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Fall04_Test1_important

Fall04_Test1_important - oftbs{ree electron Drats We begin...

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ECE 352 - Fall 2004 Test 1 Solutions ,,/ september 24' 2004 .L A particulor quanhon system is charccterized by a wtne fxnclion )ith the / follov'btgfom: *t*' -{'t'-"'' ;'l ' '' ' Io' 'rl I Erolaate A, and then determine b.Ap. We first evaluate A as ,-lr;4{r-")t,t'=nt }(, ,,,'*,,.oh=* u' =, a=S . -t-t" Now, <ir> = 0 b€cause of the qmuelv alt!9rry3yq4uqiqL atrt?a- 0 because the wave functi,ol is real. Then, .- L , 1,21 ts i,z (, _ r,: ,r!,_I. , , r6i 1 .- | ,).. ) .- | (pr\_ n,ll k, ,r,o-,' ,,-)d,_ hr,.l l1r ,r 11 z1ar \' / 16,, dxt 16 i ."15q 5h2 -h- " 83 2' and *=1. ^t7 n, = "11a. ' v2 This gives a"a, - "f1 - o.or, . . -'- \rq' - ,/ Find the fu Broglie wavelength of an electon in a semiconductor having kiietic ./ energtof0-15 eV, andamasswhichisI0
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Unformatted text preview: oftbs{ree electron Drats. We begin by finding the momentum: \\ 'h\r, ,r\ p -.'lzmE -\12.0.1.e.| .l0-''.0.l5 I.6vl0-'' = 6.61xl0-26 kg.m/ s, Then 6.626 x 10 la = 70nm . 6.61v l0 " Contider a potential tunneling barrier, vhose height is 0.3 ey and thickness is 2.0 nm. If the incidenr nve enetg) is 0.I5 eV, and the effectite mafiEt2tfa what is the transmission coefrcient? z=h = p E(k';;')' "t,h'(d) Vk- o. t-,t h,*'i x,"-f 2' We fi|st evaluate the Darameters as: = 8.86x108 , ,rrlv A f z.o.z.l.t"to-3r.0.t5.1.6x10-1e = 8.86x 108 tt ^<ra - t^-34 ,2 . E^E lzh).s.t'to 3r .0.rs.r.o,l0 Io li l'z 1/ o.os+o , to ra )z t ,/ " ^ \1-l r-[+sinh"\8.86' l0' 2. I0--]J =0.ll...
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