angstrom #------------------------------------------------------------------------- # Load DFT calcularted bandstructure and effective mass #------------------------------------------------------------------------- filename = 'InAs_nanowire.nc' # Read bulk configuration configuration = nlread(filename,BulkConfiguration)[0] # Read bandstructure bandstructure = nlread(filename,Bandstructure)[-1] # Read Effective mass effective_mass = nlread(filename,EffectiveMass)[0] meff = effective_mass.evaluate(band=1)[0][0][0] # Get the fractional kpoints kpoints = bandstructure.kpoints() # Get reciprocal lattice vectors (used to convert frational k to cartesian k) G = configuration.bravaisLattice().reciprocalVectors() # K-points in cartesian coordinates, Ang^-1 k_cart = fractional2cartesian(kpoints, G) # Get |k| as 1D array k = numpy.zeros(len(kpoints)) for ii,ki in enumerate(k_cart.inUnitsOf(Angstrom**-1)): k[ii] = (ki[0]**2 + ki[1]**2 + ki[2]**2)**0.5 # Add unit k = k*Angstrom**-1 # Get all the bands bands = bandstructure.evaluate().inUnitsOf(eV) # Energies at the Gamma-point E0 = bands[0,:] # Index of conduction band conduction_band_index = numpy.where(E0 > 0.0)[0][0] # Get the energies of the conduction band conduction_band = bands[:,conduction_band_index] # conduction band minimum cbm = min(conduction_band) # Evaluate non-parabolic model bandstructure E_non_parabolic = (-1 + (1 + 2*alpha_bulk*(hbar**2/meff_bulk*(k**2 + numpy.pi**2/(Dx)**2 + numpy.pi**2/(Dz)**2 ) ).inUnitsOf(eV) )**0.5 )/(2*alpha_bulk) # Align conduction band minimum to DFT E_non_parabolic = E_non_parabolic - min(E_non_parabolic) + cbm # Evaluate parabolic model bandstructure and align CBM E_parabolic = (0.5*hbar**2*k**2/meff_bulk).inUnitsOf(eV) + cbm # Ananlytical effective mass of slab m_slab = meff_bulk * (1 + 2*alpha_bulk*(hbar**2*numpy.pi**2/(meff_bulk)*(1/Dx**2 + 1/Dz**2 ) ).inUnitsOf(eV) )**0.5 print '' print 'Analytical nanowire mass = %.4f m_e' %m_slab.inUnitsOf(electron_mass) print 'DFT nanowire mass = %.4f m_e\n' %meff # Analytical band gap increase delta_gap = (-1 + (1 + 2*alpha_bulk*(hbar**2*numpy.pi**2/(meff_bulk)*(1/Dx**2 + 1/Dz**2 ) ).inUnitsOf(eV) )**0.5)/(2*alpha_bulk) print 'Analytical band gap increase = %.4f eV' %delta_gap print 'DFT gap change = %.4f eV' %(1.548-0.354) print '' pl.figure() pl.plot(k,conduction_band,'k',label='DFT conduction bands') pl.plot(k,bands[:,conduction_band_index+1:conduction_band_index+5],'k') pl.plot(k,E_non_parabolic,'r',label='Non-parabolic fit ') pl.plot(k,E_parabolic,'b',label='Parabolic fit') pl.xlabel('k (Ang.$^{-1}$)') pl.ylabel('Energy (eV)') pl.ylim([0,1.5]) pl.legend(loc=0)