Who discovered the electron?

A Cathode Ray Tube

Source of
Electrical
Potential

Stream of negative
particles (electrons)

Metal Plate

Gas-filled
glass tube Metal plate
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 58
 Cathode Rays
• Form when high voltage is applied across
electrodes in a partially evacuated tube.
• Originate at the cathode (negative electrode)
and move to the anode (positive electrode).
• Carry energy and can do work.
• Travel in straight lines in the absence of an
external field.
• Deflect under electric field.
J.J. Thomson- Discovery of electron
• He proved that atoms of
any element can be made
to emit tiny negative
particles.

• From this he concluded

that ALL atoms must
contain these negative
particles.

• He knew that atoms did

not have a net negative
charge and so there must
be balancing the negative
charge.
J.J. Thomson
Cathode Ray Experiment
1897 Experimentation
• Using a cathode ray tube, Thomson was able to deflect cathode
rays with an electrical field.
• The rays bent towards the positive pole, indicating that they are
negatively charged.
negative
High source of plate
voltage
_
high voltage

cathode + anode
positive
plate
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition,
1990, page 117
Hall Effect - Discovery
Observed in 1879
Discovered 18 years before the electron

Edwin Herbert Hall

• Hall voltage is produced by charge accumulation on

sidewalls
• Charge accumulation balances Lorentz Force
• Charge accumulation increases resistance

8
 A Visual Representation shows the nature of the current…

A magnetic field is applied perpendicular to the direction of electric field.

• Holes drift in a p-type bar, their path tends to be deflected.
Using vector notation, the total force on a single hole due to the electric and
magnetic fields:
In the y-direction:
The Hall effect occurs
because a charged
Remember Lorentz Force: particle moving in a
magnetic field is subject
to the Lorentz force.
 A Visual Representation shows the nature of the current…

If an electric field is not established along the width of the bar, each hole will experience a net
force (and therefore an acceleration) in the -y-direction due to magnetic field.

To maintain a steady state flow of holes down the length of the bar, the electric field must
just balance. Set net Lorentz force to zero:
 Hall Effect

The establishment of the electric field is known as the Hall effect, and the
resulting voltage is called the Hall voltage.

Drift velocity (using +q p0 for holes), the field: (remember ))

(RH : Hall coefficient)

→ Hall field is proportional to the product of the current density and the magnetic
flux density
 Hall effect

We already obtained these equations:

A measurement of the Hall voltage for a known current and magnetic field
yields a value for the hole concentration p0
 Resistivity-mobility

If a measurement of resistance R is made, the sample resistivity can be

calculated:

Since the conductivity: σ = 1/ρ, σ = qμpp0

the mobility is simply the ratio of the Hall coefficient and the resistivity:
 Hall Measurements
• Useful in the analysis of semiconductor materials.

• Measurement of the sign of the Hall voltage is a common technique

for determining if an unknown sample is p-type or n-type.

• Measurement can tell about charge carrier mobility, concentration

• Conversely, knowing the above allows for sensitive measurement of

an external B-field

(Resistant to outside contaminants unlike optical, electromechanical

testing)

14
Example

http://hyperphysics.phy-
astr.gsu.edu/hbase/magnetic/Hall.html
Please read the highlighted parts in the textbooks, Solid State Electronic Devices STREETMAN AND BANERJEE
 Excess carriers in
semiconductors

• Optical absorption
• Luminescense
• Carrier lifetime and photo-conductivity
• Diffusion of carriers
Optical absorption
• Photons with hv>Eg will excite electron hole pairs (EHP) and the
excess energy (hv-Eg) will be absorbed as heat.
• EHPs increase conductivity.
• Photons with hv<Eg will pass through unabsorbed.
• One can measure Eg in this fashion.
 Optical absorption
eV nm cm-1 THz

