Week 6: Advanced Semiconductor Laser Design Principles

Question 1

What do we want in a semiconductor laser when it comes to the electrons, holes, and optical mode?

Answer 1

We want the electrons and holes to be confined to increase the chance of radiative recombination and we want the optical mode to overlap with that region.

Question 2

How does a pn junction laser work? What happens to a pn junction laser as a function of temperature?

Answer 2

A pn junction laser works by creating an inversion layer so that the quasi-Fermi levels are separated by more than a band gap energy, satisfying the condition for stimulated emission. The threshold condition is satisfied when sufficient inversion, in terms of carrier concentration and distance, makes the optical gain greater than the loss.

As the temperature increases, the electron diffusion length and inversion layer increase, making it increasingly difficult to reach the threshold. The increase in temperature leads to more non-radiative recombination which then requires more current in order to reach inversion. This makes it really hard to achieve lasing at room temperature which makes simple pn junction lasers relatively uncommon.

Question 3

What happens to the index of refraction for high electron and hole concentrations? What does this mean for lasing? Is there a potential solution?

Answer 3

High electron and hole concentrations reduce the index of refraction. This makes it really difficult to confine the light to the active region. A potential solution is to include a small undoped region at the center of the junction, while still maintaining high concentrations of electrons and holes, until a good index profile is reached.

Question 4

What is a heterostructure laser?

Answer 4

It’s a laser that has a junction of two different materials with different band gap energies. It significantly improves performance over a homojunction laser.

Question 5

How does the difference in band gaps between the two materials in a heterostructure laser lead to improved performance?

Answer 5

The difference in band gap results in a discontinuity between the conduction and valence bands at the junction. These discontinuities are called band offsets and they actually act as barriers to carrier diffusion. The band offsets confine the carriers in the active regions, thus improving the performance.

Question 6

What is the relationship between the thickness of the active layer and the threshold current?

Answer 6

As you make the active layer thicker, there is less confinement. This means that the threshold current goes up so you’ll need more current to produce lasing.

Question 7

What is the relationship between electron concentration and threshold current density?

Answer 7

As you increase the electron concentration, the threshold current density will decrease.

Question 8

What happens to the heterojunction laser as temperature goes up? How could you reduce the temperature sensitivity?

Answer 8

As the temperature goes up, we increase the threshold current because we get leakage current from the unconfined carriers. Using two heterojunctions, we can get even better temperature insensitivity.

Question 9

How does the cavity length relate to the threshold current density?

Answer 9

A shorter cavity length will make the threshold current density go up.

Question 10

Describe the general structure of a double heterojunction laser. What kinds of operation can you get?

Answer 10

A double heterojunction layer is composed of a thin layer of a narrow band gap material sandwiched bewteen two larger bandgap materials. This confines both the majority and minority carriers in the active region. You can get continuous wave operation from these lasers at room temperature.

Question 11

Why do double heterojunction lasers perform better?

Answer 11

With double heterojunction lasers, both the conduction band and valence band have band discontinuities that results in confinement of the minority and majority carriers in the active region. The active region also has a larger refractive index meaning more light confinement in the active region. This is what makes for such great performance.

Question 12

What do unconfined holes and electrons cause in a double heterostructure semiconductor laser?

Answer 12

Unconfined electrons and holes create leakage current that flows across the heterojunction and is lost by non-radiative recombination as you approach the positive contact.

Question 13

How could you reduce the leakage current?

Answer 13

The leakage current can be reduced by increasing the band gap discontinuity.

Question 14

What determines how much field you have outside the barrier of a quantum well?

Answer 14

The extent of how much field you have outside the quantum well depends on the depth of the well.

Question 15

What happens to energy levels with a deeper well and/or a wider well?

Answer 15

As a well width increases, the energy levels will shift to lower energies. A deeper well will also lower the transition energies.

Question 16

What is a key point to remember about the transition energies as compared to band gap energy?

Answer 16

Because of the quantization of energy inside the quantum well, the transition energies will be larger than that of the band gap energy.

Question 17

How do you compute the total energy of the electrons and holes in the case of a laser with a quantum well?

Answer 17

E = E_n + (h_bar^2 / 2m) * (k_x^2 + k_y^2)

where E_n is the energy confined in the Z direction.

Question 18

How do you find the density of states in the quantum well? What does this tell you about the density of states in 2D?

Answer 18

The quantum well makes this a 2D problem because we model the z direction as an infinite well and the x and y direction as finite. This allows us to get the density of states.

We first fine the number of states as a function of E:

N = A * m* * E_f / pi * h_bar^2

Then we have that the density of states, g(E) = 1/A * dN(E) / dE = m* / pi*h_bar^2

This tells you that in two dimensions, the density of states is constant.

Question 19

How would you increase the density of states in a quantum well?

Answer 19

You would increase the density of states in a quantum well by making the wells thinner.

Question 20

Describe at a high level what it means to add a quantum well to the structure.

Answer 20

When you add a quantum well to the structure, you get quantized energy levels in the z direction, but in the x and y direction you can model these as free electrons and holes. This leads to a series of sub-bands.

Question 21

Why does adding a quantum well allow for higher gain?

Answer 21

You can get higher electron concentration at the bottom of an allowed band (one of the subbands from the quantized energy levels) which leads to higher gain. Essentially, you get higher carrier densities for a given energy.

Question 22

How does the density of states relate to the active layer thickness? How does efficiency relate to this?

Answer 22

The density of states is inversely proportional to the active layer thickness, L. When you have a smaller active layer, you increase the density of states which increases the efficiency.

Question 23

What is the optical confinement factor, Gamma? What happens to stimulated emission with a larger confinement factor?

Answer 23

The optical confinement factor is defined as the fraction of optical wave in the active layer. With a larger confinement factor, you get higher stimulated emission.

Question 24

What is the promise for a separate confinement heterostructure laser?

Answer 24

The promise is that we can provide separate control for carrier confinement and light confinement, and achieve both simultaneously.

Question 25

What is a multi-quantum well structure? How can this be coupled together to work?

Answer 25

This is a set of quantum wells that are separated by thin barriers. This can be coupled together because the electrons can tunnel from one side to another.

Question 26

Why is the threshold current in a multi-quantum well laser higher than for a single quantum well laser?

Answer 26

In the multi-quantum well structure, one has to first invert the lowest quantized level, which will have a higher density of states than a single quantum well. This requires greater threshold current.

Question 27

Why does the barrier height between wells need to be optimized?

Answer 27

If the barrier height between wells is too big, then the carrier injection is hard and that will drive up the threshold current. If the height is too small, then we won’t get the quantum effects, and instead the laser will behave like a double heteostructure.