Download Chapter3 Diode

The Devices:
Diode
[Adapted from Rabaey’s Digital Integrated Circuits, ©2002, J. Rabaey et al.]
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Goal of this chapter
•Present intuitive understanding of device operation
•Introduction of basic device equations
•Introduction of models for manual analysis
•Introduction of models for SPICE simulation
•Analysis of secondary deep-sub-micron effects
•Future trends
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Outline
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Motivation and Goals
Semiconductor Basics
Diode Structure
Operation
» Static model
– Depletion capacitance
– Carrier density profiles

Diffusion capacitance
» Dynamic response
– Switching speed

Spice model
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Semiconductor Basics  I

Electrons in intrinsic (pure) Silicon
»
»
»
»
»
covalently bonded to atoms
“juggled” between neighbors
thermally activated: density  eT
move around the lattice, if free
leave a positively charged `hole’ behind
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http://www.masstech.org/cleanenergy/solar_info/images/crystal.gif
Semiconductor Basics  II

Two types of intrinsic carriers
»
»
»
»
Electrons (ni) and holes (pi)
In an intrinsic (no doping) material, ni=pi
At 300K, ni=pi is low (1010cm-3)
Use doping to improve conductivity
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Semiconductor Basics  III

Extrinsic carriers
» Also two types of dopants (donors or acceptors)
– Donors bring electron (n-type) and become ive ions
– Acceptors bring holes (p-type) and become ive ions
» Substantially higher densities (1015cm-3)
» Majority and minority carriers
– if n>>p (n-type) electrons majority and holes minority
– Random recombination and thermal generation
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The Diode
B
A
Al
SiO
2
p
n
Cross section of pn-junction in an IC process
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N-type region
P-type region
doped with donor
impurities
(phosphorus,
arsenic)
doped with
acceptor
impurities (boron)
The Diode
Simplified structure
A
p
Al
A
n
The pn
region is
assumed to
be thin (step
or abrupt
junction)
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B
One-dimensional
representation
B
diode symbol
Different concentrations of
electrons (and holes) of the p and ntype regions cause a concentration
gradient at the boundary
Depletion Region
•Concentration Gradient causes electrons to diffuse from n to p,
and holes to diffuse from p to n
•This produces immobile ions in the vicinity of the boundary
•Region at the junction with the charged ions is called the
depletion region or space-charge region
•Charges create electric field that attracts the minority carriers,
causing them to drift
•Drift counteracts diffusion causing equilibrium ( Idrift = -Idiffusion )
hole diffusion
electron diffusion
p
n
hole drift
electron drift
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Depletion Region
•Zero bias conditions
hole diffusion
electron diffusion
p
•p more heavily doped
than n (NA > NB)
•Electric field gives rise
to potential difference in
the junction, known as
the built-in potential
(a) Current flow.
n
hole drift
electron drift
Charge
Density

+
x
Distance
-
Electrical
Field
(b) Charge density.

x
(c) Electric field.
V
Potential
-W 1
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
W2
x
(d) Electrostatic
potential.
Built-in Potential
 N A ND 
 0   T ln 

2
n
 i 
Where T is the thermal voltage
kT
T 
 26mV (at 300 K )
q
ni is the intrinsic carrier concentration for
pure Si (1.5 X 1010 cm-3 at 300K), so for
 1 
 1 
N A  1015  3 , N B  1016  3 ,
 cm 
 cm 
 10151016
 0  26 ln 
 1.5 *1010

