Electrical and Optical Properties of Materials

8/2/2019 Electrical and Optical Properties of Materials

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Electrical and optical properties

of materials


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XRF (X-ray fluorescence)

XRF is the emission ofcharacteristic secondary(or fluorescent) X-rays froma material that has beenexited by bombarding withhigh energy x-rays orgamma rays.

The energy of the emittedX-rays depends upon theatomic number of the atom(Z) and their intensitydepends upon theconcentration of the atomin the sample.


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When a photon or charged particle of sufficientenergy interacts with an atom, the atom may beexcited releasing a specific electron out of aninner, K or L shell. The outer shell electron can fallinto the vacated inner shell, releasing energy asan X-ray.


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2

Za

C

Where C= speed of light, a = constant of proportionality, is

the wavelength for each spectral line belonging to a

particular series of emission lines for each element in the

periodic table, and = a constant whose value depends on

the electronic transition series

The energy of the emitted radiation depends upon

the atomic energy level separation and on theatomic number by:


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Basic working principlePrimary photons of sufficient energy

are emitted by the x-ray tube andilluminate the sample

The matter in the sample reacts by

emitting fluorescent secondaryphotons which escape the sample.

The energy (or wavelengh or color) of the fluorescent photons is an indication about

the elemental composition of the sample. The intensity of the fluorescent beam

(number of photons per sec) is an indication of the elements concentration in thesample


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EDXRF (energy dispersive-XRF)A secondary fluorescence photon is emitted

by the sample, under the bombardment ofprimary potons emitted by the x-ray tube.

Secondary photons are emitted in all

directions.

The secondary photon enters the detector. It

is converted to an electrical impulse. Theheight (amplitude) of this pulse is directly

proportional to the energy of the incoming

photon.


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WD (wavelength diffraction)-XRF

The secondary fluorescent radiations are emitted by the sample in all directions. A

privileged direction is defined by the orientation of parallel plates forming the

primary collimator. Only radiations in that direction can go through the collimator

and reach a reflection crystal. The crystal has the property to reflect radiation with

an output angle (theta) identical to the incident angle. The reflection angle theta is

only possible if the wavelength is in close relation with the crystal 2d lattice distanceand the theta angle. The relation is known as Bragg's law


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XRF spectrums


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Photoconductivity

Photoconductivity is termed as the increase of

the electrical conductivity of a crystalline

insulator by incident electromagnetic

radiation.

because of the increase of the charge

carrier concentration due to electron-hole

formation, provided that the photon energy issufficiently high.


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Let A be the absorbtion rate of photons and R the

rate for recombination of holes and electrons. The

temporal change of the charge carrier concentration

n is:

In steady state and we obtain the steady statephotoelectron concentration

And the photoconductivity:

2RnA

dtdn

0n

R

An 0

e

R

Ane

Carrier mobility

Elementary charge


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Luminesence (e.g.Fluoresence, ,

Phosporesence)Luminescence is the emission of visible light by a substance.

It occurs when upon exposure to energy, electrons are

excited and while returning to the eletronic ground state

electron produces excess energy as a photon.

Luminescence occurs due to incident light, mechanical

impact, chemical reactions or heat input.

Luminescence is caused by the excitation of electrons of so-called activators, i.e. Impurity atoms in crystals.


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Singlet state: All electrons in the

molecule are spin-paired

Triplet state: One set of electron

spins is unpaired

The triplet state is of a lower electronic energy

than the excited singlet state.

The excess energy is

converted to

vibrational energy

The spin of an excited electron can be

reversed, leaving the molecule in an

excited tripletstateShort time

lapse ~10-8s Long decay time


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Resistivity measurement principle

A four point probe is a simple apparatus formeasuring the resistivity of semiconductor

samples. By passing a current through two

outer probes and measuring the voltage

through the inner probes allows the

measurement of the substrate resistivity.

Using the voltage and current readings from

the probe:


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The measurement of bulk resistivity is similar to that of sheet

resistivity except that a resistivity in cm-3 is reported using the

wafer thickness, t:

Where t is the layer/wafer thickness in cm.

The simple formula above works for when the wafer thickness

less than half the probe spacing (t < s/2) (Schroder). For

thicker samples the formula becomes:


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Under an imposed electric field (or voltage), thefree electrons in a metal accelerate, but are

scattered by imperfections in the crystal latticeand by the thermal vibration of the atomsthemselves. This scattering causes electrons toflow with an average drift velocity, whichdetermines the current flowing.

The electrical resistivity is dominated by thermalvibration (phonon scattering) and by soluteatoms (and vacancies) in the lattice. Dislocationsalso cause some scattering, but this is usuallyvery small compared to the effect of solute (asthe dislocation spacing is much larger than thesolute atom spacing).


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Matthiessens rule is commonly used to represent the resistivitymathematically:

(e)total = (e)t + (e)i(e)t is the intrinsic thermal response of the pure metal.(e)i is the contribution from impurities (solute, and vacancies).

The thermal contribution (e)t is approximately linear withtemperature.

The solute contribution (e)i is approximately linear with each atomtype:

(e)i = cMg(e)Mg + cZn(e)Zn + ...cx is the concentration (at%) of element x in solid solution (not

necessarily the alloy composition, as elements may also be tied up

in precipitates).xis the resistivity coefficient for element x.


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Norburys rule

The electrical resistivity increases inproportion to the square of the valence

difference of the partners.


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The effect of intermetallic phases on

resistivity

The resistivity is notably decrease upon

transition from a disordered to an ordered

state.


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Ordering transformation


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Dependence of the resistivity of

heterogeneous materials

Resistivity depends on the geometrical

arrangement of the phase mixture.

21

total

21

111

total


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p-n junction (flatband diagram)

Note that this does not automatically align the Fermi energies, EF,n and EF,p. Also, note

that this flatband diagram is not an equilibrium diagram since both electrons and

holes can lower their energy by crossing the junction. A motion of electrons andholes is therefore expected before thermal equilibrium is obtained. The diagram

shown in Figure 4.2.2 (b) is called a flatband diagram. This name refers to the

horizontal band edges. It also implies that there is no field and no net charge in the

semiconductor.
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Thermal equilibrium

To reach thermal equilibrium, electrons/holes close to the metallurgical junction diffuse

across the junction into thep-type/n-type region where hardly any electrons/holes are

present. This process leaves the ionized donors (acceptors) behind, creating a region

around the junction, which is depleted of mobile carriers. The charge due to the ionized

donors and acceptors causes an electric field, which in turn causes a drift of carriers in the

opposite direction. The diffusion of carriers continues until the drift current balances the

diffusion current, thereby reaching thermal equilibrium as indicated by a constant Fermienergy.


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Reverse/Forward bias

We now consider a p-n diode with an applied bias voltage, Va. A forward bias

corresponds to applying a positive voltage to the anode (thep-type region) relative

to the cathode (the n-type region). A reverse bias corresponds to a negative voltage

applied to the cathode. Both bias modes are illustrated with Figure 4.2.4. The

applied voltage is proportional to the difference between the Fermi energy in the n-

type andp-type quasi-neutral regions.

As a negative

voltage is applied,

the potential across

the semiconductor

increases and so

does the depletion

layer width.

As a positive

voltage is

applied, thepotential across

the

semiconductor

decreases and

with it the

depletion layer

width.
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Electrical and Optical Properties of Materials