Chapter 1

Fundamental Solid-State Principles

Metal and Insulator

The atom : Bohr’s model

Shell name

Subshell name

Subshell max

electrons

Shell max

electrons

K 1s 2 2

L 2s 2

2+6=8 2p 6

M

3s 2 2+6+10

=18 3p 6

3d 10

N

4s 2

2+6+ +10+14

=32

4p 6

4d 10

4f 14 Discrete energy levels in an atom

valence shell = the outermost shell

Principle types of crystal binding

Semiconductors contain four valence electrons

covalent bonding

Probability density function for the lowest electron energy state of an isolated hydrogen atom

Overlapping two wave functions for two atoms in close proximity to each other

Interacting two electrons results in the energy level splitting into two discrete energy levels

For a regular periodic array of N hydrogen atoms, there occur N discrete energy levels

1019 atoms in 1 eV > 10-19 eV separation

E

Interatomic distance r0

Formation of energy bands

• Si = 1s2 2s2 2p6 3s2 3p2 ~ 10 electrons occupy deep-lying energy levels close to the

nucleus and 4 valence electrons are weakly bound

• As the inter-atomic distance decreases, 3s and 3p states overlap

– At the equilibrium distance, there occur two bands ~ four quantum states per atom

in the lower band and another four quantum states in the upper band

– At T = 0, all states in the lower (valence) band is full, while the upper (conduction)

band is empty

– Bandgap energy Eg ~ width of the forbidden energy band btw the valence and

conduction bands

Bandgap energy of Silicon

atomic number = 14

Electrons in crystalline solids

Band-gap patterns

Insulators:

Metals:

The level at the bottom of the partially filled band

of Fig. 41-5 corresponds to E =0. The highest

occupied level in this band at absolute zero (T =0 K)

is called the Fermi level, and the energy

corresponding to it is called the Fermi energy EF;

for copper, EF =7.0 eV.

The electron speed corresponding to the Fermi

energy is called the Fermi velocity vF . For copper

the Fermi speed is=1.6 x106 m/s.

Semiconductors:

Fig. 41-9 (a) The band–gap pattern for a semiconductor. It resembles that of an

insulator except that here the energy gap Eg is much smaller; thus electrons,

because of their thermal agitation, have some reasonable probability of being able

to jump the gap. (b) Thermal agitation has caused a few electrons to jump the gap

from the valence band to the conduction band, leaving an equal number of holes in

the valence band.

Conduction in a semiconductor

When a valence electron absorbs enough energy, it can jump from the valence band

to the conduction band ~ “excitation” ~ creation of an electron-hole pair with a finite

life-time (“recombination”)

Moderate electrical conductance (between insulator and metallic conductor)

For example, Si, Ge, GaAs, GaP, CdS, etc

Electrical properties are varied depending on the impurities and/or defects

The electrical conductance can be tuned via doping process

Semi-Conductors

Doping ~ n-type and p-type

Doped Semiconductors:

Semiconductors

Semiconductors are crystalline materials that are characterized by specific energy bands for electrons.

Between the bands are gaps; these gaps represent

energies that electrons cannot posses. The last energy

band is the conduction band, where electrons are

mobile.

The next to the last band is the valence band, which

is the energy level associated with electrons involved

in bonding.

Nucleus

First band

Second band

Valence band

Conduction band

Energy gap

Energy gap

Energy gap

Energy

Electron and hole current

At room temperature, some electrons have enough

energy to jump into the conduction band.

After jumping the gap, these electrons are free to

drift throughout the material and form electron

current when a voltage is applied.

For every electron in the conduction band, a hole is

left behind in the valence band. Valence band

Conduction band

Energy gap

Energy

Heat

energy

Electron-

hole pair

Electron and hole current

The electrons in the conduction band and the holes in the valence band are the charge carriers. In

other words, current in the conduction band is by electrons; current in the valence band is by holes.

When an electron jumps to the conduction band, valence electrons move from hole-to-hole in the

valence band, effectively creating “hole current” shown by gray arrows.

Impurities or dopants

To increase the number of conduction band electrons, pentavalent impurities are added to pure

(intrinsic) silicon, forming an n-type semiconductor. These are elements to the right of Si on the

Periodic Table.

To increase the number of holes, trivalent impurities are added, forming a p-type semiconductor.

These are elements to the left of Si on the Periodic Table.

Si

B

Al

Ga

P

As

Sb

Ge

C

Sn

N

III IV V

In

The pn junction diode

The pn junction is basically a diode, which is a device that allows

current in only one direction. A few typical diodes are shown.

When a pn junction is formed, electrons in the n-material diffuse across

the junction and recombine with holes in the p-material.

This action continues until the voltage of the barrier repels further

diffusion. Further diffusion across the barrier requires the application of

a voltage.

~ built-in potential

Barrier potential and dynamic resistance

equivalent for a diode

Forward bias

When a pn junction is forward-biased, current is

permitted. The bias voltage pushes conduction-band

electrons in the n-region and holes in the p-region

toward the junction where they combine.

Question: Voltage와 electric potential energy 차이를

구분할 줄 아는가?

The barrier potential in the depletion region must be

overcome in order for the external source to cause

current. For a silicon diode, this is about 0.7 V.

The forward-bias causes the depletion region to be

narrow.

p-region n-region

p n

+ -

R

VBIAS

Reverse bias

When a pn junction is reverse-biased, the bias

voltage moves conduction-band electrons and holes

away from the junction, so current is prevented.

The diode effectively acts as an insulator. A relatively

few electrons manage to diffuse across the junction,

creating only a tiny reverse current (current carried

by minority carriers).

The reverse-bias causes the depletion region to widen.

p-region n-region

p n

+-VBIAS

R

Diode characteristics

The forward and reverse characteristics are shown on

a I-V characteristic curve.

In the forward bias region, current increases

dramatically after the barrier potential (0.7 V for Si)

is reached. The voltage across the diode remains

approximately equal to the barrier potential.

The reverse-biased diode effectively acts as an

insulator until breakdown is reached.

p

n

Reverse bias

Diode structure, schematic symbol, and bias circuits.

VBIAS is the bias voltage, and VB is the barrier potential.

Diode Equation

Forward and reverse currents

– pn junction current is given approximately by

– where I is the current, e is the electronic charge, V is the applied voltage, k is Boltzmann’s

constant, T is the absolute temperature and (Greek letter eta) is a constant in the range 1

to 2 determined by the junction material

– for most purposes we can assume = 1

– Thus,

exp 1s

eVI I

ηkT

-

exp 1s

eVI I

kT

-

at room temperature e/kT ~ 40 V-1

If V > +0.1 V

exp exp40s s

eVI I I V

kT

If V < -0.1 V

0 1s sI I I - -

– IS is the reverse saturation current