Intrinsic Silicon Properties

Intrinsic Silicon Properties

? Read textbook, section 3.2.1, 3.2.2, 3.2.3

? Intrinsic Semiconductors

? undoped (i.e., not n+ or p+) silicon has intrinsic charge

carriers ? electron-hole pairs are created by thermal energy ? intrinsic carrier concentration ni = 1.45x1010 cm-3,

at room temp. ? function of temperature: increase or decrease with temp? ? n = p = ni, in intrinsic (undoped) material

? n number of electrons, p number of holes

? mass-action law, np = ni2

? applies to undoped and doped material

ECE 410, Prof. A. Mason

Lecture Notes 6.1

Extrinsic Silicon Properties

? doping, adding dopants to modify material properties

? n-type = n+, add elements with extra an electron

? (arsenic, As, or phosphorus, P), Group V elements

? nn concentration of electrons in n-type material ? nn = Nd cm-3, Nd concentration of donor atoms

n-type Donor

+

P P+ electron

group V element

ion

free carrier

? pn concentration of holes in n-type material ? Nd pn = ni2, using mass-action law

n+/p+ defines region as heavily doped,

? always a lot more n than p in n-type material

typically 1016-1018 cm-3

? p-type = p+, add elements with an extra hole

less highly doped regions generally labeled n/p

? (boron, B)

(without the +)

? pp concentration of holes in p-type material ? pp = Na cm-3, Na concentration of acceptor atoms ? np concentration of electrons in p-type material ? Na np = ni2, using mass-action law

p-type Acceptor

-

B

B+ +

hole

group III element

ion

free carrier

? always a lot more p than n in p-type material

? if both Nd and Na present, nn = Nd-Na, pp=Na-Nd

do example on board

ni2 = 2.1x1020

ECE 410, Prof. A. Mason

Lecture Notes 6.2

Conduction in Semiconductors

? doping provides free charge carriers, alters conductivity

? conductivity, , in semic. w/ carrier densities n and p

? = q(nn + pp), q electron charge, q = 1.6x10-19 [Coulombs]

? mobility [cm2/V-sec], n 1360, p 480 (typical values)

? in n-type region, nn >> pn

? qnnn

? in p-type region, pp >> np

? qpnp

mobility = average velocity per Mobility often

unit electric field

assumed constant

n > p

electrons more mobile than holes conductivity of n+ > p+

but is a function of Temperature and Doping

Concentration

? resistivity, = 1/

t

? resistance of an n+ or p+ region

? R = l , A = wt

A

w

l

? drift current (flow of charge carriers in presence of an electric field, Ex)

? n/p drift current density: Jxn = n Ex = qnnnEx, Jxp = p Ex = qpppEx

? total drift current density in x direction Jx = q(nn + pp) Ex = Ex

ECE 410, Prof. A. Mason

Lecture Notes 6.3

pn Junctions: Intro

? What is a pn Junction?

contact to p-side

contact to n-side

? interface of p-type and

depletion region boundaries

p+

n+

n-type semiconductor

pn diode junction

n "well"

? junction of two materials forms a diode

p-type Si wafer

dielectric insulator (oxide)

p-type

n-type

? In the Beginning...

p-type -+ -+ - + -+ +- +- +- n-type

? ionization of dopants at material interface

-+ -+ -+ -+ -+ -+ 3

+-

+-

+-

-

+3

N acceptors/cm A

N donors/cm D

hole diffusion hole current

-

+ donor ion and electron free carrier

electron diffusion electron current

-+ acceptor ion and hole free carrier

? Diffusion -movement of charge to regions of lower concentration

? free carries diffuse out ? leave behind immobile ions ? region become depleted of

free carriers ? ions establish an electric field

? acts against diffusion

depletion region

E electric field

p-type

3

N acceptors/cm A

immobile acceptor ions (negative-charge)

-

-

++ +

++ +

++

x

x

p

n

W

n-type

3

N donors/cm D

immobile donor ions (positive-charge)

ECE 410, Prof. A. Mason

Lecture Notes 6.4

pn Junctions: Equilibrium Conditions

? Depletion Region

depletion region

E electric field

? area at pn interface void of free charges

? charge neutrality

p-type

NA 3

N acceptors/cm A

-

-

++ +

++ +

++

n-type

ND 3 N donors/cm D

?

must have equal charge on both sides

immobile acceptor ions (negative-charge)

x p

x n

immobile donor ions (positive-charge)

W

? q A xp NA = q A xn ND , A=junction area; xp, xn depth into p/n side

? xp NA = xn ND

? depletion region will extend further into the more lightly doped side

of the junction

? Built-in Potential

? diffusion of carriers leaves behind immobile charged ions

? ions create an electric field which generates a built-in potential

0

= VT

ln

NAND ni 2

? where VT = kT/q = 26mV at room temperature

ECE 410, Prof. A. Mason

Lecture Notes 6.5

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