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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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