pn2i??2.4?1013?2o?no2?1015
?2.88?1011 cm?3 (ii)po?Na?Nd?1016?7?1015 ?3?1015cm?3 nn2i??2o?p?2.4?101315
o3?10 ?1.92?1011cm?3
(b) GaAs: ni?1.8?106cm?3 (i)no?Nd?2?1015 cm
62p??1.8?10??3o2?1015?1.62?10cm?3
(ii)po?Na?N?3d?3?1015cm
62n??1.8?10?o3?1015?1.08?10?3cm?3
(c) The result implies that there is only one minority carrier in a volume of 103cm3. _______________________________________ 4.37
(a) For the donor level
nd1N?1?1?E
dd?EF?2exp???kT??? ?11?1?0.20?
2exp??0.0259?? or
nd?8.85?10?4N
d (b) We have
f1F?E??1?exp???E?E
F??kT??? Now
E?EF??E?Ec???Ec?EF? or
E?EF?kT?0.245
Then
fF?E??1
1?exp??0.245??1?0.0259?? or
fF?E??2.87?10?5
_______________________________________ 4.38
(a) Na?Nd?p-type (b) Silicon:
po?Na?Nd?2.5?1013?1?1013 or
po?1.5?1013cm?3 Then
n2i?1.5?1010n?27o?p?1.5?1013?1.5?10cm?3 o Germanium:
pNa?Nd?Na?Nd?2o?2????2????n2i
2????1.5?1013????2?????1.5?1013???2??2.4?1013???2
or
po?3.26?1013cm?3 Then
2 nn2i?2.4?1013??o?p13?1.76?1013 o3.264?10cm?3
Gallium Arsenide:
p13o?Na?Nd?1.5?10cm?3 and
nn2i?1.8?106?2o?p?13?0.216cm?3 o1.5?10_______________________________________ 4.39
(a) Nd?Na?n-type
(b) no?Nd?Na?2?1015?1.2?1015 ?8?1014cm?3
n2i?1.5?1010p?2o?n?14?2.81?105cm?3
o8?10
(c) po??N?a?Na??Nd 4?1015?N?a?1.2?1015?2?1015 ?N?a?4.8?1015cm?3
102n??1.5?10?4o4?1015?5.625?10cm?3
_______________________________________ 4.40
?n2i?1.5?1010n?2op?105?1.125?1015cm?3 o2? no?po?n-type
_______________________________________ 4.41
n2?.04?1019??6.0?1018??3?250?i?1?300??
?exp???0.66???0.0259??250300???
?1.8936?1024
?ni?1.376?1012cm?3 nn22io?p?ni?n212o?ni o4no4 ?n1o?2ni
So no?6.88?1011cm?3,
Then po?2.75?1012cm?3
pNa?Na?2o?2????2??2??ni ???12N?2a?2.752?10?2???
2????Na?24?2????1.8936?10
7.5735?1024??22.752?1012?N???Na?a??2??? 2????Na???24?2??1.8936?10 so that Na?2.064?1012cm?3
_______________________________________ 4.42
Plot
_______________________________________ 4.43
Plot
_______________________________________ 4.44
Plot
_______________________________________ 4.45
nNd?Na?Nd?Na?2o?2????2????n2i 14 1.1?1014?2?10?1.2?1014 2
?2?1014?1.2?2???1014???n2?2??i ?
1.1?1014?4?1013?2??4?1013?2?n2i
4.9?1027?1.6?1027?n2i so n13i?5.74?10cm?3
n227pi3.3?10o?n??3?1013cm?314 o1.1?10_______________________________________ 4.46
(a) Na?Nd?p-type
Majority carriers are holes
po?Na?Nd?3?1016?1.5?1016
?1.5?1016cm?3
Minority carriers are electrons
n2?10ni1.5?10?2o?p?1.5?1016?1.5?104cm?3 o(b) Boron atoms must be added
po?N?a?Na?Nd
5?1016?N?a?3?1016?1.5?1016 So N?16?3a?3.5?10cm
n?1.5?1010?2o?5?1016?4.5?103cm?3
_______________________________________ 4.47
(a) po??ni?n-type (b) pn2io?n?nn2io? opo
102n??1.5?10?o2?104?1.125?1016cm?3
?electrons are majority carriers
p4o?2?10cm?3
?holes are minority carriers (c) no?Nd?Na
1.125?1016?Nd?7?1015 so Nd?1.825?1016cm?3
_______________________________________ 4.48
E?po?Fi?EF?kTln????ni?? For Germanium T(K) kT(eV) n3i(cm?) 200 0.01727 2.16?1010 400 0.03453 8.60?1014 600 0.0518 3.82?1016 2 pN?Na?o?a2????2????n2i and N?3a?1015 cm T(K) po(cm?3) ?EFi?EF?(eV) 200 1.0?1015 0.1855 400 1.49?1015 0.01898 600 3.87?1016 0.000674 _______________________________________ 4.49
(a) E?Nc?c?EF?kTln????Nd??
