The numbers in square brackets in the right-hand margin indicate a provisional allocation of
maximum possible marks for different parts of each question.
The following may be assumed, if required:
Speed of light in vacuo c 2.998 × 108 m s-1
Planck’s constant h 6.626 × 10-34 m2 kg s-1 (≡ J s)
Boltzmann’s constant k 1.381 × 10-23 m2 kg s-2 K-1 (≡ J K-1)
Elementary charge e 1.602 × 10-19 C
Electron volt unit eV 1.602 × 10-19 J
Vacuum permittivity e
0 8.854 × 10-12 m-3 kg-1 s4 A2 (≡ F m-1)
PHAS0058/2020 CONTINUED
1
1.
(a) Draw an equivalent circuit for an organic light-emitting diode (OLED), that accounts for
both the capacitive component (i.e. the fact the active layer is sandwiched between two
electrodes in a planar sandwich structure) and the resistive component of the active layer,
and of a resistive component due to the contacts. [3]
(b) An OLED is characterised by the following properties: active area A = 4 mm2, thickness of
the active layer t = 150 nm, and relative dielectric constant of the active layer ϵ = 3. This
OLED is biased through an indium-tin oxide (ITO) connection with resistance R = 100 Ω , turnon
voltage Von = 4.0 V. In addition, it is known that the OLED carries a current density of
75 mA/cm2 when operated at a voltage V = 7 V. It is known that the anode and cathode
injection barriers at such operating voltage can be described as a resistance of 50 Ω for each
electrode. For such an operating condition answer the following questions:
i. Give the relevant values of the elements of the equivalent circuit of part (a)
above. [2]
ii. Give the maximum bandwidth (at -3 dB) of the device. [3]
iii. State if this value is realistic and acceptable. Provide a justification for your
answer. [1]
iv. State which device design parameters could be changed to increase this
bandwidth by at least two orders of magnitude, and which alteration would not
be effective to this end. Provide a justification for your answer. [4]
v. State if the effective strategies in point iv) above are compatible with solution
processing/patterning of the active layers (in particular with reference to the
use of ink-jet printing of the active layers). [1]
vi. Estimate the maximum bit transmission rate that could be achieved assuming
that in addition to the alterations to the device structures a factor of 100
increment in speed can be achieved via signal recovery methods and algorithms
designed to reduce the bit error rate (BER). [1]
vii. State which changes to the diode’s operating conditions (namely voltage and
current density) would be necessary to ensure similar light outputs, under the
changed conditions, and if these novel operating conditions are realistically
achievable. [3]
PHAS0058/2020 CONTINUED
2
2.
a) Derive a mathematical expression for the temporal dependence of the intensity of
photoluminescence emission of a fluorescent organic semiconductor following an impulsive
laser excitation, assuming that the decay mechanism is monomolecular with intrinsic
radiative rate constant kr, and in the presence of non-radiative decay channels that can be
described by an overall non-radiative rate knr. Then calculate the photoluminescence
quantum efficiency as a function of kr and knr. [4]
(b) Derive a mathematical expression for the temporal dependence of the intensity of
photoluminescence emission of a fluorescent organic semiconductor (A) following an
impulsive laser excitation, assuming again that the decay mechanism is monomolecular with
intrinsic radiative rate constant kr, but in the presence of the same non-radiative decay
channels with non-radiative rate knr (as above) and also of energy transfer (with rate kET) to a
material (B). Then calculate the photoluminescence quantum efficiency as a function of kr,
knr and kET for emission of material A only. [1]
(c) Two luminescent materials, A and B, emit in non-overlapping spectral regions of the
visible spectrum with the photoluminescence (PL) of material B being at longer wavelengths
with respect to that of material A (in either thin film or solution). Thin films of A emit with
photoluminescence quantum yield (PLQY) “#= 30 % and spectral distribution PLA. Dilute
solutions of B in toluene emit with spectrum PLB and quantum yield “$ = 95 %. When
casting a thin film of a 0.1% (by weight) blend of B in A (hint: you can safely consider this a
“dilute solid solution” of B in A), the total PLQY (i.e. due to emission by both materials) is
“$%&'( = 43 %, and the overall emission spectrum (PLBlend) is a linear combination of PLA and
PLB. The temporal decay of PLA following impulsive excitation is monoexponential with time
constant )#*’&+,= 3 ns, whereas the temporal decay of the PLA component of PLBlend has a
time constant )#*$%&'( = 2.4 ns.
