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EE105 Fall 2011 Lecture 5, Slide 1 Prof. Salahuddin, UC Berkeley
Lecture 5
OUTLINE• PN Junction Diodes
– I/V– Capacitance– Reverse Breakdown– Large and Small signal modelsReading: Chapter 2.2-2.3,3.2-3.4
EE105 Fall 2011 Lecture 5, Slide 2 Prof. Salahuddin, UC Berkeley
Recap: Law of the Junction
0 a-b
Law of the junction:
TD VV �i enapan /2)()(
EE105 Fall 2011 Lecture 5, Slide 3 Prof. Salahuddin, UC Berkeley
Recap: Minority Carrier Concentrations at the Edges of the Depletion Region
n
TDLx
A
VVi
p
ppp
eN
enxn
xnnxn
//2
0
1)(
)()(
x'
Notation:Ln electron diffusion length (cm)
nTD LxVV
nA
inpndiffn ee
LN
nqD
xd
dnqDJ //
2
, 1
0x=a
-b ;x‘=0
EE105 Fall 2011 Lecture 5, Slide 4 Prof. Salahuddin, UC Berkeley
Hole Diffusion
X’’0
pTDLxVV
pD
ipdiffp ee
LN
nqDJ //
2
,
''
1
x’’
EE105 Fall 2011 Lecture 5, Slide 5 Prof. Salahuddin, UC Berkeley
Distribution of Diffusion Current
x0 a-b
nTD LxVV
nA
indiffn ee
LN
nqDJ //
2
, 1 pTDLxVV
pD
ipdiffp ee
LN
nqDJ //
2
, 1
•Assume: No Recombination in the depletion region•Known: Total Current is the same everywhere
EE105 Fall 2011 Lecture 5, Slide 6 Prof. Salahuddin, UC Berkeley
Diode Current under Forward Bias• The current flowing across the junction is comprised
of hole diffusion and electron diffusion components:
0,0,0,0,
xdiffnxdiffpxdriftnxdriftptot JJJJJ
x0 a-b
nTD LxVV
nA
indiffn ee
LN
nqDJ //
2
, 1 pTDLxVV
pD
ipdiffp ee
LN
nqDJ //
2
, 1
J_total
EE105 Fall 2011 Lecture 5, Slide 7 Prof. Salahuddin, UC Berkeley
I-V Characteristic of a PN Junction• Current increases exponentially with applied forward
bias voltage, and “saturates” at a relatively small negative current level for reverse bias voltages.
pD
p
nA
niSS
VVSD
LN
D
LN
DAqnAJI
eII TD
2
/ 1
“Ideal diode” equation:
EE105 Fall 2011 Lecture 5, Slide 8 Prof. Salahuddin, UC Berkeley
Practical PN Junctions• Typically, pn junctions in IC devices are formed by
counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if– NA net acceptor doping on p-side (NA-ND)p-side
– ND net donor doping on n-side (ND-NA)n-side
)1( kTVqSD
DeII
Dp
p
An
niS NL
D
NL
DAqnI 2
VD (V)
I D (A
)
EE105 Fall 2011 Lecture 5, Slide 9 Prof. Salahuddin, UC Berkeley
How to make sure that current flow in a forward-biased p-n junction diode is mainly due to electrons?
EE105 Fall 2011 Lecture 5, Slide 10 Prof. Salahuddin, UC Berkeley
Diode Saturation Current IS
• IS can vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant concentrations.– typical range of values for Si PN diodes: 10-14 to 10-17 A/m2
• In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:
– If the P side is much more heavily doped,
– If the N side is much more heavily doped,
Dp
p
An
niS NL
D
NL
DAqnI 2
Dp
piS NL
DAqnI 2
An
niS NL
DAqnI 2
EE105 Fall 2011 Lecture 5, Slide 11 Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium
on the P side: xaqN
Esi
A
(see slide 3 in lecture 4)(x)
x-qNA
qND
a
-b
V(x)
xa-b
V0
0
on the N side: bxqN
Esi
D
--(1)
--(2)
DA bNaN --(3)
Let us set the reference point at x=aThen V(a)=0
V(-b)=V0; Built in potential
EE105 Fall 2011 Lecture 5, Slide 12 Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium xa
qNE
si
A V(x)
xa-b
V0
0
bxqN
Esi
D
--(1)
--(2)
DA bNaN --(3)
V(a)=0 V(-b)=V0; Built in potential
EE105 Fall 2011 Lecture 5, Slide 13 Prof. Salahuddin, UC Berkeley
Depletion Width at Equilibrium V(x)
xa-b
V0
0
EE105 Fall 2011 Lecture 5, Slide 14 Prof. Salahuddin, UC Berkeley
Depletion Width at biased conditionsV(x)
xa-b
V0
0
EE105 Fall 2011 Lecture 5, Slide 15 Prof. Salahuddin, UC Berkeley
PN Junction Depletion Capacitance• A reverse-biased PN junction can be viewed as a
capacitor, for incremental changes in applied voltage.
dep
sij W
C
si 10-12 F/cm is the permittivity of silicon
EE105 Fall 2011 Lecture 5, Slide 16 Prof. Salahuddin, UC Berkeley
Voltage-Dependent Capacitance• The depletion width (Wdep) and hence the junction
capacitance (Cj) varies with VR.
VD
EE105 Fall 2011 Lecture 5, Slide 17 Prof. Salahuddin, UC Berkeley
Reverse-Biased Diode Application• A very important application of a reverse-biased PN
junction is in a voltage controlled oscillator (VCO), which uses an LC tank. By changing VR, we can change C, which changes the oscillation frequency.
LCfres
121