fundamentos de eletrónica - ulisboa · fundamentos de eletrónica ... orange yellow blue _____ w g...

Fundamentos de Eletrónica

Carlos Ferreira FernandesInstituto Superior Técnico (IST)

Mestrado em Engenharia Eletrónica e de Computadores(MEEC)

3rd year, 1st semester2012-2013

Summary:

Semiconductors. Bonding and band diagrams. Intrinsic and extrinsic

semiconductors. Doping: donors and acceptors.

……………………………………………………………………………………...

Electric Conductivity between (106 -108 S.m-1) and (10-20 -10-8 S.m-1).

______________________________________________________________

Electric Conductivity between (106 -108 S.m-1) and (10-20 -10-8 S.m-1).

Strong temperature dependence in intrinsic semiconductors

Electric properties highly dependent on the inclusion of donor oracceptor impurities (extrinsic semiconductors)

______________________________________________________________2Ferreira Fernandesweek 1 - lesson 2

Conductivity

Material Conductivity Temperature Carrier type

______________________________________________________________

Material Conductivity

(S/m)

Temperature

dependence

Carrier type

Conductor 10 5 – 10 8 decreases Electrons

Semiconductor 10 -8 – 10 6 increases Electrons and Holes

Insulator 10 -16 – 10 -7 increases Ions and Electrons


Si

α

______________________________________________________________

-Si Si

Si

Si

Arrangement of atoms in Silicon


______________________________________________________________

The diamond crystal structure (Si,Ge)

5Ferreira Fernandes

______________________________________________________________week 1 - lesson 2

Binary Ternary

AlAs

GaAsAlxGa1-xAs

GaP

GaAsAsxP1-xGa

GaPIn Ga P

______________________________________________________________

GaP

InPInxGa1-xP

InAs

InPAsxP1-xIn

InSb

GaSbInxGa1-xSb

InAs

GaAsInxGa1-xAs

1 1

1 1

x x y y

x x y y

In Ga As P

Al Ga AS Sb

− −

− −Quaternary


______________________________________________________________

The zinc blende crystal structure (GaAs, AlAs ,InP,GaP,...)


+4 +4 +4 +4

+4 +4 +4 +4

+4 +4 +4 +4

T = 0 K

WC

WG

______________________________________________________________

+4 +4 +4 +4

T = 0 K

WV

Covalent bonding and band stucture______________________________________________________________

8Ferreira Fernandesweek 1 - lesson 2

Human eye

Infrared Red Green Violet Ultraviolet

Orange Yellow Blue

______________________________________________________________

WG and λλλλ for several semiconductor materials

Orange Yellow Blue

CdTe

InSb Pbs Ge Si GaAs CdSe GaP CdS SiC GaN ZnS

HgCdTe GaAs1-yPy

λ (µm)

6.0 3.0 2.0 1.5 1.0 0.9 0.8 0.7 0.6 0.5 0 .45 0.4 0.35

0.0 0.2 0.4 0 .6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

WG (e.V.)


+4 +4 +4

+4 +4 +4

Covalent Bonding

Valence Electrons

Two types of carriers

______________________________________________________________

+4 +4 +4

Electrons(negative charge), n

Holes(positive charge), p

In intrinsic semiconductor

n = p = ni .


• In extrinsic semiconductor

Donor Impurity (ND)

n-type semiconductor

(n > ni > p);

+4 +4 +4

+4 +5 +4

+4 +4 +4

______________________________________________________________

Acceptor impurity (NA)

p-type semiconductor

(p > ni > n).

+4 +4 +4

+4 +3 +4

+4 +4 +4

11Ferreira Fernandes

______________________________________________________________week 1 - lesson 2

• In intrinsic and non-highly doped semiconductors in thermal equilibrium it is valid:

n p = ni2

• Charge-neutrality condition

n+NA−−−− = p+ND

+

______________________________________________________________

Intrínsic n-type p-type


Thermal equilibrium

terG R=

30 0 in p n m

− = = Intrinsic Semiconductor

______________________________________________________________

0 0

20 0

i

i

n p n m

n p n

= =

=

Intrinsic Semiconductor

23/ 2 GW kTin T e

−∝


thermal equilibrium

20ter ter iG R np nn

G Rdt

∂= − = ⇒ = ⇒ =

Stationary condition under illumination

______________________________________________________________

21 1ef

iter

efter

ter

Gnp n

G

GG R

G

+ = ⇒

= +

0ter te fe r efn

G G R Gt

G Rd

∂= ++ − = =⇒

______________________________________________________________


Charge neutrality condition

( ) ( )0 00 a dq n N q p N− +ρ = = − + + +

______________________________________________________________

0 0 d an p N N+ −− = −

0 0d aN n N p+ −− = −


Summary:Conduction and Valence Band Densities. Fermi-Dirac distribution function.

Bandgap. Iinfluence of Temperature on carrier concentrations.

Fermi-Dirac Distribution Function f(W)

It describes the occupation of electrons and holes in energy

______________________________________________________________

______________________________________________________________

1

0,5

f(W)

WF

W

−=

+

1( )

1F

W W

KT

f W

eT

T

T=0

______________________________________________________________1Ferreira Fernandesweek 2- lesson 3

Indescernibility

Pauli Exclusion Principle

In Fermi level: f(WF)=0,5

Property of Fermi function: f(W)=1-f(-W)

______________________________________________________________

f(W)

1

0,5

WF

W

1-f(W)

2Ferreira Fernandes

______________________________________________________________week 2- lesson 3

Electrons in Semiconductors

• Allowed and forbidden bands alternate

• Discrete energy levels within bands

Conduction band and Valence band Density of states g(W)

π= = −* *08

( ) 2 ( )n n CVdN

g W m m W WdW h

w

______________________________________________________________

W>WC for conduction band

W<WV for valence band

π= = −* *08

( ) 2 ( )p p VVdN

g W m m W WdW h

wC

wV

g(w)

wG

3Ferreira Fernandes

______________________________________________________________week 2- lesson 3

Electron carrier density n is related to the way electrons are distributed in

the energy levels within the conduction band

Hole carrier density p is related to the non-occupied levels in the valence band

∝ ( ) ( )f Wn g W

[ ]∝ −1 ( ) ( )f W g Wp

______________________________________________________________

Fermi Level WF

– Near the middle of band gap in

intrinsic semiconductors

– Near the conduction band in n-

type semiconductors

– Near the valence band in p-type

semiconductors

wwC

wV

g(w)

wF

4Ferreira Fernandes

______________________________________________________________week 2- lesson 3

Non-degenerate Semiconductors

• WC-WF>>KT

• WF-WV>>KT

• Classic Mechanics f(W)=exp[-(W-WF)/KT]

Temperature Dependence −

=2 3GW

KTn CT e

______________________________________________________________

Intrinsic Semiconductors n=p=ni

Extrinsic n-type semiconductors (ND+>>ni) n=ND

+

p=ni2/ND

+

Extrinsic p-type semiconductors(NA->>ni) p=NA

-

n=ni2/NA

-

= KT

in CT e

5Ferreira Fernandes

______________________________________________________________week 2- lesson 3

Intrínsic

zone

Saturation

zone

Ionization

zoneLog n

Log p

Log ND

______________________________________________________________

Log ND

Log p

Log n

Log ni

1/T0∞

6Ferreira Fernandes

______________________________________________________________week 2- lesson 3

Summary:

Transport. Drift and Diffusion.

Ballistic regime

= ∑

dv

m Fdt

______________________________________________________________

______________________________________________________________

Collision-type regime

dt

= ∑

* dvm F

dt

− ∂

= π ∂

12 2*

22

h Wm

kEffective mass

______________________________________________________________


• Lattice Imperfections Vibrations(fonons)

Missing atoms

Crystal defects

Dopant atoms

Dislocations

Particle-Imperfection interactions = COLLISION

______________________________________________________________

• Weak fieldsMean velocity is proportional to the electric field

MOBILITY= −µ

n nv E

= µ

p pv E

τµ =

,, *

,

n pn p

n p

q

m

______________________________________________________________


• Ergodic Hiphotesis: average in time for a set is equivalent to the

average for a whole population at a given instant

• Thermal equilibrium

null mean velocity =∑0iv

______________________________________________________________

• DRIFTconstant electric field

F


• Ohm´s law (local form)

• DIFUSION

= σ

condJ E

( )σ = µ + µn pq n p

= −

C D gradn = −

C D gradp = ×

argJ c a C

CONDUCTIVITY

______________________________________________________________

DIFFUSION COEFFICIENT

• Einstein’s relations

= −

n nC D gradn = −p pC D gradp = ×

argdifJ c a C

= µ = µ, , ,n p n p T n pKT

D Uq

= =( 300 ) 25TU T K mV

______________________________________________________________


I A

D C

yℓ

xℓ

z

y

Hall effect.

