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Transcript of Microsoft PowerPoint - 1. CHAPTER_1 [Compatibility Mode]
p – n junction
The p-n junction is the basic element of allbipolar devices. Its main electrical property isthat it rectifies (allow current to flow easily in onedirection only).The p-n junction is often justcalled a DIODE. Applications;
>photodiode, light sensitive diode,>LED- ligth emitting diode,>varactor diode-variable capacitance diode
pp –– n junctionn junction
The p-n junction can be formed by pushing apiece of p-type silicon into close contact with apiecce of n-type silicon. But forming a p-njunction is not so simply. Because;
1) There will only be very few points of contactand any current flow would be restricted tothese few points instead of the whole surfacearea of the junction.
2) Silicon that has been exposed to the air alwayshas a thin oxide coating on its surface calledthe “native oxide”. This oxide is a very goodinsulator and will prevent current flow.
3) Bonding arrangement is interrupted at thesurface; dangling bonds.
The formation of pThe formation of p--n junction :n junction :
To overcome these surface states problems
p-n junction can be formed in the bulk of thesemiconductor, away from the surface as
much as possible.
Surface states
pp –– n junctionn junction
There is a big discontinuity in the fermi level accross thep-n junction.
EC
Eİ
EV
Ef
EC
Eİ
EV
Ef
EC
Eİ
EV
Ef
p-type n-typeEC
Eİ
EV
Ef
p-type n-type
++++++++++++++++++++++++++++++++++++++++
- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -- - - - -
HoleMovement
ElectronMovement
++++++++++++
Fixed positivespace-charge
- - - -- - - -- - - -
Fixed negativespace-charge
Ohmicend-contact
n-type p-type
Metallurgicaljunction
Lots of electrons on the left hand side of thejunction want to diffuse to the right and lots ofholes on the right hand side of the junction wantto move to the left.
The donors and acceptors fixed,don’t move(unless you heat up semiconductors, so they candiffuse) because they are elements (such asarsenic and boron) which are incorporated tolattice.
However, the electrons and holes that come fromthem are free to move.
pp –– n junctionn junction
Holes diffuse to the left of the metalurgical junction andcombine with the electrons on that side. They leave behindnegatively charged acceptor centres.
Similarly, electrons diffusing to the right will leave behindpositively charged donor centres. This diffusion process cannot go on forever. Because, the increasing amount of fixedcharge wants to electrostatically attract the carriers that aretrying to diffuse away(donor centres want to keep theelectrons and acceptor centres want to keep the holes).Equlibrium is reached.
This fixed charges produce an electric field which slowsdown the diffusion process.
This fixed charge region is known as depletion region orspace charge region which is the region the free carriershave left.
It is called as depletion region since it is depleted of freecarriers.
Idealized pIdealized p--n junctionn junction
Energy level diagram for the p-n junction in thermal equilibrium
EC
EV
Ef
p-type n-type
EC
EV
Ef
Depletion region
Hole Diffussion
Hole Drift
Electron DiffusionElectron Drift
Neutral p-region
Neutral n-region
2
( ) ( ) 0 (1)
( )
0 (2)
1 ( )
p p p
p
p p x p
pix p
J J drift J diffusion
AJ is the hole current densitycm
dpJ q pE qDdx
wherekTdEE D Einstein relation
q dx q
Thermal equilibrium; no applied field; no net currentThermal equilibrium; no applied field; no net currentflowflow
Drift current is due toelectric field at thejunction; minoritycarriers.
Diffusion current isdue the toconcentrationgradient; majoritycarriers.
ProofProof
( ) 0 ( 3 )
e x p ( ) ( )
0 ( 4 )
0
.
0 ( 5 )
ip p
i f fii
fp p
f
fn n
d E d pJ p k Td x d x
E E d Ed Ed p pp nk T d x k T d x d x
d EJ p
d x
d Ew e c o n c lu d e th a t w h ic h s ta te s th a t
d xth e F e r m i L e v e l i s a C O N S T A N T a t e q u i l ib r iu m
d EJ n
d x
The drift and diffusion currents are flowing all thetime. But, in thermal equilibrium, the net currentflow is zero since the currents oppose each other.
Under non-equilibrium condition, one of thecurrent flow mechanism is going to dominateover the other, resulting a net current flow.
The electrons that want to diffuse from the n-type layer to the p-layer have potential barier.
ProofProof
The potential barrier height accross a p-n junction isknown as the built in potential and also as the junctionpotential.
