# PHYSICS QUESTIONS

graduate2022

PX4221/PXT126

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CARDIFF UNIVERSITY EXAMINATION PAPER

Academic Year:

2016-2017

Examination Period:

Spring

Examination Paper Number:

PX4221/PXT126

Examination Paper Title:

Low Dimensional Semiconductor Devices

Duration:

2 Hours

Do not turn this page over until instructed to do so by the Senior Invigilator Structure of Examination Paper: There are 5 pages. There are four questions in total. There are no appendices. The maximum mark for the examination paper is 60 (80% of the module mark) and the mark obtainable for a question or part of a question is shown in brackets alongside the question. Students to be provided with: The following items of stationery are to be provided: 1 answer book. The following books are to be provided: Mathematical Formulae and Physical Constants. Instructions to Students: Answer THREE questions. If additional questions are attempted be clear which should be marked, otherwise only the first three written answers will be marked

Calculators which have been pre-programmed and calculators with an alphabetical keyboard are not permitted in any examinations.

The use of translation dictionaries between English or Welsh and a foreign language bearing an appropriate departmental stamp is permitted in this examination.

PX4221/PXT126

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1. (a) With the aid of an annotated sketch describe the growth technique known as Molecular Beam Epitaxy (MBE). [6]

Briefly describe how this growth technique has been used to grow Stranski-Krastanov

quantum dot nanostructures [2]

Metal Organic Chemical Vapor Deposition (MOCVD) is an alternative technique for growing

epitaxial material. What is the principal advantage of MOCVD over MBE? [1]

(b) Figure 1 below shows a shutter sequence for a III-V MBE reactor, where 1 denotes an open

shutter, and 0 denotes a closed shutter.

Sketch the conduction band and valence band edges of the heterostructure material

produced by this shutter sequence, also annotating the material layers produced.

(Assume non-degenerate doping such that Ef is at the conduction band edge and valence

band edge for n and p type doping respectively, and assume a growth rate of 1µm/hr). [5]

Figure 1. Molecular Beam Epitaxy (MBE) shutter sequence for

an active device layer growth

What might this structure be used for when a suitable voltage is applied? [1]

Assuming the material quality is good, how might you increase the efficiency of such a

device? [1]

If the barrier material is comprised of ln0.7Ga0.3As, estimate using Vegard’s law what the turn

on voltage would be for such a device. [4]

Note :

Bandgap (RT) Eg (InAs) = 0.36eV, Eg (GaAs) = 1.42eV

PX4221/PXT126

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2. (a) Assuming Anderson’s rule and Vegard’s law calculate the depth of the confining potential in meV, for holes in the valence band of a InAs/InxGa1-xAs multi QW structure where x=0.5. [5]

State whether electron and hole confinement is within the InAs or InGaAs layers, and hence

deduce what type of structure/band alignment this is. [2]

Suggest why this structure might be difficult to grow experimentally. [1]

(b) A Ga0.47In0.53As quantum well laser is designed to emit at 1.55µm at room temperature.

Using an infinite barrier approximation, where the energies of the confined states (𝐸𝑛) of a

particle of mass 𝑚∗ is given by

𝐸𝑛 = ℏ2𝑛2𝜋2

2𝑚∗𝐿2

where 𝑚∗ is the carrier effective mass, show that the width of the quantum well (L) is of the

order of 14nm. [4]

(c) With the aid of suitably defined equations and/or annotated sketches, explain how the

classical Hall effect at low field can be used to deduce the carrier density of a semiconductor

two dimensional electron gas (2DEG) sample. [5]

Describe what happens to the Hall voltage when the field is raised above the quantum limit

(𝜔𝑐𝜏𝑖 > 1), where 𝜔𝑐 is the cyclotron frequency and 𝜏𝑖 is the quantum lifetime. [3]

Note :

Bandgap Eg Eg (InAs) = 0.36eV, Eg (GaAs) = 1.42eV

Electron affinity () (InAs) =4.90eV, (GaAs) =4.07eV,

Electron effective mass (Ga0.47In0.53As) 𝑚𝑒 ∗ = 0.041𝑚0

Heavy hole effective mass (Ga0.47In0.53As) 𝑚ℎℎ ∗ = 0.470𝑚0

Rest mass of the electron 𝑚0 = 9.1x10 -31 kg

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3. (a) Figure 2 shows an idealised schematic of a Photoluminescence (PL) and a Photoluminescence Excitation (PLE) spectrum at low temperature (4K), from a GaAs/AlGaAs multi QW (MQW)

heterostructure. Assuming the excitation power is low, and assuming the infinite well

approximation, where the confinement energy (𝐸𝑛) is given by

𝐸𝑛 = ℏ2𝑛2𝜋2

2𝑚∗𝐿2

where 𝐿 is the width of the well, and 𝑚∗ is the carrier mass, estimate;

(i) the width of the well in nm [6]

(ii) the exciton binding energy in the well [4]

With reasoning, state whether this calculated well width would be an upper or lower limit to

the well width in a real GaAs/AlGaAs MQW. [2]

This MQW structure is doped. If the material is high quality what evidence indicates doping

in Figure 2, and what is the approximate Fermi energy in meV from the bottom of the first

confined sub-band of the well? [3]

Figure 2. Idealised schematic PL and PLE spectra from a

GaAs/AlGaAs multi quantum well (MQW) structure

(b) Sketch the conduction band profile of a light emitting device that uses intersubband

transitions. Briefly describe the operating principle and show on your sketch the optical

transition (either absorption OR emission). [5]

Note :

Rest mass of the electron 𝑚0 = 9.1x10 -31 kg

Electron effective mass (GaAs) 𝑚𝑒 ∗ = 0.067 m0

Heavy hole effective mass (GaAs) 𝑚ℎℎ ∗ = 0.450 m0.

Bandgap (Eg) GaAs (4K) = 1.519eV

PX4221

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4. (a) The energy states of Landau levels are given by

𝐸 = 𝐸𝑛 + (𝑛 + 1

2 )ℏ𝜔𝑐

where 𝜔𝑐 is the cyclotron frequency.

Using this and the 2D density of states given by

𝑔(𝐸)𝑑𝐸 = 𝑚∗

𝜋ℏ2 𝑑𝐸

where 𝑚∗ is the carrier effective mass, deduce the degeneracy of a Landau Level. [3]

Sketch these Landau levels on a graph of number n(E) verses energy (E), and indicate the

position of the Fermi Energy for a filling factor of 8 [4]

(b) Sketch the band diagram for a heterojunction between p-type AlGaAs and n-type GaAs

showing that this can trap a (two-dimensional) hole gas at the interface. [5]

Why would carriers in such a two dimensional system have significantly higher mobility than

bulk doped material? [1]

(c) Given that the density of states in one dimension is

𝑔(𝐸)𝑑𝐸 = 2

ℎ𝑣 =

1

𝜋ℏ √ 2𝑚∗

𝐸

where 𝑣 is the carrier velocity, consider the current through a 1D conductor between two

reservoirs of charge carriers. Demonstrate that conductance is quantised when the channel

length (l) is much smaller than the ballistic length (). [6]

Calculate the quantum unit of resistance from the ground state of this expression (n=1) [1]

Note :

Electron charge is 1.619x10-19 C, Planck’s constant ℎ=6.62x10-34 m2 kg/s,