?ln???2.8?1019??0.0259???N d??For 1014cm?3, Ec?EF?0.3249eV 1015cm?3, Ec?EF?0.2652eV 1016cm?3, Ec?EF?0.2056eV 1017cm?3, Ec?EF?0.1459eV
(b) E?Nd?F?EFi?kTln????ni??
??0.0259?ln???Nd??1.5?1010??? For 1014cm?3, EF?EFi?0.2280eV 1015cm?3, EF?EFi?0.2877eV 1016cm?3, EF?EFi?0.3473eV 1017cm?3, EF?EFi?0.4070eV _______________________________________ 4.50
2(a) nNd?Nd?o?2????2??2??ni no?1.05Nd?1.05?1015cm?3 ?1.05?1015?0.5?1015?2
? ?0.5?1015?2?n2i
so n2i?5.25?1028
Now
?3 n2?1019??1.04?1019???T?i?2.8?300??
?exp???1.12???0.0259??T300???
5.25?1028??2.912?1038??3?T??300??
?exp???12972.973??T?? By trial and error, T?536.5K (b) At T?300K,
E??N?c?c?EF?kTln??n? o?
E?ln???2.8?1019?c?EF??0.0259??1015??
?0.2652eV At T?536.5K,
kT??0.0259???536.5??300???0.046318eV
N?8?1019??536.5?3/2c?2.??300??
?6.696?1019cm?3
E?Nc?c?EF?kTln????n? o?
E?6.696?1019?c?EF??0.046318?ln????1.05?1015??
?0.5124eV then ??Ec?EF??0.2472eV (c) Closer to the intrinsic energy level.
_______________________________________ 4.51
E??p?o?Fi?EF?kTln??n? i? At T?200K, kT?0.017267eV T?400K, kT?0.034533eV T?600K, kT?0.0518eV
At T?200K,
3 n2i??2.8?1019??1.04?1019???200??300??
?exp???1.12??0.017267??
?n4i?7.638?10cm?3 At T?400K,
n2?2.8?1019i???1.04?1019??3?400??300??
?exp???1.12??0.034533?? ?ni?2.381?1012cm?3 At T?600K,
3 n2?2.8?101.04?1019?i?19????600??300?? ?exp???1.12??0.0518??
?ni?9.740?1014cm?3 At T?200K and T?400K, po?Na?3?1015cm?3 At T?600K,
2 pNa2????Na?o??2????n2i
2?3?1015?3?1015?2??????9.740?1014?2???2
?3.288?1015cm?3
Then, T?200K, EFi?EF?0.4212eV T?400K, EFi?EF?0.2465eV
T?600K, EFi?EF?0.0630eV
_______________________________________ 4.52
(a)
EkTln??Na?Fi?EF????n??0.0259?ln??Na?i????1.8?106???
For Na?1014cm?3,
EFi?EF?0.4619eV
N15a?10cm?3,
EFi?EF?0.5215eV
N16a?10cm?3,
EFi?EF?0.5811eV
Na?1017cm?3,
EFi?EF?0.6408eV (b)
?N18E???7.0?10F?E??kTln???N????a????0.0259?ln??Na?? For Na?1014cm?3,
EF?E??0.2889eV
Na?1015cm?3,
EF?E??0.2293eV
N16a?10cm?3,
EF?E??0.1697eV
Na?1017cm?3,
EF?E??0.1100eV
_______________________________________ 4.53
(a) E3?m*?Fi?Emidgap?4kTln?p??m*? n?? ?34?0.0259?ln?10? or
EFi?Emidgap??0.0447eV
(b) Impurity atoms to be added so Emidgap?EF?0.45eV (i) p-type, so add acceptor atoms (ii)
EFi?EF?0.0447?0.45?0.4947eV Then
p?EFi?EF?o?niexp???kT???
??105?exp??0.4947??0.0259??
or
po?Na?1.97?1013cm?3
_______________________________________
4.54
n???Ec?EF??o?Nd?Na?Ncexp??kT?? so
N?.8?1019?exp???0.215?d?5?1015?2?0.0259??
?5?1015?6.95?1015
or
N3d?1.2?1016cm?
_______________________________________ 4.55
(a) Silicon
(i)EE?Nc?c?F?kTln????Nd??
??0.0259?ln???2.8?1019???6?1015???0.2188eV
(ii)Ec?EF?0.2188?0.0259?0.1929eV
N???Ec?EF??d?Ncexp??kT??
??2.8?1019?exp???0.1929??0.0259??
N?3d?1.631?1016cm?N?d?6?1015 ?N??1.031?1016cm?3d Additional
donor atoms (b) GaAs
(i)E??0.0259?ln???4.7?1017?c?EF??1015??
?0.15936eV
(ii)Ec?EF?0.15936?0.0259?0.13346eV
N?????0.13346?d?4.7?1017exp?0.0259??
?2.718?1015cm?3?N?d?1015 ?N?d?1.718?1015cm?3 Additional
半导体物理与器件第四版课后习题答案(供参考)
