-
Notes from the Book
Fundamentals of Modern VLSI Devices
Book Authors: Taur and Ning
[email protected]
Last Updated: August 4, 2014
-
Contents
1 Chapter 1: Introduction 2
2 Chapter 2: Basic Device Physics 32.1 Discharge Time of a
Forward-Biased Diode . . . . . . . . . . . . . . . . . . . . . . .
. . . 32.2 Diffusion Capacitance . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 42.3 MOS Capacitors . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 52.4 Key Notes from the Chapter . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 5
3 Chapter 3: MOSFET Devices 12
4 Chapter 4: CMOS Device Design 13
5 Chapter 5: CMOS Performance Factuors 14
6 Chapter 6: Bipolar Devices 15
7 Chapter 7: Bipolar Device Design 16
8 Chapter 8: Bipolar Performance Factors 17
9 Chapter 9: Memory Devices 18
10 Chapter 10: Silicon On Insulator 19
1
-
Chapter 1
Chapter 1: Introduction
2
-
Chapter 2
Chapter 2: Basic Device Physics
2.1 Discharge Time of a Forward-Biased Diode
1. Suppose a n+-p diode with base as n-type is forward-biased
during t < 0 and reverse-biased duringt > 0. To understand
the discharge time the forward bias and reverse bias voltage is
more thanthe voltage across the depletion region which is of the
order of 1V. At t = 0, the external bias isswitched to a reverse
voltage of VR. The excess electrons in the base start to diffuse
back towardsthe depletion region of the diode. Those electrons at
the edge of depletion region of base are sweptaway by the electric
field in the depletion region towards the n+-emitter at a saturated
velocity ofabout 107 cm/s.
2. The depletion layer width is on the order of 0.1m. The
transit time across the depletion region istypically on the order
of 102s. Except for diodes of very narrow base widths, this time is
extremelyshort compared to the total time for emptying the excess
electrons out of the base region.Thus, aslong as there are
sufficient excess electrons in the base region, the reverse current
is limited not bythe diffusion of excess electrons but by the
external resistor and has a value of IR VR/R,and the slope
(dnp/dx)x=0, being proportional to IR, is approximately
constant.
3. As the excess electrons start to disharge, part of the
external voltage start so appear acrosss thep-n junction, and the
junction becomes less forward bias. Under forward bias and small
reversebias, the electron density on the p-side at the
space-charge-layer edge is given as
np(xp) = np0(xp)exp(qV app/kT )
From the above equation, it is evident that if the excess
electron concentration at the edge ofdepletion layer has decreased
by a factor of 10, the juncion voltage is changed by only 2.3kT/qor
60mV . This is consistent with our assumptions that the reverse
current remains essentiallyconstant. During this time, the diode
remains in the ON condition.
4. At t = ts, the excess electrons have been depleted to the
point that the reverse current is limitedby the diffusion of
electrons instead of by the external resistor. Rate of voltage
change across thejunction increases. Finally, when all the excess
electrons are removed, the p-n diode is completelyoff. The reverse
bias voltage appears entirely across the junction, and the reverse
current is limitedby the diode leakage current. There are two
stages in switching a diode from forward to reversebias voltage.
The first one is when reverse current is approximately constant,
and during whichthe remains in ON condition. The second one is when
the reverse current decreases exponentiallyto reverse saturation
current.
5. Discharge time for a wide-base diode: A forward-biased
wide-base diode discharges with a timeconstant approimately equal
to the minority-carrier lifetim, unless the reverse discharge
currentis much larger than the forward charging current. Even for
IR/RF = 10, the diode dischargesin a time of approximation n/10
which is larger than 10
8s for most diodes of practical dopingconcentrations. This time
is very long compared to the typical switching delays of VLSI
circuits.The important point is that it takes a long time to drain
off the excess minority carriersstored in a wide-base and turn it
off. It is important to minimize excess minority carriersstored in
forward-biased diodes if these diodes are to be switched off
fast.
