Download SAMPLE QUESTIONS_and_ANSWERS

SAMPLE QUESTIONS + Model Answer (+ approximate marking scheme)
1. (i) Electron beam lithography is an important technique for preparing nanoscale
devices both for performing measurements on nanoscale specimens and for
manufacturing devices. Describe the experimental setup and steps required for
preparing a field effect transistor from a nanowire or a carbon nanotube. [10]
Electron beam lithography (e-beam lithography) is the practice of scanning a beam of
electrons in a patterned fashion across a resist and selectively removing either exposed
or non-exposed regions of the resist. The purpose, as with photolithography, is to create
very small structures in the resist that can subsequently be transferred to the substrate
material, often by etching.
An e-beam lithography system consists of a modified scanning electron microscope
(i.e. see below). The resolution is determined by the beam width.
Experimental setup
The SEM consists of an electron gun that supplies the electrons, a condenser lens that
focuses the electron beam (i.e. the ‘spot’) onto the substrate/resist and deflectors that
allow the spot to be scanned (or ‘rastered’) over the substrate/resist. Typically the spot
position will be controlled by the deflectors which will produce a pattern under program
control.
[6]
To produce a FET from a nanotube involves patterning gold contacts from a gold film
desposited onto an insulating substrate. The nanotubes can be positioned by draping
over the substrate (typically with a nanomanipulator which is a needle moved under
piezo-electric control).
[4]
(ii) How could this setup be modified if it was required to image the nanostructure in a
transmission electron microscope ? [5]
A bit of applied thinking here – as transmission electron microscope specimens are
atomically thin (ca. 10-100nm thick) and therefore the substrate (resist) would be too
thick to observe in a TEM. Therefore it would be necessary to drill a hole in the
substrate (i.e. between the contacts !) and then drape the nanostructure between the
contacts over the whole in the substrate as in (i). The drilling can be achieved either by
electron beam lithography or by focused ion beam milling (also performed in a SEM
but using Ga+ ions as the milling medium).
[5]
(iii) Resolution in a Transmission Electron Microscope is very much greater than in an
Optical Microscope because electrons are used as an imaging medium rather than light
rays. Write down the respective equations giving the resolution for an Optical
Microscope and for a Transmission Electron Microscope. How can we maximise the
resolution of both techniques, paying close attention to all aspects of the resolution
equations. [10]
For an electron microscope the two critical equations governing resolution are the
expression for the electron wavelength (λ):
λ=
h/[2m0eV(1+eV/(2m0c2))]0.5
‐
i.e.
the
relativistic
version
where
c
is
the
speed
of
light;
e
and
m0
are
the
charge
and
rest
mass
of
the
electron
respectively
and
V
is
the
accelerating
potential
and
c
is
the
speed
of
light.
and
the
expression
for
the
minimum
resolution
which
is:
δ = 0.66 Cs1/4
λ3/4
where
δ = the smallest resolvable distance and Cs the spherical aberration coefficeint.
Essentially, there are two ways to improve the resolution (i) increase the accelerating
potential; (ii) correct Cs using a hardware aberration correction (with this, it can be tuned
to any value).
[6]
For an optical microscope
R = resolution (δ), NA = numerical aperture (FYI defined as a measure of the
acceptance angle of a lens. Higher numerical aperture means the lens gather more
diffraction orders yielding higher resolution but at the expense of depth of foc), λ
=
optical
wavelength.
The two main ways to improve the resolution of an optical microscope is to make NA
as large as possible and to use the shortest optical wavelength.
[4]
2. (i) Give a detailed explanation, referring to theory where necessary, of the analogy
between periodic atomic scale structures (think in terms of Bragg scattering behaviour)
and photonic crystals. There are one-dimensional, two-dimensional and three
dimensional photonic crystals. Can you think of analogous structures formed by atomic
scale materials ?
[12]
S ome us eful equations !
P eriodic atomic crys tals have periodic arrangements of atoms or molecules that
each represent a periodic potential to an electrons propagating through them.
Additionally, the crystal geometry dictates many of its conduction properties. For
example, Bragg diffraction conditions prohibit electron propagation in certain directions.
Additionally, gaps in energy band structure of the crystal may occur so that electrons
with certain energies are forbidden to propagate in certain directions. If the lattice
potential is strong enough, the gap might extend to all possible directions, resulting in a
complete band gap, as in a semiconductor that maintains a complete band gap
between the valance and conduction electrons.
[4]
P eriodic photonic crys tals have periodic ‘potentials’ due to lattices of macroscopic
dielectric media in place of atoms. If the dielectric constant of the materials in the crystal
are different enough, then, the absorption of light is minimal, then scattering at the
interfaces can produce many of the same phenomena for photons (i.e. light modes) as
the atomic potential does for electrons. One solution to the issue of optical control and
manipulation is thus the photonic crys tal, a low-loss periodic dielectric medium.
These can be engineered with photonic band gaps which prevent light from
propagating in certain directions with specified energies. Can get 3D Bragg scattering of
optical wavelengths.
[4]
Analogous structures to 1D photonic crystals might include nanowires or nanotubes. A
2D atomic material would include monolayer structures such as graphene. 3D atomic
cystals would include any three dimensional atomic crystal structure – e.g. Sodium
Chloride, perovskite or diamond.
[4]
(ii) The Raman effect can be summarized by the following equation:
Δν = ν0 - νs
where ν0 is the wavenumber of incident light and νs is the wavenumber of scattered
light. Explain the Stokes shift behaviour in terms of this equation with respect to a
molecule excited by a laser. How does this differ from Rayleigh Scattering and antiStokes behaviour ?
[6]
•
if
νs
>
0
(or
Stokes
shift):
the
wavenumber
of
the
scattered
light
is
less
than
that
of
the
exciting
light.
Energy
has
remained
in
the
molecule
and
the
molecule
is
in
an
excited
state.
[2]
•
if
νs
=
0
(or
Rayleigh
scatter):
the
scattered
light
has
the
same
wavenumber
as
the
incident
light
(no
energy
transfer).
Rayleigh
scattering
(after
Lord
Rayleigh)
is
applicable
to
small,
dielectric
(non‐absorbing),
spherical
without
a
particular
bound
on
particle
size
[2]
•
if
νs
<
0
or
anti‐Stokes
shift):
the
wavenumber
of
the
scattered
light
is
greater
than
that
of
the
exciting
light.
The
molecule
has
transferred
energy
to
the
scattered
light
and
was
in
an
excited
state.
[2]
(iii) The following figure is a composite spectrum including three features generally
observed in samples of Single Walled Carbon Nanotubes (SWNT) which would be
obtained using a visible Raman laser with the indicated wavelength. Explain the
significance of the three indicated features in the spectrum including any unusual
features (i.e. if any) in each of the three features.
[7]
I corresponds to the so-called “breathing mode” of the SWNT where the nanotube
expands and contracts in a breathing fashion. Can be used to characterize the diameter
of a SWNT.
[2]
II is the so-called D or “defect” band-this should not be present in a good quality carbon
nanotube sample as it indicates the presence of carbon impurities with sp3 character. [2]
III These are high energy bands (aka G bands) which are characteristic of the carbon
nanotubes and also indicate the presence of graphene-like carbon. If there are no type I
or II bands in a sample, then the sample is probably graphitic.
[3]