Basics
Crystal Structures
Junctions
Finite Barrier
Radiative Recombination
Density of States
Lasers
Photonic Crystals
 Singe Crystal Growth
Contacts

Edge Emitting Lasers

Figure 1 . Schematic diagram of a Fabry-Perot laser.

Figure 1. Shows the structure of a typical edge-emitting laser. The dimensions of the active region are 200 m m in length, 2-10 m m lateral width and 0.1 m m in transverse dimension. In reality there are many different designs of edge-emitting lasers. Current flows from the p to the type semiconductor with electrons and holes being injected in the active region. A further advantage of the double heterostructure is that the large bandgap semiconductor has a lower refractive index than that in the active region giving index guiding in the transverse direction. In the plain of the active region the emission is confined by gain guiding, where the refractive index is modified by the carrier density. The formation of a stripe contact separated by a semi-insulating regions of proton bombarded semiconductor allows the current to flow through a restricted portion of the active region. This also aid the optical confinement in the plane of the active region.

We have seen in the last section that p-n junctions can be used to create a laser. The current required to achieve lasing is enormous. This is because there is in defined region for radiative recombination to occur. Electrons and hole can just drift through the junction without recombining. A more efficient solution is to use heterostructures and double heterostructures.

A heterostructure, as the name suggests uses to different types of semiconductor with one with a larger bandgap than the other. When the two semiconductors are brought together potential barriers are formed which can confine the electrons and holes. The situation is further improved in the double heterostructure.

Figure 2 . Bandedge diagram of a NpP AlGaAs/GaAs/AlGaAs heterostructure.

Figure 2. a) shows a NpP double heterostructure, (the capital letters represent the larger bandgap semiconductors). In this case for AlGaAs/GaAs/AlGaAs in equilibrium. The Fermi level is constant across the junction and causes the band profile to bend as shown.

In Figure 2. b), the double heterostructure has been forward biased causing an injection of electrons and holes into the device, the depletion region is reduced and the bands of the N-type AlGaAs shift upwards. When the voltage is sufficient, the quasi-Fermi level for the N-type material is at the same energy and the electrons can overcome the potential barrier D E _c and flow into the p-GaAs region where they are confined by the lower bandgap material. Similarly, holes flow in from the P-type AlGaAs to the p-GaAs valence band. The electrons and holes are confined where they can combine radiatively.

Population inversion is not enough to create a laser. In order for stimulated emission to become significant, the light must interact with the electrons in the conduction band. This is achieved by creating a resonant cavity in which the light is reflected back and forth many times before leaving the cavity. If the gain equals loss, lasing will occur.

We can analyses qualitatively analyse the loss processes and calculate the minimum gain as well as the resonant cavity conditions.

The design of the cavity structures for modern heterostructure lasers can be much more complicated incorporating more than one set of cladding layers to confine the carriers (Separate Confinement Heterostructure SCH) or GRaded-INdex Separate Confinement Heterostructures (GRINSCH). Quantum well and Multiple Quantum Well (MQW) active regions have superseded bulk active-regions because of the advantages that they offer. A quantum well is formed when the width of the active region of the laser becomes comparable with the De-Broglie wavelength, (approx. 100 Å). In this situation, the electron states are no longer quasi-continuous but become separated until only a few states lie within the well. The width of the well determines the number and separation of the energy levels within the well, thus the allowed energy transitions. Radiative recombination in the quantum well is predominantly from the first energy level in the conduction band to the first energy level in the heavy-hole valence band. Therefore, the separation of the energy levels can be tailored by careful design of the well width. Another advantage of quantum well lasers is that the temperature dependence of the intrinsic threshold current (i.e. only including properties that are intrinsic to the gain medium.) is linear with temperature. ^[] Well designed quantum well lasers have low threshold currents and are very reliable with estimated lifetimes of greater than 10 ⁶ hours.

Figure 3. Wave propagation through the semiconductor cavity. An incident wave of amplitude is partially transmitted with ratio t ₁ and the right hand facet of the cavity the amplitude has attenuated exponentially and this amplitude is transmitted with ratio t ₂ . Subsequent reflections from the ends of the cavity are summed at the right hand facet from which the threshold conditions can be calculated.