3
-
6. Discharge time for a narrow-base diode: For a narrow base
diode, the recombination time isignored. The discharge time is very
small compared to n. The discharge time for a narror-basediode
lasts approximately tBIF /(IR + RF ) which, for a large IR/IF
ratio, can be much shorterthan the base transit time. Therefore, a
forward-biased narrow-base diode can be switchedoff fast.
2.2 Diffusion Capacitance
1. For a forward biased diode, in addition to the capacitance
associated with the space-charge layer,there is an important
capacitance component associated with the rearrnagement of the
excessminority carriers in the diode in response to a chaneg in
applied voltage. This minority-carriercapacitance is called
diffusion capacitance CD.
2. An n+-p wide-emitter narrow-base diode has depth or width of
the n+ emitter region is largecompared to its hole diffusion length
and the width of p-type base is small compared to its
electrondiffusion length (This diode is of interest because it
represents the emitter-base diode of an n-p-n bipolar transistor).
When a voltage Vapp is applied across the diode, an electron
current ofmagnitude In is injected from the emitter into the base
and a hole current of magnitude Ip is injectedfrom the base into
the emitter. The diode current is In + Ip. Both In and Ip are
proportional toexp(qVapp/kT ).
3. Diffusion capacitance components:
(a) In a quasisteady state, the voltage is assumed to vary
slowly in time such that the minoritycharge distribution can
respond to the applied voltage fully without any delay.
(b) When a forward bias is reduced, or when the diode is
switched to reverse bias, the electrondistribution evolves as a
function of time. Part of exccess electrons diffuses to the left
(backtowards the emitter) and part of them diffuses to the right.
The opposing electron currentsuggests that the net charge moved
through the external circuit is less than the total storedcharge at
t = 0.
(c) When ac voltage is applied across the diode, only those
electrons located sufficiently choseto the depletion-region
boundaries can keep up with the signal and get into and out of
thebase. The exact amount of such electrons depends on the signal
frequency. Similarly, if weconsider the stored holes in the
emitter, the signal following holes gives rise to a hole
currentcomponent at the base end of emitter region adn in the
external circuit. These signal-followingstored charges are
responsible for the diffusion capacitance.
(d) The exact diffusion capacitance components are derived from
a frequency depenent small-signal analysis of the current through a
diode start from the differential equations governingthe transport
of minority carriers. Appendix 6 has the derivation for
wide-emitter narror-basediode.
(e) For a wide-emitter, the low-frequency diffussion capacitance
due to the excess electrons in thenarrow-base is
CDn =qInVappkT
(W 2B
3DnB
)=
2
3
q
kTInVapptB
and that due to the excess holes in the wide-emitter is
CDp =qIpVappkT
(L2pE
2DpE
)=
1
2
q
kTIpVapppE
4. The total diffusion capacitance isCD = CDn + CDp
5. It is clear from these expressions that 2/3 of the stored
charge in the narrow-base and 1/2 of thestored charge in
wide-emitter contribute to the diffussion capacitance of a
forward-biased diode.
6. The 2/3 of the total stored stored charge in the narrow base
diffuses back to the emitter when thebase region is discharged.
This fraction is same as the fraction of total stored charge in the
basecontributing to the diffusion capacitance. In other words, one
can think of the diffusion capacitanceas coming from the portion of
the stored minority charge that is reclaimable in the form of an
accurrent as the diode respond to an ac signal.
4
-
7. It is instructive to examine the relative magnitude of the
two capacitance components
CDn(narrow base)
CDp(wide emitter)=
2
3
NENB
WBLpE
The ratio NE/NB is typically about 100 for an n+-p diode. For an
emitter with NE = 1 1020
cm3, LpE is about 0.3 m. Therefore, for a practical one-sided
diodes where the base widthis larger than 0.03 m, the ratio CDn/CDp
is much larger than unity. That is, the diffussioncapacitance of
one-sided p-n diode is dominated by the minority charge stored in
the base. Thediffusion capacitance due to minority charged stored
in the emitter is small in comparision.
