Course B - Materials for Devices Flashcards
define a dielectric material
“A dielectric material is an electrical insulator that can be polarised by an applied electric field”
give 3 polarisation mechanisms
1) electronic - distortion of an electron cloud around a nucleus
2) ionic - elastic distortion of an ionic bond
3) orientational - rotation of permanent dipole molecules
give the equation (LEARN) for dipole moment
the dipole moment between two opposite charges +q, -q, separated by r is
μ = qr
give the equations (3) for polarisation (LEARN)
Polarisation = total dipole moment per unit vol = charge per unit area
P = nμ
P = Q/A
n = dipoles per unit vol
and
P = εo E (κ-1)
give the equations (2) for the displacement field that forms when an electric field is applied to a dipole (LEARN)
D = εo E + P
D = ε E = κ εo E
give the equation for the capacitance on an empty and dielectric parallel plate capacitor (IN DATA BOOK)
Empty parallel plate
C = εo*A / L
dielectric parallel plate
C = ε*A / L
define centrosymmetric and non-centrosymmetric crystals
“Centrosymmetric crysals have an inversion centre”
“non-centrosymmetric crystals do not have an inversion centre”
give the possible polarities of a centrosymmetric crystal
- centrosymmetric crystals have NO unique directions, hence they CANNOT be polar
- whatever dipole forms on one side of the inversion centre will be perfectly cancelled by a dipole that forms on the other side
give the possible polarities of a non-centrosymmetric crystal
non-centrosymmetric crystals can be polar or non-polar
- polar if they contain a unique direction
- non-polar if they don’t
define piezoelectricity
“A change in polarisation due to the application of stress”
give the equation for the change in voltage due to stress for piezoelectric materials
ΔV = dσL/κεo
L = thickness
d = piezoelectric const.
give the necessary property of a crystal for piezoelectricity
piezoelectricity occurs in any non-centrosymmetric crystal because the positions of the charges move relative to each other
give the two effects that piezoelectric crystals are used for
Generator effect = stress changes, voltage change
motor effect = voltage change, change in shape
define pyroelectricity
“pyroelectricity is a change in polarisation due to a temperature change”
give the necessary property of a crystal for pyroelectricity
pyroelectricity only occurs in polar crystals because in non-polar crystals there is no relative motion between ions
give the equation for change in polarisation due to a temperature change for a pyroelectric crystal
ΔP = pΔT
p = pyroelectric constant
give the equation for change in voltage due to a temperature change for a pyroelectric crystal
ΔV = p Δt L / κ εo
give an example of a pyroelectric crystal and a use of pyroelectric crystals
Wurtzite = ZnS
Hex p lattice with half of tetrahedral interstices filled
only upwards pointing tetrahedrons filled so unique direction = [001]
used in burglar alarms
define ferroelectricity
“Stable, spontaneous polarisation which can be reversed by an external electric field”
when does ferroelectricity occur, what can we say about net polarisations in the absence of an electric field
- below the curie temperature Tc, the unit cell moved to a lower crystallographic symmetry
- a displacive phase transition occurs on cooling through Tc and the unit cell becomes non-centrosymmetric and gains a dipole
- even though each unit cell contains a dipole, in the absence of an electric field there will be no net dipole on a crystal (unless it has already been poled)
explain how Ferroelectricity (FE) occurs in a perovskite structure (ABO3)
in a perovskite structure (ABO3) (usually BiTiO3) FE occurs due to B atom displacement, there are large A atoms, small B atoms
- on cooling the crystal changes from cubic to tetragonal
define a domain
“A domain is a region in a material in which the polarisation is in the same direction”
what is domain wall energy
domain wall energy is the energy that arises at the boundary between different domains, it is minimised when aligned domains are next to each other