______________________________________________________________

B I

yℓ

zℓ x

e q= −F E

[ ]m q= − ×F v B

[ ]n n= −µ − µ ×v E v B

y xE v B=______________________________________________________________


−

−

−

−

−

−

−

−

−

+

+

+

+

+

+

+

+

+

n B

Fm Fe

I A

nv

C D

0HU <

z y

x

−

−

−

−

−

−

−

−

−

+

+

+

+

+

+

+

+

+

p B

Fm Fe

I A

C D

0HU >

______________________________________________________________

−

−

−

−

+

+

+

+

I

B

0HU <−

−

−

−

+

+

+

+

I

B

pv

0HU >

e q= −F E

[ ]m q= − ×F v Bqp

Rqn

Rl

IBRU HH

zHH

11=−==

______________________________________________________________


Summary:

Continuity equations

• CONTINUITY EQUATIONS

______________________________________________________________

______________________________________________________________

( )n n nn

G R divC G R D lapn div nEt

∂= − − = − + + µ

∂

( )∂= − − = − + − µ

∂

p p pp

G R divC G R D lapp div pEt

• CONTINUITY EQUATIONS

______________________________________________________________


• Time variation of carrier population inside anelementary volume is related to generation,recombination and transport mechanisms

pC

C

G

S V

CndS divCdV divCdVδ δ

= ≅∑ ∫

______________________________________________________________

nC

R

S Vδ δ

( )n n nn

G R divC G R D lapn div nEt

∂= − − = − + + µ

∂

( )∂= − − = − + − µ

∂

p p pp

G R divC G R D lapp div pEt

• Continuity equations

2Ferreira Fernandes

______________________________________________________________

week 3 - lesson 5

1. Homogeneous and neutral crystal

00 0

( )( )

n ndnrp n n

dt

−= − =

τ

( )0divC =

0 0( )dn

r n p npdt

= −

Ex: Dynamic regime in minority carrier populations under weak optical

injection

______________________________________________________________

0 0( )n

rp n ndt

= − =τ

MEAN LIFETIME FOR MINORITY CARRIERS0

1n

rpτ =

n1

n

n0

τn0t

( )0 1 0( ) n

t

n t n n n e−

τ= + −

3week 3 - lesson 5

2. Stationary regime without drift. Diffusion + recombination(minority population)

20

20 p

p

p p d pD

dx

−= +

τ

Ex: Infinity Crystal

( )0 1 0( ) p

x

Lp x p p p e

−

= + −

______________________________________________________________

( )0 1 0( ) pL

p x p p p e= + −

DiIFFUSION LENGTH L D= τ

p1

p

p0

Lp0x 4week 3 - lesson 5

Ex: Finite crystal

( ) ( )0 1 0 2 01

( )p p

p

b x xp x p p p sh p p sh

L Lbsh

L

−= + − + −

p

______________________________________________________________

p

p1

p2

p0

0 b

x

5Ferreira Fernandes

______________________________________________________________

week 3 - lesson 5

Summary:

pn Junction in thermal equilibrium. Contact potential.

HomoIsotype n+n, p+p

Anisotype pn

______________________________________________________________

______________________________________________________________

Junction

Hetero

Anisotype pn

Isotype nN, pP

Anisotype pN

JunctionAbrupt

Gradual

______________________________________________________________


• Planar process: Oxidation; Litography; Ionic implantation; metallization

______________________________________________________________

S. Sze, Physics of Semiconductor devices week 3 - lesson 6

• Thermal Equilibrium

cond df cond dfp n p p n nJ J J J J J J 0

0 0

= + = + + + == + = + + + == + = + + + == + = + + + =

Fip p p p p

dp 1 dW dpJ qp E qD qp kT

dx q dx dx

= µ − = µ − µ= µ − = µ − µ= µ − = µ − µ= µ − = µ − µ

______________________________________________________________

dx q dx dx

Fi FW W

kTip n e

−−−−

====

Fi Fdp p dW dW

dx kT dx dx

= −= −= −= −

F

p p

Fn n

dWJ 0 p 0

dx

dWJ 0 n 0

dx

==== ⇒⇒⇒⇒ µ =µ =µ =µ =

==== ⇒⇒⇒⇒ µ =µ =µ =µ =

FdW0

dx⇒⇒⇒⇒ ==== Fermi level invariant in space

3Ferreira Fernandes

______________________________________________________________

week 3 - lesson 6

D A(x) q p(x) n(x) N (x) N (x)+ −+ −+ −+ − ρ = − + −ρ = − + −ρ = − + −ρ = − + −

1E(x) (x)dx= ρ= ρ= ρ= ρ

εεεε ∫∫∫∫

V(x) E(x)dx= −= −= −= −∫∫∫∫

______________________________________________________________

NA

ND

n

p

x

4Ferreira Fernandes

______________________________________________________________

week 3 - lesson 6

xxp

xn

ρρρρ(x)

xp xn

E(x)

E0

xp xn

V(x)

VC0

______________________________________________________________

xp xn

E(x)

E0

Total Depletion

xp xn

V(x)

VC0x

xp

xn

ρρρρ(x)

DqN++++

AqN−−−−−−−−

+Q

-Q

Space Charge

5Ferreira Fernandes

______________________________________________________________

week 3 - lesson 6

Equilibrium

between drift and

diffusion ⇒⇒⇒⇒ VC0

J

xp xn

V(x)

x

WC

qVC0

Neutral p Neutral nSpace charge zone

______________________________________________________________

pdfJ

pcondJ

ndfJ

ncondJ

0

0

WF

WV

WG

WG

qVC0

6Ferreira Fernandes

______________________________________________________________

week 3 - lesson 6

(((( ))))C0 D

p0

A D A

2 V Nx

q N N N

εεεε= −= −= −= −

++++

Total Depletion

Thermal equilibrium

(((( ))))C0 A

n0

D A D

2 V Nx

q N N N

εεεε====

++++

______________________________________________________________

C0 A D0

A D

2qV N NE

N N= −= −= −= −

ε +ε +ε +ε +A D

C0 T 2i

N NV U ln

n====

Ex: 23 3A DN N 10 m−−−−= == == == = Ge 016ε = εε = εε = εε = ε 19 3

in 2,4 10 m−−−−= ×= ×= ×= ×

C0V 0,47 V==== 8n0 p0x x 6,5 10 m−−−−= − = ×= − = ×= − = ×= − = × 0E 73 kV / cm≅≅≅≅

7Ferreira Fernandes

______________________________________________________________

week 3 - lesson 6

Summary:

p-n Junction under forward and reversed bias

U

______________________________________________________________

U

I

p n

Rp Rn Rmp Rnm

( )CU RI V I= + ∆

mp p n nmR R R R R= + + +

______________________________________________________________

1Ferreira Fernandesweek 4 - lesson 7 - pt I

Assumed conditions:

• Similar equations for biased p-n and thermal equilibrium for

carrier concentrations.

• Majority concentrations similar to thermal equilibrium. Minority

______________________________________________________________

• Majority concentrations similar to thermal equilibrium. Minority

are deeply influenced by polarization

• Negligible recombination and generation rates in the depletion

region.

2Ferreira Fernandes

______________________________________________________________

week 4 - lesson 7 - pt I

1( )

1 1( ) T

V x

Unn x n e=

1( )

1 1( ) T

V x

Unp x p e

−

=

1 0n nn n≅

1 0p pp p≅

______________________________________________________________

1 0

C

T

V

Up pn n e

∆

=

1 0

C

T

V

Un np p e

∆

=

3Ferreira Fernandes

______________________________________________________________


0pn

1np

+

−−−−

Lado P Lado N

E

Lp

Ln

x

xn -xp 0

1pn

0np

x xp −

1 0 1 0( ) ( ) para

x xnLp

n n n np x p p p e x x

−−

= + − ≥

______________________________________________________________

0pn

E

Lp

Ln

x

xn -xp 0

0np

−−−− +

1 0 1 0( ) ( ) para

x xp

Lnp p p pn x n n n e x x

−−

= + − ≤

4Ferreira Fernandes

______________________________________________________________


0( ) 1

C

T

V

p n Up n

p

qD pJ x e

L

∆ = −

0( ) 1

C

T

V

n p Un p

n

qD nJ x e

L

∆ = −

( ) ( )n p n nJ x J x= ( ) ( )p p p nJ x J x=

( ) ( ) ( ) ( )p n n p p nJ x J x J x J x= = +

______________________________________________________________

( ) ( ) ( ) ( )p n n p p nJ x J x J x J x= = +

( )nJ x

( )pJ x

J

5Ferreira Fernandes

______________________________________________________________


0 0( ) 1 1

C C

T T

V V

p n n p U Up is

p n

D p D nI AJ x Aq e I e

L L

∆ ∆ = = + − = −

0 0 2p n n p p nD p D n D D

I Aq Aq n

= + = +

______________________________________________________________

0 0 2p n n p p nis i

p n p D n A

D p D n D DI Aq Aq n

L L L N L N+ −

= + = +

0 0C C C CV V V V U= − ∆ ≅ −

6Ferreira Fernandes

______________________________________________________________


UI = Pmax

I

U, ∆VC Udisr

RI

______________________________________________________________

UI = Pmax

1

C

T

V

UisI I e

∆ = −

7Ferreira Fernandes

______________________________________________________________


Summary:• Biased pn junction (2nd part).

• p-n Junction under variable conditions. Incremental parameters: Conductance.

U

______________________________________________________________

U

I

p n

Rp Rn Rmp Rnm

( )CU RI V I= + ∆

mp p n nmR R R R R= + + +

______________________________________________________________

1Ferreira Fernandesweek 4 - lesson 7 - Pt II

WC

WG

qVC

WG

−−−−

WC

WV

WG

qVC

−−−− −−−−

δδδδx

______________________________________________________________

WV

WG

−−−−

−−−−

(a) (b)

Energy bands in biased pn junction

(a) U>0 ; (b) U<0

2Ferreira Fernandes

______________________________________________________________

week 4 - lesson 7 - Pt II

I

U

T’ T

T’ > T

______________________________________________________________

U

Temperature Effects

3Ferreira Fernandes

______________________________________________________________


VM/R

ID

______________________________________________________________

DD

V UI

R

−= ln 1

DD T

is

IU U

I

= +

UDVVM

4Ferreira Fernandes

______________________________________________________________


ID

MV

R

ID R

UD sin ωMV t

p-n Junction in almost-stationary regime

(low frequency analysis or slow variations)

______________________________________________________________

UD

VM

−VM

R

− MV

R

5Ferreira Fernandes

______________________________________________________________


U, I I R

UD sin= ωMU U t

t

>M disrU U

Half-wave rectifier

______________________________________________________________

U, I

t

<M disrU U

(a)

(b

6Ferreira Fernandes

______________________________________________________________


V

VS

VS

I

I V

VS

(a) (b)

Full-wave rectifier

______________________________________________________________

U, I

t

<M disrU U

7Ferreira Fernandes

______________________________________________________________


The small-signal model

ID

I Ig

U U

′∆ ∆= ≅

∆ ∆

Incremental conductance

'D

D P

II I U g U

U

∂∆ ≅ ∆ = ∆ = ∆

∂

______________________________________________________________

UD

ID0

UD0

∆U

∆'I ∆I

U U∆ ∆ D PU∂

D is

T

I I

Ug

+=

8Ferreira Fernandes

______________________________________________________________


Summary (course 8):Dynamic analysis of p-n junction . Incremental circuit.

