Chapter 4-1 (II 2008-2009) [Compatibility Mode]

8/14/2019 Chapter 4-1 (II 2008-2009) [Compatibility Mode]

1/76

1


2/76

1. Schottky Junction

(1) Schottky diode Schottky diode is formed when a metal contactsn-type semiconductor with work function of

metal larger than semiconductor(m > n )

Definition of work function: energy differencebetween vacuum level and Fermi level.

Energy required to free an electron by

thermionic emission and photon?

Thermionic emission: work function of metal

and semiconductor .

Photon: Metal: work function; semiconductor:

When the two solids come into contact, the more energetic electrons in the CB of the

.

2

levels (just above EFm) and accumulate near the surface of the metal.


3/76

Electrons tunneling from the semiconductor leave

behind an electron-depleted region of width W in

which there are exposed positively chargeddonors in other words net ositive s ace char e.

The contact potential, called the built-in potential

V0, therefore develops between the metal and the

.

There is obviously also a built-in electric field E0 from the positive charges to

the negative charges on the metal surface.

3

Eventually this built-in potential reaches a value that prevents further

accumulation of electrons at the metal surface and an equilibrium is reached.


4/76

EFm and EFn line up.

n ecreases Ec EFn ncreases

( )

=

kT

EENn Fcc exp

The bands must bend to increase EcEFn toward

the junction.

The bending is just enough for the vacuum level

to be continuous and changing by m - n fromthe semiconductor to the metal, as this much

Far away from the junction, we, of course, still

energy is needed to take an electron across from

the semiconductor to the metal.

have an n-type semiconductor.

The PEbarrier for electrons moving from the

4

Schottky barrier height B, which is given by,FncmB == 0


5/76

Under open circuit conditions, there is no net

current flowing through the metal-semiconductor

unc on. erma em ss on a ance s reac e .

Emission probability depends on the PE barrier for

emission through the Boltzmann factor. There are

two current components due to electrons flowing

through the junction. The current due to electrons

being thermally emitted from the metal to the CB of

= kTCJB

exp11

,

4-1

Where C1 is some constant, whereas the current due

to electrons being thermally emitted from the CB of

,

=

kT

eVCJ 022 exp012circuitopen == JJJ

In equilibrium

4-2

5


6/76

Under forward bias conditions, the semiconductor

side is connected to the negative terminal.

Since the depletion region W has a much larger

resistance than the neutral n-region (outside W) and

the metal side nearl all the volta e dro is across the

depletion region.

The applied bias is in the opposite direction to the

u - n vo age 0. us 0 s re uce o 0 . Bremains unchanged. So the PE barrier for thermal

emission of electrons from the semiconductor to themetal is now e(V V).

The current J2for, due to the electron emission from the semiconductor to the metal,

is now,

( )

=kT

VVeCJ for 022 exp

6


7/76

The current J1, due to the electron emission from the metal to semiconductor

remains unchanged since B is the same. The net current is then:

( )

== expexp 02

0212

eVC

VVeCJJJ for

0 eVeV

or

=

1exp0

2

eVJ

kTkT

4-3

Where J0 is the constant that depends on the material and surface properties of the

two so s.

7


8/76

r

Schottky junction is reverse biased, then the

ositive terminal is connected to the semiconductor.

CB

B e(V0+Vr

The applied voltage Vr drops across the depletion

region since this region has very few carriers and isE

c

Ev

VB

highly resistive.

The built-in voltage V0 thus increases to V0 + Vr. The

CB to the metal becomes e(V0 + Vr), which means that

the corresponding current component becomes,

=

kTCJ rrev 022 exp

eVB 0

== kTkT 211

The net current is then:

8

== 1expexp 0212kT

eV

kT

eVCJJJ rev 4-4


9/76

Since generally V0 is typically a fraction of a volt and the reverse bias is more than a few

volts, J2

rev


10/76

(2) Schottky Junction Solar cell and photodetector

s are genera e n e ep e on reg on or

photon energy greater than energy bandgap.

Built-in field separates the EHPs. Electron toward

semiconductor and hole toward metal.

Extra electron in neutral n-region and less electron in

metal related to dark state.

Under open-circuit conditions, a voltage develops

across the Schottky junction with metal end positivean sem con uc or en nega ve.

Connected to external load, the extra electrons will

ass throu h the load toward the metal where it

replenishes the lost electrons in the metal. There isphoto energy to electric energy conversion.