The potential energy that this potential barrier correspondis
biV
pp –– n junction barrier height,n junction barrier height, biV
biqV• Electron energy is positive upwards in the energy leveldiagrams, so electron potentials are going to be measuredpositive downwards.
• The hole energies and potentials are of course positive inthe opposite directions to the electrons
EC
EV
Ef
p-type n-type
EC
EV
Ef
Depletion region
Ei
Ei
biqV
pqVnqV
Ele
ctrıo
n en
ergy
Ele
ctro
n po
tent
ial
pp –– n junction barrier heightn junction barrier height
2
e x p
ln ( 2 )
ln (3 )
,
ln ( 4 )
i fi
Ap
i
n
Dn
i
A Db i n p
i
E Ep n
k Tk T NVq n
S im i la r ly fo r Vk T NVq n
F o r fu l l io n iz a t io n th e b u i l t in v o l ta g e is a s u m o fk T N NV V Vq n
The intrinsic Fermi Level is a very useful reference level in asemiconductor.
The pThe p –– n junction barrier heightn junction barrier height
( ) (1)p i fqV E E
CurrentCurrent MechanismsMechanisms,
Diffusion of the carrierscause an electric in DR.
Drift current is due tothe presence of electricfield in DR.
Diffusion current is dueto the majority carriers.
Drift current is due tothe minority carriers.
pp –– n junction in thermal equilibriumn junction in thermal equilibriumE
lect
rıon
ener
gy
+ + ++ + ++ + +
- - - -- - - -- - - -
Neutralp-region
Neutraln-region
Hole Diffussion
Electron Diffusion
Electron Drift
Hole Drift
Field Direction
Hol
e en
ergu
y
EC
EV
Ef
DRDR
nn –– p junction at equilibriump junction at equilibrium
Ele
ctrıo
n en
ergy
+ + ++ + ++ + +
- - - -- - - -- - - -
Neutralp-region
Neutraln-region
Hole Diffussion
Electron Diffusion
Electron Drift
Hole Drift
Field Direction
Hol
e en
ergu
y
EC
EV
Ef
DRDR
When electrons and holes are diffusing from highconcentration region to the low concentration region theyboth have a potential barrier. However, in drift case ofminority carriers there is no potential barrier.
BuiltBuilt inin potentialpotential ;;
Diffusion :Diffusion :
2lni
DAbi n
NNq
kTV
At fixed , is determined by the number of and atoms.bi A DT V N N
Depletion Approximation, Electric Field and Potential for pnDepletion Approximation, Electric Field and Potential for pnjunctionjunction
+ + ++ + +
- - - -- - - -p-type n-type
Pote
ntia
l
Ele
ctric
field
Cha
rge
dens
ity
+ + ++ + +
- - - -- - - -
biVarea
mE
biqVxx
xx
xx
DepletionRegion
At equilibrium, there isno bias, i.e. no appliedvoltage.
The field takes thesame sign as thecharge
The sign of the electricfield is opposite to thatof the potential ;
nv
dVEdx
nx px
Charge density is negative on p-side and positive on n-side.
As seen from the previous diagram, the charge distributionis very nice and abrupt changes occur at the depletionregion (DR) edges. Such a junction is called as an abruptjunction since the doping abruptly changes from p- to n-type at the metallurgical junction (ideal case).
th e w id th o f th e D R o n n -s id eth e w id th o f th e D R o n p -s id e
n
p
xx
Depletion Approximation, Electric Field and Potential for pnDepletion Approximation, Electric Field and Potential for pnjunctionjunction
In reality, the charge distribution tails-off into theneutral regions, i.e. the charge distrubition is notabrupt if one goes from depletion region into theneutral region. This region is called as atransition region and since the transition region isvery thin, one can ignore the tail-off region andconsider the change being abrupt. So thisapproximation is called as DEPLETIONAPPROXIMATION.
Depletion Approximation, Electric Field and Potential for pnDepletion Approximation, Electric Field and Potential for pnjunctionjunction
The electric field is zero at the edge of the DR and increasesin negative direction. At junction charge changes its sign sodo electric field and the magnitude of the field decreases (itincreases positively).
Electric Field Diagram :
Potential Diagram :
Since the electric field is negative through the wholedepletion region ,DR, the potential will be positive throughthe DR. The potential increases slowly at left hand side butit increases rapidly on the right hand side. So the rate ofincrease of the potential is different an both sides of themetallurgical junction. This is due to the change of sign ofcharge at the junction.
