Intersubband Absorption in InAlN/GaN SuperlatticesAmanda M. Landcastle, Colin Edmunds, Oana Malis

Department of PhysicsBy growing a superlattice of alternating Indium Aluminum Nitride (InAlN) and Gallium

Nitride (GaN) layers, the quantum properties of the structure are used to achieve

energy transitions that cannot be accessed with typical semiconducting materials,

reaching the previously inaccessible 1.5-3.0 μm range. By utilizing the energy gap

difference of the two materials, a conduction band offset (CBO) arises, forming a

quantum well with quantized energy levels obeying the fundamental laws of quantum

mechanics. The InAlN is the barrier material while the GaN is the well material. The

width of the quantum well can be varied by changing the thickness of the GaN layer,

which allows the energy transitions in the well to be tailored to the goals of the

research. These transitions are known as intersubband transitions, occurring in the

energy levels of the CBO as opposed interband transitions which occur between the

energy levels in the conduction band to the valence band. The intersubband

transitions are made more likely to occur by δ-doping with silicon to push the Fermi

level closer to the conduction band which allows for easier excitations of the electrons

into the CBO to undergo the intersubband transitions. Fourier Transform Infrared

Spectroscopy is used to measure the optical properties of the superlattice. Several

geometries and measurement techniques are used to obtain spectra which can be

analyzed to further the progress of the research.

Abstract

What are semiconductors, and why are they important?

𝑓 𝐸 =1

𝑒(𝐸−𝐸𝑓)

𝑘𝑇 + 1

Fermi function predicts the probability

of an electron existing above the Fermi

Level when T is above zero kelvin.

The valence band is filled with electrons while the conduction band is empty. In a

conductor, the electrons are free to move between the valence and conduction band.

An insulator’s valence and conduction bands have a large energy gap. With the Fermi

level located an equidistance from the two bands, the energy required for an electron

to make it past the Fermi level is too high for conduction to occur.

A semiconductor’s energy gap is smaller than an insulator’s, allowing for more

conducting electrons via thermal population, but not enough for use in advanced

technological devices.

The Fermi Level is the level

at absolute zero which the

electrons cannot be excited

past. The probability of

electrons able to be excited

past the Fermi level is

determined by the Fermi

function, which is dependent

on temperature.

Doping a semiconductor means that you add

impurities to the material in order to change the

location of the Fermi level in relation to either the

conduction band or the valence band.

We use n-type doping, which increases the

conductivity of the intrinsic semiconductor by adding

electron energy levels near the conduction band.

The electrons in these energy levels can be easily

excited into the conduction band.

δ-Doping

InAlN and GaN are both intrinsic semiconductors

with different bang gaps.

The purpose of doping the InAlN/GaN superlattice is to make the excitation of

electrons into the conduction band offset more probable.

A semiconductor is δ-doped if it is grown with Molecular Beam Epitaxy and the

doped layer is smaller than the de Broglie wavelength of the electrons.

400 600 800 1000 1200

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

4.4 nm QWs

3 nm QWs

2.2 nm QWs

Absorp

tion (

arb

. units)

energy (meV)

Transition Energy Selection

The graph to the right is a plot of transition

energies observed as the well thickness is

varied. As the well layer is grown thicker, the

transition energy associated with the nth energy

level decreases, by a factor of ~1

𝐿2.

Using the infinite potential well is a good approximation for the transition energies

observed.

This is the familiar infinite square well equation for energy levels.

𝐸𝑙 ∶ energy which depends on the shape of the band

𝑚∗ ∶ effective mass

𝐿 ∶ width of the well

n: quantum number of energy level

𝐸𝑙 =ћ2𝜋2𝑛2

2𝑚∗𝐿2

Quantum Wells in Superlattice

A superlattice of InAlN and GaN is grown.

Since they have different band gap energies,

a conduction band offset (CBO) is formed. A

quantum well comes about in the CBO, and

the quantized energy levels allow for

transitions of electrons which are inaccessible

in typical semiconducting materials.

Fermi’s golden rule is used to calculate the probability of transitions per unit time

from one energy eigenstate of a quantum system into another energy eigenstate

due to a perturbation, which is the incident light.

The system begins in an eigenstate ∣ 𝑖⟩ of a given Hamiltonian to a final state ∣ 𝑓⟩, where the initial state is the ground state and the final state is the excited state.

Intersubband Transitions

Interband transitions occur between the

conduction and valence bands, so the

transition energy is determined by the

material properties.

Electrons are either thermally excited or optically pumped to the bottom of the

conduction band and are then excited into the conduction band offset where

they interact with the intersubband transitions.

Intersubband transitions occur in the

quantized energy levels of the quantum

well, allowing access to energies that

are not dependent on the band gap

energy of the material.

Intersubband Absorption

Fermi’s Golden Rule – rate of absorption

𝛼 = ћ𝜔𝑊𝑎𝑏𝑠

𝑃

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑣𝑜𝑙𝑢𝑚𝑒

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎

P is the optical intensity in 𝑊

𝑐𝑚2

Absorption coefficient

• Purdue University Department of Physics• Dr. Oana Malis, Purdue University• Colin Edmunds, Purdue University

• National Science Foundation (NSF)• The College at Brockport: State University

of New York

Acknowledgements

Sample 052813a – InAlN – 14.8% Indium

Fourier Transform Infrared Spectroscopy is used to

find the absorption spectra for the sample. Direct

absorption measurement is used first. Photoinduced

absorption is used when electrons need to be

optically pumped in order to make more

intersubband transitions. This increases the

absorption.

Growth Scheme

Direct Absorption Method

No Gaussian or Lorentzian peak is

seen in either spectra, so no

absorption is observed.

Photoinduced Absorption Method

The doping scheme for this sample was thought to be optimal, so the fact that there was no

absorption was curious. The sample was mounted to indium film in the attempt to shift the

electromagnetic interference wave to be maximum at the quantum well surface. A simulation

of this concept is illustrated below.

The incident light undergoes total internal reflection within the sample. This leads to light

bouncing off the sides and interfering with itself. These interferences cause the ripples in the

image above. When the light waves interfere, a maximum is formed when constructive

interference occurs. Mounting the sample to indium should work because the complex index

of refraction for indium with the 2μm wavelength we are using is

ñ 2𝜇𝑚 = 2.97 + 14.5𝑖

This changes the boundary conditions and leads to a maximum at the semiconductor-metal

interface. This method worked, as seen in the spectrum above. There was absorption

observed at the energy expected. We were not able to recreate these results, but it shows

promise.

Conclusions and Future Work

The reason for InAlN/GaN not working is attributed

to inhomogeneities, referred to as InAlN nanorods,

embedded in the barrier materials of the

superlattice. This shows that the charge density

becomes localized in the nanorod, while the

superlattice remains relatively depleted. A high

charge density is needed for absorption.