10


11/76

For photon energy less than bandgap, what happen?

The photon will excite an electron from Fermi level

of metal overB into CB of semiconductor. In this

case photon energy must be greater than B.

reverse biased Schottky junction,

- 0

V0+Vr and thus increase the drift velocity

of the EHPs in the depletion region.

Shorten the transit time required to crossthe depletion width.

11

photodetector.


12/76

(3) Ohmic contactAn Ohmic contact is a junction between metal and

The work function of the metal m is smaller thanthe work function n of the semiconductor.

.

The electrons (around EFm) tunnel into thesemiconductor in search of lower energy levels,

.

Consequently many electrons pile in the CB of the

semiconductor prevent further electrons tunnelingfrom the metal.

n increases, the Ec-EFn decreases and the energy

band bends downward.

The conduction electrons immediately on either side

of the junction (at EFm and Ec) have about the same

12

when they cross the junction in either direction under

the influence of an electric field.


13/76

Accumulation RegionOhmic Contact

BulkSemiconductor

Ec

E

CB

EFm

EFn

VB

-e a

After Contact

It is clear that the excess electrons in the accumulation region increase the

conductivity of the semiconductor in this region. When a voltage is applied to the

structure, the voltage drops across the higher resistance region, which is the bulk

.

comparatively high concentrations of electrons compared with the bulk of the

semiconductor. The current is therefore determined by the resistance of the bulk

region.

13


14/76

2.pn Junction

Metallurgical junction between n-type and p-type

. pen c rcu

Hole concentration gradient (p n): ppo pno

no po

Hole diffusion p n, Electron diffusion n p

Depletion region or space charge layer(SCL) is

formed due to the recombination of diffused carriers

(Note: pn = ni2 everywhere, without applied bias orphotoexcitation)

14


15/76

An internal electrical field E formed in the x direction

This field drives both hole and electrons in the opposite

directions of their diffusion.

At last, the equilibrium is reached when the hole andelectron diffusion rate is balanced by the hole and

.

The net space charge density in the depletion region (-

W


16/76

Gauss law relates Field (E) to net space charge density

)(net x

dx

d=

E

Field in depletion region

Permittivity of the medium =0r

( )

p

x

WxWdxx

p


17/76

( )0


18/76

Relationship between V0 and the doping parameter(Na, Nd)

=

kTNEN exp0Boltzmann statistics:

0,

ratio of the electron concentration in p type and n typesemiconductor is

n

=

kTnn

p 0

0

exp

, ,

=

eVpn 00 expp0

0 kTnkT

18

nann0

0

0

0

=

=pn pene

4-8


19/76

lnandln 000

0

=

= npp

e

kTV

n

n

e

kTV

pn

apii

n Npnn

p === 022

0 ;dnn 0

ln2

0

=

da

i

NNn

ekTV 4-9

Clearly V0 is related to the dopant and material properties viaNa, Ndand ni

The built-in voltage (V0)is the voltage across a pn junction, going from P- to n-type

semiconductor in open circuit. It is not the voltage cross the diode, which is made

up of V0 as well as contact potentials at metal-semiconductor junction at electrodes.

19


20/76

2.2 Forward bias

The applied voltage Vdecrease the potential barrier

0 0-diffuse to left and right.

This results in more holes diffusion to n-side and

more e ec rons us on o p-s e- n ec on o

excess of minority carriers.

By using Boltzmann statistics, the hole concentration

( )

( )

= kTVVe

pp pon0

exp0

pn a x = x= n s

=

eVpn 00 exp

At open circuit

( )

=kTeVpp non exp0 p

p0

20

pp0 and pn0 are hole concentration in p-type

and n-type semiconductors


21/76

Electrons are similarly injected from the n-side

- . x=-Wp is given by:

eV

=

kT

nn pop exp

n 0 is electron concentration in p-type semiconductors

eV

( )

=

=

eVnn

kTpp

o

non

exp0

exp4-10

Law of the Junction: relationship between

minority carrier concentrations and voltage in

pnjunction

The current due to the hole diffusion in n-side and electron diffusion in p-side

21

(diffusion of minority carriers) can be maintained through a pn junction under

forward bias.


22/76

Assume that the length of the p- and n- regions are

longer than the minority carrier diffusion length.

-

= nn

xpxp exp)0()(

h

whereLh is the hole diffusion length, defined by in which h is the mean

-hhh DL =

.