Depletion Approximation, Electric Field and Potential for pnDepletion Approximation, Electric Field and Potential for pnjunctionjunction
+ + ++ + +
- - - -- - - - p-typen-type
+ + ++ + +
- - - -- - - -
biVarea mE
xx
xx
xx
DepletionRegion
Field direction is positive x direction
Field direction
Depletion Approximation, Electric Field and Potential for npDepletion Approximation, Electric Field and Potential for npjunctionjunction
Pote
ntia
l
E
lect
ric
field
Cha
rge
dens
ity
Abrupt junctionAbrupt junction
+ + ++ + +
- - - -- - - -p-type n-type
Cha
rge
dens
ity + + ++ + +
- - - -- - - -
xx
DepletionRegion
pxnx
• The amount of uncoverednegative charge on the left handside of the junction must beequal to the amount of positivecharge on the right hand side ofthe metalurgical junction.Overall space-charge neutralitycondition;
A p D nN x N x
w
pnDA xxNN when
The higher doped side of the junctionhas the narrower depletion width
xxnn and xxpp is the width of the depletion layer on the n-sideand p-side of the junction, respectively.
Unequal impurity concentration results an unequaldepletion layer widths by means of the charge neutralitycondition;
Abrupt junctionAbrupt junction
nDpA xNxN ..
W = total depletionregion
When (unequal impurity concentrations) and , W
D A
p n p
N Nx x x
Abrupt junctionAbrupt junction
When WA D n p nN N x x x
• Depletion layer widths for n-side and p-side
)(21
)(21
DA
DAbiSi
Ap
DA
DAbiSi
Dn
NNqNNV
Nx
NNqNNV
Nx
Abrupt junctionAbrupt junction
F o r e q u a l d o p i n g d e n s i t i e s W
T o t a l d e p le t i o n l a y e r w i d t h , W
21 1( )( )
2 ( )
n p
S i b i A D
A D A D
S i b i A D
A D
x x
V N NWN N q N N
V N NWq N N
Abrupt junctionAbrupt junction
12 permittivity of vacuum 8 85 10 relative permittivity of Silicon 11 9
, and W depends on , and
ln
-Si o r o
r
n p A D bi
Abi
. x F/m.
x x N N V
kT N NVq
2D
in
OneOne--Sided abrupt pSided abrupt p--n junctionn junction
+ + ++ + +
--p-type n-type
+ + ++ + +
--
xx
nxpx
+ + ++ + +
- - - -- - - -
DepletionRegion
Abrupt pAbrupt p--n junctionn junction
DA NN heavily doped p-type
neglectedbecanpx
OneOne--Sided abrupt pSided abrupt p--n junctionn junction
D
2 21 1
2 obtain a similar equation for W
in the case of N
Si bi A D Si bi A Dn
D A D D A
Si bip
D
A
V N N V N NW xN q N N N qN
VW xqN
N
neglegtedsince NA>>ND
One-sided abrupt junction
OneOne--Sided abrupt pSided abrupt p--n junctionn junction
+ + ++ + +
--p-type n-type
Pote
ntia
l
E
lect
ric
field
Cha
rge
dens
ity
+ + ++ + +
--
biVarea
mE
biqVxx
xx
xx
nxpx
Electric field
-x direction
Appliying bias to pAppliying bias to p--n junctionn junction
p n
+ -
forward bias
p n
- +
reverse bias
How current flows through the p-njunction when a bias (voltage) isapplied.
The current flows all the time whenevera voltage source is connected to thediode. But the current flows rapidly inforward bias, however a very smallconstant current flows in reverse biascase.
There is no turn-on voltage because current flows in anycase. However , the turn-on voltage can be defined as theforward bias required to produce a given amount of forwardcurrent.
If 1 m A is required for the circuit to work, 0.7 volt can becalled as turn-on voltage.
Appliying bias to pAppliying bias to p--n junctionn junction
VVbb II00
VVbb ; Breakdown voltage
II0 ;0 ; Reverse saturation current
Forward BiasForward BiasReverse BiasReverse BiasI(current)
V(voltage)
Appliying bias to pAppliying bias to p--n junctionn junction
+ - - +
p n p n p n
biqV
biV
Fbi VVq
Fbi VV
bi rq V V
Rbi VV
+ ++ +
- -- -
++
--
+ ++ +
- -- -
Pote
ntia
l Ene
rgy
Zero Bias Forward Bias Reverse Bias
Ec
EvEv Ev
Ec Ec
When a voltage is applied to a diode , bands moveand the behaviour of the bands with appliedforward and reverse fields are shown in previousdiagram.
