solid state electronic devices example 5-3 find an expression for the electron current in the n-type...
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Solid State Electronic Devices
Example 5-3Example 5-3Find an expression for the electron current in the n-type material of a forward-biased p-n junction.
side. p theintojunction theacross electrons of injection theand holes, injected
theion with recombinatfor electrons of supplying theincludes expression This
)1()1()()(
is materialn in thecurrent electron theThus
)1()(
is siden on thecurrent hole The
)1(
iscurrent totalThe
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n
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Lx
p
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kTqVLxn
p
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kTqVp
n
nn
p
p
enL
Dpe
L
DqAxIIxI
eepL
DqAxI
enL
Dp
L
DqAI
pn
pn
Solid State Electronic Devices
3. 3. Reverse Bias3. 3. Reverse Bias
Fig. 18. Reverse-biased p-n junction: minority carrier
distributions near the reverse-biased junction
pnpn
r
Lxn
p
pLxn
p
pn
nkTVq
nn
r
r
epL
DqAep
L
DqAp
pepp
q
kTV
VV
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)(
)1(
When
n respect to with biased negatively p
If
Physically, extraction occurs because
minority carriers at the edges of the
depletion region are swept down the
barrier at the junction by the E field,
and holes in the n region diffuse toward
the junction.
Solid State Electronic Devices
Example 5-4Example 5-4
Consider a volume of n-type material of area A, with a length of one hole
diffusion length Lp. The rate of thermal generation of holes within the
volume is
Assume that each thermally generated hole diffuses out of the volume
before it can recombine. The resulting hole current is I=qALppn/τp, which is
the same as the saturation current for a p+-n junction. We conclude that
saturation current is due to the collection of minority carriers thermally
generated within a diffusion length of the junction.
p
nnnrirth
p
np
ppnng
pAL
2 since
Solid State Electronic Devices
4. Reverse-bias Breakdown4. Reverse-bias Breakdown
< Preface >< Preface >
• If the current is not limited externally, the junction can be damaged by excessive
reverse current, which overheats the device as the maximum power rating is
exceeded.
• It is important to remember, however, that such destruction of the device is not
necessarily due to mechanisms unique to reverse breakdown.
• The first mechanism, called the Zener effect, is operative at low voltages(up to a few
volts reverse bias).
• The breakdown occurs at higher voltages(from a few volts to thousands of volts), the
mechanism is avalanche breakdown.
Solid State Electronic Devices
4. 1. Zener Breakdown4. 1. Zener Breakdown
Fig. 20. The Zener effect: (a) heavily doped junction at equilibrium; (b) reverse bias with
electron tunneling from p to n; (c) I-V characteristic
Heavily doped junction → High electric fields → Tunneling effect occurs
High electric field makes steep energy band, and reverse bias makes narrower width of barrier.
Solid State Electronic Devices
4. 2. Avalanche Breakdown4. 2. Avalanche Breakdown
Fig. 21. Electron-hole pairs created by impact ionization : (a) a single ionizing collision by an
incoming electron in the depletion region of the junction; (b) primary, and tertiary collisions
• Lightly doping
• Breakdown mechanism is the impact ionization of host atoms by energetic carriers.
nbr
in
out
n
inout
VVM
P
PPPn
n
M
PPPnn
)/(1
11
1
1
tion)multiplica (Electron
...)1(
32
32
Solid State Electronic Devices
4. 2. Avalanche Breakdown4. 2. Avalanche Breakdown
Fig. 22. Variation of avalanche breakdown voltage in abrupt p+-n junctions, as a function of
donor concentration on the n side, for several semiconductors.
• In general, the critical reverse
voltage for breakdown increases
with the band gap of the material,
since more energy is required for an
ionizing collision.
• Vbr decreases as the doping
increases, as Fig. indicates.
Solid State Electronic Devices
4. 3. Rectifiers4. 3. Rectifiers
Fig. 23. Piecewise-linear approximations of junction diode characteristics : (a) the ideal
diode; (b) ideal diode with an offset voltage; (c) ideal diode with an offset voltage and a
resistance to account for slope in the forward characteristic.