Excess minority carrier concentrationnonn pxpxp = )()(

The hole diffusion current density JD,hole is therefore

( ) ( )'' xpdxdp nn ==''

,

dxdxo e

)

= n

hholeD

xp

eDJ

'exp0

22

hh

,


23/76

The total current anywhere in the device is constant.

The total current =JD,hole(x=Wn) + D, elec (x=-Wp).

eD, n

h

holeD p

L

=

( ) ( )= ppp nnn 00 0

( )

=

kT

eVpp non exp0

= 1exp0

, kT

eV

L

peD

J

nh

holeD

Thermal equilibrium hole concentrationpn0 is related to the donor concentrations by

22

Nnp d

i

n

in

0

0 ==

23

= 1exp2

,

kT

eV

NL

neDJ

dh

ihholeD


24/76

= 1exp2

,kT

eV

NL

neDJ

dh

ihholeD

Hole diffusion current in n-region

= 1exp

2 eVneD ieSimilarly, the electron diffusion,

aecurren

Total current across the device is

=+= 1exp,,kT

eVJJJJ soelecDholeD 4-11

2

i

ae

e

dh

hso n

NL

eD

NL

eDJ

+=

4-12

Equation 4-12 is the familiar diode equation and frequently called the Shockley equation.

24


25/76

2.3 Reversed bias

Applied voltage increases the built-in potential

barrier and thus electric field in SCL is larger than

the built-in internal fieldE0. but there is a small

reverse current.

Small amount of holes on the n-side near the SCL

become extracted and swept by the field across SCLover to the p-side.

eV

Junction law with reversed bias

( )

=

=

eVnn

kTpp

o

non

exp0

expSmall diffusion current due

to concentration gradient

eDeD

Reverse saturation current density is

25

i

aedh

so nNLNL

= 4-13


26/76

2.4 Depletion layer capacitance of thepnjunction

De letion re ion of a n unction has ositive andnegative charges separated over distance W

similar to parallel plate.

apac tance n para e p ate = =

Capacitance in the depletion region depends on

e vo age. ncremen a capac ance =

( )( )2/1

2

+

=oda VVNN

W

From Eq. 4-7, depletion region width is;a

V is positive for forward bias and negative for reverse bias

WeNWeNQ pand == AeNAeNWWW adpn +=+=

2/1

26

+=+=

da

oda

adNeNAeNAeN

W


27/76

( )( )2/1

2

+

=+= oda

NeN

VVNN

eN

Q

eN

QW

aa

( ) ANNeAdQ da 2/1

( )( ) WNNVVdV

dao

dep =

+

==2/1

2

Cde is given by the same expression as that for the parallel plate capacitor , A/W, but

-

with W being voltage dependent According to the definition of the capacitance of

parallel plate

The voltage dependence of the depletion capacitance

is utilized in Varactor diodes, which are employed

as voltage-dependent capacitors in tuning circuits.

The incremental capacitances of the

27

depletion region increases with forward

bias and decreases with reverse bias.


28/76

2.5 Reverse breakdown: Avalanche and Zener

break breakdown

When the reverse voltage increases to a critical

value, the reverse current is substantially

increased.

This phenomenon is called pn junction breakdown, which is caused either by the Avalanche

ReverseI-Vcharacteristics of apn

junction.

.

Avalanche breakdown: as the reverse bias increase,

the electric field in depletion region is so large that

thermally generated EHPs can gain enough energy

to ionize the host Si atoms. EHPs new EHPs.

28


29/76

Zener breakdown mechanism:

Heavily doped pn junctions have narrow depletion

widths, and thus large electric field in this region

Reverse bias will lower down the CB in n-side.

c (n-side)< v (p-side), electrons tunneling from p

to n-side, lead to current. This process is called

Zener effect.

Zener breakdown mechanism

29


30/76

3. Bipolar Junction transistor (BJT)

Common base (CB) DC characteristics

+ n p

BE C

(a)

Emitter Base Collector

Heavily doped p-region (p+): emitter

Lightly doped n-region (n): Base

Lightly doped p-region (p): Collector

width.

30


31/76

BE CEmitter Base Collector

pn(0)

pn(x)n (0)

E

ICIE

x

pno

WEB WBCWB

npo

I

np(x)(b)

CBEB

Under normal and active conditions, the base-emitter (BE) is forwarded biasedand the base-collector (BC) junction is reverse biased. Base is common to both

the emitter and collector.