Consider a semiconductor laser cavity of length L with a plane wave with complex propagation constant

and amplitude E incident on the left hand side of the cavity. The ratio of transmitted to incident light is t ₁ and the ratio of transmitted to incident fields at the left is taken as t ₂ . The ratio of reflected to incident fields with the optical cavity is r ₁ exp( i q ₁ ) at the left-hand mirror and r ₂ exp( i q ₂ ) at the right-hand mirror. For a low loss medium, the phase shifts q ₁ and q ₂ are small and are generally neglected.

Without time dependence, the plane wave electric field is such that E _x is t _i E _i at the first transmition boundary t ₁ E _i exp( - K L ) just inside the right boundary. The first portion of the field transmitted at the right boundary is t ₁ t ₂ E _i exp( - K L ). The next portion of the wave transmitted is at the right boundary becomes t ₁ t ₂ r ₁ r ₂ E _i exp( -3 K L ) and so on. Addition of these transmitted fields gives:

The sum is a geometric progression which permits the last equation to be written as

When the denominator of the last equation tends to zero, the condition of a finite transmitted wave E _t with zero E _i is obtained, which is the condition for oscillation. Therefore the oscillation condition is reached when

The substituting the term for K defined above and remembering that k ₀ =2 p / l ₀ and also k = a l ₀ /4 p into the resonance condition we obtain:

The absorption term has been written as the difference between the gain and the losses a _i . The condition for oscillation represents a wave making a round trip of 2L inside the cavity to the starting plane with the same amplitude and phase, within a multiple of 2 p . The amplitude condition is:

This more usually written,

where R = R ₁ = r ₁ r ₁ ^* = R ₂ = r ₂ r ₂ ^* is the power reflectivity. For cleaved semiconductor facets in GaAs R~0.3. An additional factor which is often included is the optical confinement factor G which measures the ratio of the emission mode within the active region. For bulk edge emitting lasers this is close to unity but for quantum well lasers it is considerably smaller (about 0.1).

The phase condition becomes:

which reduces to

A resonance occurs when an integer number of half-wavelength l ₀ will fit into the cavity.

Figure 4. Schematic laser cavity showing the first three modes.

For example in a GaAs cavity of 200 m m in length there will be around 1600 modes. The longitudinal mode separation is given by differentiating

(2)

For adjacent modes, q=-1 and the substituting equation (1).

(3)

To a first approximation, d n /d l is small therefore

(4)

with L>> l the mode spacing is rather small and many modes will fit into the cavity of the laser. The diagram shows the emission spectra of an edge emitting laser just below threshold. The closely space modes are superimposed on the spontaneous emission profile. As the current is increased to just above threshold one lasing mode becomes dominant.

Figure 5. Emission spectra of an edge-emitting laser below threshold and above.

Since the spontaneous emission spectrum is rather broad, several modes compete to become the dominant lasing mode and this mode can switch or mode hop while operating. This characteristic is most undesirable in lasers for telecommunications.

Vertical Cavity Surface Emitting Lasers (VCSELs)

The vertical cavity surface emitting laser has many potential advantages over the edge-emitting lasers. Its design allows the chips to be manufactured and tested on a single wafer. Large arrays of devices can be created exploiting methods such as 'flip' chip optical interconnects and optical neural network applications to become possible. In the telecommunications industry, the VCSEL's uniform, single mode beam profile is desirable for coupling into optical fibres. However, concomitent with these advantages come a number of problems particularly in the fabrication and operation at high powers. In this section, we look at the structure and operation of these devices and discuss the problems facing the designer of such devices.