Incremental parameters. Conductance and differential capacitances.

______________________________________________________________

10-Out-2012 Ferreira Fernandes 1

U

I

p n

Rp Rn Rmp Rnm

______________________________________________________________

p-n junction in variable regime. Incremental parameters.

ID

Incremental conductance

' D

D P

II I U g U

U

∂∆ ≅ ∆ = ∆ = ∆

∂

______________________________________________________________

UD

ID0

UD0

∆U

∆'I ∆I

I Ig

U U

′∆ ∆= ≅

∆ ∆

D PU∂

D is

T

I I

Ug

+=

2Ferreira Fernandes

______________________________________________________________

10-Out-2012

Transition Capacitance

n n n nT

n

Q dQ dQ dxC

u du dx du

−δ= ≅ − = −

δ

( )nn D D

dQA x AqN AqN

dx

+= ρ = ≅

______________________________________________________________


n D D

ndx

( )( )

1

20

2 1

2

n AC

D A D

dx NV U

du qN N N

−ε = − −

+

( )( )

1

202

A DT C

A D

qN NC A V U

N N

−ε= −

+______________________________________________________________

______________________________________________________________

−

−

− −

−

+

+

+ +

+

p n

U

CT

Transition capacitance


______________________________________________________________

U

ρ

x xn

xp

δQn

δQp

U

CT0

VC0

______________________________________________________________

Diffusion Capacitance

( )0( ) cosMu t U U t= + ω + α = τS T DQ I

DdISdQC g= = τ = τ


______________________________________________________________

D

D

dISS T TdV

D

dQC g

dV= = τ = τ

Transit time depends on the carrier lifetime

______________________________________________________________

1np

+

−−−−

Lado P Lado N

E


______________________________________________________________

0pn

−−−−

L p

L n

x

x n-x p 0

______________________________________________________________

p-n Junction: Commutation Regime

iD


______________________________________________________________

uD

− + −

+

A B

S

E E

R

______________________________________________________________

0pn

1np

+

−−−−

Lado P Lado N

E

Lp

Ln

x

1pn

0np


______________________________________________________________

xn -xp 0

0pn

E

Lp

Ln

x

xn -xp 0

0np

+

−−−−

______________________________________________________________

u

t t0

−E

+E


______________________________________________________________

lado n lado p n

p

x x’

pn0 np0

t t

______________________________________________________________

−−−−

Stationary characteristic I(U) for a Si diode

Summary (courses 9 and 10):Si p-n junction. Stationary characteristic I(U).

15 e 17-Out-2012 Ferreira Fernandes 1

______________________________________________________________

(i) For reversed bias, the current does not saturates in −−−−Iis

(i) For forward bias, the current increase with voltage is slower, for small

currents.

______________________________________________________________

( ) ( )inI qRAl U q Al U= = −

I

U

G isI I I= +


______________________________________________________________

( ) ( )2

iG

nI qRAl U q Al U= = −

τ

( )( )

2

G

is n p i

I l U N

I D D n=

+ τ

0,1 (Ge)

300 (Si)

U

______________________________________________________________

2

2T

U

UiR S

kTnI qAR A e

E

π= =

τ1T

U

UD is RI I e I

= − +


______________________________________________________________

( )( ) 20

( )

2 T

R T

Udif

Un p C i

I U l U N

I

D D V U n e

π=

τ + −

IR

Idif

I

U

______________________________________________________________

Temperature effect

3

2 22 0 10 /

G

T

U W qU

U kTR iI I n e T e U kT q

−−

≅ ∝ ∝ < <

2 310 /

G

T

U W qU

U kTdif iI I n e T e U kT q

−−

≅ ∝ ∝ >> ID


______________________________________________________________

UD

T

______________________________________________________________

( )( )

1

20

2

A DT C

A D

qN NC A V

N NU

−ε= −

+

Conductance

is

T

D II

Ug

+=

Transition capacitance

dQ


______________________________________________________________

= = τ = τD

D

dISS T TdV

D

dQC g

dVDiffusion capacitance

Incremental parameters depend on the DC bias

______________________________________________________________

EXAMPLE:

Consider the circuit of the figure and assume that Iis=1 nA andU(t)= U0+UMcosωωωωt (V). Calculate the diode current when

a) U0=20V and UM=10mV b) U0=20V and UM=20mV

c) U0=50V and UM=10mV d) U0=0V and UM=10mV

e)U0=0V and UM=10V

Say in qualitatively way how varies a) if ωωωω=1MHz

_______________________________________________________(sol: a) I(t)=20+0.01 cosωt (mA) b) I(t)=20+0,0 2cosωt (mA)

c) I(t)=50+0,01cosωt (mA) d) I(t)=0,4 cosωt (nA)


c) I(t)=50+0,01cosωt (mA) d) I(t)=0,4 cosωt (nA)

e)I(t)=10cosωt (mA) in the positive half-cycle and I(t)=0 in the negative half-cycle

(half-wave rectifier)

For high frequencies the capacitive effects exist and should be considered in the

diode models. The current is in advance (positive phase), when compared to the

input voltage waveform (phase null). I ( t) R = 1 0 0 0 Ω

U ( t)

______________________________________________________________

______________________________________________________________

Summary (course 11):

Bipolar Junction Transistor Ebers Moll equationsBipolar Junction Transistor. Ebers-Moll equations

p n p

E C

p pAcceptors Donors CContacts


B

ND NA ND

n

NA

np np

p

p

p

A – área transversal x

IE IC

IB

E C

UCUE

E C p n p IE IC

B

IE IC

(a)

B IB UE UC

IB

E

B

C

UCUE


B

(b

______________________________________________________________

Conventions adopted in this course that are common to p-n-pand to n-p-n

1. In the symbol the arrow is in emitter terminal directed from p to n asin a diode;

2. Reference for voltages: Theses are referenced from p-side to n-sideof the colector-base and emitter-base junctions. Therefore they arepositive (negative) for forward (reversed)-biased;

3. Rference for currents: The emitter current is taken with the directionof the arrow. If it enters (leaves) the other two leave (enter) theof the arrow. If it enters (leaves) the other two leave (enter) thetransistor. Therefore we can assume that the KCL is given byIE=IB+IC;

4. Dissipated power is important in the active zone. In cut zoneti ll th t i th t ti th ltpractically there are no currents; in the saturation zone the voltages

are negligible;5. In the active zone the emitted power in the transistor is practically

the power in the collector junction and it is given by –(Uc.Ic).

17-Out-2012 Ferreira Fernandes 3______________________________________________________________

p j g y ( )

______________________________________________________________

IE IC E C

A – área transversal x IB

E

B

C

UCUE

E C p n p IE IC

IE IC E C

(a)

B IB UE UC

IB

B

UCUE

(b(b


What is represented in the Figure?


And now?


Now, I think noone doubts…


⎧

1 1

CE

T TE ES R CS

UUU UI I e I e

⎧ ⎛ ⎞⎛ ⎞⎪ ⎜ ⎟⎜ ⎟⎪ ⎜ ⎟⎜ ⎟= − −α −⎪ ⎜ ⎟⎜ ⎟

Ebers-Moll

equations E ES R CS⎪ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎪ ⎝ ⎠ ⎝ ⎠⎪⎪

⎨

equations

1 1

CE

T T

UUU UI I I

⎨⎪ ⎛ ⎞⎛ ⎞⎪ ⎜ ⎟⎜ ⎟⎪ ⎜ ⎟⎜ ⎟1 1T T

C F ES CSI I e I e⎪ ⎜ ⎟⎜ ⎟= α − − −⎪ ⎜ ⎟⎜ ⎟⎪ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎪⎩

( )pBpB

BpBCSRESF LbshL

pAqDII

/'0== αα

⎞⎛

( )⎟⎟⎠⎞

⎜⎜⎝

⎛+=

pBpB

BpB

nE

EnEES LbthL

pDL

nDAqI

/'00

( )⎟⎟⎠⎞

⎜⎜⎝

⎛+=

pBpB

BpB

nC

CnCCS LbthL

pDL

nDAqI

/'00

______________________________________________________________

( )1/ cosh '/

'

pBF

b L

LD n b

⎡ ⎤⎣ ⎦α =

⎛ ⎞0

0

'1 pBnE E

pB nE B pB

LD n bthD L p L⎛ ⎞

+ ⎜ ⎟⎜ ⎟⎝ ⎠

.

( )1/ cosh '/

'

pBR

B

b L

LD n b

⎡ ⎤⎣ ⎦α =

⎛ ⎞⎜ ⎟0

01 pBnC C

pB nC B pB

LD n bthD L p L⎛ ⎞

+ ⎜ ⎟⎜ ⎟⎝ ⎠

Short base

NE > NB > NC

9Ferreira Fernandes______________________________________________________________

17-Out-2012

______________________________________________________________

( )1 1E TU UE ESI I e= − 1F EIα

IE IC

1R CIαIB

U

( )1 1C TU UC CSI I e= −

UCUE


17-Out-2012

______________________________________________________________

Derived equations. Direct and reversed Current gains. Emitter Yield. Transport factor.