The emitter is heavily doped, the BE depletion region WEB extends almostentirely into the base. The base and collectors have comparable doping, so the

base-collector depletion region WBC extends to both sides.

31


32/76

Ex

BE CEmitter Base Collector

pn(0)

pn(x)

p

np(0)

ICIE

n (x)(b)

WEB WBCWB

npo

IB VCBVEB

EB junction is forward biased, holes are injected into the base and electrons into

the emitter.

Hole injection into the base far exceeds the electron injection into the emitter

because the emitter is heavily doped. So can assume that the emitter current is

entirely due to holes injected from the emitter into the base.

Injected holes into the base must diffuse toward the collector junction because

there is a hole concentration gradient in the base.

32

( )

=kT

eVpp EBnn exp0 0 ( ) 0Bn Wp


33/76

Assuming no holes are lost by recombination in the base, then all the injected

.

When the holes reach the collector junction, they are quickly swept across into the

collector by the internal field in WBC. The collector current is the same to the

emitter current.

The difference is that the collector current flows through a larger voltage

CB.

collector circuit.

To evaluate the emitter current we must know the hole concentration rofile xnacross the base. Because base is narrow, we can assume pn(x) profile is a straight

line.

B

n

h

n

nhE WeADdxpeADI 0 ==

33

( )

=kT

pp EBnn exp0 0

=kT

eV

W

peADI EB

B

nhE exp

0


34/76

currentemitterTotal += without considerin the recombinatione ec rono e

The emitter injection efficiency:

holeEI

A small number of the diffusing holes in the narrow base inevitably become lost by

( ) ( )electronEholeE II +=

recom nat on w t t e arge num er o e ectrons, t e ase transport actor T

CCT

II ==

34

Eo eE

E

C

I

I

=Collector-base current transfer ratio of transistor- isdefined as


35/76

h s e o e e me n e ase, h s e pro a y per un me a a o ewill recombine and disappear. t is the time for a hole diffuse across WB

is the time for a hole diffuse across W = W 2/2D

1- t / h is the probability of not recombining, so

h

tT

= 1

0.999-0.99ofrangein the;1 h

t

=

35

ase curren s ( ) ( ) CEEh

EholeE

h

electronEB =

+=

+=


36/76

The ratio of the collector current to the base current is the current gain of the transistor

t

h

B

C

I

I

==

1

Leak current in the collector-base junction-ICBO

( ) CBOEB

CBOEC

IIIIII

=+=

1

36

what constitutes the transistor action is the control ofIEand henceICby VEB


37/76

dcI-Vcharacteristics of the n

bipolar transistor (exaggerated

to highlight various effects)

(x)

n(0)

Base

pn(x)

SCL IC increases slightly with VCB even when IE is

constant. (WHY?)

V = -10 V

VCB

= -5 V

VCB is increased, WBC also increases.

Consequently the base width gets slightly

narrower, leading to a slightly shorter base transit

time t

.

= t1

37

WBCWB

W'B

W'BC

h

The base width modulation by VCB is called theEarly effect.


38/76

Common base amplifier

eVeAD The input signal is the ac voltage veb applied in

=

kTWBE exp series with the dc bias VEB across the EB, and

then modulates the injected hole junction pn(0)

up and down.

large change in IE and then IC.This can be used to obtain

voltage amplification.IE changed IC changed

38


39/76

The change in IC can be converted to a voltage change by using a resistor RC, so

CCCCCB IRVV +=

The out ut si nal volta e v corres onds to the chan e in V

ECCCCBcb IRIRVv ===

The variation in the emitter current IE depends on VEB,

EE

I

eI

=

=eVpeAD

IEBnh

E exp0

EB

Input resistance re is output signal is

B

( )mAIeIkT

I

Vr

EEE

EBe

25

===

e

ebCECcb

r

vRIRv ==

39

Voltage amplification is

e

C

eb

cbV

rv

vA ==


40/76

Junction field effect transistor (JFET)

Gate

GBasic structure

p+

DS n-channeln

DrainSource

DS

Circuit symbol

forn-channel FET

p

p

+

Depletion

regionG

Cross section nDepletion

Metal electrode

Insulation

(SiO )

S DG

p+

n

S Dn-channel

n

Channel

regions

n-channel p

c ness p

(a)

Basic structure: An n-type semiconductor slab is provided with contacts at its

40

. .

