Lecture 17a

PN Junctions and Diodes

18-322 Fall 2003Reading: Section 3.2

Lecture 17a

Crystalline Silicon

Si

Si

Si Si

Si

Si

Si

Si

Si

SiSi Si SiSi

SiSi Si SiSi

SiSi Si SiSi

Si

Covalent bond filled with an electron

NOTE:2D representation

of 3D reality

Lecture 17a

Generation and Recombination

Si

Si

Si Si

Si

Si

Si

Si

Si

SiSi Si SiSi

SiSi Si SiSi

SiSi Si SiSi

Si

Hole

Free electron(-q)

(+q)Electron-hole pairs

appear:Generation

Pairs disappear:Recombination

Lecture 17a

Holes and Electrons

Called Carriers

They’re both mobileHoles move by “swapping” missing electronWith an electric field:Holes move in positive directionElectrons move in negative direction

E

Lecture 17a

Intrinsic Semiconductors

Electron concentration: nHole concentration: p

n = pIntrinsic concentration: ni (T)

ni = 1010 cm-3 at 300Kn0 p0 = ni

2

Only 1 in 20 trillion bonds broken!

Lecture 17a

Doping with Impurities

Donor impurities:Elements that “donate” electronsHave 5 valence electrons in outer orbitExample: Phosphorus

Acceptor impurities:Elements that “accept” electronsHave 3 valence electronsExample: Boron

Lecture 17a

Donors

Si

Si

Si Si

Si

Si

Si

Si

Si

PSi Si SiSi

SiSi Si SiSi

SiSi Si SiSi

Si

Free electron(-q)

(+q)

Donor Ions:Positive charge

Immobile

Donated electronmobile

N-type silicon

Lecture 17a

Acceptor

Si

Si

Si Si

Si

Si

Si

Si

Si

BSi Si SiSi

SiSi Si SiSi

SiSi Si SiSi

Si

(-q)

(+q) Hole

Acceptor Ions:Negative charge

Immobile

Donated holemobile

P-type silicon

Lecture 17a

N-type Semiconductors

Donor concentration: Nd

Dominates over intrinsic: Nd >> ni

n0 = Nd

Still holds: n0 p0 = ni2

p0 = ni2 / Nd

Majority carriers: electronsMinority carriers: holes

Lecture 17a

P-type Semiconductor

Acceptor concentration: Na

p0 = Na

Still holds: n0 p0 = ni2

n0 = ni2 / Na

Majority carriers: holesMinority carriers: electrons

Lecture 17a

Carrier Transport

E

Carriers “drift”

Apply an electric field: EAverage electron velocity “drift velocity”

Vdn = - µn E

Lecture 17a

Carrier Mobility

Electron Mobility: µn

Function of temperature: T ⇑ -> µn ⇓Function of total doping: (Na + Nd) ⇑ -> µn ⇓

Hole Mobility: µp

µp ≈ µn / 2.5

Holes don’t move as fast as electrons

Lecture 17a

N-type Resistance

Lt

W

Current: Coulombs per secondCharge: ND * q * tWLRate: Vdn / L = µn E / L = µn V / L2

Resistance: V/I = L / (ND * q * µn * tW)

Lecture 17a

Resistance

R = Constant * L/WTypical Measure: Ω per (per square)

Six Squares

Lecture 17a

The Junction

ppo

npo x

nno

pno

1018 cm-31016 cm-3

100 cm-3 104 cm-3

log n, pMajority Carriers (holes)NA

P - type N - type

Majority Carriers (electrons)ND

Lecture 17a

At Absolute Zero:

ppo

npo x

nno

pno

N - type

Majority Carriers (electrons)ND

1018 cm-31016 cm-3

100 cm-3 104 cm-3

Majority Carriers (holes)NA

P - type

Lecture 17a

Diffusion

P-type

Hole Diffusion

N-type

Electron Diffusion

Lecture 17a

Depletion Region

Few Majority Carriers(only fixed ions)

P-type N-type

Lecture 17a

Depletion Region

N-type

-+

P-type

xp xn

qND Charge Density

qNA

xnxp

NAND

=

Lecture 17a

Built In Potential

P-type N-type

-Charge Density+

Electric Field

Potential

Lecture 17a

Built In Potential

φ = φT ln [NA ND / ni2 ]

Charge without applied voltageNot really measurableField creates current opposite to diffusion

Drift!

Lecture 17a

In Equilibrium

Hole Diffusion

Electron Diffusion

Hole DriftElectron Drift

P-type N-type

Lecture 17a

Reverse BiasReverse Bias: Make N-type Higher voltage

Increases field.Increases DRIFT current!

Hole Diffusion

BUT:There aren’t many carriers

available for drift this direction

(free holes in N,free electrons in P)

Hole DriftElectron DriftP-type N-type

Electron Diffusion

Lecture 17a

Forward BiasForward Bias: Make P-type Higher voltage

Decreases fieldDecreases DRIFT current!

Hole Diffusion

Hole DriftElectron DriftP-type N-type

Depletion region shrinksMore carriers to diffuse

increased diffusion current

Electron Diffusion

Lecture 17a

Ideal Diode Behavior

-Is

ID ID = IS [ e (V/VT) -1 ]

VT = kT/q = 26mV @ 300K

V

Lecture 17a

Diode Models

Physical ModelsIdeal Diode Equations“On” voltage: VD

Determine a voltage when current is “large”Typical value: 0.6V - 0.7V

+

V

-

+- VD

V < VD V > VD