Conversion 1 1240 8065.6 241.8

Factors*

Example- CdSe (1.74 eV→713 nm) will pass all IR while GaP (2.26 eV →549
nm) will pass green light and all longer wavelengths.
Solar Energy Spectrum

• Power reaching earth 1.37 KW/m2

 eV nm cm-1 THz
Ultraviolet (UV) 124 - 3.26 10 - 380 1000000 - 26300 30000 - 789

Visible Violet 3.26 - 2.85 380 - 435 26300 - 23000 789 - 689
Blue 2.85 - 2.48 435 - 500 23000 - 20000 689 - 600
Cyan 2.48 - 2.38 500 - 520 20000 - 19200 600 - 577
Green 2.38 - 2.19 520 - 565 19200 - 17700 577 - 531
Yellow 2.19 - 2.10 565 - 590 17700 - 16900 531 - 508
Orange 2.10 - 1.98 590 - 625 16900 - 16000 508 - 480
Red 1.98 - 1.65 625 - 750 16000 - 13300 480 - 400

Near Infrared (NIR) 1.65 - 0.496 750 - 2500 13300 - 4000 400 - 120

Mid-Infrared (MIR) 496 - 124 meV 2.5 - 10 µm 4000 - 1000 120 - 30

Far Infrared (FIR) 124 - 12.4 meV 10 - 100 µm 1000 - 100 30 - 3.0

Terahertz Regime 41.4 - 1.24 meV 30 µm - 1 mm 334 - 10 10 - 0.3

Luminescense

• Luminescence is emission of light by a substance not

resulting from heat; it is thus a form of cold body radiation.
• It can be caused by chemical reactions, electrical energy,
subatomic motions, or stress on a crystal.
• Light may be given off as EHPs recombine and shed the
excess energy.
• You can create EHPs (that will recombine) in different ways
• Photoluminescense
• Cathodeluminescense
• Electroeluminescense

23
Luminescense
• Photoluminescense
• Shine monochromatic light larger than the bandgap
of the material and measure frequency spectrum of
emitted photons. Characterization tool.
• Cathodeluminescense
• Excite material with accelerated electrons. The
electrons beam can be pointed to various parts of
the structure. Characterization tool. (Except for ZnS
on light bulbs and TV screens.)

24
Luminescense
• Photoluminescense
• Shine monochromatic light larger than the bandgap
of the material and measure frequency spectrum of
emitted photons. Characterization tool.
Fluorescent Lamp
A fluorescent lamp is a low weight mercury vapour lamp that uses
fluorescence to deliver visible light. An electric current in the gas
energizes mercury vapor which delivers ultraviolet radiation through
discharge process and the ultraviolet radiation causes the phosphor
coating of the lamp inner wall to radiate visible light.

https://www.electrical4u.com/fluorescent-lamp-
its-working-principle/
Luminescense
• Cathodeluminescense
• Excite material with accelerated electrons. The
electrons beam can be pointed to various parts of
the structure. The effect is also used as a
characterization tool.

