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I -^ I
largest Eg^ :^ 2ns^ ,^ 3.6^ EV
i - 24
a =^ -^ =^ o^ - 3441M
smallest Eg :^ In^ Sb^ ,^ o^
- 24
d--^ -^ =^ 6.89mm
O' 18
Al 's (^) Eg 2 corresponding
Ga compounds Eg > the corresponding
In compounds
Eg. I - 2 Nearest atom (^) are at (^) separation :^ I×J5t5t# = 4- 330ft
Radius of each atom =^ IX^ 4- 330ft^ =^2.^ 165ft
Volume of each^ atom :^ ¥ IT^ (^2 -^16573 =^42 -^ 5A^ 's Number of atoms^ per cube :^ it 8 ×+8= Packing fraction^ : 42-5× 21533
Maximum (^) packing fraction :^ 68% (^) #
- (^3)
a) x Y Z^ b^ ) X^ Y 2
(^6 4 3 )^ ( z i^ 2)
' '^4 # of atoms in (^) unit (^) cell as (^) =(8x¥g ) -11= £3 =^ I^ -^6 X^ 1022am
x 10-7^ cm I^5 Area of Clio^ )^ plane =^ (^ a^ JI^ ) a =^ JI ( (^25) )
of (^) atoms =^ It^ (4×4) =^2
Density =^2
o -^2
JJ (^25 )
16
= oc7o7n2XlO#
=^ 5.6×^10
" (^) " cm ' ' 25 Nearest (^) neighbour atoms (^) along (^) body diagonal : (^) Tay 2 Radius :^ TJ
9 =^ 2-17 (^) Ao l - 5
Densities of^ Si^ ,^ GaAs
si :^ a^ =^ 5.43×10-8^ cm (^) , (^8) atoms 1 cell 8 8
=
= 5 - lo " cm
density i5.1022cm-3.28.IO/m#=2.33g/cm 602 × 1023 mo f
Volume of^ unit cell =^ as^ =^ (^125 )A3^ =^ 1.25×10-22^ cm^
3
Number of^ atoms^ tanit^ cell^ =^ 8kg^ )^ -161^ 's)^4
Volume density =
,,z¥
atoms 1cm^ 's
= (^312) × (^1022) atoms 1cm (^).
- 8 BEES
-••⑥EB
- T•⑧⑧ ' 111 ' ' (^) l l (^) l (^) l
¥*o¥¥,
? .^.
• ⑧OI -^ - -0*80 -^ -^ -^ -^ - Ao⑧@
/
(l^ l^ O^ )
I - 9) •• • •^ • O O^ OJSC lattice
%.la#ini.::i:te.dne
Of the^ front shaded point
O O O
I - 10
a) fcc lattice a =^ 5.34A
number of (^) atoms (^) per ( 100 )^ surface =^ 4.^ Tt^ +^ I^ =^2 atoms atoms (^) per (^100 )^ surface (^) area = 2- = 6.78× (^1014) cm^ '
( 534AM
b) nearest neighbour distance in Inp
Fifita
ta lattice with a =^5 -^87
nearest : 12.52 =^ 5.87ft (^). 52 2
= 4-15 Ao
" " 7 NaCl density
Nat : atomic. weight 23 glmol , radius th
Cli ' :
atomic weight 35.5^ glmol , radius I^ -^ 8A
unit cell with a =^ 2.8A
Na and Ys^ Cl per unit cell :(^ I ° 237 -1¥. 35 - 5)
602 × 1023
sc : ante::::^ see:'m :O : stance (^).. (^). ÷÷E¥: ' ".
' cc :
::::: ::::^ ÷:: :^ ÷. ÷÷F:÷ ' tu : ::::::c:::^ is::::^ : ÷÷7÷÷ "'
l - 14 )
em (^).
#¥¥EA
I - 15 )
SC :^ atoms / cell :^8 ×+8^ =^1
nearest neighbour :^ a
atom (^) sphere volume :^ ( E^ ) 's
=^ HI
6 unit (^) cell volume :^ g^3 fraction occupied :^ I. (^) HII
I
= GI =^ O'^52 bcc :^ atoms (^) hell =^8 × 4 t^ I^ =^2 nearest (^) neighbour = AIB atom (^) sphere volume =^4 ( (^) Ey B) 3 =^ H53sa3_ 16
unit cell^ volume^ =^ a
} it. Ba 's
fraction occupied =^ - 2.^ IT =-^ IT^53 =^0168
a 3 8 diamond :^ atom hell i^ 4+4= nearest neighbour^ :^1453 atom (^) sphere volume^ :^ 4¥^ ( ALI ) ' = ABI 128 unit cell Volume^ :^ a ' it (^53) a^3
fraction occupid^ :^ =
Hy÷
6 ' 14ft - K t 5.66 A ( t - K) = 5.87 A
x =^ o^ - 44
At (^) Sb o. 44A so. 56 lattice matches In P (^) and has Eg =L. GeV.
5- 87A x t 545 Cl - K) =^ 5-
x =^ 0.
Iho - 48 Ga o 's - P^ lattice matches GaAs and has
Eg = 2 -^ O^ ev
a) (^) Assume Cs^ =^ Kd CL (^) throughout the (^) growth.
Thus initial Concentration of P should be :
16 10 = 2-86×^1016 cm
b) The P concentration is so small that the volume
of (^) melt can^ be calculated from (^) the (^) weight of si
500090ft =^2146 cm 3 of^ Si
2- 3391cm 3
2- (^86) × (^1016) cm^ -3^ × 2146 cm^3 = 6 - 14 × (^1019) atom 's P 19 6.14× 102 × 312 =^ 3.16×10-^
y
of P
b - 02 ×^1023
since the^ P^ concentration^ in the
growing crystal^ is
only about^ one^ -^ third^ of^ that^ in^ the^ melt,^ Si^ is
used (^) up more^ rapidly than P (^) in (^) the growth
. Thus the melt
becomes richer in P^ as the
growth proceeds^ ,
and the
crystal is^ doped more^ heavily in^ the^ latter^ stages of (^) growth.^ This^ assume that led^ is^ not varied (^) ; g more uniformly doped (^) ingot can^ be^ grown (^) by (^) varying the pull rate appropriately
- modern (^) Goehr (^) al ski growth system use^ computer^ controls (^) to vary the^ temperature, pull rate (^) , and^ other (^) parameters to^ achieve (^) fairly uniformly (^) doped ingots.