……………………………………………………………………………................…

( )0C F E CB CI I I U= α − δ ( )0 1EB F R ESI I= −α α

( )0E R C EB EI I I U= α + δ

( )0EB F R ES

( )00 01

1CB

CE F CBII I= = +β

( )0C F B CE CI I I U= β − δ

( )0 01CE F CBF−α

( )00 01EB

EC R EBII I= = +β

( )0E R B EC EI I I U= −β + δ

( )0 011EC R EB

RI I+β

−α


17-Out-2012

______________________________________________________________

CIΔ EIΔC

CF U const

EI =α =Δ E

ER U const

CI =α =Δ

CC

F U constB

II =

Δβ =

Δ EE

R U constB

II =

Δβ = −

Δ

Fα α1

FF

F

αβ =

−α 1R

RR

αβ =

−α


17-Out-2012

______________________________________________________________p n p

(a)

Donors

x

Acceptors Acceptors

x (b)

x (c)

(d)

(e)

qUC

qUE


17-Out-2012

______________________________________________________________

1 0

E TU UBE Bp p e=

p n p

E B C

nC0 1 0

E TU UE En n e= pB0

nE0

x1 0

C TU UC Cn n e=

1 0C TU U

BC Bp p e=


17-Out-2012

______________________________________________________________

Emitter yeld

0CpE

UpE nE

JJ J =γ =

+ 0

1'1 pBnE ELD n bth

D L p L

γ =+pE nE

0pB nE B pBD L p L

Transport Factor

0CpC

UpE

JJ =θ = −

α = γ×θ

Current Gain

Fα = γ×θ


17-Out-2012

______________________________________________________________

E C R R G G

IE IC R+D R+D

B

IB

R – Recombination; G – Generation; D - Diffusion


17-Out-2012

______________________________________________________________

Zonas de funcionamento:

DIRECT ACTIVE ZONE Emitter – Base Junction: FCollector – Base Junction: R

SATURATION Emitter – Base Junction: FSATURATION Emitter – Base Junction: FCollector – Base Junction: F

CUT ZONE Emitter – Base Junction: RCollector – Base Junction: R

Ex: p-n-p in Active zone UEB>0 ; UCB<0Ex: p n p in Active zone UEB>0 ; UCB<0

n-p-n in Active zone UEB<0 ; UCB>0


______________________________________________________________

Summary: (course 12)

Common emitter circuit. Degenerate emitter circuit. Early effect.

______________________________________________________________

iC

uRC

iB RBuC RC

EB uE

iE

uCE

EC

iE~ vb


______________________________________________________________

______________________________________________________________

IC

Output characteristic (n-p-n)

( )1 R BI+ β ΔICE0

ZAI Disrupção da

junção emissora

( )1 R BI+ β Δ

UCE 0BI =

1 0BI >

1F BIβ

UEC0

UCE0

IEC0

1B

2 1 1 0B B B BI I I I= + Δ > >

F BIβ ΔDisrupção da junção colectora

Saturação

Zona Activa Directa (ZAD) (a)

_____________________________________________________________2Ferreira Fernandes24-Out-2012

0C F B CEI I I≅ β − ( ) 01C R B ECI I I≅ − +β +

( ) ( )010 l F B CEI I

U I U+ −β ( 0) lnU I U= ≅ α

I U U

( ) ( )( )

0

00 ln

1F B CE

CE C TF B R CE

U I UI I

β= =

+ −β α( 0) lnCE C T RU I U= ≅ α

Input Characteristic IB CE TU U−

0CEU =0CEU >

Active Zone

UEdisr.

IB0

Emitter base di ti

UE

Active Zone (ZAD) Corte

disruption

(b) ( )

( ) ( ) ( ) ( ) ( ) 01 1 1B F ES E R CS F ES E BI I U I I U I= − −α δ + −α = − −α δ + 3

______________________________________________________________

Early effect

______________________________________________________________

0

0 'pB nE B

FnE E

D L pD n b

β ≅

IC

Early Voltage

UCE

IB=const.

Ferreira Fernandes 424-Out-2012

______________________________________________________________

iC

uRC

Montagem de emissor comum

iB

EB

RBuC

uE uCE

EC

RC

iE

CE

~vb

i

uRC

iB RBuC

iC

E

RC

EB uE

iE

uCE

EC

~vbRE CE


______________________________________________________________

IC

P’

IC

P

IC

P

______________________________________________________________

P

UCE

P

UCE

P’ P

UCE

P’

(EB) (EC) (RC)

IC IC IC

P

P’

P

P’ P

P’

UCE

(RB)

UCE

(βF)

UCE

(RE)


______________________________________________________________

______________________________________________________________

Summary (courses 13 and 14)

Transistor in variable regime. Incremental model.

π Hybrid incremental model

Incremental components i i i u uIncremental components ie, ib, ic, ue, uc

Transístor in the active zoneTransístor in the active zone


______________________________________________________________

______________________________________________________________

Incremental model -π híbrido

B Cib

B C

vπ rπ gmvπ ≡ rπ βib

E E

π = βm bg v i = ⇒ = βb gr rv iπ βm bg v iπ π π= ⇒ = βmb gr rv i

⎞∂= ⎟∂ ⎠

Cm

IgV = ⇒ = =

BEBE TT

VV UU CS

C SII eI I e na Z A D g⎟∂ ⎠

mBE P.F.R.

gV = ⇒ = =C S m

T TI I e na Z.A.D. g

U U= C

mT

Ig

UTU______________________________________________________________

2Ferreira Fernandes29 e 31-Out-2012

______________________________________________________________

Incremental model T model

C Ci g

gmvbe αieα =e m bei g v

=v r iB

re

≡ B

re

ie

=be e ev r i

= αm eg rvbe

r0 r0

E E

m eg

π β ββ

r 1 ( )= + βr r 1thereforeπ β β= = = + β

βα+ β

e1

r1

( )π = + βer r 1

N ti th t i ti ll i br i −1gNotice that is practically given by=e be er v i 1mg____________________________________________ __________________


______________________________________________________________

In the model incremental resistor r0 is given by the curve slopes in the active zone

⎛ ⎞= +⎜ ⎟

⎝ ⎠

BE

T

VU CE

C ESA

VI I e 1

VVA = Early voltage

⎝ ⎠AV

Slope − = ≅+C C

A C

10

E AVr

I IV VA CE A

VIC≅ A

0C

r VI

IC

VCE-VA______________________________________________________________4Ferreira Fernandes29 e 31-Out-2012

______________________________________________________________

B C

rπ gmvπ r0vπ

E

Early effect

Capacitive effectsCapacitive effects______________________________________________________________


______________________________________________________________

Ex: Integrated circuits transístors with base and collector in short-

i it B

C≅ ≅ ⇒CE BEV V 0,7 Z.A.D.

circuit B

EIncremental model

C ≡ B C ≡ BC

rπ gmvπ r0vπ ≡ rπ gm r0 ≡

E

−1mg

E EE

−π>> >> 1

0 mr r g pois π = βmg r

In the incremental point of view the transistor behaves as a resistance when colector and base are directly linked 6

______________________________________________________________

Common emitter circuit

RC

iB RB1 uC

iC

ECB

uE

iE

vO

RB2

EC

~ vi

0; ;C Am m

I Vg r g rU I π= = =β

T CU I

( ) ( )0 0 1 2// ; // ; // //V m C out C in B BA g R r R R r R R R rπ= − = =

29 e 31-Out-2012 Ferreira Fernandes 7______________________________________________________________

C itt i it______________________________________________________________

Common emitter circuit (degenerated emitter)

RC

iB RB1 uC

iC

CB uE

iE

vO

RB2

EC

~ vi

( ) ( )1 2; // // 11

CV in B B E

E

RA R R R r Rr R ππ

β= − = + +β⎡ ⎤⎣ ⎦+ +β( ) Eπ β

( ) 0; // 1 //CV out C m E

E

RA R R r g r RR π⎡ ⎤≅ − = +⎣ ⎦


______________________________________________________________

______________________________________________________________

• Common collector circuit• (emitter follower)

( )( )( )( )

0

0

1 // //;

1 // //E L

VE L

R R rA

r R R rπ

+β=

+ +β

( )( )01 // //in E LR r R R rπ= + +β

( )0// // ; / 11

Gout E e e

RR R r r r rπ⎛ ⎞

≅ + = +β⎜ ⎟+β⎝ ⎠β⎝ ⎠• Buffer• Emitter follower (non-inverter and unit gain voltage)

29 e 31-Out-2012 Ferreira Fernandes 9______________________________________________________________

Summary (course 15):JFET.

______________________________________________________________

G1

UDS UGS1

IG1

xp p+

ID IS D S

n 2a

xn

UGS2 IG2

G

– ionized donors ionizados– ionized acceptors

p+

G21 2 0= = =GS GS DSU U U

______________________________________________________________5 Nov 2012

______________________________________________________________

UDS IG

G

ID IS D S

n

y

L

a xn (y)

( )02 1

=+

c An

D A D

V Nxq N N Nεx

y

V1V2 J

V = const. xn(y)

V3 V4

Vn . . .