8. The effect of heavy doping, when included, will increase the
amount of charge stored and hencethe diffusion capacitance. Since
heavy doping effect is larger in the more heavily doped emitterthan
in the base, it will make the ratio CDn/CDp smaller. This affect
the switching speed. Theexpression with heavy doping is shown
as
CDn(narrow base)
CDp(wide emitter)=
2
3
(n2ieBn2ieE
)(NENB
)WBLpE
Therefore, the heavy-doping effects cannot be ignored in any
quantitative modeling of the switchingspeed of a diode.
2.3 MOS Capacitors
1. Energy band diagram of an MOS system
(a) Before we discuss the energy band diagram of an MOS device,
it is necessary to first introducethe concept of free electron
level and work function which play key roles in the relative
energyband placement when two different materials are brought into
contact. The free electronlevel is defined as the energy level
above which the electron is free, i.e., no longer bonded tothe
lattice. In silicon, the free electron level is 4.05 eV above the
conduction band edge. Inother words, an electron at the conduction
band edge must gain an additional energy of 4.05eV (called electron
affinity in order to break loose from the crystal field of silicon.
The freeelectron level in silicon dioxide is 0.95 eV above its
conduction band. The work function isdefined as the difference
between the free electron level and the Fermi level. For a
p-typesilicon, the work function, qs can be expressed as:
qs = q+Eg2
+ qB
where B is the difference between the Fermi potential and the
intrinsic Fermi potential.
(b) When two different materials ar brought into contact, they
must share the same free electronlevel at the interface.
(c) Under flatband condition, there is no field in all three
materials. If metal work function is lessthan the silicon
substrate, we need to apply negative gate voltage, (s m) ms,
withrespect to the substrate. In general, the flatband voltage of
an MOS device is given by
Vfb = (m s) QoxCox
where Qox is oxide charge per unit area and Cox is the oxide
capacitance per unit area.
(d) The electron affinity, q, is the material property which
depends only on the type of semicon-ductor and does not change with
either the location or the doping type.
2. Gate voltage and surface potential
2.4 Key Notes from the Chapter
1. The most important result of the application of quantum
mechanics to the descriptio of electronicsin a solid is that the
allowed energy levels of electrons are grouped into bands. The
bands areseparated by regions of energy that the electrons in the
solid cannot possess: forbidden gaps.
5
-
2. The energy of electrons in the conduction band increases
upward, while energy of the holes in thevalence band increases
downward.
3. The bandgap decreases slightly as the temperature increases,
with a temperature coefficient ofdEg/dT 2.73 104 eV/K.
4. When two systems are in thermal equilibrium with no current
flow between them, their Fermilevels must be equal. A direction
extension is that, or a continuous region of metals
and/orsemiconductors in contact, the Fermi level at theermal
equilibrium is flat, i.e., spatially constant,throughout the
region.
5. The electrical conductivity of an exterinsic semiconductor is
dominated by the type and concen-tration of the impurity atoms, or
dopants.
6. In terms of energy-band diagrams, donors add allowed electon
states in the bandgap close to theconduction-band edge, while
acceptors add allowed states just above te valence-band edge.
7. The Fermi level in n-type semiconductor moves up towards the
conduction band, consistent withthe increase in electron density.
On the other hand, the Fermi level in p-type semiconductor
movesdown towards the valence band, consistent with the increase in
hole density. The exact position ofFermi level depends on both the
ionization energy and the concentration of dopants.
8. It is seen that as the temperature increases, the Fermi level
approaches the intrinsic value nearmidgap.
9. The distance between the Fermi level and the intrinsic Fermi
level near the midgap is a logarithmicfunction of doping
concentration.
10. The Fermi level moves into the conduction band for n+
semiconductor and into the valence bandfor p+ semiconductor. In
addition, when impurity concentration is higher than 1018
1019cm3,the donor levels braoden into bands. This results in an
effective decrease in the ionization energyuntil finally the
impurity band merges with the conduction (or valence) band and the
ionizationenergy become zero. Under these circumstances, the
silicon is said to be degenerate.
