Energy Materials - Petra Cameron

What is the Fermi level?

The energy level that has a 50% probability of being occupied at the thermal equilibrium.

In a metal at 0 K, what is the Fermi level?

The highest occupied energy level.

What does the wavevector k represent?

The momentum and direction of an electron wave.

What is the relationship between momentum and wavevector?

$$\text{p}=ħ\text{k}$$

What is the density of states (DOS)?

The number of available electronic states at a given energy.

What does density of states (DOS) tell you?

How many states exist at a particular energy.

What does the Fermi-Dirac distribution tell you?

The probability that a state is occupied by an electron.

How do you calculate the number of occupied electronic states?

Occupied states = N(E) × f(E), where N(E) is density of states and f(E) is Fermi-Dirac distribution.

What is the occupancy probability when E = EF?

f(EF) = 0.5 so the Fermi level corresponds to 50% occupancy.

What is the first Brillouin zone?

The unit cell of reciprocal space containing all unique k-values required to describe electron behaviour in a crystal.

For a 1d crystal, what is the range of k-values in the first Brillouin zone?

$-\frac{\pi}{a}\le k\le\frac{\pi}{a}$ where a is lattice spacing.

Why is the first Brillouin zone important?

It contains all unique electron wavevectors needed to describe the crystal.

What determines the number of bands in a crystal?

The number of bands is approximately equal to the number of basis orbitals in the unit cell.

What causes bands to widen?

Greater orbital overlap between neighbouring atoms.

Why do band gaps form?

Electron-nucleus interactions remove degeneracy and split energy levels.

What is a metal?

A material with partially filled bands or overlapping bands.

What is a semiconductor?

A material with a small band gap.

What is an insulator?

A material with a large band gap.

Why is graphene conductive?

Its pi and pi* bands touch at the K-point.

What is $\text{k}_{B}\text{T}$ at room temperature?

Approximately 0.026 eV

What is the band gap of silicon?

Approximately 1.1 eV

Why does silicon have a smaller band gap than diamond?

Larger atomic spacing causes less orbital overlap and less splitting.

What is a direct band gap?

A transition requiring no change in k.

What is an indirect band gap?

A transition requiring a change in k and a phonon.

Why are direct-gap materials good for LEDs?

Radiative recombination is more likely.

What is effective mass?

A measure of how carriers behave in a crystal.

What does high curvature mean?

Small effective mass and high carrier mobility.

What is a hole?

A missing electron in the valence band that behaves as a positive charge carrier.

What is photoconductivity?

An increase in conductivity caused by light-generated charge carriers.

At the Fermi level, what is the occupancy probability?

0.5

What is an intrinsic semconductor?

An undoped semiconductor

What is n-type doping?

Adding Group V dopants (e.g. phosphorus)

What is p-type doping?

Adding Group III dopants (e.g. boron)

What type of states do n-type dopants introduct?

Donor states

What type of states do p-type dopants introduce?

Acceptor states

What are the majority carriers in n-type materials?

Electrons

What are the majority carriers in p-type materials?

Holes

What happens to the Fermi level in n-type silicon?

It moves towards the conduction band

What happens to the Fermi level in p-type silicon?

It moves towards the valence band

What is the work function?

The minimum energy needed to remove an electron from the Fermi level to the vacuum level

What forms when p-type and n-type semiconductors are joined?

A depletion region

What causes the depletion region?

Diffusion and recombination of electrons and holes

What remains inside the depletion region?

Immobile ionised dopants

What creates the built-in voltage?

The electric field generated by charged dopants

What is true of the Fermi level at equilibrium in a p-n junction?

It is constant throughout the junction

Why do the bands bend in a p-n junction?

To maintain a constant Fermi level at equilibrium

What happens during forward bias?

The depletion region narrows and current increases

What happens during reverse bias?

The depletion region widens and current decreases

Why does a diode rectify current?

Forward bias lowers the barrier while reverse bias raises it

What is a BJT?

A device containing two p-n junctions

What is a MOSFET?

A transistor whose conductivity is controlled by gate voltage

Why is an n-channel MOSFET normally off?

No conducting channel exists until an inversion layer forms

What is a solar cell?

An illuminated p-n junction that converts light into electricity

What condition is needed for light absorption?

$$h\nu\ge E_{g}$$

What does the built-in field do in a solar cell?

Separates electrons and holes before recombination

What is $\text{V}_{OC}$?

Open-circuit voltage

What is $\text{I}_{SC}$?

Short-circuit current

What is the Shockley-Queisser limit?

The maximum theoretical efficiency of a single-junction solar cell

Why can low-energy photons not contribute?

They are not absorbed

Why can high-energy photons waste energy?

Excess energy is lost as heat

What is recombination?

Process where electron from conduction band falls into a hole in the valence band

What are the three major recombination mechanisms?

1. Radiative

2. Shockley-Read-Hall

3. Auger

Which recombination mechanism involves defects?

Shockley-Read-Hall recombination

Which recombination mechanism emits light?

Radiative recombination

What is the general formula of a perovskite?

$$ABX_3$$

What is an exciton?

A bound electron-hole pair

Why do excitons form in organic semiconductors?

Low dielectric constants lead to strong electron-hole attraction

Why are donor-acceptor interfaces needed?

To split excitons into free charges

What is a bulk heterojunction?

A nanoscale donor-acceptor mixture with a very large interfacial area

Why do bulk heterojunctions improve OPV performace?

They increase exciton separation and reduce recombination

What is the key LED reaction?

$$e^{-}+h^{+}\rightarrow h\nu$$

What is the solar cell equivalent reaction?

$$h\nu\rightarrow e^{-}+h^{+}$$

What is an OLED?

Organic light-emitting diode

What is a QLED?

A device using semiconductor quantum dots as light emitters