( )( )

02 1−=

+c GSP A

D A D

V U Naq N N N

ε

x

V1

J

x

______________________________________________________________5 Nov 2012

______________________________________________________________

( )2 1

=+

cp A

D A D

V Naq N N Nε

(Pinch-off)GSPU

2

0 1⎡ ⎤⎛ ⎞⎢ ⎥= − ⎜ ⎟⎢ ⎥⎝ ⎠

GSP CaU V

⎢ ⎥⎝ ⎠⎣ ⎦nx

______________________________________________________________5 Nov 2012

______________________________________________________________

( )D DI J S y=

( ) ( )2 nS y a x y b= −⎡ ⎤⎣ ⎦

3/ 2 3/ 2⎡ ⎤⎛ ⎞ ⎛ ⎞

Non-saturation or triode zone3/ 2 3/ 2

0 02 223 3

DS C GS DS C GSD CP

CP CP CP

U V U U V UabI VL V V V

⎡ ⎤⎛ ⎞ ⎛ ⎞− + −⎢ ⎥= − +⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

σ

S t ti3/ 2

0 01 223 3sat

C GS C GSD CP

CP CP

ab V U V UI VL V V

⎡ ⎤⎛ ⎞− −⎢ ⎥= − + + ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

σ

Saturation zone

CP CP⎢ ⎥⎝ ⎠⎣ ⎦3/ 2

2 22 13 3

sat sat

sat

DS DSD CP

CP CP

U UabI VL V V

⎡ ⎤⎛ ⎞⎢ ⎥= − + −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

σ3 3CP CPL V V⎢ ⎥⎝ ⎠⎣ ⎦______________________________________________________________

5 Nov 2012

I______________________________________________________________

ID

UGS1 UGS2

UGS3 1 2 2 3Δ = − = −GS GS GS GS GSU U U U U

3 4

0= − =

Δ >

…GS GS

GS

U UU

UDSUDS

0= − = − +satDS GS GSP GS C CPU U U U V Vsat

______________________________________________________________5 Nov 2012

______________________________________________________________

( )=

∂∂= D

GSU constDS

Im U PFR

g ( )=

∂∂= D

DSU constGS

Ids U PFR

gDS

ID

UGS1 UGS2

UGS3 1 2 2 3

3 4

0

Δ = − = −

= − =

Δ >

…GS GS GS GS GS

GS GS

GS

U U U U UU U

U

UDS

______________________________________________________________5 Nov 2012

i______________________________________________________________

id

D G

gmugs

ugs uds

gm gs

S

DG

rds

DG

ugs gmugs

SS______________________________________________________________

5 Nov 2012

______________________________________________________________

T i →Vco decreases, Decreases the transition zone length,Increases channel depth

T increases ⎯→⎯Decreases the electron mobility

D D D

Simbology

G

D

G

D

G1

D

G2

S S S

(a) (b) (c)

______________________________________________________________5 Nov 2012

• Homogeneous semiconductor

R = d an p N N+ −− = −Electric neutralityRS

=σ

20 0 = ip n nThermal equilibrium

R G G G+

0 0 iq

Stationary situation with uniform illumination

tot ter efR rnp G G G= = = +

2 1 efi

ter

Gpn n

G⎛ ⎞

= +⎜ ⎟⎝ ⎠

07 Nov 2012 Ferreira Fernandes 1

ter⎝ ⎠

• Semicondutores homogéneos2 1 ef

iG

pn nG

⎛ ⎞= +⎜ ⎟Internal photoelectric effect i

terp

G⎜ ⎟⎝ ⎠

( ) ( )1,423eV= = ≥ ⇒ = ≥G G

cW hf h W W W

( )pn pnq μ+μ=σ

( ) ( )eV

m≥ ⇒ ≥

λ λ μG GW hf h W W W

Conductivity

Intrinsic conductivity ( )i i n pqnσ = μ + μ Increases with T

e D nqN +σ = μ

2 GWn N N exp ⎛ ⎞= −⎜ ⎟ 2 3 GWn T exp ⎛ ⎞∝ ⎜ ⎟

Decreases with TExtrinsic Conductivity e D n

e A p

qqN −

μ

σ = μ

07 Nov 2012 2

i C Vn N N expkT

= ⎜ ⎟⎝ ⎠ in T exp

kT∝ −⎜ ⎟

⎝ ⎠

• Homogeneous Semicondutors:

• Intrinsic F i L l i th iddl f th• Intrinsic – Fermi Level in the middle of the gap

• Extrinsic:– n-Type – Fermi Level approaches Conduction band– p -Type– Fermi Level approaches Valence bandHighly extrinsic (Nimp>>ni)

2 24;

2D D i

D

N N nn n N

+ +++ +

= ≅

2 24;

2A A i

A

N N np p N

− −−+ +

= ≅2

07 Nov 2012 3Ferreira Fernandes

• Fermi-Dirac Function

f(W)f(W)

1

T

T=0

0,5

WW

T

WF

KTWf F 05,0)( ≠=KTWWWfWWWf 00)(1)( KTWWWfWWWf FF 00)(;1)( =>=<=


• Homogeneous semiconductors

C FW WN −⎛ ⎞⎜ ⎟

F VW WN −⎛ ⎞⎜ ⎟

C FCn N exp

kT⎛ ⎞= −⎜ ⎟⎝ ⎠

F VVp N exp

kT⎛ ⎞= −⎜ ⎟⎝ ⎠ Zona

intrínseca Zona de

Saturação Zona de

ionizaçãoLog n

Log N

Log p

Log ND

Log pLog n

Log p

Log n i

1/T0∞

i

1/T0 ∞


• Continuity equation. Dynamical situation. Neutral cristal and uniform illunination

dn0 0( )dn r n p np

dt= −

Ex: Dynamical regime for minority carriers. Weak illumination

00 0

( )( )n

n ndn rp n ndt

−= − =

τ

1MEAN LIFETIME FOR MINORITY

0

1n rpτ =

n ( )0 1 0( ) n

t

n t n n n e−τ= + −

n1

n0

( )0 1 0( )

τn0t07 Nov 2012 6

Stationary regime without drift. Diffusion with recombination(minority carriers)

20

20 pp

p p d pDdx

−= +

τ

Ex: Infinite crystalEx: Infinite crystal

( )0 1 0( ) p

xLp x p p p e

−= + −

DIFFUSION LENGTH L D= τ

pp1

p

p0

Lp0x

07 Nov 2012 7

02( ) c a dqV N N− +

• P-n Junção (thermal equilibrium)

02(0) c a d

d a

qV N NEN N+ −=

+ε

0 0n p⎛ ⎞

02 c a d

a d

V N Nq N N

− +

− ++

=ε

0 00 2ln n p

c Ti

n pV u

n

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠

E(x)

xp0 xn0

V(x) ρ(x)

DqN+

xp0 xn0

E0

VC0 x

xp0

xn0

Dq

N

+Q

-Q

E0AqN−−


• p n Junction (bias):• p-n Junction (bias):– Electric field increses with reversed biasing– Depletion zone length increases with reversed biasing– Small Forward voltages (about 1V, depending on the material)

DUu

⎛ ⎞⎜ ⎟ 2p nD DI A

⎛ ⎞⎜ ⎟

Small Forward voltages (about 1V, depending on the material)– Negligible Reversed currents

1TuD isI I e⎜ ⎟= −

⎜ ⎟⎝ ⎠

2

0 0

p nis i

p n n pI Aq n

L n L p= +⎜ ⎟⎜ ⎟

⎝ ⎠

DU⎛ ⎞ I

1 se 0

0

DTnu

D dif R isI I I I e U

I I I U

⎛ ⎞⎜ ⎟= + = − >⎜ ⎟⎝ ⎠ UI = Pmax

U RIse 0D is GI I I U= − + <

UI = Pmax

U, ΔVC Udisr RI


p n J nction ( ariable regime)

DU

• p-n Junction (variable regime)

TnuT is

dT

I eCnu

=τ

0D isD I IIg

U nU⎛ ⎞ +∂

= =⎜ ⎟∂⎝ ⎠

PFR( , )D DI U

D TPFRU nU∂⎝ ⎠

1

( ) ( )1202

A DT C D

A D

qN NC A V UN N

−ε= −

+


J ti ( l t t ti i )• p-n Junction (almost-stationary regime)

ID R

ID

MVR

UDsinωMV t

UD−VM UD

VM

− MVR


S mmar______________________________________________________________Summary:

MOS-FET. Qualitativ description. N-channel and p-channel MOS. Enhancement and depletion MOS. Simbology.

G metal

UDS

UGS

n+ n+

IG D

ID

S

IS d Insultor

n n

2n xp L

UBS

p

B

______________________________________________________________12 Nov 1Ferreira Fernandes

______________________________________________________________

DS GSU U<<

UDS

UGS ID

ID

n+ n+ UGS = const.

UDS


______________________________________________________________

≈DS GSU U

UGS

UDS

ID

+ +

ID

n+ n+

UGS = const.

UDS


______________________________________________________________

min lim= − = −DS GS GD GS GSU U U U U

UGS

UDS

UGS

ID ID

UGS = const.

n+ n+

p

UDS


______________________________________________________________

0<DSU

UGS

UDS

UGS

ID ID

UDS

n+ n+

UGS p


______________________________________________________________

Stationary Characteristics voltage-current in a MOSFET

UGS4

ID 0

4 3 2 1

≤

> > > >GS T

GS GS GS GS T

U VU U U U V

UGS4

UGS3

U

UGS1

UGS2

UGS0 UDS

UGS0

UGS4UGS4


______________________________________________________________

Energy

MetalOxid

Semiconductor

W

≈ ≈

WC0

WF

WC0

W0 WF0

W

x -a 0

WCM WV0


______________________________________________________________

ρ Metal Semiconductor Oxid Charge Distribution

+Q -Q

x-a d

−− AqN E Metal SemiconductorOxid

ES0

E0 xElectric Field

x -a d


______________________________________________________________ V Metal Semiconductor Oxid

VMS

Potencial distribution

φS

V0x

Wx

-a d

Energy DistributionMetal

Oxid

Semiconductor

≈ ≈

WC0

W

( )0 0 022 2 lninv

i FS T

W W pW Uq q n

φ−Δ

= = =x

-a

W0WF0

WV0

inviq q nx

0 d ______________________________________________________________12 Nov 9Ferreira Fernandes

ρ ______________________________________________________________

ρ Metal Semiconductor Oxid

+Q QB

x -a dmax

Qn

lim BD inv inv

OS OXB BGS GS S MS S

OX OX OX OX

Q QQ QU U VC C C C

φ φ= − + = − − − − +

D D D D

G

Enhancement

G

depletion

G

Enhancement

G

depletion

B B B B

S S S S ______________________________________________________________

n-Channel p-channel

12 Nov 10Ferreira Fernandes

S______________________________________________________________

Summary:Zones in MOSFET. Incremental components for MOSFET. Differential capacities. Body p p yeffect.

