1.8 Double Heterostructures

1.8 Explain how a double heterostructure works. Who are the Nobel prize winners for this invention?

A double heterostructure is a sandwich of one material between another material. It is a PIN junction, and the material of the intrinsic region of the PIN junction is a material with a smaller bandgap than the P and N regions. This structure…

  • Enables direct current injection via trapping of carriers
  • Light is generated in the intrinsic region where carriers are recombined.
  • Light is confined for a resonator feedback system as the intrinsic region layer serves as a waveguide.
  • It can be assumed that nearly all carriers recombine in the intrinsic region.

Nobel prize winners are (2000): Jack Kilby (1/2), Zhores Alferov (1/4), Herbert Kroemer (1/4)


Electronic Recombination/Generation Mechanisms (1.6, 1.7)

1.6. List and explain all the basic electronic recombination/generation mechanisms. Which one is required for lasers to operate?

  • Spontaneous Recombination
  • Stimulated Emission
  • Photon Absorption
  • Non-radiative Recombination

1.7 Describe the main ways of non-radiative recombination in semiconductor lasers/

Non-radiative recombination:

  • A conduction band electron and a valence band hole recombine without generating photons
  • Energy dissipated by heat or kinetic energy
  1. Non-radiative recombination by crystal defects, surfaces:
  • Electron and hold recombine but do not generate photon
  • Proportional to carrier density N
  • Caused by surface, point defect, interface, etc

2. Auger Recombination:

  • Energy from recombination is transferred to another electron or hole instead of photon generation
  • Proportional to carrier density N^3.
  • Energy from electron and hole is transferred to a third particle.

1.3 Advantages and disadvantages Diode Lasers have relative to gas ore solid-state lasers

1.3 List three advantages and three disadvantages diode lasers have relative to gas or solid-state lasers.

1.4 What are the most common applications of diode lasers? Can you think of any other applications that are not mentioned in the text? (Diode Lasers and Photonic Integrated Circuits 2nd Edition)

  • CD/DVD, optical mice, blu-ray
  • Fiber optic comms
  • PICs in optical networks
  • Medical, OCT
  • Remote sensing, LIDAR, gyroscopes

Lasers (Principle)

Define the necessary elements of a laser cavity.

A laser generates and amplifies light. This is achieved using an optical gain medium, a resonant optical cavity, and pumping (electrical or optical).

The material of the gain medium absorbs radiation in the desired wavelength. However, when the material is pumped by electrical or optical energy, the material is excited to a non-equilibrium energy level. In the state of non-equilibrium, the incident radiation is amplified instead of absorbed. As the non-equilibrium state electrons enter a de-excitation state, radiation is generated.

Inside the resonant cavity, standing waves or modes form at wavelengths of multiples of twice the cavity length. As the gain of a mode overcome its losses, that mode is emitted.

Very often a single mode is desired. This is achieved using the mirror design of the cavity, spectral filtering elements in the cavity, and the spectral response of the gain medium.

Types of lasers include the diode/semiconductor laser, fiber lasers, gas lasers, solid-state lasers, and dye lasers.

Diode lasers can be pumped directly using electrical current and are more efficient. Efficiencies of diode lasers are in the range of 50%.

Potential Wells and Bound Electrons

Wavefunctions describe the motion of particles such as electrons. However, electrons are usually confined by some manner of potential distributions. This is the case for atoms as well as arrays of atoms that form solids. In such cases, the wavefunction extends throughout the solid. Solving the Schroedinger’s equation analytically for such cases is incredibly complicated, even for periodically repeating lattices. One pattern that occurs however is a potential well, or a depression in potential which confines an electron. By coupling multiple wells, a periodic potential can be described that more closely resembles a periodic wavefunction in real crystals.

In an approximation, electrons in solids behave similarly to free electrons, but with an altered mass or effective mass. These electrons in solids have solutions which are described using the E-k relationship.

For a one-dimensional potential well, we can recognize three regions. Lets assume the well is 6nm in width and the height of the well is 1eV. We can find the general solutions of the potential well for each region.

General solutions to the potential well:

The potential well can have two solutions: an odd and even solution.

The energy levels associated with the wavefunctions of the potential well are then calculated.

The following matlab code further demonstrates an important concept, which is the number of allowed states in a potential well.

Wavefunctions and Uncertainty Principle

The wave or state functions describes the motion and properties of a particle, such as an electron or photon. The magnitude squared of the wave-function is the probability density of finding a particle in a volume.

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The Uncertainty Principle defines the limits of accuracy as a relationship between position and momentum.

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The expected value of an observation, such as the presence of a particle in a volume is calculated via an operator.

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The Schroedinger equation describes the motion of particles according to quantum mechanics.

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The Schroedinger equation can be separated into the time dependent and and spatially dependent forms. The time-independent, spatially dependent form solution is as follows.

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