sem 2 exam 16

Question 1

What is the probability of a quantum state being occupied by an electron when E = Ef?

Answer 1

1/2 regardless of temperature

Question 2

Why is the photon absorption coefficient proportional to √(hν - Eg)?

Answer 2

Because of density of states (3D)

Question 3

For a semiconductor at the end of the derivation of the 3D density of states function, √E becomes what?

Answer 3

√E ⇒ √(E -Eg)

Question 4

How accurate is the infinite well approximation for the first 3 energy levels?

Answer 4

It’s a reasonable approximation for E1, doubtful for E2 and not valid for E3

Question 5

What is the general solution for the time independent Schrodinger equation when V(x) = 0 ?

Answer 5

ψ(x) = Asin(kx) + Bcos(kx)

Question 6

What is x when the wavefunction is continuous?

Answer 6

When ψ is continuous, x = 0.

Question 7

For a Dirac comb potential, what is potential V(x) given by at x=0 ?

Answer 7

−αδ(x)

Question 8

Why does g(E)δ(E) = n(k)δk ?

Answer 8

Because of the differential quotient.

Question 9

What are the features of the Dirac z-function?

Answer 9

|cos(ka)| has to be < 1 and therefore leads to forbidden and allowed regions known as energy gaps and bands respectively. This is characteristic of periodic solids such as semiconductors.

Question 10

What is the separation of the super lattice of quantum wells used for a quantum well laser?

Answer 10

10 nm

Question 11

How is a population inversion achieved for a quantum well laser?

Answer 11

Electrical injection of carriers traps them in the quantum wells, quantum mechanical tunnelling happens at a faster rate than recombination.

Question 12

When does lasing occur for a quantum well laser?

Answer 12

When the wells are in a suitable optical cavity with aperture.

Question 13

How do you show that a set of states cannot be cloned?

Answer 13

Demonstrate they aren’t orthogonal.

Question 14

When are two states orthogonal?

Answer 14

When their inner product is equal to zero.

Question 15

What does a CNOT gate do in terms of its input and output?

Answer 15

When |A> IS 0, B remains the same.

When |A> is 1, B is inverted. A always remains the same.

Question 16

When the input of a Hadamard gate is |0 0>, what is the output?

Answer 16

(|0 0> + |1 1>)/√2 = |β00>

Question 17

When the input of a Hadamard gate is |0 1>, what is the output?

Answer 17

(|0 1> + |1 0>)/√2 = |β01>

Question 18

When the input of a Hadamard gate is |1 0>, what is the output?

Answer 18

(|0 0> - |1 1>)/√2 = |β10>

Question 19

When the input of a hadamard gate is |1 1>, what is the output?

Answer 19

(|0 1> - |1 0>)/√2 = |β01>

Question 20

Why is reduced dimensionality preferable for optoelectronics devices in terms of the density of states?

Answer 20

In general, the number of states near the band edge increases significantly for reduced dimensionality and hence potential for better device performance.

Question 21

How can a 2D electron gas be created in a quantum well, using a GaAs/AlGaAs semiconductor heterostructure?

Answer 21

A 2D electron gas can be created at the interface between doped (n-type) and intrinsic GaAs. Therefore using n-AlGaAs/GaAs/n-AlGaAs creates a quantum well in which electrons become trapped.

Question 22

If the barrier is 300 meV, is the infinite well model more valid for electrons or holes?

Answer 22

It is more valid for heavy holes than for electrons and light holes.

Question 23

How does the dispersion relation of a free electron differ from that of a quantum well?

Answer 23

The free electron follows a path that is not quantised as the infinite square well is.

Question 24

What is a bell state?

Answer 24

A bell state is when two qubits are entangled and can be given by:

(|0 1> +|1 0>)/√2