( ) ( )CS y x y b=

( ) ( ) ( , )

0( )

ˆ, ( , ) ( , )Cx y dV x yD y n dy

S y

I J u dS qbn x y x y dx= − =∫ ∫ μ( )y

( )( ) ( )*

0( , ) ( , ) ( )Cx ydV y dV y

D n n ndy dyI b qn x y x y dx b Q y= = −∫ μ μ

*

0( ) ( )DSU

nD nI b Q y dV y

L= − ∫

μ ( ) ( ) ( )n S BQ y Q y Q y= −

( ) 2B S A SQ y q N −= − ε φ

Ferreira Fernandes 1

( )invB S A SQ y q φ

______________________________________________________________19 Nov

______________________________________________________________

limsatDS DS GS GSU U U U≤ = −

Triode or non-saturation zone

( )lim

2*

2OX DS

D n GS GS DSC UI b U U U

L⎡ ⎤

= − −⎢ ⎥⎣ ⎦

μ

limsatDS DS GS GS

2L ⎣ ⎦

U U U U≥ = −

Saturation zone

( )lim

* 2

2sat

n OXD D GS GS

b CI I U UL

= = −μ

limsatDS DS GS GSU U U U≥ =

( )2L______________________________________________________________

2Ferreira Fernandes19 Nov

______________________________________________________________

1DSU

1DSUID

1

Non- Saturation

ID1

Non Saturation

Saturation

Saturation

UGS

cut

l imGSU UGSlimGSU

cut


19 Nov

______________________________________________________________

ID

0 ≤GS TU V

UGS4

UGS3 U

4 3 2 1> > > >GS GS GS GS TU U U U V

UGS2

UGS1

UUGS0

UDS

UGS0

UGS4


19 Nov

______________________________________________________________

Body effect

DI1 0BSU = 2 0BSU < 3 2BS BSU U<

U Cte= .DSU Cte=

GSU1TV 2TV 3TV1TV 2TV 3TV


19 Nov

______________________________________________________________

MOS: Variable Regime

( ) ( )0 0 0...D D

D D GS GS DS DSI II I U U U U

U U⎛ ⎞ ⎛ ⎞∂ ∂

= + − + − +⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠( ) ( )0 0 0D D GS GS DS DS

GS DSPFR PFRU U⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

g ( )*bgm

*b C U

( )lim

*n OX GS GS Dd Ss

b C U U UL

g = − −μNon-saturation zone

*m n OX DSg b C U

L= μ

0dsg =

Saturation Zone ( ) ( )lim

* satm

Dn OX GS GS

GS GS

Ib C U UL U U

g = − =−

μ( )limGS GS


19 Nov

______________________________________________________________

Incremental Model

id D G

ugs

gmugs rds

uds

S


19 Nov

______________________________________________________________

( )1satD D DSI I U= +λ

1Sds D dsg I r−= =λ

Body effect

D G

rds ugs

gmugs sbm sbg u

S

Ferreira Fernandes 8______________________________________________________________

19 Nov

______________________________________________________________

( )⎡ ⎤

Capacitive effects

( )lim

( )GSn OX GSQ y C U U V y⎡ ⎤= − −⎣ ⎦

* ( )( ) dV yI b Q ( )y L

Q Q d=

∫( )( )D n nyI b Q y

dy= − μ

0

( )total ny

Q Q y dy=

= ∫

3/ 22A LI⎡ ⎤⎛ ⎞2 323 E E

Dtotal OX GS GS

D

A LIQ C U UI A

⎡ ⎤⎛ ⎞= − − −⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦

( )( )

3 3

2 2

23

E E

E E

GD GStotal OX

GD GS

U UQ C L

U U

−=

−


( )E E

19 Nov

______________________________________________________________

2 3gs OXC C=Saturation zone

0gdC =

D

G Cgd

Cgs gmugs

S


S

19 Nov

______________________________________________________________

Summary:Applications: Inverter. Amplifier

APPLICATIONS MOS: INVERTER

pp p

UI

RD

D U

t

EDD

UDUi

D

Tr

S

G RG

UD

t

______________________________________________________________21 Nov

______________________________________________________________

APLICATIONS MOS: AMPLIFIER

ui

RD 1

20 V1

12 k

DD

D

ER kR

== Ω= ΩR1

ui

tD

EDDD

Tr

2 1,5 k5,5 FG

RC

= Ω= μ

1

CG G

t

uDuD

ui S R2 ~

t0m D

i

v g Rv

= −

______________________________________________________________21 Nov

R

______________________________________________________________ RD

ID (mA)

EDRG = 10 kΩ

G

D ID

I1

UDS

P

0

1

1

ED

EG=10 V

G

S

IG

UGS

RSUGS(V)0-1 S

(a) (b) ID

Q

O

( )*D D SE R R+

( )D D SE R R+

2 VGSU =

U

O

UDS*DE DE ODSU

QDSU______________________________________________________________21 Nov

______________________________________________________________

RG

G

ΔUDS

D ΔID

ΔU

ΔEG ~ ΔUGS

RS

RD S

gmΔUGS

G GS S DE U R IΔ = Δ + Δ Δ = ΔD m GSI g U

( )DS m D D SU g I R RΔ = − Δ +( )PFR lim= −m GS GSg A U U

( )1

+Δ=−

Δ +m S DDS g R RU

E g R1Δ +G m SE g R______________________________________________________________

21 Nov

______________________________________________________________

Summary:Thyristor. Stationary characteristic I(U). SCR.TRIAC. DIAC. GTO.

I E

II

I

B IL

IH

UUB0

H

Current-voltage characterístic of a thyristor in the 1st quadrant

Ferreira Fernandes 1

Current voltage characterístic of a thyristor in the 1st quadrant______________________________________________________________

14 Nov

______________________________________________________________

A

A

IA

IA

IUE1

A

U

J1

J2

p (1)

n (2)

IB1

IC1

IC2UC1

UAJ2

J3 p (3)

n (4) IB2

UC2

K

K

IE2

K

UE2

(a) (b) K


14 Nov

______________________________________________________________

1024 1024

( )3mD AN N −

1022

1020

(1) (2) (3) (4)

0 x

50 μm 150 μm 50 μm30 μm50 μm 150 μm 50 μm30 μm

Doping profile in a thyristor

101 2 1 2

2 seCD A D

qVE N N N≅ >>ε

303 3 4 3

2 seCA D A

qVE N N N≅ >>εε ε


14 Nov

A______________________________________________________________

A

IA

A

IA

IUE1

J1

J2

p (1)

n (2)

IB1

IC1

IC2UC1

Un (2)

J ′ UJ2

J3 p (3)

IB2

UC2

U

p (3)

n (4)

2J ′ U

KIE2

K

UE2

(a) (b)

A KI I= 1 2 01 02A F A F K CB CBI I I I I= + + +α α0

1CB

AT

II =−α1 Tα


14 Nov

______________________________________________________________

A A

SCR

A

IA

(1)

1EAI I=

IB1

G

UA

J1

J2

J3

p (1)

p (3)

n (2) IC1

IC2IG

K

J3 n (4)

IB2

2 KEI I=IK

UGG

IG

K 2 KEI I

K (a) (b)

2 0

1F G CB

AT

I II +=

−α

αA G KI I I+ =1 Tα


14 Nov

______________________________________________________________

II

IA

IG>0IG>0

IG=0 IG<0

I UAUB3 UB2 UB1

1 TG AI I−=

αα 2Fα


14 Nov

______________________________________________________________

AI

IG

A G K RI I I I+ = +

KI

G ( )2 0

1F G R CB

AT

I I II

− +=

−α

αIR

1 RII I I I I I⎛ ⎞

+ + +⎜ ⎟ θ1 RA G K R K K

K

I I I I I II

+ = + = + =⎜ ⎟⎝ ⎠

θ

' 22

FF =

ααθθ


14 Nov

IA

p

n ( )11 AI−αElectrons

1 AIα

ICB01 Holes

IG

p

2 KIα

ICB02

( )21 KI−α

n

IK 814 Nov

______________________________________________________________

n

A

IA

TRIACn (1) p (2)

n (3)

A G TRIAC

I

p (4)

UAK K

IA

n (5)

n (6)

I

UB1

−UB2 UAK

G K

UGK


14 Nov

28 Nov 1Ferreira Fernandes

______________________________________________________________

Summary:DIAC. Dynamical aspects in thyristors. GTOGTO.____________________________________________________________

DIACLarge Base

I

I(U) symmetrical

I(U) continuous

p

n U

U

UR

p UJ

______________________________________________________________2Ferreira Fernandes28 Nov

______________________________________________________________

DIAC

I

I

II

UR

UJ UR+UJ

I

UL

−UL U

U


______________________________________________________________

IA

Dynamical aspects in the commutation OFF-ON in the SCR

IAmax 0,9 IAmax

t 0,1 IAmax

UG ta tc

tLtL

t 0,1 UGmax

tL=turn-on time (minimum time to put J2 forward biased); ( p );ta= delay time; tc=rising time (depends on the load)______________________________________________________________


