basic operation of a (heterojunction) bipolar transistor
TRANSCRIPT
Lecture 5: HBT DC Properties
2014-01-28 1 Lecture 5, High Speed Devices 2014
•Basic operation of a (Heterojunction) Bipolar Transistor •Abrupt and graded junctions •Base current components •Quasi-Electric Field
Reading Guide: 143-162: 170-177
Basic Operation of a Bipolar Transistor
2014-01-28 2 Lecture 6, High Speed Devices 2014
N In
P
p+
+ In
0.5
3G
a 0.4
7A
s
n In
0.5
3G
a 0.4
7A
s
Emitter Base Collector
VBC VBE
1) Base-Collector junction reversed biased (very small current)
2) Emitter-Base junction forward biased.
3) Electrons/holes diffuse between emitter and base – controlled by VBE!
4) Electrons flow out of collector – IC(VBE).
5) Some electrons recombine in the base – hole current IB(VBE)
Common Emitter Operation
2014-01-28 3 Lecture 6, High Speed Devices 2014
0 1 2 3 4
0
0.02
0.04
0.06
0.08
0.1
Vce
(V)
Kolle
kto
rstr
öm
(A
)
VBE=0.781V
VBE=0.798V
VBE=0.810V
VBE=0.816V
VBE=0.0V
VBE
+
-
VCE
+
-
IB
IC VCE(sat)
• VBE is the input voltage • IB the input current • IC the output current How do we calculate: IC(VBE) IB(VBE) Current gain b: IC/IB
-VBC=VCE-VBE
Homo&Graded Short-base Junctions – without recombination
2014-01-28 4 Lecture 5, High Speed Devices 2014
dn(0) dn(XB)=0 Emitter Base Collector
01exp
1exp0
0
0
kT
qVnXn
kT
qVnn
BCB
BE
d
d
No recombination tn ~ ∞ XB,E<<Ln,p
dp(0)
kT
qV
N
n
X
DqAI
kT
qV
N
n
X
DqAI
be
d
WG
i
E
pE
dBp
be
a
NG
i
B
nBdC
exp
exp
2
2
kT
E
N
N
X
X
D
D
I
I g
B
E
B
E
pE
nB
Bp
C expb
From the ni terms
IB usually dominated by recombination!
Large current gain even if NB>>NE
We will see that NB should be high: NB≈ 1020 cm-3
Typical HBT has b ~ 20-100.
x XB 0 XE
Example b for InGaAs/InP HBT – no recombination
2014-01-28 5 Lecture 5, High Speed Devices 2014
kT
E
N
N
X
X
D
D
I
I g
B
E
B
E
pE
nB
Bp
C expb
InP In0.53Ga0.47As
Eg (eV) 1.35 0.76
µn,min (cm2/Vs) 1500
µp,maj (cm2/Vs) 150
ND (cm-3) 1017 -
NA (cm-3) 1019
XE (nm) 150
XB (nm) 30
Base current components
2014-01-28 6 Lecture 5, High Speed Devices 2014
Emitter
SCR
Base
1 2 3 4 5
1. Back injected holes – negligible in a well designed HBT
2. Recombination in the space-charge-zone 3. Recombination in the base bulk region 4. Recombination at base contact interface 5. Recombination at base surface
Collector
IB
Every time an electron is ”lost” – replaced through the base current – IB.