Appliying bias to pAppliying bias to p--n junctionn junction
voltagereverse voltageforward
R
F
VV
Junction potential reduced Enhanced hole diffusion from p-side to n-side compared
with the equilibrium case. Enhanced electron diffusion from n-side to p-side compared
with the equilibrium case. Drift current flow is similar to the equilibrium case. Overall, a large diffusion current is able to flow. Mnemonic. Connect positive terminal to p-side for forward
bias.
Forward BiasForward Bias
Drift current is very similar to that of the equilibrium case.This current is due to the minority carriers on each side ofthe junction and the movement minority carriers is due tothe built in field accross the depletion region.
Junction potential increased Reduced hole diffusion from p-side to n-side compared with
the equilibrium case. Reduced electron diffusion from n-side to p-side compared
with the equilibrium case Drift current flow is similar to the equilibrium case. Overall a very small reverse saturation current flows. Mnemonic. Connect positive terminal to n-side for reverse
bias.
Reverse BiasReverse Bias
Qualitative explanation of forward biasQualitative explanation of forward bias
+ -
p n++
--
ppnn
ppnono
nnpopo
npnp
p-n junction in forward bias
Junction potential is reducedfrom VVbibi to VVbibi--VVFF..
By forward biasing a largenumber of electrons areinjected from n-side to p-sideaccross the depletion regionand these electrons becomeminority carriers on p-side,and the minority recombinewith majority holes so that thenumber of injected minorityelectrons decreases (decays)exponentially with distanceinto the p-side.
Car
rier
Den
sity
Similarly, by forward biasing a large number ofholes are injected from p-side to n-side acrossthe DR. These holes become minority carriers atthe depletion region edge at the n-side so thattheir number (number of injected excess holes)decreases with distance into the neutral n-side.
In summary, by forward biasing in fact oneinjects minority carriers to the opposite sides.These injected minorites recombine withmajorities.
Qualitative explanation of forward biasQualitative explanation of forward bias
How does current flow occur if all the injectedminorities recombine with majorities ?
If there is no carrier; no current flow occurs. Consider the role of ohmic contacts at both ends
of p-n junction. The lost majority carriers are replaced by the
majority carriers coming in from ohmic contactsto maintain the charge neutrality.
The sum of the hole and electron currents flowingthrough the ohmic contacts makes up the totalcurrent flowing through the external circuit.
Qualitative explanation of forward biasQualitative explanation of forward bias
“o” subscript denotes the equilibrium carrierconcentration.
Ideal diode equationIdeal diode equation
material.type-ninionconcentratholemequilibriu
material.type-pinionconcentratholemequilibriu
material.type-pinionconcentratelectronmequilibriumaterial.type-ninionconcentratelectronmequilibriu
no
po
po
no
ppnn
2. inpn
At equilibrium case ( no bias )
Ideal diode equationIdeal diode equation
)2(.
)1(.
.
2
2
2
materialtypepnpnmaterialtypennpn
npn
ipopo
inono
i
Ideal diode equationIdeal diode equation
2
22
ln assuming full ionization
; majority carriers
.ln . for n-type
ln exp (3)
A Dbi
i
A po D no
po nobi no no i
i
po bibi po no
no
kT N NVq n
N p N n
p nkTV n p nq n
p qVkTV p pq p kT
Ideal diode equationIdeal diode equation
22
, (2)
.ln .
ln exp (4)
po nobi po po i
i
no bibi no po
po
Similarly from equation
p nkTV n p nq n
n qVkTV n nq n kT
This equation gives us the equilibrium majority carrier concentration.
Ideal diode equationIdeal diode equation
What happens when a voltage appears across the p-n junction ?
Equations (3) and (4) still valid but you should drop (0)subscript and change VVbibi with
i.i. VVbibi –– VVFF if a forward bias is applied.ii.ii. VVbibi + V+ VRR if a reverse bias is applied.if a reverse bias is applied.
VVFF :: forward voltageVVR :R : reverse voltageWith these biases, the carrier densities change from equilibrium
carrier densities to non- equilibrium carrier densities.
Ideal diode equationIdeal diode equation
Non-equilibrium majority carrier concentration in forwardbias;
( )e x p
F o r e x a m p le ; f o r r e v e r s e b i a s
( )e x p
b i Fp n
n
b i Rn p
q V Vp pk T
n
q V Vn nk T
• When a voltage is applied; the equilibrium nno changes tothe non equilibrium nn.