Two faces of the n-type are heavily p-type doped (gates).


41/76

1. VGS = 0

ch

x

VDS

0BA

p+

n

GVGS= 0

ID = 6 mAn

Depletion

region n-channel

VDS = 1 V

(a)

VDS >0 ID from D to S positive voltage along the n channel

more reversely biased from A to Bdepletion region extend more into

41

e c anne rom o .

VDS width of depletion region

channel resistance


42/76

- AB DS.therefore does not increase linearly with VDS.

ID

(mA)

VGS

= 010

VDS(sat)

= VP

IDSS

VGS

=-2V

VGS

=-4VVDS(sat) = VP+VGS

VGS

=-5V

IDS

0 4 8 120

VDS

42


43/76

G

ID = 10.1 mAG

ID = 10 mA

DS

Pinched off

channel

A

P

DS

VDS=10V

(c)

VDS = VP= 5 V

(b)

DS ncreases urt er, t e two ep et on reg ons meet at po nt . e c anne s

then said to be pinched off. The voltage VP is called the pinch-off voltage.

The inch-off volta e is e ual to the ma nitude of reverse bias needed acrossthe p+n junctions to make them just touch at the drain end.

PGD VV =

VGS = 0 , s o VGD = -VDS and pinch off occurs when VDS = VP.

The drain current does not increase significantly with V when V > V .

43

G


44/76

GPinchedoff channel

DSE

ID = 10 mA

AP

Lchlpo

VDS> 5 V

Beyond VDS = VP, there is a short pinched-off channel of length lpo.

There is a very strong electric field E in this region in the D to S direction.

ectrons n t e n-c anne r t towar , an w en t ey arr ve at , t ey are

swept across the pinched-off channel by E. Consequently the drain current is

actually determined by the resistance of the conducting n-channel over Lchfrom A to P and not b the inched-off channel.

44


45/76

As VDS increases, most of the additional voltage simply drops across lpo as this

.toward A.

Point P must still be at a potential VPbecause it is this potential that just makes

the depletion layers touch. Thus the voltage drop across Lch remains as VP, then,

AP

PD

R

VI =

RAP is determined by Lch, which decreases slightly with VDS, ID increases

slightly with VDS. In many cases, ID is conveniently taken to be saturated at a

.

45


46/76

2. VGS< 0 (for example, -2 V)

GVGS =-2V

p+G

ID = 1.8 mA

VGS =-2V GVGS =-2V

ID = 3.6 mA

DS

VDS = 0 V

A BnDS

VDS = 1 V

DS

VDS = 3 VPinched offP

(a) (b) (c)

V = 0, the +n unctions are now reverse-biased from the start, the channel isnarrower, and the channel resistance is now larger than in the VGS = 0.

VDS= 1 V, the p+n junctions are now progressively more reverse-biased from VGS at

=GD GS DS .

If the pinch-off voltage is 5 V, now we only need VDS= 3 V to pinch off the channel.

46

Beyond pinch off, ID is nearly saturated just as VGS = 0, but its magnitude is

obviously smaller as the thickness of the channel at A is smaller.


47/76

ID

(mA) VDS(sat) = VP

VGS = 010 IDSS

VGS =-2VV

GS=-4V

5

VDS(sat)

= VP

+VGS

IDS

0 4 8 120

VGS

=-5V

V

DS

In the presence of VGS, the pinch off occurs at VDS = VDS(sat),

( ) GSPsatDS VVV +=

For VDS > VDS(Sat), ( ) GSPsatDSSD

V

VV

V

VI

+== RAP depends on VGS.

47If VGS

= -VP

(-5V), whole channel is closed. VGS(off)

.


48/76

IDS is relatively independent of VDS and is controlled by VGS. This control is only

possible if VDS > VDS(sat).

2

)off(

1

=

GS

GSDSSDS

V

VII

Field effect: By changing VGS, varies the depletion layer and hence the resistance

of the channel.

48

JFET Amplifier


49/76

p

JFET transistor action is the control of IDSby VGS

The ac source-vac connected in serials with dc bias-VGG modulate the VGSup and downaround VGG. The variation of vgs converted into the variation of the drain current by

resistanceRD and the current variation is not quite symmetric as that in the input signal.

