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LAMPIRAN

Lampiran 1 File perhitungan struktur pita elektronik dan DOS graphene #PERHITUNGAN STRUKTUR PITA ELEKTRONIK & DOS MATERIAL

GRAPHENE (ILHAM MASHORI)

from pythtb import * %matplotlib inline

# lattice vectors and orbital positions lat=[[1.0, 0.0], [0.5, np.sqrt(3.0)/2.0]] orb=[[1./3., 1./3.], [2./3., 2./3.]]

# two-dimensional Thigt-Binding model gra=tb_model(2, 2, lat, orb)

# set model parameters delta=0.0

t=1.0

# define hopping between orbitals gra.set_onsite([-delta,delta]) gra.set_hop(t, 0, 1, [ 0, 0]) gra.set_hop(t, 1, 0, [ 1, 0]) gra.set_hop(t, 1, 0, [ 0, 1])

# solve model on a path in k-space

k=[[0.0, 0.0],[1./3., 2./3.],[0.5,0.5],[0.0, 0.0]] (k_vec,k_dist,k_node)=gra.k_path(k, 100) evals=gra.solve_all(k_vec) # plot bandstructure import matplotlib.pyplot as plt fig, ax = plt.subplots() plt.hlines(0,0,2,color='r',linestyle='--') ax.plot(k_dist,evals[0,:],linewidth=2) ax.plot(k_dist,evals[1,:],linewidth=2) ax.set_xticks(k_node) ax.set_xticklabels(["$\Gamma$","K","M","$\Gamma$"])

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ax.set_xlim(k_node[0],k_node[-1]) # add vertical lines at node positions for n in range(len(k_node)): ax.axvline(x=k_node[n],linewidth=0.5, color='k') # put title ax.set_xlabel("Path in K-Space") ax.set_ylabel("Band Energy") fig.savefig("bandsgraphene.png") print() print('---') print('starting DOS calculation')

print('---') print('Calculating DOS...')

# calculate density of states

# first solve the model on a mesh and return all energies kmesh=59

kpts=[]

for i in range(kmesh): for j in range(kmesh):

kpts.append([float(i)/float(kmesh),float(j)/float(kmesh)]) # solve the model on this mesh

evals=gra.solve_all(kpts) # flatten completely the matrix evals=evals.flatten()

print (kmesh) # plotting DOS

print('Plotting DOS...') # now plot density of states fig, ax = plt.subplots()

counts,bins,bars = ax.hist(evals,200,range=(-4.,4.)) print(counts)

print(len(counts)) print(bins) print(len(bins)) print(bars) ax.set_ylim(0.0,140.0) # put title

ax.set_title("Graphene model density of states") ax.set_xlabel("Band energy")

ax.set_ylabel("Number of states") # make an PDF figure of a plot fig.tight_layout()

fig.savefig("Graphene_dos.pdf") print('Done.\n')

#Grafik Garis DOS

# MEMBUAT GRAFIK GARIS PADA DOS GRAPHENE y=( 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 37., 48., 36., 30., 48., 42., 30., 42., 48., 36., 42., 36., 42., 42., 36., 54., 36., 60., 24., 66., 36., 54., 30., 72., 42., 30., 60., 30., 72., 30., 66., 48., 42., 72., 36., 60., 60., 30., 84., 48., 72., 60., 54., 96., 54., 48., 108., 60., 126., 96., 96., 120., 48., 102., 36., 42., 78., 24., 30., 60., 12., 48., 12., 24., 36., 18., 30., 0., 12., 18., 12., 6., 0., 6., 0., 0, 0., 6., 0., 6., 12., 18., 12., 0., 30., 18., 36., 24., 12., 48., 12., 60., 30., 24., 78., 42., 36., 102., 48., 120., 96., 96., 126., 60., 108., 48., 54., 96., 54., 60., 72., 48., 84., 30., 60., 60., 36., 72., 42., 48., 66., 30., 72., 30., 60., 30., 42., 72., 30., 54., 36., 66., 24., 60., 36., 54., 36., 42., 42., 36., 42., 36., 48., 42., 30., 42., 48., 30., 36., 48., 36., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.) print(len(y)) x=(-4., -3.96, -3.92, -3.88, -3.84, -3.8, -3.76, -3.72, -3.68, -3.64, -3.6, -3.56, -3.52, -3.48, -3.44, -3.4, -3.36, -3.32, -3.28, -3.24, -3.2, -3.16, -3.12, -3.08, -3.04, -3., -2.96, -2.92, -2.88, -2.84, -2.8, -2.76, -2.72, -2.68, -2.64, -2.6 , -2.56, -2.52, -2.48, -2.44, -2.4, -2.36, -2.32, -2.28 ,-2.24, -2.2, -2.16, -2.12, -2.08, -2.04, -2., -1.96, -1.92, -1.88, -1.84, -1.8, -1.76, -1.72, -1.68, -1.64,