11. Carrier transport or current flow in semiconductor is driven
by two different mechanisms: (a) thedrift of carriers, which is
caused by the presence of an electric field, and (b) the diffusion
of carriers,which is caused by an electron or hole concentration
gradient in semiconductor.
12. Electron mobility is approximately three times the hole
mobility, since the effective mass of electronsin the conduction
band is much higher than that of holes in the valence band.
13. At low impurity levels, the mobilities are mainly limited by
carrier collisions with the lattice oracoustic phonons. As doping
concentration increases beyond 10151016, collisions with the
charded(ionized) impurity atoms through Coulomb interaction become
more and more important and themobilities decrease.
14. At high temperatures, the mobility tends to be limited by
lattice scattering and is proportionalto T3/2, relatively
insensitive to the doping concentraion. At low temperatures, the
mobility ishigher, but is a strong function of doping concentration
as it becomes more limited by impurityscattering.
15. In the inversion layer of a MOSFET device, the current flow
is goverened by the surface mobility,which is much lower than the
bulk mobility. This is mainly due to additional scattering
mechanismsbetween the carriers and the Si-SiO2 interface in the
presence of high electric fields normal to thesurface.
16. The linear velocity-field relationship discussed above is
valid only when the electric field is not toohigh and the carriers
are in thermal equilibrium with the lattice. At high fields, the
average carrierenergy increases and carriers lose their energy by
optical phonon emission nearly as fast as theygain it from the
field. This results in a decrease of the mobility as the field
increases until finallythe drift velocity reaches a limiting value,
vsat 107cm/s. This phenomenon is called velocitysaturation.
6
-
17. Saturation velocity of holes is similar to slightly lower
than that of electrons, but saturation forholes takes place at a
much higher field because of their lower mobility.
18. For more highly doped material, low-field mobilities are
lower because of impurity scattering.However, saturaion velocity
remains essentially the same, independent of impurity
concentration.
19. There is a weak dependence of vsat on temperature. It
decreases slightly as the temperatureincreases.
20. One of the key equations governing the operation of VLSI
devices is Poissons equation. It comesfrom Maxwells first equation
which in turn is based on Coulombs law for electrostatic force of
acharge distribution. Poissons equation is expressed in terms of
the electrostatic potential, whichis defined as the potential
energy of carriers divided by the electronic charge q.
21. Total current, which is the sum of drift and diffusion
current, is proportional to the gradient of theFermi potential
instead of proportional to the electric field. For a connected
system of metals and/orsemiconductors in thermal equilibrium with
no current flow, the Fermi level is flat, i.e., spatiallyconstant,
throughout the system. It is important to keep in mind that Fermi
level difference is thedriving force for current flow, much like
voltage difference drives currents in a circuit.
22. Since, the system is not in termal equilibrium, the Fermi
level is not well defined. The electrondistribution function is no
longer a function of energy only. It becomes asymmetric in the
currentflow directios to favor population of the electronic states
with a forward momentum. It is thenuseful to consider a local Fermi
level based on the local equilibrium state at any given point.
So,one can introduce separate Fermi levels for electrons and holes,
respectively, and they are calledquasi-Fermi levels.
23. The electron denisity in the conduction band can be
calculated as if the Fermi level is at Efn andthe hole density in
the valence band can be calculated as if the Fermi level is at Efp.
The gradientof electron quasi-Fermi potential drives the electron
current and the gradient of hole quasi-Fermipotential drives the
hole current.
24. Continuity equations are based on the conseration of mobile
charge.
25. At thermal equilibrium, the generation rate is equal to the
recombination rate and np = n2i , themass-action law.
26. Under low-injection conditions, the recombination rate is
inversely proportional to the minority-carrier life-time which is
in the range of 104 109 s, depending on the quality of the
siliconcrystal.
27. The minority-carrier diffusion length, which is the average
distance a minority carrier travels beforeit recombines with a
majority carrier, is given by L =
(D ), where D is the diffusion coefficient of
minority carrier. Since diffusion length is much larger than the
active dimension of a VLSI device,generation-recombination in
general plays very little role in device operation. Only a few
specialcircumstances, such as CMOS latch-up, the SOI floating-body
effect, junction leakage current, andradiation-induced soft error,
must the generation-recombination mechanism be taken into
account.
