ECE495N-F08-HW_8_solution

# ECE495N-F08-HW_8_sol - HW_8_solution Problem 1(a-Transmission 2 ° Eigenvalues I O 0 0:5 1 15 Transmission-—>(b 0 0:5 1 Transmission-—>(C

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Unformatted text preview: HW_8_solution Problem 1 (a) -Transmission 2 ° Eigenvalues I O 0 0:5 1 15 Transmission -—-> (b) 0 0:5 1 Transmission -—-> (C) Problem 1: % 1D transmission clear all g=l;zplus=i*1e-12;Np=5;to=l; H=—t0*diag(ones(l,Np—1),l)—t0*diag(ones(1,Np—1),—1); L=diag([l zeros(l,Np~1)]);R=diag([zeros(1,Np—1) 1]); ii=l;dE=0.0025;for EE=-2.5:dE:+2.5 %sig=—i*0.5*g; ck=—(EE+zplus)/(2*t0);ka=acos(ck);sig=-t0*exp(i*ka); sigl=sig*L;sig2=sig*R; gam1=i*(sigl—sigl');gam2=i*(sig2—sig2'); G=inv(((EE+zplus)*eye(Np))—H—sigl—si92); A=i*(G-G');Dl(ii)=A(l,1);D2(ii)=A(2,2); TM(ii)=real(trace(gam1*G*gam2*G'))i E(ii)=EE;ii=ii+1; end [V,D]=eig(H);diag(D); X=1.05*ones(l,Np); hold on h=plot(TM,E,'r'); set(h,'linewidth',[2.0]) %h=plot(X,diag(D),'rx'); %Set(h,'linewidth',[4.01) %h=plot(X,diag(D),'bo'); set(gca,'Fontsize',[36]) x1abel(' Transmission ———> W ylabel(' Energy ( eV ) ~~~> ‘) grid on (C) H E G \\ Ana‘yt’fcoxl [o] — 3.1; cc: [ca €X¥W\$ST¢I1 2‘ = Z}: VIE) f5 V" Hag +Mn\$ngsTmﬂ (taleV) EEK,“ H" :‘—.:2,-]’| [E-O+é~‘co \ 1-!- +0 CT"! k& “=0 e 1 (using E =—L+°Ccs lta T15 E. virusvnlcox~ A - *3- 5 lev ) Problem 2 (a) (C) o analytical —numerica| .----.....u.._..---........— 0.5 1 Transmission ---> o 6 10 transmission clear all zplus=i*le—12;Np=50;t0=1; H=—t0*diag(ones(1,Np—1),1)—t0*diag(ones(1,Np—l),—1); L=diag([1 zeros(1,Np—1)]);R=diag([zeros(1,Np—1) 1]); H(25,25)=2; ii=1;dE=0.0025;for EE=~2:dE:+2 %sig=—i*0.5*g; Ck=—(EE+zp1us)/(2*t0);ka=acos(ck);sig=—t0*exp(i*ka); T(ii)=rea1(1/(1+(H(25,25)/2/tO/sin(ka))AZ)); sigl=sig*L;sigz=sig*R; gam1=i*(sig1-sigl');gam2=i*(sigZ—sigz'); G=inv(((EE+zplus)*eye(Np))—H—sigl—sigz); Gn=G*gam1*G'; A=i*(G—G');D=real(diag(A))./2/pi;n=real(diag(Gn))./2/pi; TM(ii)=real(trace(gam1*G*gam2*G')); E(ii)=EE;ii=ii+1; end hold on h=plot(T,E,'ro'); h=plot(TM,E,'b'); set(h,'linewidth',[4.0]) set(gca,'Fontsize',[36]) ylabel(' Energy (eV) ———> ') xlabel(' Transmission -——> ') grid on C Aﬂod Wisp-2.: gﬁm ‘ eXFres sTon z, 1’ Y2 -.= V15) “LI ‘1‘ 3-7";ng Ltirzfj 9‘"; gﬁ‘l k“ T —= Tm, E v. arm“: -— “g ‘i .n H 7,1,0 6’!!! k“ er’ybﬂ i —' LI g‘EﬂkM 2— (Zfo 67" k“) u’+ (new H )z .— .— 231}, 57” k“ gr “We. ‘h‘ﬂnSVhTSSTOTL [*tejkaj (ﬁr/12V, U21QV) (’hf —2.’:E: é-LeV): ( ,U-— 7:: h S‘fn Lox Problem 3 —NEGF Semi-classical Problem 3: % 1D Quasi—Fermi level clear all g=1; zplus=i*le-12 ;Np=50 ,'t0=1; H=-t0*diag(ones(1,Np-1),1)—t0*diag(ones(1,Np—1),—1); L=diag([1 zeros(1,Np—l)]);R=diag([zeros(1,Np—l) 1]); H(25,25)=2; EE=-1; %sig=—i*0.5*g; ck=—(EE+zplus)/(2*t0);ka=acos(ck);sig=—t0*exp(i*ka); sigl=sig*L;sig2=sig*R; gam1=i*(sig1-sigl');gam2=i*(sigZ—si92'); G=inv(((EE+zplus)*eye(Np))—H—sig1—sig2); Gn=G*gaml*G'; A=i*(G—G');D=real(diag(A))./2/pi;n=real(diag(Gn))./2/pi; TM=real(trace(gam1*G*gam2*G')); V=[(1—TM/2)*ones(l,25) (TM/2)*ones(l,25)]; hold on h=plot(n./D,'b'); h=plot(V,'r'); set(h,‘linewidth‘,[2.0]) set(gca,'Fontsize',[36]) ylabel(' F —-—> H xlabel(' Point # ———> ') grid on ...
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## This note was uploaded on 12/30/2010 for the course ECE 495N taught by Professor S.datta during the Spring '08 term at Indiana University-Purdue University Fort Wayne.

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ECE495N-F08-HW_8_sol - HW_8_solution Problem 1(a-Transmission 2 ° Eigenvalues I O 0 0:5 1 15 Transmission-—>(b 0 0:5 1 Transmission-—>(C

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