• Most forward-biased diodes exhibit an offset voltage E0, which can be approximated in a
circuit model by a battery in series with the ideal diode and resister R.
Solid State Electronic Devices
4. 3. Rectifiers4. 3. Rectifiers
Fig. 24. Beveled edge and guard ring to prevent edge breakdown under reverse bias : (a)
diode with beveled edge; (b) closeup view of edge, showing reduction of depletion region
near the bevel; (c) guard ring
A short, lightly doped region → The reason of punch-through
It is possible for W to increase until it fills the entire length of this region.
→ The result of punch-through is a breakdown below the value of Vbr
Solid State Electronic Devices
4. 4. Breakdown Diode4. 4. Breakdown Diode
Fig. 26. A breakdown diode : (a) I-V characteristic; (b) application as a voltage regulator
• It is designed for a specific breakdown voltage(higher doping). Such diodes are also called
Zener diodes(several hundred voltages).
• It can be used as voltage regulators in circuits with varying inputs.
Solid State Electronic Devices
5. Transient and A-C Conditions5. Transient and A-C Conditions
< Preface >< Preface >
• Since most solid state devices are used for switching or for processing a-c
signals, we cannot claim to understand p-n junctions without knowing at
least the basics of time dependent processes.
• In this section we investigate the important influence of excess carriers in
transient and a-c problems.
• The switching of a diode from its forward state to its reverse state is
analyzed to illustrate a typical transient problem.
Solid State Electronic Devices
5. 1. Time Variation of Stored Charge5. 1. Time Variation of Stored Charge
Fig. 4-16. Current entering and leaving a volume ΔxA.
p
pp
xxx
p
x
xxJxJ
qt
p
)()(1
equation continuity The :ion recombinat andDiffusion
Jp(x)
Jp(x+Δx)Δx
Rate of increase of hole concentra- recombination
Hole buildup tion in ΔxA per unit time rate
t
txpq
txpq
x
txJ
p
p
),(),(),(
eq. above from t timeandx position at
current theof component each obtain can We
Fig. 4-16
x
ppp dx
t
txptxpqxJJ
0
),(),()()0(
obtain t toat time sidesboth integratecan We
Solid State Electronic Devices
5. 1. Time Variation of Stored Charge5. 1. Time Variation of Stored Charge
carriersminority providing : (2) (1)
: carriers excess decreasingor Increasing (2)
/ : carriers excess ofion Recombinat (1)
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dt
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Q
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txiti
p
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p
p
p
nnnnp
np
Solid State Electronic Devices
5. 1. Time Variation of Stored Charge5. 1. Time Variation of Stored Charge
Fig. 27. Effects of a step turn-off transient in a p+-n diode: (a) current through the diode; (b)
decay of stored charge in the n-region; (c) excess hole distribution in the n-region as a
function of time during the transient.
Stored charges are
recombination with electrons
ptpp
p
pp
pppp
pp
p
p
p
eItQ
s
IsQ
IssQsQ
IQti
dt
tdQtQti
/)(
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)()(1
0
)0(,0)0(
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ionrecombinatafter charges stored ofon distributiCarrier
Solid State Electronic Devices
5. 1. Time Variation of Stored Charge5. 1. Time Variation of Stored Charge
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instant,any at charge stored for the have We
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n
p
pn
pn
t
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p
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Lxnp
Lxnn
n
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kTtqvnn
epqAL
I
q
kTtv
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tQeptptpqALdxetpqAtQ
etptxp
tv
p
p
eptp
Solid State Electronic Devices
5. 2. Reverse Recovery Transient5. 2. Reverse Recovery Transient
Fig. 28. Stored delay time in a p+-n diode: (a) circuit and input square wave; (b) hole
distribution in the n-region as a function of time during the transient; (c) variation of current
and voltage with time; (d) sketch of transient current and voltage on the device I-V
characteristic
= p(xn)-pn
t=0, p-n diode has forward-bias.
