Semiconductor Device Physics

Lecture 2Dr. Gaurav Trivedi,EEE Department,

IIT Guwahati

Electronic Properties of SiSilicon 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,

e = –1.602 10–19 CHoles are positively charged,

p = +1.602 10–19 C

The concentration (number of atom/cm3) of conduction electrons & holes in a semiconductor can be influenced in several ways:Adding special impurity atoms (dopants)Applying an electric fieldChanging the temperature Irradiation

S i S i S i

S i S i S i

S i S i S i

Si Si Si

Si Si Si

Si Si Si

Hole

Conductionelectron

Bond Model of Electrons and Holes

When an electron breaks loose and becomes a conduction electron, then a hole is created.

2-D Representation

What is a Hole?A hole is a positive charge associated with a half-filled covalent bond.A hole is treated as a positively charged mobile particle in the

semiconductor.

Conduction Electron and Hole of Pure Si

ni = intrinsic carrierconcentration

ni ≈ 1010 cm–3 at room temperature

• Covalent (shared e–) bonds exists between Si atoms in a crystal.

• Since the e– are loosely bound, some will be free at any T, creating hole-electron pairs.

Energy states(in Si atom)

Si: From Atom to Crystal

• The highest mostly-filled band is the valence band.

• The lowest mostly-empty band is the conduction band.

Energy bands(in Si crystal)

Ec

EvEle

ctr

on

en

erg

y

• For Silicon at 300 K, EG = 1.12 eV• 1 eV = 1.6 x 10–19 J

EG, band gap energy

Energy Band Diagram

Simplified version of energy band model, indicating:Lowest possible conduction band energy (Ec)Highest possible valence band energy (Ev)

Ec and Ev are separated by the band gap energy EG.

Semiconductor Ge Si GaAs DiamondBand gap (eV) 0.66 1.12 1.42 6.0

Measuring Band Gap EnergyEG can be determined from the minimum energy (hn) of photons that

can be absorbed by the semiconductor.This amount of energy equals the energy required to move a single

electron from valence band to conduction band.

Photon

photon energy: h n = EG

Ec

Ev

Electron

Hole

Band gap energies

Carriers

Completely filled or empty bands do not allow current flow, because no carriers available.

Broken covalent bonds produce carriers (electrons and holes) and make current flow possible.

The excited electron moves from valence band to conduction band.Conduction band is not completely empty anymore. Valence band is not completely filled anymore.

Band Gap and Material Classification

E c

E v

EG = 1.12 eV

Si Metal

Ev

E c

EE

c

vE c

EG= ~8 eV

SiO2

E v

Insulators have large band gap EG.Semiconductors have relatively small band gap EG.Metals have very narrow band gap EG .

Even, in some cases conduction band is partially filled,Ev > Ec.

Carrier Numbers in Intrinsic Material

More new notations are presented now:n : number of electrons/cm3

p : number of holes/cm3

ni : intrinsic carrier concentration In a pure semiconductor, n = p = ni.At room temperature,

ni = 2 106 /cm3 in GaAs ni = 1 1010 /cm3 in Si ni = 2 1013 /cm3 in Ge

Manipulation of Carrier Numbers – Doping

Donors: P, As, SbAcceptors: B, Ga, In, Al

By substituting a Si atom with a special impurity atom (elements from Group III or Group V), a hole or conduction electron can be created.

Doping Silicon with Acceptors

Al– is immobile

Example: Aluminium atom is doped into the Si crystal.

The Al atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”.

The hole is free to roam around the Si lattice, and as a moving positive charge, the hole carries current.

Doping Silicon with Donors

P+ is immobile

Example: Phosphor atom is doped into the Si crystal.

The loosely bounded fifth valence electron of the P atom can “break free” easily and becomes a mobile conducting electron.

This electron contributes in current conduction.

Ec

Donor LevelED

Donor ionization energy

Ev

Acceptor LevelEA

Acceptor ionization energy

+

▬

▬

+

Ionization energy of selected donors and acceptors in Silicon

Acceptors

Ionization energy of dopant Sb P As B Al InEC – ED or EA – EV (meV) 39 45 54 45 67 160

Donors

Donor / Acceptor Levels (Band Model)

Dopant Ionization (Band Model)

Donor atoms

Acceptor atoms

Carrier-Related Terminology

Donor: impurity atom that increases n (conducting electron).Acceptor: impurity atom that increases p (hole).

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: undoped semiconductor n = p = ni.Extrinsic semiconductor: doped semiconductor.

Ec

Ev

DE

Density of States

E

Ec

Ev

gc(E)

gv(E)

density of states g(E)

g(E) is the number of states per cm3 per eV.g(E)dE is the number of states per cm3 in the energy range between

E and E+dE).

Ec

Ev

DE

* *n n c

c 2 3

2( )

m m E Eg E

h

* *p p v

v 2 3

2( )

m m E Eg E

h

E Ec

E Ev

*n

*n o*p o

31o

: effective mass of electron

For Silicon at 300 K,1.180.81

9.1 10 kg

m

m mm m

m

mo: electron rest mass

Density of States

Near the band edges:

E

Ec

Ev

gc(E)

gv(E)density of states g(E)

F( ) /

1( )

1 E E kTf E

e

F

F

F

If , ( ) 0If , ( ) 1If , ( ) 1 2

E E f EE E f EE E f E

k : Boltzmann constantT : temperature in Kelvin

Fermi FunctionThe probability that an available state at an energy E will be

occupied by an electron is specified by the following probability distribution function:

EF is called the Fermi energy or the Fermi level.

Effect of Temperature on f(E)

Effect of Temperature on f(E)

Energy banddiagram

Density ofstates

Probabilityof occupancy

Carrier distribution

Equilibrium Distribution of Carriers

n(E) is obtained by multiplying gc(E) and f(E),p(E) is obtained by multiplying gv(E) and 1–f(E).

Intrinsic semiconductor material

Energy banddiagram

Density ofStates

Probabilityof occupancy

Carrier distribution

Equilibrium Distribution of Carriers

n-type semiconductor material

Energy banddiagram

Density ofStates

Probabilityof occupancy

Carrier distribution

Equilibrium Distribution of Carriers

p-type semiconductor material

Important Constants

Electronic charge, q = 1.610–19 CPermittivity of free space, εo = 8.85410–12 F/mBoltzmann constant, k = 8.6210–5 eV/KPlanck constant, h = 4.1410–15 eVsFree electron mass, mo = 9.110–31 kgThermal energy, kT = 0.02586 eV (at 300 K)Thermal voltage, kT/q = 0.02586 V (at 300 K)