“There is an energy associated with the interface between differently aligned domains, hence it’s more efficient to have the same domains next to each other”
what is stray field energy
when there are large domains of the same polarisation, there is an energy cost as a field forms
UE = 1/2 ε E^2
what can we say about the size of domains given the two energy factors at play
- it is a balance between domain wall energy and stray field energy
what can we say about the angles between domains in a single crystal
- the angles between domains in a single crystal depend on the symmetry of the crystal and the preferred dipole direction
what can we say about the orientation of FE dipoles in a polycrystal when in an external electric field
they will align on the crystallographic direction closest to that of the field
explain hysteresis in a FE crystal, give the 6 stages, how do the domain walls move
- hysteresis occurs when a cycling E field is applied to an FE
consider a graph of P (on Y) against E (on X):
1) start at origin, unpolarised, dipoles point in many directions, no field
2) field applied, domains in the same direction as E field grow as this is more energy efficient, polarisation increases, irreversible domain wall motion
3) saturation polarisation Psat is reached, all domains aligned with E field
4) E field removed, polarisation remains as the sample has been ‘poled’
5) field is reversed, domain wall motion starts to occur in opposite direction, polarisation decreases, E = Ecoercive at point where P = 0
6) same as 3 but in opposite direction
give some uses of ferroelectrics
- as piezo or pyro electrics
- as dielectrics
- memory devices, +P and -P can be used as 0,1 in computing
when (considering electron shells) does magnetism occur
- Partially filled electron shells
give the equation for a magnetic moment (IN DATA BOOK)
m = IA
I = current (A)
A = area (m^3)
give two equations for magnetism
M = m/V
M = χ H
χ = susceptibility (unit-less)
H = mag. field strength
define diamagnetism
“Change in orbital motion of electrons due to applied B field”
- all atoms are diamagnetic
- V weak effect
- not permanent
- electron orbits change to oppose applied field
- χ = -ve, V small
define paramagnetism
- some electrons in partially filled shells, dipoles exist
- they are isolated/ non-interacted
- with no field there is no magnetisation
- when field, moments align with field
- χ = +ve, v small
define ferromagnetism
- many unpaired electrons, strong interaction between moments
- moments align with each other, lowest exchange interaction energy
- moments align with an external applied field, orientation becomes permanent, large M
- χ = large, +ve
define antiferromagnetism
- many unpaired electrons, strong interaction between moments
- antiparallel moments are lowest energy
- sets of antiparallel moments exactly cancel
- net M = 0
- χ = small, +ve
define ferrimagnetism
- moments exist, strong interaction between moments
- antiparallel moments form
- moments on sub-lattices not equal so net magnetisation
what is exchange interaction energy, how does it link to ferromagnets
- comes from Pauli exclusion principle
- lowest energy is where electrons have the same spin part but different spacial parts
- means misaligned moments are higher energy
- Ferromagnets form at lower temperatures because EIE ‘wins’ over thermal energy to give aligned moments
Define magnetocrystalline anisotropy
the interaction between the crystal lattice and the magnetic moments mean energy can be higher or lower depending on direction of B fields
easy axis = easy to magnetise on this direction, Msat reached at lower field
Hard axis = harder to magnetise on this direction, Msat reached at higher field
define shape anisotropy (linking to magnetism)
- it is easier to magnetise along the length of an object
define magnetostriction
“a change in shape when a material is magnetised”
Λ = magnetostriction coeff = fractional change in length when magnetisation from 0 —> Msat
why may ferromagnets not necessarily be magnetised
- Ferromagnetic materials are not necessarily magnetised as stray fields have an energy cost
- so different domains form, each domain is magnetised but in different directions