28. In contrast to the minority-carrier lifetime, the
majority-carrier response time is very short in asemiconductor,
which is typically on the order of 1012 s. It is much shorter than
most deviceswitching times.
29. Near the physical junction, the energy-bands are bent in
order to maintain energy-band continuitybetween the p-region and
the n-region. The band bending implies an electric field, E =
di/dx,in this transition region. This electric field causes a drift
component of electron and hole currentsto flow. On both sides of
the band-bending region, the energy bands are flat and there is no
electricfield. These regions are referred to as the quasineutral
regions.
30. The build-in potential, i, is proportional to the difference
between the energy bands on the p-sideand the corresponding energy
bands on the n-side, qi = Ec(p-side) Ec(n-side).
31. A region is called quasi-neutral if the net +ve and -ve
charge densities are equal in their gradientsuch that there is no
electric field in the region.
7
-
32. Abrupt junctions have step change in doping impurities. The
abrupt-junction is reasonable formodern VLSI devices, where the use
of ion implantation for doping the junctions followed by
low-thermal-cycle diffusion and/or annealing, results in junctions
that are fairly abrupt. Besides, theabrupt-junction approximation
often leads to closed-form solutions which render the device
physicsmuch easier to understand.
33. The electrostatic potential i(x) is independent of x in the
uniformly doped quasineutral regions.Within the band-bending
region, i(x) changes from being Eip/q at the p-region end of the
theband-bending region to being Ein at the n-region end of the
band-bending region. Within theband-bending region, the electron
density drops very rapidly as i(x) changes, being equal to
theionized donor density at the n-region end. Thus, the density of
electrons within the band-bendingregion is negligible compared to
the density of ionized donors except for a very narrow
regionadjacent the quasi-neutral n-region where q(i f ) is less
than about 3kT . Similarly, within theband-bending region, the
density of holes is negligible compared to the density of ionized
acceptorsexcept for a very narrow region adjacent to the
quasi-neutral p-region.
34. A closed-form solution to Poissons equation can be obtained
if the electron and hole densitiesare assumed to be negligible in
the entire band-bending region. This is called the
depletion-approximation.
35. The depletion-layer widths, xp amd xn, are dependent on the
donor concentration Nd on the n-sideand the acceptor concentration
Na on the p-side, as well as on the applied voltage Vapp, across
thejunction.
36. The depletion approximation is quite accurate for all
applied voltages except at large forwardbiases, where the
mobile-charge densities are not negligible compared to the ionized
impurityconcentrations in the transition region. Since transition
region is not charge-neutral, it is alsoreferred to as the
space-charge region or space-charge layer.
37. Total space charge inside the n-side of the depletion region
is equal to the total space charge insidethe p-side of the
depletion region.
38. The built-in potential represents an energy barrier limiting
the flow of electrons from the n-side tothe p-side and flow of
holes from p-side to the n-side. Under reverse bias, applied
voltage increasesthis barrier. This barrier is reduced under
forward bias conditions.
39. A quasineutral region has a finite resistivity determined by
its dopant impurity concentration.When a current, I, flows in a
region of finite resistivity, there is a corresponding voltage
drop, orIR drop, along the current path. If IR drop in the
quasineutral regions are not negligible, thenVapp should be
replaced by V
app.
40. A diode has rectifying current-voltage characteristics,
being conducting when it is forward biased,and non-conducting when
it is reversed biased.
41. The depletion-layer capacitance of a diode is equivalent to
a parallel-plate capacitor of separationWd and dielectric constant
si. Physically, this capacitance is due to the majority carriers at
theedges of the depletion layer, not the space charge within the
depletion region, respond to changesin the applied voltage.
42. When the density of mobile carriers is comparable to or
larger than the densities of ionized donorsor acceptors, the
boundaries of the space-charge region are no longer well
defined.
