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Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Current Flow
emitter current (iE) – is current which flows across EBJ Flows “out” of emitter lead
minority carriers – in p‐type region. These electrons will be injected from emitter into base. Opposite direction.
Because base is thin, concentration of excess minority carriers within it will exhibit constant gradient.
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Straight line represents constant gradient.
00
( ) concentration of minority carriers a position x (where 0 represents EBJ boundary) thermal‐equilibrium value of minority carrier (elect
/
ron) concentration in base
0
reg
(eq6.1) 0 BE
pp
Tv
nn
Vp
x
n e
pn
pn
00
0
ionvoltage applied across base‐emitter junction
thermal voltage (constant)
ppBE
pT
nn
nv
V
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Current Flow
Concentration of minority carrier np at boundary EBJ is defined by (6.1).
Concentration of minority carriers np at boundary of CBJis zero. Positive vCB causes these electrons to be swept across junction.
00
( ) concentration of minority carriers a position x (where 0 represents EBJ boundary) thermal‐equilibrium value of minority carrier
/
(electron) concentration in ase
0
b
(eq6 0.1)
pp
BE T
x
n
v V
n
pn e
pn
pn
0
00
regionvoltage applied across base‐emitter junction
thermal voltage (constant)
ppE
pB
T
nn
nv
V
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Current Flow
Tapered minority‐carrierconcentration profile exists.
It causes electrons injected into base to diffuse through base toward collector.
As such, electron diffusion current (In) exists.
cross‐sectiona area of the base‐emitter junction magnitude of the electr
this simplificationmay be made ifgradient assumedto be straight line
(e
(eq6.2)
q6.2)
0
E
pn E n
pE n
Aq
n
dn xI A qD
dxdn
AI qDW
on charge electron diffusivity in base
width of basenD
W
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Current Flow
Some “diffusing” electrons will combine with holes(majority carriers in base).
Base is thin, however, and recombination is minimal. Recombination does, however, cause gradient to take slightly curved shape. The straight line is assumed.
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
00
( ) concentration of minority carriers a position x (where 0 represents EBJ boundary) thermal‐equilibrium value of minority carrier (elect
/
ron) concentration in base
0
reg
(eq6.1) 0 BE
pp
Tv
nn
Vp
x
n e
pn
pn
00
0
ionvoltage applied across base‐emitter junction
thermal voltage (constant)
ppBE
pT
nn
nv
V
Recombination causes actual gradient to be curved, not straight.
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Collector Current
It is observed that most diffusing electrons will reach boundary of collector‐basedepletion region.
Because collector is more positive than base, these electrons are swept into collector. collector current (iC) is approximately equal to In.
iC = In
intrinsic carrier density doping concentration of base
/
0
2
(eq6.3)
saturation current:
(eq6.4)
BE Tv VC S
E
n
n pS
E n iS
A
iNA
i I
A qD nI
W
A qD nI
W N
e
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Collector Current
Magnitude of iC is independent of vCB. As long as collector is positive, with respect to base.
saturation current (IS) – is inversely proportional to W and directly proportional to area of EBJ. Typically between 10‐12 and 10‐18A Also referred to as scale current.
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Base Current
base current (iB) – composed of two components: ib1 – due to holes injected from base region into emitter. ib2 – due to holes that have to be supplied by external circuit to replace those recombined.
transistor parameter
/
(eq6.5)
(eq6.6) BE T
CB
v VSB
ii
Ii
e
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The Base Current
common‐emitter current gain () – is influenced by two factors: width of base region (W) relative doping of base emitter regions (NA/ND)
High Value of thin base (small W in nano‐meters) lightly doped base / heavily doped emitter (small NA/ND)
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
The EmitterCurrent
All current which enters transistor must leave. iE = iC + iB
Equations (6.7) through (6.13) expand upon this idea.
this expression is generated through combination of (6.5) and (6.7)
/(eq6.8/6.9)
(eq6.10)
(eq6.11
1
)
1
BE T
C
v VE C S
C E
i
i i I
i i
e
this parameter is reffered
/
toas
(eq6.13)
(eq6.1
1 1
2)
,
BE Tv VSE
Ii
common‐base current gain
e
Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)
Exercises 6.1, 6.2, 6.3 (page 315 on 7th edition textbook)