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_______________________________________ 4.21
(a) kT??0.0259???375??300???0.032375eV
3/2n??1019???375?o?2.8?300??exp???0.28??0.032375?? ?6.86?1015 cm?3
EF?E??Eg??Ec?EF??1.12?0.28 ?0.840eV
p?04?1019??3/2?375?o?1.?300??exp???0.840??0.032375?? ?7.84?107cm?3
(b) E?N?c?c?EF?kTln???n? o?
??0.0259?ln???2.8?1019???6.862?1015??
?0.2153eV
EF?E??1.12?0.2153?0.9047eV
p????0.904668?o?1.04?1019exp??0.0259?? ?7.04?103cm?3
_______________________________________ 4.22 (a) p-type
(b) EEg1.12F?E??4?4?0.28eV
p?N???EF?E???o?exp??kT?? ??1.04?1019?exp???0.28??0.0259??
?2.10?1014cm?3 Ec?EF?Eg??EF?E?? ?1.12?0.28?0.84eV
n?N???Ec?EF??ocexp??kT?? ??2.8?1019?exp???0.84??0.0259?? ?2.30?105cm?3
_______________________________________ 4.23
(a) n?EF?EFi?o?niexp??kT?? ??1.5?1010?exp??0.22??0.0259??
?7.33?1013cm?3
pn?EFi?EF?o?iexp??kT?? ??1.5?1010?exp???0.22??0.0259??
?3.07?106cm?3
(b) nn?E?EFi?o?iexp?F?kT??
??1.8?106?exp??0.22??0.0259?? ?8.80?109cm?3
p?E?EF?o?niexp?Fi?kT??
??1.8?106?exp???0.22??0.0259?? ?3.68?102cm?3
_______________________________________ 4.24
(a) E?N???F?E??kTln???po??
??1.04?1019?0.0259?ln????5?1015???
?0.1979eV
(b)
Ec?EF?Eg??EF?E?? ?1.12?0.19788?0.92212eV
(c) n?2.8?1019?exp???0.92212?o??0.0259?? 文档鉴赏
?9.66?103cm?3 (d) Holes
(e) Eln??p?o?Fi?EF?kT??n?? i
??0.0259?ln???5?1015???1.5?1010??
?0.3294eV _______________________________________ 4.25
kT??0.0259???400??300???0.034533eV
N?19??400?3/2??1.04?10??300??
?1.601?1019cm?3
N?19??400?3/2c?2.8?10??300??
?4.3109?1019cm?3?
n2i?4.3109?1019??1.601?1019?
?exp???1.12??0.034533?? ?5.6702?1024
?ni?2.381?1012cm?3 (a)
EE?N??F???kTln????po?? ??0.034533?ln???1.601?1019 ??5?1015???
?0.2787eV (b) Ec?EF?1.12?0.27873?0.84127eV
(c)
n?4.3109?1019?exp???0.84127?o??0.034533??
?1.134?109cm?3 (d) Holes
(e) E?po?Fi?EF?kTln????n? i?
??0.034533?ln??5?1015????2.381?1012??
?0.2642eV _______________________________________ 4.26
(a) p??0.25?o??7?1018?exp??0.0259??
?4.50?1014cm?3
Ec?EF?1.42?0.25?1.17eV
n??exp???1.17?o?4.7?1017?0.0259??
?1.13?10?2cm?3 (b) kT?0.034533eV /2 N?400????7?1018?3??300??
?1.078?1019cm?3 Nc??3/24.7?1017???400??300??
?7.236?1017cm?3 E?N??F?E??kTln????po??
??0.034533?ln???1.078?1019???4.50?1014??
?0.3482eV
Ec?EF?1.42?0.3482?1.072eV
n????1.07177?o?7.236?1017exp??0.034533?? ?2.40?104cm?3
_____________________________________ 4.27
(a) p??1.04?1019?exp???0.25?o?0.0259??
?6.68?1014cm?3
Ec?EF?1.12?0.25?0.870eV
n??0.870?o??2.8?1019?exp??0.0259??
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no?7.23?104cm?3 (b)
kT?0.034533eV
N?400????3/21.04?1019???300??
?1.601?1019cm?3 3/2 Nc??2.8?1019???400??300??
?4.311?1019cm?3
EkTln??N???F?E????po??
?0.034533?ln???1.601?1019???6.68?1014???
?0.3482eV
Ec?EF?1.12?0.3482?0.7718eV
n?4.311?1019?exp???0.77175?o??0.034533??
?8.49?109cm?3
_______________________________________ 4.28
(a) n2o??NcF1/2??F?
For EF?Ec?kT2,
?EF?EcF?kT?kT2kT?0.5 ThenF1/2??F??1.0
no?2??2.8?1019??1.0?
?3.16?1019cm?3
(b) n2o??NcF1/2??F? ?2??4.7?1017??1.0?