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
mV  638mV
2


Forward Bias
hole diffusion
electron diffusion
p
n
hole drift
electron drift
+
-
•Applied potential lowers the potential barrier, Idiffusion > I drift
•Mobile carriers drift through the dep. region into neutral regions
•become excess minority carriers and diffuse towards terminals
•Read about drift and diffusion currents at:
•http://ece-www.colorado.edu/~bart/book/book/chapter2/ch2_10.htm
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Forward Bias
n p (x)
pn (x)
Lp
pn0
np0
-Wp
p-region
-W1 0
W2
Metal contact to n-region
pn (W2)
minority carrier concentration
Wn
n-region
diffusion
Typically avoided in Digital ICs
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x
Reverse Bias
hole diffusion
electron diffusion
p
n
hole drift
electron drift
-
+
•Applied potential increases the potential barrier
•Diffusion current is reduced
•Diode works in the reverse bias with a very small drift current
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pn0
np0
n p0
-Wp
p-region
-W1 0
Wn
W2
n-region
diffusion
The Dominant Operation Mode
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Metal contact to n-region
Reverse Bias
x
Models for Manual Analysis
+
ID = IS(eV D/T – 1)
VD
ID
+
+
VD
–
(a) Ideal diode model
•Accurate
•Strongly non-linear
•Prevents fast DC bias
calculations
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–
VDon
–
(b) First-order diode model
•Conducting diode replaced
by voltage source VDon=0.7V
•Good for first order
approximation
Typical Diode Parameters
Geometry, doping and material
constants lumped in Is
Diffusion coefficient
minority carrier concentration
+
VD
ID = IS(eV D/T – 1)
–
•Dn=25 cm2/sec
•Dp=10cm2/sec
•Wn=5 mm
•Wp=0.7 mm
•W2=0.15 mm
•W1=0.03 mm
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I S  qAD ( WnpWn 02  W pn Wp 01 )
D p
typical value
I S  10 17 A / mm 2
D n
Diode Current
VDon  0.7V
VDon  0.7V
Ideal diode equation:
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Depletion Capacitance

Due to depletion charges
» VD changes space charge
» Forms a capacitor Cj
– Charge modulated by voltage

Ideality factor (m) depends on
junction gradient
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Equivalent Capacitances  I

Linearize diode capacitances
» Cj is a non-linear function of VD
– When bias changes then Cj also changes
– Hard to use in manual analyses
» Instead use equivalent capacitance
– Gives the same total charge for a given VD transition
» Equivalent depletion capacitance
– Must be worked out for a given V1V2 transition
Q j Q j (V2 )  Q j (V1 )
Ceq 

 K eqC j 0
VD
V2  V1
 0m (0  V2 )1m  (0  V1 )1m 
K eq 
(V2  V1 )(1  m)
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Equivalent Capacitances  II
» Equivalent diffusion capacitance
– Must be worked out for currents at given V1V2 transition
Q j
I D (V2 )  I D (V1 )
Cd (V2 )  Cd (V1 )
Ceq 
 T
 T
VD
V2  V1
V2  V1

Ceq depends on process constants and {V1,V2}
» Example:
– for AD=0.5 mm2 Cj0=2 fF/mm2, 0=0.64 V and m=0.5
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then Keq0.622 and Ceq1.24 fF/mm2 if switched between 0 and -2.5 V
So unit capacitance Cj 0.9 fF/mm2 or Cj 0.45 fF for the total diode area
Secondary Effects: Breakdown

Cannot bear too large reverse biases
» Drift field in depletion region will get extremely large
» Minority carriers caught in this large field will get very energetic
– Energetic carriers can knock atoms and create a new n-p pair
– These carriers will get energetic, too, and so on: thus large currents!
0.1

Two types
» Avalanche breakdown
ID (A)
– Above mechanism
» Zener breakdown
– More complicated
0

–0.1
–25.0
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–15.0
–5.0
VD (V)
0
5.0
Can damage diode
Diode SPICE Model

Required for circuit simulations
» Must capture important characteristics but also remain efficient
» Extra parameter in the model: n (emission coefficient, 1 n 2)
– Fixes non-ideal behavior due to broken assumptions
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Additional series resistance accounts for body+contact
Nonlinear capacitance includes both CD and Cj
I D  I S (eVD /nT 1)
RS
+
VD
-
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ID
CD
SPICE Parameters
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Often supplied by the fab to the designer
» If not must be measured and fit the parameters
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Assumes default values, if not explicitly defined
Pay attention to the units and spelling
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