Chapter 15 1

OutlineReading: Livingston, Chapter 15.1-15.3

A Review of Semiconductors Intrinsic Semiconductors

Electrons in Conduction Band and Holes in Valence Band Intrinsic carrier concentration Fermi Energy

Extrinsic Semiconductors Dopants Complete ionization NeNh product

Chapter 15 2

Semiconductors: Review

Semiconductors have electrical and optical properties between metals and insulators.

Chapter 15 3

Chapter 15 4

Intrinsic Semiconductors

Chapter 15

Ze(E)

Zh(E)

2/1)()( gee EECEZ =Amend equations used for metals

2/1)()( ECEZ hh =

3

2/3*)2(4hmC ee

= 3

2/3* )2(4hmC hh

=

TkEE BFeEF /)(1

1)(+

=

Chapter 15 5

Total # of Electrons in Conduction Band

=g

BF

E

TkEEgee dEeEECN

/)(2/1)(

=

0

)](1)[( dEEFEZN hh

Total # of Hole in Valence Band

TkEECe

BFgeNN /)( =

TkEVh

BFeNN /=

3

2/3* )2(2h

TkmN BeC

=

3

2/3* )2(2h

TkmN BhV

=

Chapter 15 6

Eliminate EF from the Equation

Chapter 15 7

Intrinsic Carrier Concentration Bandgap and Temperature

7

( ) TkEVCi BgeNNN 2/2/1 =

Chapter 15 8

Example: Fermi Level in Intrinsic Semiconductor

Chapter 15 8

Where is the Fermi level in intrinsic GaAs? How far is it from midgap? The bandgap of GaAs is 1.42 eV.

Material me*/mo mh*/moSi 0.26 0.39Ge 0.55 0.37

GaAs 0.068 0.54

Chapter 15 9

Example: Intrinsic Carrier Concentration and Bandgap

Which semiconductor has the largest intrinsic carrier concentration?

Ec

Ev

Ec

EvEg = 5 eV

Eg = 1 eV

Chapter 15 10

Example: Conductivity in Intrinsic Semiconductor

Calculate the conductivity of intrinsic silicon at room temperature for e = 0.15 m2V-1s-1 and h = 0.05 m2V-1s-1. Assume me* = 0.26mo, mh* = 0.39mo, and Eg = 1.1 eV.

Chapter 15 11

Extrinsic Semiconductors

Chapter 15 12

Extrinsic Semiconductors (cont.)

Ze(E)

Zh(E)

Ze(E)

Zh(E)

Chapter 15 13

Extrinsic Semiconductors (cont.)For extrinsic semiconductors

Chapter 15 14

Example: Carriers in an Extrinsic SemiconductorIf you add 1017 donor atoms/cm3 to a semiconductor with a 0.6 eV bandgap, what will be the charge carrier concentrations in the valence and conduction bands at T = 300K? Where is the Fermi level before and after doping? Assume that the donors are fully ionized and that both the hole effective mass and electron effective mass have the mass of a free electron.

Chapter 15 15

Chapter 15 16

Example: Conductivity in Extrinsic SemiconductorWhat is the conductivity of a silicon crystal doped with 5 x 1013 cm-3 atoms of As? ni = 1010 cm-3, e = 1350 cm2V-1s-1, and h = 450 cm2V-1s-1. Assume all dopants are ionized.

Chapter 15 17

Semiconductors: How to Get Electrons into Conduction Band (and Holes in the Valence Band)

1. Thermal Excitation

2. Optical Excitation

3. Dopants

Chapter 15 18

Review Questions

1. Define intrinsic and extrinsic semiconductor.2. What is a hole?3. Where is the Fermi energy in an intrinsic semiconductor?4. If an intrinsic semiconductor has 1010 cm-3 holes, how many

electrons does it have?5. What is the majority carrier in n-type material?6. What is the minority carrier in p-type material?7. Donors are added to ________ type material?8. Where, in general, is the Fermi energy in a p-type semiconductor ,

above or below Eg/2? And a n-type semiconductor?9. Assuming complete ionization, what is the electron concentration in

an n-type semiconductor with 1010 cm-3 donor atoms?10. What does the product of NeNh equal? Does this apply to intrinsic

or extrinsic semiconductors?11. List 3 ways to excite electrons into the conduction band.

Chapter 15 19

Important Equations2/1)()( gee EECEZ =

3

2/3*)2(4hmC ee

=

2/1)()( ECEZ hh =

3

2/3* )2(4hmC hh

=

TkEE BFeEF /)(1

1)(+

=

TkEECe

BFgeNN /)( =

3

2/3* )2(2h

TkmN BeC

=

TkEVh

BFeNN /=

3

2/3* )2(2h

TkmN BhV

=

( ) TkEVCi BgeNNN 2/2/1 =hei NNN =

2

*

*

ln4

32 e

hBgF m

mTkEE += hhee eNeN +=