______________________________________________________________

Uext

Dynamical aspects in the commutation ON-OFF (SCR)

UA

t

t

IA

t

trc trp

t

trcorte

trc=current recovery time (to block J1 or J3); trp=gate recovery time (remove carriers from the bases);

Tr=typical recovery times 10 to 100 μs28 Nov 5

______________________________________________________________

GTOGate controls commutation in both directions

Natural commutation in ACNatural commutation in AC

Forced commutation in CC (Increase of load or short circuit)

GTO- commutation also with gate negative pulses

GTO vs BJT: Advantages:

currents in the order of kA and voltages of kVKeeps in the ON state without gate current

D i l bi di ti l t i th l iDynamical bi-dimentional aspects in the analysis

During the cut the transversal section with current decreases progressively


T l A t i GTO______________________________________________________________

IG/2 IG/2 IK

Transversal Aspects in GTO

J3 U1

S/2 S/2 n

J1

J2

J3 U1

U2 Wp

Wn

p

n

J1 p

IA

1’ 2’ 3’ 3 2 1


______________________________________________________________

IA

t

Dynamical aspects ON-OFF

IA0

0,9 IA0

stntt

0,1 IA0t

Settlement time – Time to remove of carriers from base p and from th d j ti ( d S t b t 2 Ldif)cathod juction (reduce S to about 2 Ldif)

Evanescent time – Time to remove holes from base n


______________________________________________________________

A

G

II

β =Current gain in cut

( )2 2

1 ln 2 1 ln 4 1SL L Lt t⎡ ⎤⎛ ⎞ ⎛ ⎞

β + β+ β+⎢ ⎥⎜ ⎟ ⎜ ⎟

Settlement time

( ) 2 2 21 ln 2 1 ln 4 1S tpp p p

t tW W W

= β− + −β+ − −β+⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦2

1 4 Lβ +Maximum current gain in cut max 21 4

pWβ = +

2

2n

tnWtD

=

Maximum current gain in cut

Evanescent time2tn

pD

Short Base Decrease the evanescent time Small block voltages; High α______________________________________________________________


______________________________________________________________

Typical values

On voltage 2,7 V7On Current density 107 A/m2

Delay time 5,5 μsRising time 0,6 μsSettlement time 3,9 μsSettlement time 3,9 μsEvanescent time 0,9 μsCurrent gain in cut 7


3 Dez 1Ferreira Fernandes

______________________________________________________________

Summary:Compound SemicondutorsCompound Semicondutors

……………………………………………………………………………................…

BinaryBinaryCompound Semicondutors Ternary

Quaternary

III–V – GaAsBinarySemicondutors II–VI – ZnO

IV–VI – PbS

Ex: Famíly III-VGroup III – Al, Ga, InGroup V P As SbGroup V – P, As, Sb

______________________________________________________________2Ferreira Fernandes3 Dez

______________________________________________________________

Zincoblenda (Z) lattice(2 cubic lattice face-centered)(2 cubic lattice face centered)

1 atom III in the center

4 atoms V in the nodes

Elementar (8 atoms)

4 atoms III

14 atoms V (8 in the nodes

6 in the center of faces)


3 Dez

______________________________________________________________

aa

Zincoblenda structure.Elementary latticeZincoblenda structure.Elementary lattice


3 Dez

______________________________________________________________

• Ternary compounds – combination of bynaries with a common element

(AB+BC)

Substract – GaAs, InP, GaP, InSb

(Lattice constants almost equal ⇒ good matching)

Properties:

a (x) = x a + (1-x) aaABC(x) = x aAB + (1-x) aBC

WG(x) = WG1 + bx + cx2

Ternary properties ≠ Linear combination of the properties of the correspondent binaries. Ex: μ, WG


3 Dez

______________________________________________________________

Semicondutor Symbol

ElementarGe

Si

AlP

AlAs

GaN

Binary (III-V) GaP

GaAs

InP

InAs

AlxGa1-xAs

AlxIn1-xAs

GTernary GaAs1-xPx

GaxIn1-xAs

GaxIn1-xP

Al Ga As SbQuaternary

AlxGa1-xAsySb1-y

GaxIn1-xAs1-yPy63 Dez

______________________________________________________________

• Quaternary

A1-xBxCyD1-y

A B – group IIIA,B group IIIC,D – group V

Possibility of varying W keeping aPossibility of varying WG keeping apractically constant

Application: optical communications (1 3 < λ < 1 55 μm): InGaAsP matchedApplication: optical communications (1,3 < λ < 1,55 μm): InGaAsP matched to InP

binaries

ACAD ⇒ Quaternary A B C Dbinaries BCBD

⇒ Quaternary A1-xBxCyD1-y

Q(x, y) = (1-x)y BAC + (1-x) (1-y) BAD + xy BBC + x(1-y) BBD( y) ( )y AC ( ) ( y) AD y BC ( y) BD


______________________________________________________________

6 1

6,2

a (Å)

-

- .

.

InAs

InP5,9

6,1

6,0

-

-

-

.

GaAs5 6

5,7

5,8 -

-

.

.

GaP5,4

5,5

5,6 -

-

-

Band gap and lattice parameters for InGaAsP compounds.

0,5 1,0 1,5 2,0 2,5WG (eV)| | | |

Band gap and lattice parameters for InGaAsP compounds.

Matched to InP and to GaAs83 Dez

______________________________________________________________

Heterojunctions

Vácuo

WC1 WC2

WF1

χ1 WS1

χ2

WS2 δ1

WG1WG2

WF2 WV1 WV2

δ2

WG1

(a)

WC

WG2

ΔWC

WF WV WG1

ΔWV

(b) ______________________________________________________________

3 Dec

WΔ 1 2CWΔ = χ −χ 2 1C V G GW W W WΔ + Δ = −

( ) ( ) WWWWWWWWV SSVGCGFF

C2112112221

0−

=−−Δ+

=−+Δ−

=−

=δδδδ

W WWG2

qqqqC0

1 20

S SC

W WV

q−

= WG1 WG1 WG2

(a) (b) 21 SS WW =

21 χχ > 0>Δ CW

WG1

WG2

WG1 WG2

GWΔ>− 21 χχ .0<Δ VW

(c) (d) 3 Dec

WW <______________________________________________________________

12 SWSW <

(a) (b)

0;0 <Δ>Δ VWCW 0;0 >Δ>Δ VWCW

(c) (d)

00 ΔΔ WW 00 >Δ<Δ WW0;0 <Δ<Δ VWCW 0;0 >Δ<Δ VWCW______________________________________________________________

3 Dec

______________________________________________________________

E(x)

xp0 xn0

V(x) ρ(x)

DqN+

Q xp0 xn0

VC0 x

xp0

xn0

+Q

-Q

AqN−−

______________________________________________________________3 Dec

______________________________________________________________

Rectifier junctions- isotype ou heterotype

SpSn WW <

WW

Ohmic junctions - heterotype

SpSn WW >

______________________________________________________________3 Dec

______________________________________________________________

HeterojunctionsHeterojunctions

Band diagrams for isotype or heterotypeheterojunctions

Application examples

______________________________________________________________3 Dec

______________________________________________________________

0W – Electronic affinity

χ

SW

y

– Work function

cW

W

– Lower limit of conduction band

– Upper limit of valence bandFW

W

GW – Band gap

– Fermi level

VW

Work Function ( )s C FW W W= χ + −

______________________________________________________________3 Dec

______________________________________________________________

Isotype n-n Heterojuntion

0W 0W

2χ2SW 2cqV

1cqV

cqV1χ

1SW 2cW

2FW

2SW 2cq0W

WcWΔ1cW

1FW

1GW

2GW FW1GW

2GW

cW

1vW 2vW1 2

2G

vW

vWΔ

v

______________________________________________________________3 Dec

______________________________________________________________

anisotype p-n Heterojuntion

0W

χ

0W

nχSnW 2cqV

1cqV

cqVW

W

pχ SpW CnW

FnW

Sn0W

cWcWΔ 2cqV1cqVcW

CpW

GpW

GnW FWGpW

GnW

c

vWΔ

pφ nφ

FW

VW

FpW

VpW VnWp n

vW

______________________________________________________________3 Dec

______________________________________________________________

Work function ( )s C FW W W= χ + −

qV W W= −Contact potential

s C F

0 1 2C s sqV W W= −Contact potential

WΔ = χ χ = ΔχConduction band discontinuity C p nWΔ = χ −χ = ΔχConduction band discontinuity

Valence Band discontinuity W W WΔ = Δ ΔValence Band discontinuity V G CW W WΔ = Δ −Δ

______________________________________________________________3 Dec

______________________________________________________________

WC W

WC WC

WFWF WF n n n n

VW ′ VW ′

WF

n n

VW ′

WV

WV WV

R R Direct BandType I Type II

______________________________________________________________3 Dec

______________________________________________________________

W

WC

WC

WC

n p n p n p

WF WF

WF

n p n p n p

WV

WV

WV

NR R Direct Band

Type I Type II

______________________________________________________________3 Dec

l l

______________________________________________________________Application examples

Abrupt Heterojunction p-p formed by GaAs with

1 1/ 0,1a VN N = and 1x xAl Ga As− with 2 2/ 0,01a VN N =C l l t t t f Al th t l d t th fl t b d

1x xAl Ga As−( ) 4,07 1,1x xχ = −

Calculate x content of Al that leads to the flat band condition

( ) , ,χ1,42 1,25GW x= +

1 2

0

GaAs

0, 45 . .eV0

Al0,41Ga0,59As

∫∫ ∫∫ ∫∫ ∫∫

2 1,93 . .GW eV=

CW1 4,07 . .eVχ =

1 1,42 . .GW eV=1 0,06 . .eVφ = 1 5, 43 . .SW eV=

CW

2 5, 43 . .SW eV=

FW

VW FW

VW0,12 . .eV

0,06 . .eV

______________________________________________________________3 Dec

4 07 V 0 1N N______________________________________________________________

Heterojunction with semicondutor 1: 1 1,4 . .GW eV= 1 4,07 . .eVχ = 1 1 0,1d cN N =semicondutor 2: 2 1,6 . .GW eV= 2 3,8 . .eVχ = 2 2 0,1a VN N =Represent the band diagram in thermal equilibrium and say if the junction is ohmic or rectifier..

n dN + p aN −

E

2 5,34 . .SW eV= 2 3,8 . .eVχ =

0 1,21 . .CqV eV=

∫∫ ∫∫ ∫∫

∫∫ ∫∫

2 1,6 . .GW eV=

1 4,13 . .SW eV=

0,27 e.V. 1 4,07 . .eVχ =

W2vW

2 0,06 . .eVφ =

0,07 e.V.