Recombination terms for bulk base
2014-01-28 7 Lecture 5, High Speed Devices 2014
Radiative recombination Shockley-Read-Hall (SRH) Auger
n
AugerSRHrad
nnUUUU
t0
Base: ni<<n<<p
tn: total recombination life time
Radiative SRH Auger
The base of a HBT has high doping level NA > 1019 cm-3. tn can become very short! tn ≈ 1-100 pS for NA = 1019 - 1020 cm-3
InGaAs recombination time (tn)
Homo&Graded Short-base Junctions – with recombination
2014-01-28 8 Lecture 5, High Speed Devices 2014
n(0) n(XB)=0 Emitter Base Collector
01exp
exp1exp0
0
00
kT
qVnXn
kT
qVn
kT
qVnn
BCB
BEBE
No recombination tn ~ 0 XB<<Ln
p(0)
𝜁𝐷𝐶 =1
𝐷𝑛𝜏𝑛= 1/𝐿𝑛
𝜕2𝑛
𝜕𝑥2− 𝜁𝐷𝐶
2 𝑛 = 0
𝑛𝑑𝑐 𝑥 = 𝑛 0sinh 𝜁𝐷𝐶(𝑋𝐵 − 𝑥)
sinh 𝜁𝐷𝐶(𝑋𝐵)
sinh 𝑥 =𝑒𝑥 − 𝑒−𝑥
2
cosh 𝑥 =𝑒𝑥 + 𝑒−𝑥
2
x XB 0 XE
𝐼𝐶 = 𝑞𝐴𝑐𝐷𝑛 ∙𝑑𝑛
𝑑𝑥𝑥=𝑋𝐵 𝐼𝐸 = 𝑞𝐴𝑐𝐷𝑛 ∙
𝑑𝑛
𝑑𝑥𝑥=0
Homo&Graded Short-base Junctions: Current gain
2014-01-28 9 Lecture 5, High Speed Devices 2014
dn(0) dn(XB)=0 Emitter Base Collector
dp(0) 𝑛𝑑𝑐 𝑥 = 𝑛 0sinh 𝜁𝐷𝐶(𝑋𝐵 − 𝑥)
sinh 𝜁𝐷𝐶(𝑋𝐵)
sinh 𝑥 =𝑒𝑥 − 𝑒−𝑥
2
cosh 𝑥 =𝑒𝑥 + 𝑒−𝑥
2
𝛼𝑇 =𝐼𝐶𝐼𝐸≈
1
1 +𝑋𝐵2
2𝐷𝑛𝜏𝑛
𝛽 =𝐼𝐶𝐼𝐵≈
1
1 − 𝛼𝑇=2𝐷𝑛𝜏𝑛
𝑋𝐵2 ≡
𝜏𝑛𝜏𝑏
Base Transport Factor:
Common emitter current gain:
High Gain: • Thin Base • High mobility • Long life time
𝜏𝑏 =𝑄𝐵𝐼𝐶
= 𝑞𝐴𝐸 𝑛 𝑥 𝑑𝑥 𝑋𝐵0
𝐼𝐶 Base Transport Factor
𝑑
𝑑𝑥sinh 𝑥 = cosh (𝑥)
cosh 𝑥 ≈ 1 +𝑥2
2+ 𝑂 𝑥4
Ideality Factor – Bipolar Transistor
2014-01-28 10 Lecture 5, High Speed Devices 2014
kT
qV
N
n
X
DqAI be
a
NG
i
B
nBdC exp
2
kT
qVI be
baseB exp,Recombination inside neutral base layer
kT
qVI be
RLOB2
exp,
VBE
log
(I C
,I B)
Recombination inside space-charge region
𝐼𝐵 = 𝐼𝐵,𝑅𝐿𝑂 + 𝐼𝐵,𝑏𝑎𝑠𝑒
Total base current:
1 minute exercise – Gummel Plot
2014-01-28 11 Lecture 5, High Speed Devices 2014
VBE
log
(I C
,I B)
VBE b
How does b vary with Vbe?
Abrupt Junction
2014-01-28 12 Lecture 5, High Speed Devices 2014
kT
E
N
N
X
X
D
D
I
I v
B
E
B
E
pE
nB
Bp
C expb
Electron current set by potential spike and diffusion across base (complicated) Hole curent set by diffusion Potential barrier for electrons ~fbi
Potential barrier for holes ~fbi+Ev
fbi
fbi
Ev
Correction due to limited thermal velocity
2014-01-28 13 Lecture 5, High Speed Devices 2014
Diffusion is due to thermal motion of electrons: vdiff < vthermal
Jdiff = qn(XB)vthermal : Must be some electrons at XB for a diffusion current to flow!
0 10 20 30 40 500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
7
Vd
iff (c
m/s
)
Base Thickness (nm)
n(0) n(XB)=0?? Base Collector
0,00 BdiffB
B
ndiff XqnvXnn
X
qDJ
thnB
ndiff
vDX
nqDJ
/
0
*
2
m
kTvth
vdiff=Dn/XB
Modern HBTs have XB<30 nm So this correction can be important! However – more complicated math!
vth
Calculation for InGaAs base
n(XB)=0
(1)
(1)
2 minute excercise
2014-01-28 14 Lecture 5, High Speed Devices 2014
0 XB
dn(x)
Consider two HBTs with two different minority carrier concentrations in the base: 1) Are the collector currents the same?
2) Which one has the highest b?
Dn=Dn
tn=tn
(2)
(1)
Base electric field
2014-01-28 15 Lecture 5, High Speed Devices 2014
Introduce an (quasi) electric field in the base region – diffusion and drift For a constant electric field, eB
xn
kT
q
dx
xdnqDJ B
nc
ecc JxJ )(
xX
kT
q
q
kT
qD
Jxn B
B
Bn
c e
eexp1
Same current – smaller n(x) as compared with pure diffusion!
Possible to achieve higher b
Lower QB better high frequency properties!