what are domain/bloch walls in ferromagnets, what are the two factors which determine how wide/narrow they are
“A domain wall or Bloch wall is a transition between two differently oriented domains in a ferromagnet”
1) exchange interaction energy (EIE)
- lowest when misaligned spins are apart
- encourages wide Bloch walls
2) magnetocrystalline anisotropy energy
- lowest when moments align with the easy axis of the material
- minimised by aligning spins with preferred directions so encourages narrow walls
actual width determined by balance of these
give the stages of ferromagnetic hysteresis
consider an M (magnetisation) (on Y) against H (magnetic field) (on X) graph
1) no net magnetisation, many different domains all aligned with easy axis
2) as H increases, domain walls move, M increases, irreversible due to domain wall pinning
3) whole sample aligns on easy axis as 1 domain
4) moves away from easy axis to align with H, Msat reached
5) applied field reduced, M decreases as moments align with easy axis again
6) field reversed, domain growth in opposite direction
7) M = 0, many different domains, then repeats in opposite direction
what is the spinel structure
- Fcc oxygen sublattice conventional cell
- 4 octahedral interstices - 1/2 are occupied by trivalent ions (Al3+)
- 8 tetrahedral interstices - 1/8 occupied by divalent ions (Mg2+)
what is the inverse spinel structure, what is its significance
- same as spinel structure but now consider Fe(2+)O Fe(3+)O3
- Fe2+ is in an octahedral interstice
- Fe3+ are half in octahedral interstices and half in tetrahedral interstices
- the Fe3+ magnetisations cancel as the octahedral and tetrahedral interstices point in opposite direction
- the Fe2+ give an overall magnetisation
- it is Ferrimagnetic
define ionic mobility
“Ions/Atoms aren’t stationary on their lattice sites, they can migrate through the lattice by swapping positions with other ions through vacant sites”
what are the main two factors on ionic mobility (just state)
1) number density of vacant sites
2) energy barrier between sites
explain the factor of number density of vacant sites on ionic mobility, give the two types of defect that lead to vacant sites
- we can either have vacancy defects where an atom/ion is missing or an interstitial defect where there is an extra atom in an interstice
this leads to:
1) Shottky defect: A- vacancy, B+ vacancy
2) Frenkel defect: B+ vacancy, B+ interstitial
explain the factor of energy barrier between sites on ionic mobility, give the equations which determine this
- for an ion to be able to move through a lattice, it must be able to overcome the energy barrier, Q
- mobility or diffusivity, D, depends upon probability it can overcome barrier
- defined by Arrhenius
D = Do exp(-Q/RT)
D = Do exp(-Q/kT)
D = diffusivity
when can we have a net current flow from ionic mobility/ which two things will create a net current flow
1) a concentration gradient of ions or vacancies - leads to diffusion current
2) an electric field, E, leads to drift current
explain how a diffusion current (ionic motion) forms and give the suitable equations for it
- we can define J, diffusion flux, number of ions crossing a unit area per unit time
J = I/A = -D dn/dx
ions diffuse DOWN a conc. grad so -ve
diffusion current density (Am^-2) = jdiff = -qD dn/dx
- this ONLY applies to steady state diffusion in a uniform conc. grad.
explain how a drift current forms (ionic motion) and give the suitable equations for it
- if an electric field E is applied then the energy barrier to ionic motion increases in one direction and decreases in the other,
drift current density given by
jdrift = -σ dv/dx = σE
how can drift currents and conc. grads be manipulated to show that applying an electric field leads to a conc. grad
we know
n = no exp(-qV/kT)
dn/dx = (-q/kt) n dv/dx = (qn/kt) E
so applying an electric field leads to a conc. grad.
derive the nernst-einstein eq.
- we know that appying an electric field leads to a drift current, it also encourages a conc. grad which leads to a diffusion current
- at equil, they are equal and opposite
qD dn/dx = σE
qd (qnE/kT) = σE
σ/D = nq^2/kT
this is nernst-einstein eq.
