EE 5340 Semiconductor Device Theory Lecture 19 – Spring 2011 Professor Ronald L. Carter
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EE 5340Semiconductor Device TheoryLecture 19 – Spring 2011
Professor Ronald L. Carterronc@uta.edu
http://www.uta.edu/ronc
©rlc L19-31Mar2011
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Test 2 – Tuesday 05Apr11• 11 AM Room 129 ERB• Covering Lectures 11 to19• Open book - 1 legal text or ref.,
only.• You may write notes in your book.• Calculator allowed• A cover sheet will be included with
full instructions. For examples see http://www.uta.edu/ronc/5340/tests/.
npn BJT currents in the forward active region ©RLC
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IC =
JCAC
IB=-(IE+IC )
JnE JnC
IE = -JEAE
JRB=JnE-JnC
JpE
JGC
JREJpC
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E current equations mode npn BJT (w/o
gen/rec)
ditto. , L/xsinh
V/VfexpL/xtanhV/Vfexp
LnqDJ
dir. x' in , 1VVexpL/xtanhL
pqDJ
xxnqDJ- ,x'
'xp-qDJ
BBtBC
BBtBE
BB0B
nE
tBE
EEEE0E
pE
0xB
BnE0x'
EEpE
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C current equations in npn BJT (w/o gen/rec)
BB
tBC
BB
tBE
B
B0BnC
tBC
CCC
C0CpC
xxB
BnC0x"
CCpC
LxVVf
LxVVf
LnqDJ
1VV
LxLpqDJ-
xxnqDJ- ,x"
xpqDJ-B
/tanh/exp
/sinh/exp
exp/tanh
"
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Ebers-Moll Model(Neglecting G-R curr)
(Fig. 9.30*)
-JEAE=IE JCAC=IC
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Source of Ebers-Moll Equations (E)
tBE
FF
BBB
B0B
tBC
RR
E
ES
BBB
B0B
EEE
E0EES
BB
tBC
BB
tBE
B
B0BnE
t
BE
EEE
E0EpE
EEnEpEE
V/VfexpJ
L/xsinhLnqD
V/VfexpJ
AI
L/xtanhLnqD
L/xtanhLpqDJ
L/xsinhV/Vfexp
L/xtanhV/Vfexp
LnqDJ
1VVexp
L/xtanhLpqDJ
A/IJJJ
αα
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Source of Ebers-Moll Equations (C)
tBC
RR
BBB
B0B
tBE
FF
C
CS
BBB
B0B
CCC
C0CCS
BB
tBE
BB
tBC
B
B0BnC
t
BC
CCC
C0CpC
CCnCpCC
V/VfexpJ
L/xsinhLnqD
V/VfexpJ
AI
L/xtanhLnqD
L/xtanhLpqDJ
L/xsinhV/Vfexp
L/xtanhV/Vfexp
LnqDJ
1VVexp
L/xtanhLpqDJ-
A/IJJJ
αα
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E-M model equations
BB
BC2i
CSRSESFBB
BE2i
S
tBC
CSRt
BEESE
tBE
ESFt
BCCSC
xNDAqnIIIxN
DAqnI gives iprelationsh yreciprocit The
VVfIV
VfII
VVfIV
VfII
expexp
expexp
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Fig. 9.30*
-JEAE
= IE
JCAC
= IC
E
B
C
RIR FIF
Ebers-Moll Model (Neglecting G-R curr)
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E-M linking current model
ECCCCTEC
I-III
CBt
BCRS
REC
IV
VfexpII
tBE
FS
FCC
EB
VVfexpII
I
B
E
C
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tBC
tBESEC
tBCS
tBE
FSE
tBES
tBC
RSC
S
VVexpV
VexpII
branch E-C the links"" that current TheV
VfexpIVVfexpII
VVfexpIV
VfexpII
become eqns. M-E the ,I of terms In
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E-M linking current model (cont)
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E-M linking current model (cont)
EBECE
CBECC
FF
Ft
BEFS
EB
RR
Rt
BCRS
CB
I-II andIII sdefinition with eqns
M-E the for values same the give still
1 with VVfexpII
& 1 with VVfexpII
:Similarly
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More non-ideal effects in BJTs
a Base-width modulation (FA: xB changes with changes in VBC)
a Current crowding in 2-dim base• High-level injection (minority
carriers g.t. dopant - especially in the base).