Assumption; low level injectionAssumption; low level injection
• For low level injection; the number of injected minorities ismuch less than the number of the majorities. That is theinjected minority carriers do not upset the majority carrierequilibrium densities.
pop
non
ppnn
• Non equilibrium electron concentration in n-type when aforward bias is applied ,
( )exp non-equilibrium.bi Fn p
q V Vn nkT
Ideal diode equationIdeal diode equation
( ) (5)
exp (6)
bi Fn no no p
bino po
q V Vn n n nkT
qVn nkT
combining (5) and (6)
( )exp expbi F bip po
q V V qVn nkT kT
Ideal diode equationIdeal diode equation
poexp and subtracting n from both sides
exp 1
the excess concentration of minority electronsover the equilibrium concentration at the edge of the DR
Fp po
p po po n
n
qVn nkT
qVn n nkT
Solving for non-equilibrium electron concentration in p-typematerial, i.e. np
Ideal diode equationIdeal diode equation
Similarly ,
exp 1 the non-equilibriumn no no pqVp p pkT
the excess concentration of minority holes
over the equilibrium concentration at the edge of the DRp
Forward-bias diode; injection of minority carriers across DR
+ -
p n++
--
BB
ppnono
nnpopo
AA
nnnono
pppopo
point A
point Bp po
n no
n np p
lnlp
• is the distance from DR edge into p-side
• is the distance from DR edge into n-sidep
n
ll
When a forward bias is applied; majoritycarriers are injected across DR andappear as a minority carrier at the edgeof DR on opposite side. These minoritieswill diffuse in field free opposite-regiontowards ohmic contact. Since ohmiccontact is a long way away, minoritycarriers decay exponentially withdistance in this region until it reaches toits equilibrium value.
Exponential decay of injected minority carriers on oppositeExponential decay of injected minority carriers on oppositesidessides
The excess injected minorities decay exponentially as
p
( ) (0 ) e x p
( ) (0 ) e x p
a n d L a re d iffu s io n le n g th s
fo r e le c tro n s a n d h o le s
pp
n
nn
p
n
lp l n
L
ln l pL
L
Number of Injected Minority Holes Across The Depletion RegionNumber of Injected Minority Holes Across The Depletion Region
• By means of forward-biasing a p-n junctiondiode, the holes diffuse from left to right accrossthe DR and they become minority carriers.
• These holes recombine with majority electronswhen they are moving towards ohmic constants.
• So, the number of minority holes on the n-regiondecreases exponentially towards the ohmiccontact. The number of injected minorityholes;excess holes;
( ) (0) exp( )nn
p
lp l pL
Distance into then regionfrom the Depletion Region
Diffusion Length forholes
Number of Injected Minority Holes Across The Depletion RegionNumber of Injected Minority Holes Across The Depletion Region
point A
( ) (0)exp( )
(0) exp( ) 1
(0) exp 1
p po
pp
n
po
no
n n
ln l n
L
qVn nkT
qVp pkT
Ideal diode equationIdeal diode equation
• Similarly by means offorward biasing a p-njunction, the majorityelectrons are injectedfrom right to left acrossthe Depletion Region.These injected electronsbecome minorities at theDepletion Region edge onthe p-side, and theyrecombine with themajority holes. When theymove into the neutral p-side, the number ofinjected excess electronsdecreases exponentially.
)exp(1)exp()(
)exp()0()(
n
ppopn
n
pnpn
Ll
kTqVnl
Ll
l
Ideal diode equationIdeal diode equationDiffusion current density for electrons ;
( ) exp 1 exp
( 0) exp 1 Minus sign shows that electron current
density is
n po pn n n p
n n
n pon p
n
D n ldn d qVJ qD qD n l qdx dx L kT L
qD n qVJ lL kT
in opposite direction to increasing .That is in the positive x direction.
Similarly for holes;pl
( 0) exp 1
The total current density;
exp 1
p nop n p
p
n po p noTotal n p
n p
qD pdp qVJ l qDdx L kT
D n D p qVJ J J qL L kT
Ideal diode equationIdeal diode equation
exp 1 exp 1
multiplying by area ;
exp 1
n po p noTotal o
n p
o
D n D p qV qVJ q JL L kT kT
qVI IkT
Ideal diode equationIdeal diode equation
This equation is valid for both forward and reverse biases; just change theThis equation is valid for both forward and reverse biases; just change thesign of V.sign of V.