27
Luminescense
• Electroeluminescense
• Excess electrons and holes that are supplied by a
current or voltage source recombine to produce
light.
• LEDs, LASERS
• While the other methods are characterization tools this
method of creating luminescence is used in end use
devices.
 Luminescense
• Chemiluminescence, a result of a chemical reaction
• Bioluminescence, emission as a result of biochemical reaction by a living organism
• Electrochemiluminescence, a result of an electrochemical reaction
• Crystalloluminescence, produced during crystallization
• Electroluminescence, a result of an electric current passed through a substance
• Cathodoluminescence, a result of a luminescent material being struck by the electrons
• Mechanoluminescence, a result of a mechanical action on a solid
• Triboluminescence, generated when bonds in a material are broken when that material is scratched,
crushed, or rubbed
• Fractoluminescence, generated when bonds in certain crystals are broken by fractures
• Piezoluminescence, produced by the action of pressure on certain solids
• Sonoluminescence, a result of imploding bubbles in a liquid when excited by sound
• Photoluminescence, a result of absorption of photons
• Fluorescence, photoluminescence as a result of singlet–singlet electronic relaxation (typical lifetime:
nanoseconds)
• Phosphorescence, photoluminescence as a result of triplet–singlet electronic relaxation (typical lifetime:
milliseconds to hours)
• Radioluminescence, a result of bombardment by ionizing radiation
• Thermoluminescence, the re-emission of absorbed energy when a substance is heated
• Cryoluminescence, the emission of light when an object is cooled (an example of this is wulfenite)
 Recombination process
• Direct recombination of electrons and holes
• Electron drops from conduction band to the valence band
and recombines with a hole without any change in
momentum (E vs K) .
• The energy difference is used up in an emitted photon.
• This process occurs at a certain rate in the form of how
long does a free electron or hole remain free before it
recombines (tn or tp)
• tn or tp are dependent on doping level, crystal quality
and temperature.
Band-to-Band
Carrier lifetime and photo-conductivity

• Indirect recombination; Trapping

• The probability of a direct recombination is small in Si and Ge.
• A trapping level is needed. No photons generated just
phonons (lattice vibrations)
• Minority carrier lifetime dominates recombination process.

R-G Center
 Carrier lifetime and photo-conductivity
Indirect recombination; Auger:
• The excess energy given off by an electron
recombining with a hole is given to a second Auger
electron (in either band) instead of just emitting
the energy as a photon.
• The newly excited electron then gives up its
additional energy in a series of collisions with the
lattice, relaxing back to the edge of the band.
• Thus, this effect is a result of interactions
between multiple particles, including multiple
electrons and a hole.
• This process can also occur with multiple holes
and one electron, depending on whether charge
carriers in the valence or conduction band are
involved.
The Auger effect is a process by which electrons with characteristic
energies are ejected from atoms in response to a downward transition by
another electron in the atom.
Direct vs. Indirect Band Gap Materials
E-k Diagrams

Little change in momentum Large change in momentum

is required for recombination is required for recombination
→ momentum is conserved by → momentum is conserved by
photon emission phonon + photon emission
EE130 Lecture 8, Slide 34
Carrier lifetime and photo-conductivity
• The Fermi level (EF) is
only meaningful at
n = ni e ( Fn − Ei ) / kT
thermal equilibrium. n = n0 + n
• Under excitation we use
n = t n g op
the quasi Fermi level to
denote excess hole and
electron concentrations. ( Ei − F p ) / KT
p = ni e
p = p0 + p
p = t p g op
Fermi energy
• The Fermi energy is a concept in quantum mechanics usually referring to the
energy difference between the highest and lowest occupied single-particle states in
a quantum system of non-interacting fermions at absolute zero temperature. In
a Fermi gas the lowest occupied state is taken to have zero kinetic energy,
whereas in a metal the lowest occupied state is typically taken to mean the bottom
of the conduction band.

• Confusingly, the term "Fermi energy" is often used to refer to a different but closely
related concept, the Fermi level (also called electrochemical potential). There are a
few key differences between the Fermi level and Fermi energy:

• The Fermi energy is only defined at absolute zero, while the Fermi level is defined
for any temperature.

• The Fermi energy is an energy difference (usually corresponding to a kinetic

energy), whereas the Fermi level is a total energy level including kinetic energy
and potential energy.

• The Fermi energy can only be defined for non-interacting fermions (where the
potential energy or band edge is a static, well defined quantity), whereas the Fermi
level (the electrochemical potential of an electron) remains well defined even in
complex interacting systems, at thermodynamic equilibrium.
Diffusion of carriers

• Diffusion process
• The random motion of similar particles from a
volume with high particle density to volumes with
lower particle density
• A gradient in the doping level will cause electron or
hole flow, which causes an electric field to build up
until the force from the gradient equals the force of
the electric field.
• no current will flow at equilibrium

37
 Diffusion of carriers

• Diffusion process
• t is the mean free time that 1/2 of the particle will enter
the next dx segment.
• l is the mean free path of a particle between collisions.