various arrhenius plots can be made with this
what is the general purpose of doping zirconia with Yttria to make YSZ
- it stabilises the cubic Zirconia phase over a much larger temperature range
what occurs (atomic level) when we make YSZ
- fluorite structure
- Y2O3 is added to ZrO2
- Y3+ but Zr4+
- so when two Zr4+ are replaced by two Y3+ there is a charge disparity
- to conserve charge, when this occurs, an oxygen vacancy is formed so ionic motion can occur
give an example (other than YSZ) of an ionic conductor
δ-Bi2O3
- same fluorite structure as YSZ
- Bi sublattice is FCC
On average in each unit cell:
- 8 tetrahedral oxygen sites
- 6 oxygens filling
- 2 oxygen vacancies
- so ionic motion can occur
explain the use of ionic conductors in oxygen concentration cells, explain how an oxygen concentration cell works
- two electrodes both containing oxygen but at different partial pressures
- YSZ solid electrolyte in between, which oxygen ions can move through to balance the partial pressures
reaction at cathode (reduction) = O2(g) + 4e- —> 2O(2-)
reaction at anode (oxidation) = 2O(2-) —> O2(g) + 4e-
then electrons move through external circuit back to cathode
E = -RT/4F ln(p(O2)(II) / p(O2)(I))
(Nernst eq.) (in data book)
explain the use of ionic conductors in lambda sensors/ how lambda sensors work
- fitted to exhaust systems to measure oxygen levels and adjust fuel levels to maximise efficiency, minimise emissions
- exhaust gas enters exhaust manifold, there are permeable Pt electrodes around a YSZ electrolyte and a heater the other side
- voltage across electrodes is measured
- this gives a difference in partial pressures between exhaust and atmosphere
- linked to computer which adjusts air-fuel ratio to give complete stoichiometric combustion
how does an oxygen pump work
- same as an oxygen conc. cell but this time potential is applied to drive O2 from low conc. to high conc. area
how do fuel cells work/ what is their general structure
“Fuel cells produce energy by direct oxidation of fuel”
general structure:
- Anode (porous) - must be electrically conductive
- Cathode (porous) - must be electrically conductive
- electrolyte, must be oxygen conductive but low e- conductive
what are some types of fuel cells/ different electrolytes, different fuels
YSZ as electrolyte, O(2-) conducting, needs high operating temps
or
Polymer electrolyte membrane, H+ conducting, need Pt catalysts
either H2(g) as fuel or CH4(g) as fuel
1/2 cell reactions can usually be derived
give the advantages and disadvantages of fuel cells
Advs:
- high efficiency
- little noise
- if no C in fuel then no CO2 emissions
- can run continuously if fuel is always provided
Disadvs:
- H2(g) storage challenging
how can we derive the rms length of a polymer chain
if we model the polymer as a series of shorter rigid segments of length l, and that they can rotate freely where they join then
if chain stretched out then l=nl
Rn = (n)Σri
R(n-1) = (n-1)Σri
Rn = R(n-1) + rn
averaged we conclude <Rn> = 0 so we do rms
Rn = <R^2 n>^1/2
Rn ^2 = (R(n-1) + rn) dot (R(n-1) + rn) = R^2 (n-1) + 2(R(n-1) dot rn) + rn ^2
= R^2 (n-1) + (2R(n-1) l cosγ) + l^2
cosγ = 0</Rn>
so by induction
<Rn ^2> = nl^2
so rms length is sqrt(n)l
what is the Kuhn length/ how can we use it
- our rms model for polymer length does not consider how not all C-C bonds can rotate freely
- Hence we make the model more accurate by defining Lk (the Kuhn length) as the length below which the chain is effectively straight
- we consider a fewer number of larger segments
what are liquid crystals
- crystalline materials have long-range order so are anisotropic
- non-crystalline materials and liquids are generally isotropic
- Liquid crystals are anisotropic liquids where their anisotropy comes from their molecular shape
- liquid crystals often consist of rod-shaped molecules with a long rigid axis
- they are free to flow so have no long range positional order
- there is some orientational order as their long axes remain roughly parallel
what is a nematic LC structure
- no positional oder
- long range orientational order, they tend to align along a common axis, the director D
- anisotropic
- the degree of orientational order decreases with temp
define the order parameter
a parameter used to describe the degree of orientational order
Q = (3<cos^2(θ)> -1) / 2
all aligned - Q = 1
all random - Q = 0
difference between polarised and unpolarised light
- polarised light has oscillations in 1 direction
- unpolarised light has oscillations in many directions
define the refractive index, n, of a material
n = c/v
c = speed of light in vacuum
v = speed of light in material
what occurs to EM waves on passing through polymers, how does this change at higher temps
- EM waves passing through a polymer will couple to electron density in the molecules
- it will usually couple more strongly in one direction than another
at high temps:
- randomly aligned molecules so non net effect
at lower temps:
- one direction couples more so has a higher refractive index
what are the fast and slow axes of a material, what are PVDs
- the direction in which light couples strongly is the slow axis, light travels slower
- the direction in which light couples weakly is the fast axis, light travels quicker
- These directions are perpendicular, both to each other and to the propagation direction
- they are called the PVDs, (permitted vibration directions)
define birefringence
“Birefringence is the property of a material where refractive index depends on the polarisation and propagation directions of light”
birefringence = Δn
what are polarisers
“polarisers are materials which only allow a specific polarisation of light to pass through”
- usually polymer films with polymers uniaxially aligned
- 2 polarising filters perp to each other let no light through
what occurs when polarised light passes through birefringent materials, include suitable eqs.