43. Many modern VLSI devices operate at very high electric
fields within the depletion regions ofsome of their p-n diodes. In
fact, the junction fields are often so high that determinental
high-field effects, such as avalanche multiplication and
hot-carrier effects, limit the attainable deviceand circuit
performance. To overcome the constraints imposed by high fields in
a diode, devicedesigners often introduce a thin but lightly doped
region between the n- and p-sides. Introductionof a lightly doped
layer between the n- and p-regions of a diode reduces the maximum
electric fieldin the junction.
44. Simple and closed-form equations relating the electron and
hole densities and currents to the appliedvoltage can be obtained
under these approximations
8
-
(a) Quasineutrality
(b) Low-level injection
45. For a forward biased diode, we have an excess of minority
carriers at the boundaries of the quasineu-tral regions. For a
reverse biased diode, we have a depletion of minority carriers at
the boundariesof the quasineutral regions.
46. The current-voltage characteristics of a one-sided diode are
determined primarily by the transportof minority carriers in
lightly doped side.
47. Minority carrier current is inversely proportional to the
doping concentration. Thus, in a one-sideddiode, the
minority-carrier current in the lightly doped side is much larger
than that in the heavilydoped side. The diode current is dominated
by the flow of minority carriers in the lightly dopedside of the
diode, while minority-carrier current in the heavily doped side
usually can be neglectedin comparision. Th effect of heavy doping
can increase the minority-carrier curernt flowing inthe lightly
doped region is substantially. However, if the width of an emitter
is not larger thanits minority-carrier diffusion length, the
minority-carrier current flow in the emitter may not
benegligible.
48. In a forward-biased n+p diode, both the excess
minority-carrier concentration and the minority-carrier current
increase exponentially with the applied voltage.
49. The reverse bias causes a gradual depletion of electrons in
the p-region near the depletion-regionboundary, and this electron
concenration gradient causes an electron current to flow from
thequasineutral p-region towards the depletion region. This is the
electron diffusion component of theleakage current in a reverse
biased diode. It is also referred to as the electron saturation
currentof diode. Total diffusion leakage current in a diode is the
sum of the electron and hole saturationcurrents. Notice that the
diffusion leakage current is independent of the applied
voltage.
50. A diode is wide-based if its base width if large compared to
the minority carrier diffusion length inthe base. For a
forward-biased wide-base diode, the excess minority-carrier
concentration decreasesexponentially with distance from the
depletion region boundary, and the minority-carrier current
isindependent of the base-width. For a reverse-biased wide-base
diode, the minority-carrier electronsit the base within a diffusion
length of the depletion-region boundary diffuse towards the
depletionregion, with a saturation current density which is
independent of the base width.
51. A diode is called narrow-base if its base width is small
compared to the minority-carrier diffusionlength in the base. For
narrow-base diode, both forward and reverse biases, the
minority-carriercurrent density in a narrow-base n+ p diode
increases as base width is reduced.
52. A diode has a shallow emitter if the minority-carrier
diffusion length in the emitter is comparableto or smaller than the
width of the emitter region. The width of the emitter region of a
pn diodeis also referred to as the junction depth. Therefore, a
shallow-emitter diode is also a pn junctionhaving an electrically
shallow junction. When W/L in the emitter, the minority-carrier
current inthe emitter increases very rapidly as the emitter depth
decreases. Typical p diodes in modernVLSI devices should be treated
as shallow-junction diodes.
53. There are effective means for reducing the minority-carrier
current in a shallow-emitter diode. Forexample a shallow emitter
can be contacted using a doped polysilicon layer instead of a metal
ormetal silicide layer.
54. In practical silicon diodes, the space-charge region current
is not negligible at reverse bias and lowforward-bias. For an n+ p
diode, high injection occurs when np approaches Na where Na isthe
acceptor concentration of the p-side. At high injection, IR drops
in the quasineutral regionscan be significant. The onset of high
injection can be pushed to higher voltage by increasing Na.The
applied voltage Vapp reduced to V
app = Vapp IR. The difference between Vapp and V app is
contained in the ideality factor, m. When m is unity, the
current is considered ideal. A forwarddiode current is ideal except
at very small and very large forward biases. The nonideality at
smallforward bias is caused by the space-charge-region current.