−2
− l dn( x) dn( x) dn( x) dn( x)
n ( x) = −
= − Dn , Jn ( diff .) = − ( − q ) Dn = + qDn
2t dx dx dx dx
−2
− l dp ( x) dp ( x) dp ( x) dp ( x)
 p ( x) = −
= − D p , Jp ( diff .) = − ( + q ) D p = + qD p
2t dx dx dx dx

38
Continuity equation

• Rate of hole build up = increase of hole

concentration in the volume - the
recombination rate

p 1 Jp p
=− −
t q x t p
n 1 Jn n
= −
t q x t n

39
 When the current is carried strictly by diffusion (negligible drift), we can
replace the currents for diffusion current; for example, for electron
diffusion we have:

Substituting this into Eq. (4-3lb) we obtain the diffusion equation for
electrons:

and similarly for holes,

Diffusion length

• Lp is the average distance a hole will move

before recombining.
• Ln is the average distance an electron will
move before recombining.

Ln  Dnt n
L p  D pt p
41
Direct Recombination of
Electrons and Holes
Energy levels of impurities in Si. The
energies are measured from the nearest
band edge (Ev or Ec); donor levels are
designated by a plus sign and acceptors by
a minus sign.
 PN Junction (Diode)

• When N-type and P-type dopants are introduced side-by side in a semiconductor, a PN junction
or a diode is formed.
• In order to understand the operation of a diode, it is necessary to study its three operation
regions: equilibrium, reverse bias, and forward bias.
• Because each side of the junction contains an excess of holes or electrons compared to the
other side, there exists a large concentration gradient. Therefore, a diffusion current flows across
the junction from each side.
• As free electrons and holes diffuse across the junction, a region of fixed ions is left behind. This
region is known as the “depletion region.”
• The fixed ions in depletion region create an electric field that results in a drift current.
 PN Junction (Diode)

• After its formation;

• the p side has a large number of free holes and the n side an excess of free electrons.
• Due to their mutual repulsion, the free electrons of n side are diffused in all directions.
• Some of them can traverse the junction, creating an atom with a positive charge on the n side.
• When the electron enters the p side, it recombines with a hole (as holes are the majority carriers
at the p side), generating a negative ion. This means that each electron that traverses the p − n
junction generates a couple of ions, one negative on the n side and one positive on the p side.
• After some time, around the junction almost all electrons and holes recombine, creating a
negative charged zone on the p side and a positive charged zone on the n side.
• These two zones create a potential barrier that counteracts the diffusion of the electrons from the
n side to the p side.
 PN Junction (Diode)

As free electrons and holes diffuse across the junction, a region of fixed ions is left behind. This
region is known as the “depletion region.”

The fixed ions in depletion region create an electric field that results in a drift
current.
At equilibrium, the drift current flowing in one direction cancels out the diffusion
current flowing in the opposite direction, creating a net current of zero.

Because of the electric field across the junction, there exists a built-in potential.
1 Which is not related to cold body radiation?
A) Phosphorus (a chemical element with symbol P) emits light.
A) When a material is heated, it starts emitting light.
A) Electrons and holes recombine and lose energy as heat.
A) A television that uses a cathode ray tube.
A) Materials re-emit light that they absorb, which takes relatively long time.

Answer: When a material is heated, it starts emitting light.

2 Which of the following are used when finding the carrier concentration in a semiconductor?
A) Density of states and Bose-Einstein function
A) Function Continuity equation and current density equation
A) Maxwell-Boltzmann distribution function and Fermi Dirac Distribution Function
A) Diffusion and drift functions
A) Density of states and Fermi Dirac Distribution

Answer: Density of states and Fermi Dirac Distribution