49DDSDDDS RIVV =The voltage across DS is


50/76

V =18 V andR =2000

The peak-to-peak voltage amplification is:

( )( ) ( )

6.56.23

=

==

=

pkpkdsDSpkpkV

vVA

..pkpkgsGS

The negative sign represent the fact that the output and input voltages are out-of-

50

phase by 180o.

Mutual transconductance -gm: for the small signal about dc values, the variation IDS


51/76

gm g , DSdue to VGSabout the dc value.

gs

d

GS

DS

GS

DSm

v

i

V

I

dV

dI ==

g idis the change in the drain current

with its dc value and called output

signal current.

2

)off(

1

=GS

GSDSSDS

VVII

[ ] 2/121

2 DSDSSGSDSSDSm

IIVIdI

=

==g )off()off()off( GSGSGSGS

viiRv == ;-

gsmDdDdsvRiRv

=

=

==)(

51

m

gsgsgs vvv

M t l id i d t fi ld ff t t i t (MOSFET)


52/76

Metal-oxide-semiconductor field effect transistor (MOSFET)

1. Field effect and inversion

Fixed metal ionsx

Metal

Metal

C(a) V E

+Q

- Q

MobileelectronsCharge density

Two metal lates. Volta e is a lied char es + and a ear on the lates andthere is an electric field.

In the top plate E displaces electrons from surface into the bulk to expose

In the lower plate E displaces electrons from bulk into the surface to form -Q

52

Due to metal has more than enough electrons on surface, electrical field does not

penetrate into the metal and terminates at the metal surface.


53/76

Metal

x

V(b)WE

Depletionregion

+Q

- Q

p-typesemiconductor

If the lower plate is a p-type semiconductor, it is apparent that we do not sufficient

number of negative acceptors at the surface to generate the charge Q.

Therefore, we must expose negative acceptors in the bilk, which means that thee mus pene ra e n o e sem con uc or. o es n e sur ace reg on ecome

repelled toward the bulk and thereby expose more negative acceptors.

region, called depletion region.

53

x


54/76

(c)

x

Wa

Conduction

V> Vth E Wn

nvers onlayer +Q

- Q

ep e onregion

Voltage increases further, -Q also increases, as the field becomes stronger and

penetrates more into the semiconductor. Eventually, it is more difficult to make up

Q by simply extending the depletion layer width Wa into the bulk.

th ,

electrons into the depletion layer and form a thin layer of width Wn near the surface.

This layer is called inversion layer.

Further increase in the voltage does not change Wa

but simply increase Wn

.

These electrons are from both minority carriers and breaking of Si-Si bonds.

54

2 Enhancement MOSFET


55/76

2. Enhancement MOSFET

meta - nsu ator-sem structure s orme etween a p-type an an e ectro e

(gate). The insulator is SiO2.

There two n+ doped regions at the ends of the MOS device that form the source (S)

and drain (D).

Without voltage, S to D is an npn structure that is always reverse biased. If the+

55

, DSjunction between the drain and the substrate. As the MOSFET device is not

normally used with a negative VDS

, we will not consider this polarity.

VDS


56/76

VGS

= 3 VVDS

Vth

= 4 VID

= 0 ID

S G D

p n+

n+ Depletion

region

VDS

(a) Below threshold VGS

< Vth

and VDS

> 0

VGS < Vth, a depletion region is formed under the gate. No current from S to D for

DS.

VGS

= 8 V

VDS

= 0.5 V

Vth = 4 V

ID

= 1 mA ID

S G D

n+

n+

n-channel is the

(b) Above threshold VGS

> Vth

and VDS

< VDS(sat)

VDS

nA B

VGS > Vth, an n-channel inversion layer is formed under the gate, linking the two n+

regions. If a small VDS is applied, a drain current flows,

56chn

DSD

R

VI

=

VDS

= 0.5 V


57/76

V = 8 V

DS

I = 1 mA I

S G D

n+

n+

n-channel is the

th

=

(b) Above threshold VGS

> Vth

and VDS

< VDS(sat)

VDS

nA B

p inversion layer

The voltage variation along the channel is from zero at A (source end) to VDS at B

(drain end).

- GS GD GS DS .

depends only on VGS.

, , .

channel gets narrower from A to B and its resistance Rn-ch increases with VDS.