Polarised light passing through a birefringent material is resolved into 2 components:
- 1 along fast axis
- 1 along slow axis
- ONLY along PVDs
- unless perfectly aligned to 1 PVD then no splitting
the difference in speeds of light along each PVD creates an optical path difference (OPD)
ΔT = Δnt/c = phase difference
OPD = tΔn
t = thickness
δ/2π = Δnt / λ
what occurs when there is a birefringent sample between two polarisers, which wavelengths of light are removed, which remain
- light passes through polariser, polarised light remains, it then passes into material and splits into two components
- as passing through birefringent sample OPD occurs
- if OPD is λ/2 then δ = π radians, 180° so polarisation of light is rotated through 90 degrees and it can pass through the second polariser, light is transmitted
- if OPD is nλ then δ = 2nπ radians, n(360°) so polarisation does not change and it cannot pass through the analyser so is removed
what occurs when white light passes through two crossed polars and a birefringent material
- white light is formed from all possible λs
- phase difference δ depends on λ
when between crossed polars:
- most λs pass through
- certain λs where OPD = nλ don’t
- these colours are removed and the resultant colour is observed
- these can be analysed using the michel-levy chart
what are extinction positons
- this occurs when the incident polarised light has a plane of polarisation parallel to one of the PVDs
- it simply passes directly along a PVD and no OPD occurs
- it is not rotated
- it will be moved by the analyser
how can we determine the sign of birefringence
- add a compensator of a known birefringence
- align both sample and compensator so that PVDs are at 45 degrees to polariser/analyser
Addition:
- if the fast axes of sample and compensator and slow axes of sample and compensator align then greater OPD, colour higher on michel-levy chart
Subtraction:
- if fast axis of sample aligns with slow axis of compensator and vice versa then lower OPD, and colour lower on michel-levy chart
are LCs birefringent, what are their PVDs
LCs are birefringent, their PVDs are para and perp. to the director
what is a smectic LC
the molecules arrange in layers
what is a chiral nematic LC
- contains a helical twist
- greater twist at higher temps
- also greater twist for shorter molecules
explain the structure of an LCD
- the director of an LC can be made to lie in a particular direction by creating grooves on a surface it is in contact with
- if a nematic LC is sandwiched between two plates with perp grooves then it twists across the sandwich and makes a twisted nematic structure
explain the on/off states of an LCD
ON: light enters through bottom polariser, twisted by nematic structure, makes it aligned with top polariser, passes through top polariser as normal, light fully transmitted
OFF: electric field applied, the molecules tend to align with the field, Freedericksz transition, molecules near plates align with grooves, molecules in middle become vertical, no twisting, no light transmission
Can a resultant voltage occur on a piezoelectric polycrystal without it being Ferroelectric,
what about a single crystal?
- If polycrystalline, the induced polarization would occur in different directions in the differently oriented grains
- this leads to zero net polarization, and
hence zero voltage - therefore to obtain a resultant voltage it must be ferroelectric and poled
- single crystals can display piezoelectricity without poling so no ferroelectricity is required