?5.30?1017cm?3
_______________________________________ 4.29
po?2?N?F1/2???F? 5?1019?2??1.04?1019?F1/2???F?
So F1/2???F??4.26 We find ???3.0?E??EFFkT
E??EF??3.0??0.0259??0.0777eV
_______________________________________ 4.30
(a) ?E?Ec4kTF?FkT?kT?4
Then F1/2??F??6.0 no?2?NcF1/2??F? ?219??2.8?10??6.0?
?1.90?1020cm?3
(b) n2o???4.7?1017??6.0?
?3.18?1018cm?3
_______________________________________ 4.31
For the electron concentration n?E??gc?E?fF?E?
The Boltzmann approximation applies, so n?E?4??2m*?n?3/2h3E?Ec
?exp????E?EF???kT?? or
n?E??4??2m*n?3/2h3exp????Ec?EF???kT??
?kTE?Ec???E?Ec?kTexp???kT?? Define
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x?E?EckT Then
n?E??n?x??Kxexp??x? To find maximum n?E??n?x?, set
dn?x??0?K??12x?1/2dx?exp??x? ?x1/2??1?exp??x????
or
0?Kx?1/2exp??x???1??2?x??
which yields
x?12?E?EckT?E?E1c?2kT
For the hole concentration p?E??g??E??1?fF?E??
Using the Boltzmann approximation p?E??4??2m*2p?3/h3E??E
?exp????EF?E???kT?? or
p?E??4??2m*?3/2ph3exp????EF?E????kT??
?kTE??EkTexp????E??E???kT?? Define
x??E??EkT
Then
p?x???K?x?exp??x?? To find maximum value of p?E??p?x??,
set
dp?x??dx??0 Using the results from above,
we find the maximum at
E?E1??2kT
_______________________________________
4.32 (a) Silicon: We have
n???Ec?EF??o?Ncexp??kT?? We can write
Ec?EF??Ec?Ed???Ed?EF? For
Ec?Ed?0.045eV and
Ed?EF?3kTeV we can write
n??1019?exp???0.045?o?2.8?0.0259?3??
??2.8?1019?exp??4.737? or
no?2.45?1017cm?3 We also have
p?N???EF?E???o?exp??kT?? Again, we can write
EF?E???EF?Ea???Ea?E?? For
EF?Ea?3kT and
Ea?E??0.045eV Then
p???0.045?o?1.04?1019exp?????3?0.0259?? ?1.04?1019exp??4.737? or
po?9.12?1016cm?3 (b) GaAs: assume Ec?Ed?0.0058eV Then
n????0.0058o?4.7?1017exp??0.0259?3?? ??? ?4.7?1017exp??3.224? or
no?1.87?1016cm?3
Assume Ea?E??0.0345eV Then
p????0.0345o?7?1018exp??0.0259?3??? ??7?1018?exp??4.332?
or
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po?9.20?1016cm?3
_______________________________________ 4.33
Plot
_______________________________________ 4.34
(a)
p3o?4?15?1015?3?1015cm? n?1.5?1010?2o?3?1015?7.5?104cm?3
(b)
no?Nd?3?1016cm?3
102 p?1.5?10?o?3?1016?7.5?103cm?3
(c)
no?po?n10i?1.5?10cm?3
(d) n219i??2.8?10??31.04?1019???375??300??
?exp????1.12??300????0.0259??375???
?ni?7.334?1011cm?3 p15o?Na?4?10cm?3 ?
112n?7.334?10?o4?1015?1.34?108cm?3
(e) n2i??2.8?1019??1.04?1019??3?450??300??
?exp????1.12??300????0.0259??450???
?ni?1.722?1013cm?3
142n1014?10?o?2??????1.722?1013?2???2
?1.029?1014cm?3
p?1.722?1013?2o?1.029?1014?2.88?1012cm?3
_______________________________________ 4.35
(a)
po?Na?Nd?4?1015?1015
?3?1015cm?3
n2i?1.8?106n?2o?p?10?3cm?3
o3?1015?1.08?(b)
n16o?Nd?3?10cm?3
p?1.8?106?2?4o?3?1016?1.08?10cm?3
(c)
no?po?ni?1.8?106cm?3
(d) n2??4.7?1017i??7.0?1018??3?375??300??
?exp????1.42??300????0.0259??375???
?ni?7.580?108cm?3 po?N3a?4?1015cm? ?
82n?7.580?10?o4?1015?1.44?102cm?3
(e) n2i??4.7?1017??7.0?1018??3?450??300??
?exp??
??1.42??300????0.0259??450???
?n?3i?3.853?1010cm no?Nd?1014cm?3
102p??3.853?10?o1014?1.48?107cm?3
_______________________________________ 4.36 (a) Ge: ni?2.4?1013cm?3
(i)nN?Nd?2o?d2????2????n2i
?2?1015?2?1015?22?????2.4?2???1013??2
or
no?Nd?2?1015cm?3
半导体物理与器件第四版课后习题答案4