Space charge region current leads tom 2. The nonideality with m 2
at very large forward bias is due to high injection effect, IRdrop.
At intermediate voltages, we have 1 < m < 2.
9
-
55. Finite resistivity of the p- and n-regions results in
voltage drops between the ohmic contacts andthe junction. Finite
resistivity effect is important only at very large forward biases.
At large biases,it is not easy to clearly tell if the nonideality
is caused by series resistance or by high injection.It may be
combination of both. However, when m > 2, we know that the
series resistance effectdominates because the high injection effect
by itself has an ideality factor of no larger than 2.
56. Series resistance effects can be reduced by increasing the
diode doping concentrations, particularlythe doping concentration
of the base side of the diode. Increasing doping concentration also
delaysthe onset of high injection. Degradation of ideality factor
is usually observable only at low forwardbiases and only in diodes
having significant amounts of generation-recombination centers in
thespace-charge region.
57. For a reverse-biased diode, the total leakage current is the
sum of the space-charge-region satura-tion current and the
diffusion saturation current. Temperature dependence of diffusion
saturationcurrent is dominated by the temperature dependence of the
n2i factor, which is proportional toexp(Eg/kT ) where Eg is bandgap
energy. The space-charge-region leakage current, being
pro-portional to ni, has a temperature dependence of exp(Eg/2kT ).
In othe words, the diffusionleakage current has an activation
energy of about 1.1 eV while the generation-recombination leak-age
current has an activation energy of about 0.5 eV. Therefore, the
diffusion leakage current, dueto its larger activation energy, is
usually larger than the generaion-recombination leakage
current(space-charge-region saturation current) at elevated
temperatures.
58. The diffusion leakage current is independent of reverse-bias
voltage. The space-charge-region cur-rent is proportional to the
space-charge-layer width which increases with reverse-bias
voltage.
59. There is a capacitance associated with the depletion layer
of a diode. As the diode is switchedoff (zero-biased or
reverse-biased) to on (forward-biased), it takes some time before
the diode isturned on and reaches the steady state. This time is
associated with charging up the depletion-layer capacitor and
filling up the p- and n-regions with excess minority carriers.
Similarly, when adiode is switched from the on state to off state,
it takes some time before the diode is turned off.This time is
associated with discharging the depletion-layer capacitor and
discharging the excessminority carriers stored in the p- and
n-regions. The minority-carrier response time, or
dielectricrelaxation time, is negligibly short, on the order of
1012 s.
60. As doping concentration of the lightly doped side of a
one-sided pn junction increases, depletionlayer capacitance
increases but depletion layer width decreases.
61. For a narror-base diode, all the minority carriers can
travel across the base region without recom-bining. The
base-transit-time is equal to the average time for the minority
carriers to traverse thenarrow base region.
62. Modern n p n bipolar transistors typically have base widths
of about 0.1 m, and a peak basedoping concentration of about 21018
cm3. The corresponding minority electron mobility is about300
cm2/V-s. The base-transit-time is therefore less than 1 1011 s,
which is extremely shortcompared with the corresponding
minority-carrier lifetime on the order of 1107 s. Recombinationis
negligible in the base layers of modern bipolar transistors.
63. A time t = 0, the external bias is switched to a reverse
voltage of VR. The excess electrons in thebase start ti diffuse
back towards the depletion region of the diode. Those electrons at
the edgeof the depletion region are swept away by the electric
field in the depletion region towards the n+
emitter at a saturated velocity of about 107 cm/s. The depletion
layer width is typically on theorder of 0.1 m. The transit time
across the depletion region is typically on the order of 1012
s. Except for diodes of very narrow widths, this time is
extremely short compared to the totaltime for emptying the excess
electrons out of the base region. Thus, as long as there are
sufficientexcess electrons in the base region, the reverse current
is limited not by the diffusion of excesselectrons but by the
external resistor and has a value of IR VR/R and the slope
(dnp/dx)x=0,being proportional to IR, is approximately constant. At
t = ts, the excess electrons have beendepleted to the point that
the reverse current is limited by the diffusion of electrons
instead of bythe external resistor. The rate of voltage change
across the junction increases. Finally, when allthe excess
electrons are removed, the p n junction is completely off. The
external reverse-biasvoltage appears entirely across the junction,
and the reverse current is limited by the diode leakagecurrent.