57

VDS

= 4V


58/76

VDS

4V

S G D

VGS

= 8 V

P

(c) Above threshold VGS

> Vth

and saturation, VDS

= VDS(sat)

VDS

ID

IDS

A

D= . m

p

n+

n+ DS(sat)

Eventually when the gate to n-channel voltage at B decreases to just below Vth, the

inversion layer at B disappears and a depletion layer is exposed. The n-channel

becomes pinched off at this point P. This occurs when VDS= VDS(sat), satisfying,

( ) thsatDSGSGD VVVV ==

When the driftin electrons in the n-channel reach P the lar e E within the narrow

depletion layer at P sweeps the electrons across into the n

+

drain. The current islimited by the supply of electrons from the n-channel to the depletion layer at P,

which means that it is limited by the effective resistance of the n-channel between

58

an .

VDS

= 10 V


59/76

VGS

= 8 VI

D

ID

= 4.5 mA

S G D

n+

n+

VDS

A

P'

p

When VDS exceeds VDS(sat), the additional VDS drops mainly across the highly

res st ve ep et on ayer at P, w c exten s s g t y to P towar A. At P, t e gate

to channel voltage must still be just Vth as this is the voltage required to just pinch

off the channel.

The resistance of the channel from A to P does not change significantly with

increasing VDS, which means that the drain current is then nearly saturated at IDS,

( )

chnAP

satDSDSDR

VII

'

59


60/76

(b) Dependence ofID on VGSat a given VDS(> VDS(sat))

As VDS(sat) depends on VGS, so does IDS. There is a slight increase in IDS with VDSbeyond VDS(sat).

The term enhancement refers to the fact that a gate voltage exceeding Vth isrequired to enhance a conducting channel between the source and drain.

60

Experimental relationship between I and V is:


61/76

Experimental relationship betweenIDSand VGSis:

( )2thGSDS VVKI =

ox2Lt

ZK e

=For ideal MOSFET,Kcan be expressed as:

where e is the electron drift mobility in the channel,L andZare the length and

width of the gate controlling the channel, and and tox are the permittivity (ro) andthickness of the oxide insulation under the gate

2

DSGSDS

=th

Where is a constant that is typically 0.01 V-1.

61

Light emitting diodes (LED)


62/76

g g

Light emitting diodes (LED) are simple optoelectronic devices that have applications in

display devices such as tail-lights in automobiles, traffic lights and also for optical

communications.

(1) Fundamentals of the operation of the light emitting diodes

62

The LED is a p-n junction that operates under forward bias Electrons are injected


63/76

The LED is a p-n junction that operates under forward bias. Electrons are injected

- - , ,opposite direction. Electrons injected into p-type semiconductor are minority carriers

there and would recombine with the holes either in the space charge region or beyond

the space charge region. As the result, if the recombination is radiative a light quantum

(photon) is emitted. The same happens with hole that penetrate into n-type material

where they are minority carrier. The emitted light quanta have to escape from thedevice without absorption, therefore one of the electrodes has to be made transparent.

(2) Typical setup of LED

63

(3) Efficiency of the device


64/76

c ency o e ev ce s pro uce y e com na on o severa ac ors

a. Internal efficiency of the radiative process

This component of the efficiency depends on the paraeters of the materials and the

quality of the interface. It is preferable to use direct bandgap materials with lowradiative lifetime. Non-radiative lifetime has to be made as big as possible. It depends

.

b. Injection efficiency

Since a photon emitted deep in the buried layers of the device has larger probability to

be absorbed in the semiconductor it is desirable to concentrate emission closer to the

ransparen e ec ro e. sua y e ransparen e ec ro e s o e n ec ng. ere ore,

is desirable to have high efficiency of the electron component of the current. Theinjection efficiency is defined as the ratio of the electron component of the current

to the total current through the p-n junction.

64

In order to make the injection efficiency as large as possible the concentration of


65/76

-

in the p-type semiconductor. The choice of the acceptor concentration in the p-type

half of the device should be optimized taking into account the fact that decreasing the

p-type doping helps to make the electron injection larger, but at the same time it

ncreases t e ra at ve et me.

c. External efficiency

The external efficiency of an LED quantifies the efficiency of conversion of electric

energy into an emitted external optical energy. The emitted photons have to leave the

device and therefore the optics of the device should be designed with great care.

interfaces and (c) Emission at such angle to the surface that the light undergoes total

internal reflection.

(4) Materials used for the LEDs

Efficient LEDs require high radiative recombination rate as compared to the non-

radiative recombination. Hi hl efficient devices use the direct band a

65

semiconductors. Another important requirement for the material is the availability of

the suitable substrate.