Ideal diode equationIdeal diode equation
• Change V with –V for reverse bias. When qV>a few kT;exponential term goes to zero as
VVBB II00
VVBB ; Breakdown voltage
II0 ;0 ; Reverse saturation current
Forward BiasForward Bias
Reverse BiasReverse Bias
oII Reverse saturation currentexp 1oqVI IkT
Current
Voltage
Forward bias current densitiesForward bias current densities
+ -
p n
ln=0lp=0
Ohmic contact
pntotal JJJ
pJnJCur
rent
den
sity
Jtotal is constant through thewhole diode.
Minority current densitiesdecreases exponentially intothe the neutral sides whereasthe current densities due tothe majorities increase into theneutral sides.
pp--n junction in reverse biasn junction in reverse bias
• Depletion region gets bigger withincreasing reverse bias.
• Reverse bias prevents largediffusion current to flow throughthe diode.
• However; reverse bias doesn’tprevent the small current flowdue to the minority carrier. Thepresence of large electric fieldacross the DR extracts almost allthe minority holes from the n-region and minority electronsfrom the p-region.
• This flow of minority carriersacross the junction constitudes I0,the reverse saturation current.
• These minorities are generatedthermally.
- +
p n
ln=0lp=0
pntotal JJJ
pJnJ
Cur
rent
den
sity
Car
rier d
ensi
ty
pnnp
pnonpo
pp--n junction in reverse biasn junction in reverse bias
• The flow of these minorities produces the reversesaturation current and this current increasesexponentially with temperature but it is independent ofapplied reverse voltage.
VVbb II00
VVBB ; Breakdown voltage
II0 ;0 ; Reverse saturation current
Forward BiasForward Bias
Reverse BiasReverse BiasDrift current
I(current)
V(voltage)
Junction breakdown or reverse breakdownJunction breakdown or reverse breakdown
• An applied reverse bias (voltage) will result in a smallcurrent to flow through the device.
• At a particular high voltage value, which is called asbreakdown voltage VB, large currents start to flow. If thereis no current limiting resistor which is connected in seriesto the diode, the diode will be destroyed. There are twophysical effects which cause this breakdown.
1)1) ZenerZener breakdownbreakdown is observed in highly doped p-njunctions and occurs for voltages of about 5 V or less.
2)2) AvalancheAvalanche breakdownbreakdown is observed in less highly dopedp-n junctions.
Zener breakdownZener breakdown
• Zener breakdown occurs at highly doped p-njunctions with a tunneling mechanism.
• In a highly doped p-n junction the conductionand valance bands on opposite side of thejunction become so close during the reverse-biasthat the electrons on the p-side can tunnel fromdirectly VB into the CB on the n-side.
Avalanche BreakdownAvalanche Breakdown
• Avalanche breakdown mechanism occurs whenelectrons and holes moving through the DR andacquire sufficient energy from the electric fieldto break a bond i.e. create electron-hole pairsby colliding with atomic electrons within thedepletion region.
• The newly created electrons and holes move inopposite directions due to the electric field andthereby add to the existing reverse bias current.This is the most important breakdownmechanism in p-n junction.
Depletion CapacitanceDepletion Capacitance
• When a reverse bias is applied to p-n junction diode, thedepletion region width, W, increases. This cause an increasein the number of the uncovered space charge in depletionregion.
• Whereas when a forward bias is applied depletion regionwidth of the p-n junction diode decreases so the amount ofthe uncovered space charge decreases as well.
• So the p-n junction diode behaves as a device in which theamount of charge in depletion region depends on the voltageacross the device. So it looks like a capacitor with acapacitance.
Depletion CapacitanceDepletion Capacitance
Capacitance of a diode varies with WW (Depletion Region width)
WW (DR width varies width applied voltage VV )
VQC
Charge stored incoloumbs
Voltage across thecapacitor in volts
Capacitancein farads
Depletion CapacitanceDepletion Capacitance
2
Capacitance per unit area of a diode ;
For one-sided abrupt junction; e.g.
SiDEP
A D n n
A p D n
FCW cm
N N x W xN x N x
2 fo r
T h e ap p lica tio n o f reve rse b ia s ;
2 ( )2 ( )
S i S i S i b iD E P n A D
n D
S i S i DD E P
b i RS i b i R
D
VC x N NW x q N
q NCV VV V
q N
Depletion CapacitanceDepletion Capacitance2
2
If one makes measurements and draw 1against the voltage ; built-in voltage anddoping density of low-doped side of the diode fromthe intercept and slope.
2( )1
2
R
bi R
Si D
S
C - V /CV obtain
V VC q N
slopeq
2 ln( )A Dbi
i D i
kT N NVN q n