50 -1.6, -1.56, -1.52 ,-1.48, -1.44, -1.4, -1.36, -1.32, -1.28, -1.24, -1.2, -1.16, -1.12, -1.08 ,-1.04, -1., -0.96, -0.92, -0.88, -0.84, -0.8, -0.76, -0.72, -0.68, -0.64, -0.6, -0.56, -0.52, -0.48, -0.44, -0.4, -0.36, -0.32, -0.28, -0.24, -0.2, -0.16, -0.12, -0.08, -0.04, 0., 0.04, 0.08, 0.12, 0.16, 0.2, 0.24, 0.28, 0.32, 0.36, 0.4, 0.44, 0.48, 0.52, 0.56, 0.6, 0.64, 0.68, 0.72, 0.76, 0.8, 0.84, 0.88, 0.92, 0.96, 1., 1.04, 1.08, 1.12, 1.16, 1.2, 1.24, 1.28, 1.32, 1.36, 1.4, 1.44, 1.48, 1.52, 1.56, 1.6, 1.64, 1.68, 1.72, 1.76, 1.8, 1.84, 1.88, 1.92, 1.96, 2., 2.04, 2.08, 2.12, 2.16, 2.2, 2.24, 2.28, 2.32, 2.36, 2.4, 2.44, 2.48, 2.52, 2.56, 2.6, 2.64, 2.68, 2.72, 2.76, 2.8, 2.84, 2.88, 2.92, 2.96, 3., 3.04, 3.08, 3.12, 3.16, 3.2, 3.24, 3.28, 3.32, 3.36, 3.4, 3.44, 3.48, 3.52 , 3.56, 3.6, 3.64, 3.68, 3.72, 3.76, 3.8, 3.84, 3.88, 3.92, 3.96, 4. ) print(len(x))

# now plot density of states import matplotlib.pyplot as plt

from scipy.interpolate import splrep,splev fig, ax = plt.subplots()

# put title

ax.set_xlabel("Energy (eV)")

ax.set_ylabel("Density of States (1 / eV)") plt.text(0.1,113,"μ") plt.vlines(0,0,115,color='r',linestyle='--') ax.set_ylim(0,120.0) bspl = splrep(x,y,s=40000) bspl_y = splev(x,bspl) plt.plot(x,bspl_y) plt.show()

# make an PDF figure of a plot fig.tight_layout()

fig.savefig("GrapheneDOS.png") print('Done.\n')

Lampiran 2 File perhitungan karakteristik termoelektrik graphene #PERHITUNGAN KARAKTERISTIK TERMOELEKTRIK GRAPHENE

from __future__ import division from scipy import integrate import numpy as np mu = 6.835937499999999e-5 T = 200.0 * 8.621738e-5 v = 1e+6 tau = 1e-14 E = xE q = 1

dfermi = -np.exp((E - mu)/(T))/(T*(np.exp((E - mu)/(T)) + 1)**2) L = []

for i in range (3) :

func = tau * v**2 * yDOS * -dfermi * (E - mu)**i j = integrate.trapz(func, E) print('L','(',i,')',' = ', j) L.append(j) L = np.array(L) #rumus seebeck S = L[1]/(q*T*L[0]) print('Seebeck Coef = ',S) #termal konduktivitas kappa_e=(L[2]-(L[1]**2/L[0]))*(1/T) print('kappa_e = ',kappa_e) sigma=(L[2]-kappa_e*T)/((S**2)*(T**2)) print('sigma = ',sigma) ZT= ((((S**2)*sigma)/kappa_e)*T) print('Figure of Merit=',ZT)

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Lampiran 3 File grafik karakteristik termoelektrik graphene

#PERHITUNGAN SEEBECK, Konduktivitas Termal, Konduktansi Listrik, dan ZT import numpy as np xx=([200,250,300,350,400,450,500,550,600,650,700,750,800,850,900]) yy=([0.0143230628745862,0.00853330768546766,0.0056082557742676035, 0.00402863134491746,0.003134893511013128,0.00260147124636047, 0.0022588286543981755,0.00201822841924204,0.0018340463134383447, 0.00168333013468192,0.0015546494030743577,0.00144220067675734, 0.0013428255964603951,0.00125457233456609,0.0011760356031282437]) # now plot density of states

import matplotlib.pyplot as plt

from scipy.interpolate import splrep,splev fig, ax = plt.subplots() # put title ax.set_xlabel("Temperatur (K)") ax.set_ylabel("S (μV/K)") ax.set_ylim(0,0.016) ax.set_xlim(0,900) plt.plot(xx,yy,linewidth=2.5,color='g',marker='o') plt.show()

# make an PDF figure of a plot fig.tight_layout()

fig.savefig("seebeck.png") print('Done.\n')