EE105 Fall 2011Lecture 2, Slide 1Prof. Salahuddin, UC Berkeley Lecture 2 OUTLINE Semiconductor Basics Reading: Chapter 2

EE105 Fall 2011 Lecture 2, Slide 1 Prof. Salahuddin, UC Berkeley

Lecture 2

OUTLINE• Semiconductor Basics

Reading: Chapter 2


Announcement

• Office Hours for tomorrow is cancelled(ONLY for this week)

There will be office hours on Friday (2P-3P)(ONLY for this week)

Thursday’s class will start at 4P(ONLY for this week)


What is a Semiconductor?• Low resistivity => “conductor”• High resistivity => “insulator”• Intermediate resistivity => “semiconductor”

– conductivity lies between that of conductors and insulators– generally crystalline in structure for IC devices

• In recent years, however, non-crystalline semiconductors have become commercially very important

polycrystalline amorphous crystalline


Semiconductor Materials

Gallium(Ga)

Phosphorus(P)


Energy Band Description

•For current flow, one needs to have electrons in the conduction band or holes in the valence band

•Completely full or completely empty bands cannot carry current


Energy Band Description

Current due to electron flow and hole flow will add up


Silicon• Atomic density: 5 x 1022 atoms/cm3

• Si has four valence electrons. Therefore, it can form covalent bonds with four of its nearest neighbors.

• When temperature goes up, electrons can become free to move about the Si lattice.


Electronic Properties of Si Silicon is a semiconductor material.

– Pure Si has a relatively high electrical resistivity at room temperature.

There are 2 types of mobile charge-carriers in Si:– Conduction electrons are negatively charged;– Holes are positively charged.

The concentration (#/cm3) of conduction electrons & holes in a semiconductor can be modulated in several ways:

• by adding special impurity atoms ( dopants )• by applying an electric field• by changing the temperature• by irradiation


Electron-Hole Pair Generation• When a conduction electron is thermally generated,

a “hole” is also generated.• A hole is associated with a positive charge, and is

free to move about the Si lattice as well.


Carrier Concentrations in Intrinsic Si• The “band-gap energy” Eg is the amount of energy

needed to remove an electron from a covalent bond. • The concentration of conduction electrons in intrinsic

silicon, ni, depends exponentially on Eg and the absolute temperature (T):

600Kat /101

300Kat /101

/2

exp102.5

315

310

32/315

cmelectronsn

cmelectronsn

cmelectronskT

ETn

i

i

gi


Doping (N type)• Si can be “doped” with other elements to change its

electrical properties.• For example, if Si is doped with phosphorus (P), each

P atom can donate a conduction electron, so that the Si lattice has more electrons than holes, i.e. it becomes “N type”:

Notation:n = conduction electron concentration


Doping (P type)• If Si is doped with Boron (B), each B atom can accept

an electron (creating a hole), so that the Si lattice has more holes than conduction electrons, i.e. it becomes “P type”:

Notation:p = hole concentration


Terminologydonor: impurity atom that increases n

acceptor: impurity atom that increases p

N-type material: contains more electrons than holes

P-type material: contains more holes than electrons

majority carrier: the most abundant carrier

minority carrier: the least abundant carrier

intrinsic semiconductor: n = p = ni

extrinsic semiconductor: doped semiconductor


Intrinsic vs. Extrinsic Semiconductor


Electron and Hole Concentrations• Under thermal equilibrium conditions, the product

of the conduction-electron density and the hole density is ALWAYS equal to the square of ni:

2

innp

P-type material

A

i

A

N

nn

Np2

D

i

D

N

np

Nn2

N-type material


Dopant Compensation• An N-type semiconductor can be converted into P-

type material by counter-doping it with acceptors such that NA > ND.

• A compensated semiconductor material has both acceptors and donors.

P-type material(NA > ND)

DA

i

DA

NN

nn

NNp

2

AD

i

AD

NN

np

NNn

2

N-type material (ND > NA)


Doping

What is the electron and hole density if you dope Si with Boron to 1018 /cm3 ?


Charges in a Semiconductor• Negative charges:

– Conduction electrons (density = n)– Ionized acceptor atoms (density = NA)

• Positive charges:– Holes (density = p)– Ionized donor atoms (density = ND)

• The net charge density (C/cm3) in a semiconductor is AD NNnpq


Carrier Drift• The process in which charged particles move because

of an electric field is called drift. • Charged particles within a semiconductor move with

an average velocity proportional to the electric field.– The proportionality constant is the carrier mobility.

Ev

Ev

ne

ph

Notation:p hole mobility (cm2/V·s)n electron mobility (cm2/V·s)

Hole velocity

Electron velocity


Velocity Saturation• In reality, carrier velocities saturate at an upper limit,

called the saturation velocity (vsat).

E

vE

v

bv

bE

sat

sat

0

0

0

0

1

1


Drift Current• Drift current is proportional to the carrier velocity

and carrier concentration:

Hole current per unit area (i.e. current density) Jp,drift = q p vh

Total current Jp,drift= Q/t

Q= total charge contained in the volume shown to the rightt= time taken by Q to cross the volume

Q=qp(in cm3)X Volume=qpAL=qpAvht


Conductivity and Resistivity• In a semiconductor, both electrons and holes

conduct current:

• The conductivity of a semiconductor is– Unit: mho/cm

• The resistivity of a semiconductor is– Unit: ohm-cm

EEnpqJ

EqnEqpJJJ

EqnJEqpJ

npdrifttot

npdriftndriftpdrifttot

ndriftnpdriftp

)(

)(

,

,,,

,,

np qnqp

1


• Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015 cm-3 and boron to a concentration of 6x1017 cm-3.

Resistivity Example

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EE105 Fall 2011Lecture 2, Slide 1Prof. Salahuddin, UC Berkeley Lecture 2 OUTLINE Semiconductor Basics Reading: Chapter 2