Ir=-E/R, when stored charges are
totally recombination.
It’s desirable that tsd is small
compared with the switching time.
Solid State Electronic Devices
5. 2. Reverse Recovery Transient5. 2. Reverse Recovery Transient
Fig. 28. Effects of storage delay time on switching signal: (a) switching voltage; (b) diode current
2
1
sd
sd
erf
lifetime.carrier theis gdeterminin parameter critical The
e.delay tim storage is
rf
fpsd II
Iτt
t
t
Solid State Electronic Devices
Example 5-5Example 5-5At the time t=0 the current is switched to –Ir at a forward biased p+-n diode.Apply appropriate boundary condition and quasi-steady state approximation to find the tsd.
)/1(/1)(
)()(
ms, transforLaplace Using
0,for t )()(
)(
47),-(5 Eq. From
p
r
p
pfp
pfpp
pr
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p
p
ss
I
s
IsQ
IssQsQ
s
I
IQdt
tdQtQti
r
fp
rf
rpsd
sd
trfr
p
pn
npp
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I
I
II
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pp
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:obtain weand , when zero equal set to is This
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52),-(5 Eq.in as )()( that Assuming
])([
)1()(
/
/
//
Solid State Electronic Devices
5. 3. Switching Diodes5. 3. Switching Diodes
• A diode with fast switching properties → either store very little charge in the
neutral regions for steady forward currents, or have a very short carrier lifetime, or
both.
The methods to improve the switching speed of a diode.The methods to improve the switching speed of a diode.
1. To add efficient recombination centers to the bulk material. For Si diodes, Au
doping is useful for this purpose. The carrier lifetime varies with the reciprocal of
the recombination center concentration.
2. To make the lightly doped neutral region shorter than a minority carrier diffusion
length. This is the narrow base diode. In this case the stored charge for forward
conduction is very small, since most of the injected carriers diffuse through the
lightly doped region to the end contact. → Very little time required to eliminate the
stored charge in the narrow neutral region.
Solid State Electronic Devices
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5. 4. Capacitance of p-n Junctions5. 4. Capacitance of p-n Junctions
1) Junction capacitance : dominant under reverse bias
2) Charge storage capacitance : dominant under forward bias
dV
dQC Junction CapacitanceJunction Capacitance
Solid State Electronic Devices
5. 4. Capacitance of p-n Junctions5. 4. Capacitance of p-n Junctions
tmeasuremen ecapacitanc t viameasuremenion concentrat doping
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W
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p+ n
xp0 xn0
Solid State Electronic Devices
switching good/circuit frequency -highin junction
n-p biased-forwardfor effect switchinglimit ecapacitanc storage charge The
econductanc c-a
charge stored in this changes small todue eCapacitanc
ondistributi hole injected in the charge stored
currentsteady a with biased Forward
/
/2
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dV
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dV
dIG
IkT
qepAL
kT
q
dV
dQC
epqALLpqAIQ
s
kTqV
p
nps
ppkTqV
npp
s
kTqVnppnpp
5. 4. Capacitance of p-n Junctions5. 4. Capacitance of p-n Junctions
Charge Storage CapacitanceCharge Storage Capacitance
Solid State Electronic Devices
5. 4. Capacitance of p-n Junctions5. 4. Capacitance of p-n Junctions
Fig. 30. Depletion capacitance of a junction: (a) p+-n junction showing variation of depletion
edge on n side with reverse bias. Electrically, the structure looks like a parallel plate capacitor
whose dielectric is the depletion region, and the plates are the space charge neutral regions; (b)
variation of depletion capacitance with reverse bias.
Solid State Electronic Devices
5. 4. Capacitance of p-n Junctions5. 4. Capacitance of p-n Junctions
Fig. 31. Diffusion capacitance in p-n junctions. (a) Steady-state minority carrier distribution for a
forward bias, V, and reduced forward bias, V-ΔV in a long diode; (b) minority carrier distributions
in a short diode; (c) diffusion capacitance as a function of forward bias in long and short diodes.