\ ~ll C tll' 나 I C:\..Ll \.l ll~.
" 11 <.l l I~ \..V VaJelH oonct1ng?
. ·~ u 』 '-- C -.. rH )w in g the
~. \\?hat is 1neant by a subst1tut1onal impur ity in a crysta l? What i
s meant bY an 1nter
impun ty >.
~titi al
6. \\'hat i~ 1neant by epitax ial growt h?
7. \\~hy dt)eS the thenn al oxida t1on of silico n occur at the Si- SiO
o,id~ ha~ formed'?
2 interface even after an
PROBLElVIS
Section 1.3
Spac e Latt ices
1.1
Oeten nine the nurnb er ot ato1ns per unit cell in a (a) face-c entere d cubic
, (h) bo<l ycenter ed cubic . and (c) dian1 ond lattice .
1.1
The lattice const ant of GaAs is 5.65 A. Deter mine the numb er of Ga atom~
and A'>
atnm~ per cnr~.
1.3
Deten nine the volut ne densi ty of germa nium atoms in a germa nium semi
condu ctor
The lattice const ant of genna nium is 5.65 A.
W
Assu1ne tl1at each aton1 is a hard spher e with the surfac e of each atom in
contac t with
the surfac e of its neare st neigh bor. Deter mine the perce ntage of total un
it cell volu me
tl1at is occup ied in (a) a simpl e cubic lattice , (b) a face-c entere d cubi c latti
ce. (cJ a
body- cente red cubic lattice , and (d) a diamo nd lattice .
Consi der GaAs . What is the distan ce (cente r-to-c enter) betwe en neares t Ga
and A'i atom 、
1.5
1.6
)
A 1naterial. with a volum e of 1 cm3, is comp osed of an fcc lattice with a
lattice con'itan t
of 2.5 n1.n1. The .. atoms " in this mater ial are actual ly coffee bean s. Assum
e the coffee
氐미1s are hard spher es with each bean touch ing its neare st nei
ghbor. Determi ne the
Yolmne of coffee after the coffee beans have been groun d. (Ass ume 100
percent packing
densit y of the groun d coffee .)
땄\ lf the l aruce const ant of silico n is 5.43 A , calcu late (a) the di stance fro
m the center 1)I
one sibco n ato1n to the cente r of its neare st neigh bor, (b) the numb er de
nsit: ol . . ilicl 비
J.ton1s ( #/cm3 ), and (c) the mass densi ty (gram s/cm3) of silicon.
1.8 A c~ ·stal is comp osed of two eleme nts, A and B. The
basic cry stal stru cture j.., '1 1,ll.:、 L도
center ed cubic with eleme nt A at each of the come rs and eleme nt B in the face plJnt' .
The effect i ve radius of eleme nt A is 1.02 A. Assum e the eleme nts arc harJ :,.,phcrc.., \\. ith
the surfac e of each A-typ e atom in conta ct with the surfac e of it s n carc \ t) pc n~igh납 r bor. Calcu late (a ) the n1axi1nu1n radius of the B-typ e atom thal will fit
into thi~ 、 tru e ture 미1 d (b) the volum e densi ty (#/en갑) of both A-typ e atoms and B-typ
c atom~ .
1.22 J)ctc nnin c th e dcn"l it y of va lcnc.:c clc<.: tn ,n ~ in
~,i l v<;.r. A \'-tUrn<.; <,il vcr i\ ,, , ,mpl,:,, ciJhic
~ tt1..1 c t urc .
1.23 Detern1in c the ~n glc between the tctr<1hC<.Jral
h<,rid \ of <.1 ~ilic<,n lattic..c.
Section 1.S
Imp erfe ctio ns and Imp uri ties in Solids
1.24 (a) If 4 Y I 01 6 ar~enic at<>m s per cm 'i arc adde
d t<, intrin 이 c c., ilicon a<.. a c., uh~titutionat
imp urity, determine wha t percentage of the sjjicon
atom ~ are di ~pla.ced in the ,ing lc
cry~tal lattice . (h) Repeat part (a) if 2 / ) 0 15 boron
atom ~ per cm are added t<J
intri n sic ~i licon .
(a) Pho spho ru s atom s at a concentration o f 5 x 1016 cm
· , arc added lfJ a purt: samp,e
of intri n sic silicon. Assume the pho sphorus at<Jm ~
are di ~tri·buted homogcncou~ly
thro ugh out the silic on sample. Wha t i~ the fraction
by weig ht of ph o\ph oru \'! ,h , l f
boro n atom ~, at a concentration of 101x cm - 3,. are
added to the mater1al in part {aJ.
determine the frac tion by weig ht of boron.
1.26 If 2 x 101 5 gold atom s per cm :, are added to intri
nsic ~iJ icon a~ a <., ub<.,ti tutional
imp urity and are di strib uted unif orm ly thro ugh out
the ~cm icon duc tor, determine: ll~c
di stance between gold atoms in term s of the silic on
latti ce con~tant. ( A~~u mc the
gold atom s are dist ribu ted in a rect ang ular or cub
ic array. )
I
RE AD IN G 1-'IST
1. AzaroJJ , L . V. , and J. J. Bro phy. Elec tron ic Processe
s
Mc( :iraw -Hi JJ , 1963 .
in Mat eriu /, . Nt. . \\ Yl)r\.. :
2. CampbeJJ , S. A. The Sf'ience and /:,'nRin<'erin R
ofM icro r l,·ct roni c Fuh ricollc>ll.
New York: ()xf ord U nivc r~ity Pre~~ , 1996 .