• Emitter Bandgap narrowing (NE ~ density of states at cond. band. edge)
• Junction breakdown at BC junction
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Recombination/Generation
Currents (FA)
CBCB
BCeff,
1gen
BCeff,BCbiC
BCgen
BCiGC
1rec
BEt
BErec
iBERE
NNNNN and
rate, ionrecombinat the is and DR CB
the is qNVV2W where ,2
WqnJ
.rate ionrecombinat the is and DR
EB the is W where ,V2Vexp2
nqWJ
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FA npn figure of merit – emitter efficiency
1L/x and L/x if ,xDNxDN1
L/xtanhLDnL/xtanhLDp1
VV if ,J/J11
JJJ
EEBB1
EBEBEB
1
EEEB0BBBBE0E
tBEnEPEPEnE
nE
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FA npn figure of merit – base transport factor
2
BB
BBtBE
BBtBET
BBtBCtBE
nE
nCT
Lx1L
x0L
x , Lx1
LxVV1LxVV
Lx and VV , VV For
. JJ factor, transport base The
coshlim/cosh
/cosh/exp/cosh/exp
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FA npn figure of merit – recombination factor
BB1
tBE
0BBOBBEi
nE1
0
BEtBE
0iBER
RnEnE
pERnEpEnE
Lx for ,V2VexpDn2
xxn1
,J from rate, ionrecombinat the is and DR
EB the is x where ,V2Vexp2
nqxJ
JJJ
JJJJJ
factor, Recomb
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Common base current gain, F
TpEREnE
pEnE
nEnC
pEnEnE
EpCGC
pEREnEnC
EC
pEREnE
pCGCnC
EC
0
JJJJJ
JJ
JJJ as
Factors .I of fctns not are J and J
since , JJJJ
II :signal small
JJJJJJ
II gain, current DC
T
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Common base current gain, F (continued)
1
tBE
0BBOBBEi
2B
2B
EBEBEB
1
tBE
0BBOBBEi
1
2B
2B
BBtBEBBtBE
T
1
EBEBEB
1
EEEB0BBBBE0E
V2VexpDn2
xxnL2
xxDNxDN1
V2VexpDn2
xxn1
L2x1L/xcoshV/Vexp1
L/xcoshV/Vexp
xDNxDN1L/xtanhLDn
L/xtanhLDp1
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Common emitter current gain, F
lim. , V2VexpDn2
xxn , xDNxDN
L2x
lim. , V2VexpDn2
xxn , L2x
xDNxDN
limited. or limited is BJT a Usually,V2VexpDn2
xxnL2
xxDNxDN
1 so , 1 ; III with ,II
TtBE
0BBOBBEi
EBEBEB
2B
2B
tBE
0BBOBBEi
2B
2B
EBEBEB
T
1
tBE
0BBOBBEi
2B
2B
EBEBEB
00
0CBEBC
0
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Common base current gain, F (cont.)
1
tBE
0BBOBBEi
2B
2B
EBEBEB
1
tBE
0BBOBBEi
1
2B
2B
BBtBEBBtBE
T
1
EBEBEB
1
EEEB0BBBBE0E
V2VexpDn2
xxnL2
xxDNxDN1
V2VexpDn2
xxn1
L2x1L/xcoshV/Vexp1
L/xcoshV/Vexp
xDNxDN1L/xtanhLDn
L/xtanhLDp1
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Common emitter current gain, F
lim. , V2VexpDn2
xxn , xDNxDN
L2x
lim. , V2VexpDn2
xxn , L2
xxDNxDN
limited. or limited is BJT a Usually,V2VexpDn2
xxnL2
xxDNxDN
1 so , 1 ; III with ,II
TtBE
0BBOBBEi
EBEBEB
2B
2B
tBE
0BBOBBEi
2B
2B
EBEBEB
T
1
tBE
0BBOBBEi
2B
2B
EBEBEB
00
0CBEBC
0
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References* Semiconductor Physics and
Devices, 2nd ed., by Neamen, Irwin, Boston, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.
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