def calc_conductance(energies,transmission,temperature=300*Kelvin,mu=0*eV): """ Calculates the conductance for a given transmission. """ energies = energies.inUnitsOf(eV) mu = mu.inUnitsOf(eV) beta = 1/(temperature*boltzmann_constant).inUnitsOf(eV) arg = (energies-mu)*beta arg = numpy.where(arg > 50.0, 50.0, arg) dFdE = beta*numpy.exp(arg)/(numpy.exp(arg) + 1)**2 G = numpy.trapz(transmission*dFdE,energies) return G*2*elementary_charge**2/planck_constant #*******************************************************************# # # # USER DEFINED PARAMETERS # # # #*******************************************************************# #------------------------ # # DOPING # #------------------------ # # List of doping densities corresponding to the input file above # doping_densities = [1e14,1e15,1e16,1e17,1e18,1e19,1e20,1e21] # # Number of Si atoms in unit cell # nua0 = 48 # # Length of unit cell in z-direction # Lz = 5.431*Angstrom # # Volume of each atom in a bulk Si crystal # atom_volume = 0.5*40.039*Angstrom**3 # #------------------------ # # HDF5 FILES # #------------------------ # # Files with band structures for the doping levels in above list # doping_files = [ # 'sinw_doping_1e+14.hdf5', # 'sinw_doping_1e+15.hdf5', # 'sinw_doping_1e+16.hdf5', # 'sinw_doping_1e+17.hdf5', # 'sinw_doping_1e+18.hdf5', # 'sinw_doping_1e+19.hdf5', # 'sinw_doping_1e+20.hdf5', # 'sinw_doping_1e+21.hdf5', # ] # #------------------------ # # DATA FILE TO LOAD # #------------------------ # # File for saving calculated data for later analysis # loadfile = 'sinw.pckl' # # PNG or PDF file with plot # pngfile = 'mobility.png' # #------------------------ # # MOBILITY # #------------------------ # # Set a nanowire length of 1 micron # L = 10000*Angstrom # # Set the temperature # temperature = 300*Kelvin # # Conduction band index # conduction_band_index = 113 # # # #*******************************************************************# # # # NO CHANGES NEEDED BELOW # # # #*******************************************************************# #==================================================================== # Consistency check #==================================================================== if not len(doping_densities) == len(doping_files): raise Error("The number of specified doping levels does not match the number of specified band structure files.") #==================================================================== # Load previously saved data #==================================================================== import pickle f = open(loadfile, 'r') (E,Ec0,T0,T_doped,Tave,Rc,Rave,Rs) = pickle.load(f) f.close() #==================================================================== # Calculate mobility and conductance vs doping concentration #==================================================================== # Volume of one Si atom in units of cm^3 atom_volume_cm = atom_volume.inUnitsOf(Units.cm**3) # Cross sectional Area A = nua0*atom_volume/Lz # Lists of mobilities and conductances mobilities = [] mobilities_pristine = [] conductances = [] conductances_pristine = [] # Loop over doping densities for doping_density,doping_file in zip(doping_densities,doping_files): # Load band structure for given doping density bandstructure = nlread(doping_file, Bandstructure)[-1] bands = bandstructure.evaluate().inUnitsOf(eV) # Fermi level relative to conduction band edge fermi_level = -bands[0,conduction_band_index] # Calculate conduction band electron density Ne = doping_density*atom_volume_cm*nua0 # Charge density n = (charge in one unit cell)/(length of unit cell) n = Ne/Lz # Average distance between two dopant atoms dopant_distance = 1.0/(doping_density * atom_volume_cm * nua0)*Lz # Resistance (in units of h/(2e^2) ) of a wire with lenght L R_L = Rs*float(L/dopant_distance) + Rc # Transmision of wire with length L T = 1/(R_L) # Conductance of wire with length L conductance = calc_conductance(E*eV,T,temperature=temperature,mu=(Ec0+fermi_level)*eV) # Conductivity of wire with length L conductivity = conductance*L # Conductance of pristine wire conductance_pristine = calc_conductance(E*eV,T0,temperature=temperature,mu=(Ec0+fermi_level)*eV) # Conductivity of pristine wire with length L conductivity_pristine = conductance_pristine*L # Mobility mu = sigma/(e*n) of wire with length L with defects mobility = (conductivity/(1*elementary_charge*n)).inUnitsOf(Meter**2/(Volt*Second))*10**4 # Mobility of pristine wire mobility_pristine = (conductivity_pristine/(1*elementary_charge*n)).inUnitsOf(Meter**2/(Volt*Second))*10**4 # Save conductances and mobilities in lists mobilities.append(mobility) mobilities_pristine.append(mobility_pristine) conductances.append(conductance.inUnitsOf(G0)) conductances_pristine.append(conductance_pristine.inUnitsOf(G0)) #==================================================================== # Plotting results #==================================================================== import matplotlib.pyplot as plt fig = plt.figure(figsize=(6,7)) ax1 = fig.add_subplot(211) ax2 = fig.add_subplot(212, sharex=ax1) # Plot mobilities ax1.plot(doping_densities,mobilities,'ro-',ms=8,label='Dopant scattering') ax1.plot(doping_densities,mobilities_pristine,'ks-',ms=8,label='Pristine') ax1.set_xscale('log') ax1.set_yscale('log') ax1.set_ylabel(r'Mobility ($cm^2/(Vs)$)') ax1.set_xscale('log') ax1.set_yscale('log') ax1.legend(loc=3) # Plot conductances ax2.plot(doping_densities,conductances ,'ro-',ms=8,label='Dopant scattering') ax2.plot(doping_densities,conductances_pristine,'ks-',ms=8,label='Pristine') ax2.set_xlabel(r'Doping density ($cm^{-3}$)') ax2.set_ylabel(r'Conductance ($2e^2/h$)') ax2.set_yscale('log') # Finalize figure plt.tight_layout() plt.savefig(pngfile) plt.show()