Derive an expression for the energy transfer efficiency (defined as the number of excitons
transferred from A to B per unit exciton initially generated on A by the impulsive excitation)
as a function of )#*’&+, and )#*$%&'(. Use this expression to calculate the numerical value of
the transfer efficiency for the case given above. [4]
PHAS0058/2020 CONTINUED
3
(d) State if the concentration of 0.1 wt% in the blend above is sufficiently dilute to suppress
all aggregation quenching and provide a quantitative, numerical justification, derived from
the numbers above for your conclusion. [3]
PHAS0058/2020 CONTINUED
4
3.
(a) A molecule is characterised by a perfectly spherical shape. State if it is possible that a
large ensemble of such molecules displays LC behaviour. Justify your answer. [2]
(b) An X-ray diffraction experiment of a liquid crystal (LC) sample has returned the diffraction
pattern depicted in figure 1 below with the outer (partial) halo occurring at ‘inverse distance’
q1= 6.28 Å-1 from the centre of the diffractogram and the inner points at “inverse distance”
q2 = 0.1256 Å-1 from the centre of the diffractogram. State if the mesogens responsible for
this diffractogram can be classified as calamitic or else. In addition, give the name of the LC
phase that can be inferred from such details, and a pictorial representation of the molecular
ordering. Also calculate the dimensions of the LC molecule. [6]
(c) A liquid crystal phase is constituted by domains in each of which the mesogens are
isotropically distributed with respect to the azimuthal angle φ, but perfectly oriented at a colatitude
angle ϑ0= ./6, as measured with respect to the vertical axis of the considered
reference frame. First, draw a sketch of the mesogens’ spatial distribution. Also give a
quantitative expression for the distribution function as a function of both ϑ and φ. Then,
assuming that all domains are identical, and after giving the general integral expression of
the order parameter S, write the equation needed to calculate the order parameter for this
specific system. Then calculate the value of the expression. [7]
Figure 1
PHAS0058/2020 CONTINUED
5
4.
(a) State the difference between the ideal classes of ferroelectrics undergoing “displacive”
and “order-disorder” transitions. [2]
(b) State what is the macroscopic order parameter for ferroelectrics in Landau’s theory and
give a quantitative definition. [2]
(c) Calculate the polarisation volume density arising as a result of the displacements
indicated for the crystal, schematically indicated (as a two-dimensional projection) in the
image below and undergoing a transition from cubic to tetragonal structure (represented on
the left- and right-hand sides in the figure below, respectively). Hint: this can be considered
a model for barium titanate – black filled circles represent Ba2+, white circles O2-, and the
grey central circle Ti4+ ions. [6]
(d) A graphene layer is to be used as hole-injection contact in an organic light-emitting diode
which has an emitter with a highest occupied molecular orbital lying 5.2 34 below the
vacuum level. Assume the work function of pristine graphene to be ” = 4.6 34. Determine
the type of extrinsic doping and the carrier concentration (number density) of the graphene
sheet that is necessary to achieve to make this hole-injecting contact ohmic. State if the
obtained value is reasonable, and justify your answer in relation to the value of Avogadro’s
number, under the hypothesis that the density of graphene is comparable to that of water.
[5]
9 pm
9 pm
6 pm 6 pm
6 pm
-2
-2
-2
-2 -2
+2
+2 +2
+2
+4
0.398 nm 0.403 nm 0.398 nm
0.398 nm
END OF PAPER
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