PHT.301 Physics of Semiconductor Devices

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Introduction

Electrons in crystals

Intrinsic Semiconductors

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Transport

pn junctions

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Laser Diode

A laser diode is a Light Emitting Diode (LED) in an optical cavity. The optical cavity consists of two mirrors arranged so that standing waves of light can exist between the mirrors. For the standing waves, there are nodes at the surfaces of the mirrors which leads to the condition that the distance between the mirrors $L$ is an integer times half a wavelength. When the laser diode is turned on, the LED sends out light by spontaneous emission. The photons generated by spontaneous emission travel in random directions with photon energies within a few $k_BT$ of the bandgap energy of the semiconductor. Some of these photons have the right wavelength and direction to enter a cavity mode and start bouncing back and forth between the mirrors. Typically, several cavity modes become occupied with photons and these consequently cause stimulated emission. In stimulated emission, a photon stimulates a electron to fall from the conduction band to the valence band and emit a photon into the same quantum state as the initial photon. Photons in the same quantum state have the same wavelength, the same propagation vector, the same polarization, and the same phase. The rate for stimulated emission depends on the number of photons already in that cavity mode,

$$ \Gamma_{i\,\text{stimulated}} = N_{i}\Gamma_{\text{spontaneous}}.$$

Here $N_i$ is the number of photons in cavity mode $i$. The inverse of the rate, $1/\Gamma_{\text{stimulated}}$, has units of seconds and is the average time for an electron-hole pair to recombine and produce a photon in the mode $i$. When the current flowing through the diode is low, few photons are generated so the number of photons in each mode is small and the stimulated emission is not much faster than spontaneous emission. As the current increases, the number of photons that enter the cavity modes increase and stimulated emission occurs at a faster rate than spontaneous emission. This is why laser diodes have a threshold current density. There must be enough photons in the optical cavity so that stimulated emission dominates over spontaneous emission. The cavity mode with the most photons in it causes the most stimulated emission and gets the most photons to join this mode. Eventually the light output is predominantly stimulated emission from one cavity mode.

Two common types of laser diodes are the Edge-emitting laser and the Vertically Cavity Surface Emitting Laser (VCSEL).

Edge emitting laser
Edge emitting lasers usually include a double heterojunction where there is an active layer with a smaller-bandgap semiconductor between the n-doped and p-doped layers which both are larger-bandgap semiconductors. When it is forward biased electrons are injected into the conduction band of the active region and holes are injected into the valence band of the active region. These recombine and emit light. The active region is designed to have a higher index of refraction than the surrounding material so the light is guided parallel to the surface by internal reflection inside the active material like in an optical fiber. Confining the light like this is how fiber lasers achieve high gain. The mirrors that form the optical cavity can either be Distributed Bragg Reflectors (DBR) or they can just use the reflection from the cleaved surface of the crystal. In a distributed Bragg reflector, the waveguide that guides the light is modulated periodically such that there are reflections at each period of the modulation. The period is chosen so that the reflections at the laser light frequency add constructively. If the modulation of the waveguide is long enough, all of the light will be reflected. The other way to make a mirror is to cleave the crystalline semiconductor along a plane perpendicular to the direction of the waveguide. When the light reaches the cleaved surface of the semiconductor, part of the light is transmitted and part is reflected. This is called Fresnel reflection.

Components of a laser pointer

This laser pointer is an edge emitting laser.



The components of a laser pointer. The semiconducting chip is about 300 μm × 250 μm × 100 μm.



Side view of the laser diode.

Vertically Cavity Surface Emitting Laser (VCSEL)
Vertically Cavity Surface Emitting Laser emit the laser light perpendicular to the substrate. VSCELs have a layered structure with an active layer that emits the light sandwiched between two multilayer Distributed Bragg Reflectors (DBR) which act as mirrors.



Drawing of a VCSEL by Robert Fabro.

The DBRs are dielectric mirrors that are multilayers of two different semiconductors with different band gaps. The bandgaps of both of these layers is larger than the photon energy of the laser light so that the mirrors are transparent to the laser light. At every interface between the two semiconductors, some of the light is reflected and some is transmitted due to the differences in the indices of refraction of the layers. The thicknesses of the layers are chosen so that the reflections from the interfaces of light with the laser wavelength all add constructively. There are enough layers in the lower Bragg reflector to reflect all of the light. The upper Bragg reflector has fewer layers so that some light escapes vertically.

One of the DBRs is p-doped and the other is n-doped. When they are biased, electrons are injected into the conduction band of the undoped active layer and holes are injected into the valence band of the active layer. The active layer semiconductor has a smaller bandgap than the semiconductor layers that make up the mirrors so the electrons and holes get trapped in this thin active layer which is designed to be at a maximum of the light intensity of the optical cavity. The high light intensity promotes stimulated emission as the electrons recombine with the holes. The active layer can be thought of as a quantum well if it is thin enough that the separation in energy levels is comparable to the thermal energy $k_BT$.