1 0,06 . .eVφ =1 1, 4 . .GW eV=

FW

______________________________________________________________3 Dec

______________________________________________________________

Heterojunction bipolar transistor.

2 22 22 2

0 0iE iB

E B iE iB GE GBAE DB

n nn p n n W WN N <<<< ⇒ << ⇒ ⇒ >

1

0

0

1'1 thpE nB E

B E B B

D L b pD L L n

γ =⎛ ⎞

+ ⎜ ⎟⎝ ⎠ 0nB pE nB BD L L n⎝ ⎠

21' Eb L<< → γ = 2

2'1

nEpE iE A

nB pE D iB

b LD n NbD L N n

<< → γ+


______________________________________________________________

eBase Colector Base EmissorN N N N> >

Base more doped⇒ smaller b ⇒ θ ~1,

eBase Colector Base EmissorN N N N> >

⇒ Base resistance decreases

Since the transition regions are larger in emitter and collector zonesSince the transition regions are larger in emitter and collector zones

decreases the transition capacities of both junctions.

1iB iEn n>> ⇒ γ ≅ ⇒ α ≅ θ


5 Dez

______________________________________________________________

Increase NBase

Decreases RB increases fT

NBase

Decreases b Decreases RB

Increases θ increases αF

D E l ff t

Decreasing NEmissor

Decreases Early effect

g Emissor

NColector Decreases CTE andCTC increases fT

Diminuir |U |Diminuir |UDisrp|


5 Dez

1Ferreira Fernandes10 Dec

______________________________________________________________

Summary:

Optoelectronic Devices. Photodiode. Solar cellp

Photodiode

______________________________________________________________

1T

UU

is ilumI I e Iη⎛ ⎞⎜ ⎟= − −⎜ ⎟⎝ ⎠

I

U⎜ ⎟⎝ ⎠ U

Iilum

( )ilum efI G Aql U=

I

UU

____________________________________________________________2Ferreira Fernandes10 Dec

______________________________________________________________

I (μA)

80

0 4 0 2 0 2

40

0 4U (V)

φ

2φ

-0,4 -0,2 0,2 0,4

2φ

3φ


______________________________________________________________ E(x)

N

ND(x)

n(x) NA(x)

p(x)

n=p=ni xxw

Zona de depleção

(a) (b)

p i n − +

contacts Anti reflexion layer

luz

SiO2p

electrões buracos

fotões

SiO2

n+

Depleted zone(i or weakly doped)

Metalic contact

(c) (d) 410 Dec Ferreira Fernandes

______________________________________________________________

I

I

Solar Cell

I

Gef U

UR VCA VM

U

IM ICC

PM


______________________________________________________________

1 1MT

VUM ilumV Ie

⎛ ⎞+ = +⎜ ⎟

max maxP PFFP V I

= =1 1T

eU Iis

+ = +⎜ ⎟⎝ ⎠ ref CA CCP V I

Solar Panel I

U

Solar Panel

Panel Cell

I U


______________________________________________________________

1sU R I

UT silum is

U R II I I eR

−η

⎡ ⎤ −⎢ ⎥= − + − +⎢ ⎥⎣ ⎦ pR⎢ ⎥⎣ ⎦

I

U

I

U I

U

Rs

.

Rs

Rp

Rp

Iilum

I

U

p

T

(a) (b)

U

T

( )(c)____________________________________________________________

7Ferreira Fernandes10 Dec

M t lli t t______________________________________________________________

Canti-reflexion layer

Metallic contact

n

light

n

p

n

p

Metallic contact

0 2ln lnA D A D GC T T

C Vi

N N N N WV U UN N qn

⎛ ⎞ ⎛ ⎞= = +⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠ C Vi q⎝ ⎠⎝ ⎠

( )max CA CC

d d

P FF V IP P

η = = −rad radP P


ln 1CCCA T

is

IV U

I⎛ ⎞

= +⎜ ⎟⎝ ⎠

______________________________________________________________

⎝ ⎠

1 1 GWpn kT

is C VA D

DDI qA N N eN N

−⎛ ⎞⎜ ⎟= +⎜ ⎟τ τ⎝ ⎠n A p DN N⎜ ⎟τ τ⎝ ⎠

light

rugosidadeA

Optical path

B 910 Dec Ferreira Fernandes

Ph t t i tPhototransistor

R

E

ICB0

E

Emitter (p)

Base (n)

Collector (p)

0p Cn

Phototransistor

(Open emitter)

0p En

0n BpEL

CL

1010 Dec Ferreira Fernandes

R ICE0

Phototransistor

Emitter Base Collector

E (Open Base)

Emitter (p)

Base(n)

Collector(p)

0p Cn

CL

0p En

0n BpEL

0p E


( ) ( )0 0 01C F E F C CE CI I I I U= β + + β − δ

Anti-reflexion layer SiO2

Collector

Emitter

SiO2 n+ n+

High optical gain region

S b t t Si ( )

1210 Dec

Substrate Si (p)

Ferreira Fernandes

______________________________________________________________

Phototransistor and equivalent model

C C

pnp E

npn E


12 Dez Ferreira Fernandes

______________________________________________________________

Summary:LEDs and LASERs.

(LEDs)1 are devices that convert electric energy inlight

______________________________________________________________

light.

____________________________________________________________12 Dez Ferreira Fernandes

______________________________________________________________

The conversion is related to electronictransitions followed by the photonemission with wavelengths compatible

ith th i ti d

f,λ

with the energy variations occurredGT R WGφ

GaPGaAs

GW f ch h= =GaAs0,3P0,

7

G fλ

WG characteristic of materialf λ caracteristic of radiation

λ (μ )m

0,6 0,7 0,8 0,9 1,0

Light spectra in LEDs

f, λ caracteristic of radiation

Light spectra in LEDs____________________________________________________________


______________________________________________________________

Current-voltage stationary characteristic in a LED


______________________________________________________________

Current-power characteristicin a LED

FE IWP η=0 FE Iq

P η=0


______________________________________________________________

SLM laser DFB

3 a 6 nm 300 a 600 GHz

LED

FP <0,001 nm<100 MHz

50 a 100 nm5 a 10 THz λ

ÚÚ ÚÚ

LASER D(ps/km×nm)

Δλ (nm)

λ (μm)

B(Mb/s)

BL(GHz×km)

FP 17 5 155 100 10 DFB 17 0 1 155 5000 500DFB 17 0,1 155 5000 500


______________________________________________________________

Optical Couplers

Entrada Saídahf

Entradahf

Entrada EntradaSaída

(a) (b)(a) (b)

Emitter – GaAs (infrared)( )Detector - Si


______________________________________________________________ %

100

80

GaP:N GaAs GaAs:Si

80

60 GaAs0.15P0.85:N

Díodo de Ge

bilid

ade

Olho humano

40

20

Díodo de Si

GaAs0.35P0.65:N

Sens

ib

0 200 500 1000 1500 2000 nm

Ultra Luz Infra-Vermelho Infra-Vermelho

GaAs0.6P0.4

Violeta Visível Próx. Med. λ

Sensibility of Ge, Si diodes and human eye to the emitted radiation from several compound

dsemiconductors____________________________________________________________


______________________________________________________________

Electric scheme and structure of an optical coupler


______________________________________________________________

I

Optical coupler circuit

FI

DRCR

CI

+

− E

U

1U

CEU

CU

DU

EIEU


______________________________________________________________

Output characteristics of an optical coupler


______________________________________________________________

Transfer characteristic Current Transfer ratio as a function of tempereture


Fundamentos de ElectrónicaHomogeneous Materials

Fundamentos de Electrónica

Resistances Photoresistances

Intrinsic resistances Extrinsic resistances

Isotype junctions

Hetero type junctions Rectifier junctions

Díode

Homojunctions

LEDs

Junctions

H t j ti

PhotodíodesSollar cells

Painéis solares

LASERs

Isotype junctions

19 DezOhmic contacts

HeterojunctionsRectifier junctions

yp j

Hetero type junctions

F d t d El t ó i

H j ti

Fundamentos de Electrónica

(Bipolar)Junctions Bipolar Transistors

BJT pnpHomojunctions

( )

Heterojunctions

BJT npn

UnipolarJFET

FET

Reforço P-MOSFET

19 DezN-MOSFETDepletion

Fundamentos deFundamentos de Electrónica

Thyristors

4 layer diodes

Thyristors

4 layer diodesGTO

SCR DIAC

TRIAC

19 Dez

O t l t iElectronic Devices Optoelectronic Devices

UnipolarPMOS

JFET

p

GTODIAC

NMOSPhototiristor

Bipolar

SCRDIAC

TRIAC

LED

LASER

4 layer diode

Díode photo-transistor

Optical Coupler

19 DezPhotodíodo

Solar cell

BJT-npn

BJT-pnp

p

Solar pannel

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