10
-
64. Discharge time for a wide-base diode: A forward-biased diode
discharges with a time constantapproximately equal to the
minority-carrier lifetime, unless the reverse discharge current is
muchlarger than the forward charging current. It takes a long time
to drain off the excess minoritycarriers stored in a wide-base
diode and turn it off. It is important to minimize excess
minoritycarriers stored in forward-biased diodes if these diodes
are to be switched off fast.
65. Discharge time of a narrow-base diode: For a narrow base
diode, recombination current can beignored. A narrow-base diode
discharges in a time very small compared to n, lifetime of
minority-carrier electrons in p-region. The discharge time for a
narror-base diode can be much shorter thanthe base transit time. A
complex but closed-form solution can be obtained in the large
IR/IFratio. A comples but closed-form solution can be obtained in
the large IR/IF limit, which showsthat most of the charge has come
out by about tB/3. The important point is that a
forward-biasednarror-base diode can be switched off fast.
66. Diffusion capacitance: Let us understand the diffusion
capacitance for an n+ p wide-emitternarrow-base diode, i.e., a
diode where the depth or width of the n+ emitte region is large
comparedto its hole diffusion length and the width of the p-type
base region is small compared to its electrondiffusion length. When
forward bias is reduced, or when diode is switched to reverse bias,
theelectron distribution evolves as a function of time. Part of the
excess electrons diffuses to the left(back towards the emitter) and
part of them diffuses to the right. The opposing electron
currentssuggest that the net charge moved through the external
circuit in the discharge process is less thanthe total stored
charge. When ac voltage is applied across the diode, only those
electrons locatedsufficiently close to the depletion-region
boundaries can keep up with the signal and get into andout of the
base. The exact amount depends on the signal freqency. Similarly,
if we consider thestored holes in the emitter, the signal-following
holes in the n+ emitter give rise to a hole currentcomponent at the
base end of the emitter region and in the external circuit. These
signal-followingstored charges are responsible for the diffusion
capacitance. The 2/3 of the stored charge in thenarrow base and 1/2
of the stored charge in the wide emitter contribute to the
diffusion capacitanceof a forward-biased diode. The diffusion
capacitance of a one-sided p n diode is dominated bythe minority
charge stored in the base of the diode. The diffusion capacitance
due to the minoritycharge stored in the emitter is small in
comparision. The effect of heavy doping, when included,will
increase the amount of stored charge and hence the diffusion
capacitance.
67.
11
-
Chapter 3
Chapter 3: MOSFET Devices
12
-
Chapter 4
Chapter 4: CMOS Device Design
13
-
Chapter 5
Chapter 5: CMOS PerformanceFactuors
14
-
Chapter 6
Chapter 6: Bipolar Devices
15
-
Chapter 7
Chapter 7: Bipolar Device Design
16
-
Chapter 8
Chapter 8: Bipolar PerformanceFactors
17
-
Chapter 9
Chapter 9: Memory Devices
18
-
Chapter 10
Chapter 10: Silicon On Insulator
19
Chapter 1: IntroductionChapter 2: Basic Device PhysicsDischarge
Time of a Forward-Biased DiodeDiffusion CapacitanceMOS
CapacitorsKey Notes from the Chapter
Chapter 3: MOSFET DevicesChapter 4: CMOS Device DesignChapter 5:
CMOS Performance FactuorsChapter 6: Bipolar DevicesChapter 7:
Bipolar Device DesignChapter 8: Bipolar Performance FactorsChapter
9: Memory DevicesChapter 10: Silicon On Insulator