Materials with direct bandgap Suitable

b

Emission remarks


66/76

substrate energy

range (eV)

AlxGa1-xAs

Eg = 1.424 + 1.247x; x < 0.45

GaAs 1.424 to 1.9

GaP with doping GaP 2.21 (i) GaP: N (565 nm-yellow-

green)

(ii) GaP:Zn, O (640nm-red)

GaAs1-xPx

Eg = 1.424 + 1.150x + 0.176x2;

x < 0.45

InP 1.424 to

1.977

(i) GaAs0.6P0.4 (650nm-

red) (ii) GaAs0.35P0.65: N

(620nm-orange) (III)

GaAs0.15P0.85: N (590nm:

ye ow

In1-xGaxAsyP1-y, x = 0.47

Eg = 1.35 0.72y + 0.12 y2 for all y.

InP 0.8 to 1.35 Use for communication

applications

In1-xGaxNEg = x

2 + 0.33x + 2.07 for all x13% latticematched with

Sapphire

2.07 to 3.4 Latest technology for bluelight emission (displays,

memories).

66

(5) Heterojunction high-intensity LEDs


67/76

Homojunction- A pn junction between two same bandgap semiconductors.Heterojunction- A pn junction between two different bandgap semiconductors.

Double heterostructure LED: increaseing the

intensity of the output light

(a) A double heterostructure diode has two

junctions which are between two different

bandgap semiconductors (GaAs and AlGaAs).(b) A simplified energy band diagram with

exaggerated features. EF must be uniform. (c)

Forward biased simplified energy band

. .

illustration of photons escaping reabsorption inthe AlGaAs layer and being emitted from the

device.

67

(6) LED characteristics


68/76

to the bandgap energy.

The relative light intensity versus photon energy or wavelength is an important

characteristics of LED.

The linewidth of the output spectrum or is defined as the width between half-

68

.

The output spectrum from an LED depends not only on the semiconductor material but

also on the structure of the pn-junction diode, including the dopant concentration levels.

Solar cells


69/76

pn junction with a very narrow and moreheavily doped n-region

The electrodes attached to the n-side must

allow illumination to enter the device and at

.

An open circuit voltage-photovoltaic voltage

develops between the terminals of the device

ue o e movemen o s

photogenerated..

Electron diffusion length in Si is longer than the

o e us on engt .

Open circuit zero net current two oppositecurrents one is due to the hoto enerated EHPs

69

the other is due to the photovoltaic voltage

(injection of minority carriers-forward bias)

photocurrent


70/76

Photogenerated carriers within the volumeLh+ W+ L ive rise to a hotocurrent if the

terminals of the device are shorted.

crystalline Si

- . - .

Wavelength greater

than 1.1 m iswasted. (25% for

absorbed near the crystalsurface-being lost by

recombination in surface

Anti-reflection

coating is notperfect, (80-90%

Device

itself

70

reg on more e ects -

Upper limit of the solar cell using single crystal of Si is about 24-26%.


71/76

np phsc

Light intensityPhotocurrent generated by light

Constant that depends on the particular device

V due to the hotocurrent assin throu h R.

Forward bias, reducing the built-in potential and leading to the

m nor y carr ers n ec on, d

= 1expkT

eVII od

whereIo is the reverse saturation current and is the ideality factor: 1 - 2

+= 1expphkT

III o

Solar cellI-V


72/76

AApplying external bias

TypicalI-Vcharacteristics of a Si solar cell.

The short circuit current isIph and the open

c rcu vo age s OC.


73/76

VI =

=

eV

p

kTo

By solving the two equation simultaneously, the actual currentIand Vin

the circuit can be obtained.

73

Load line construction method can easily find theIand V.


74/76

VI = I-V characteristics in this equation is a straight line with a

negative slope -1/R, called load line.

Point P satisfy both equations and the therefore represent the operation

oint of the circuit.

Fill factor-FF


75/76

The power delivered to the load isPout=IV. The maximum delivered power can be

obtained by changing the R or the intensity of illumination. WhereI=Im and V=Vm

FFV

mm=

The FF is a measure of the closeness of the solar cellI-Vcurve to the rectangular

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005)

shape (the ideal shape).


76/76

Chapter 4-1 (II 2008-2009) [Compatibility Mode]

Documents

Transcript of Chapter 4-1 (II 2008-2009) [Compatibility Mode]