The earliest VCSEL was reported in 1965 by Melngailis ^[1,2] . It consisted of a n ⁺ pp ⁺ junction of InSb. When cooled to 10 K and subjected to a magnetic field to confine the carriers, the device emitted coherent radiation at a wavelength of around 5.2 m m. Later, other groups reported on the grating surface emission ^[3,4] , Near infra-red emission close to telecommunications wavelength of 1.5 m m was achieved by Iga, Soda, et al in 1979 ^[4] at the Tokyo Institute of Technology. These early VCSEL devices had metallic mirrors with resulting high threshold current densities (44 kAcm ^-2 ) and were cooled using liquid Nitrogen. Epitaxial mirrors for GaAs/AlGaAs VCSELs were pioneered in 1983 ^[5] , with the pulsed room temperatures VCSELs being produced in the laboratory one year later ^[6] . Reduction in the threshold current density was connected with reduction in the active volume of the cavity. Today, GaAs/AlGaAs VCSELs with oxide current confinement have threshold currents as low as 40 m A. ^[7]

Structure

There are many designs of VCSEL structure however, they all have certain common aspects in common. The cavity length of VCSELs is very short typically 1-3 wavelengths of the emitted light. As a result, in a single pass of the cavity, a photon has a small chance of a triggering a stimulated emission event at low carrier densities. Therefore, VCSELs require highly reflective mirrors to be efficient. In edge-emitting lasers, the reflectivity of the facets is about 30%. For VCSELs, the reflectivity required for low threshold currents is greater than 99.9%. Such a high reflectivtiy can not be acheived by the use of metalic mirrors. VCSELs make use Distributed Bragg Reflectors. (DBRs). These are formed by laying down alternating layers of semiconductor or dielectric materials with a difference in refractive index. At the dispersion minima for optical fibres, semiconductor materials used for DBRs have a small difference in refractive index therefore many periods are required. Since the DBR layers also carry the current in the device, more layers increase the resistance of the device therefore discipation of heat and growth may become a problem if the device is poorly designed. Some designs are shown below showing the evolution VCSELs:

(a) Metalic Reflector VCSEL	(b) Etched Well VCSEL
(c) Air Post VCSEL	(d) Burried Regrowth VCSEL

Cavity Issues

Today, most VCSEL devices employ quantum wells within the cavity. By depositing a thin layer of semiconductor with a slightly smaller band gap, one can not only define a region for recombination to occur, one can control over the optical properties of the device. Discrete energy levels are formed in the conduction and valence bands. Transitions from the conduction band to valence band energy levels occur from states that have the same value of n. Say, CC1-HH1 or CC1-LH1. The power obtained from a single quantum well is low. Multiple quantum wells may be grown within the cavity to increase power obtained. The position of  the quantum wells is crucial if one is to maximise the gain of the device. Consider a standing wave in a cavity, with maximum amplitude 2P _av at the anti-nodes and a spatially varying gain g(z), then the effective gain is given by:

If we consider the case of a quantum well structure, where the gain medium is placed at a standing wave anti-node.

Distributed Bragg Reflectors (DBRs)

The reduced cavity length in VCSELs and the addition of quantum wells significantly reduces the probability of stimulated emission in a single pass of the cavity. The light within the cavity must be reflected back into the cavity many more times than with a Fabry Perot laser. The average time the photons spend within the cavity is known as the photon lifetime. The reflectivity of the mirrors must be very high to increase the photon lifetime and thus the time of interaction with the excited electron states. As an example, we obtain an estimate of the reflectivity that is required for these mirrors, we can apply some optimistic values to the gain threshold condition for a single quantum well device. Threshold gain occurs where the optical gain equals the optical loss.

Expressed in terms of the gain:

Where a is the absorption coefficient, L _QW and L _cav are the lengths of the gain region, and the quantum well respectively. R1 and R2 are the mirror reflectivities. Assuming an ideal device with no absorption. A final liberty will be to let R ₁ = R ₂ =R. Using a best case gain of 1000cm ^-1 give a mirror reflectivity of 99.95%. Metallic mirrors are limited to a reflectivity of ~98% and so for such small active regions are useless. Dielectric materials and semiconductors have a very low absorption coefficient for photons with energies below the bandgap energy of the material. If two dielectric materials, with a differing refractive index are placed together to form a junction, light will be reflected at the discontinuity. The amount of light reflected off one such boundary is small. However, if layers of alternating semiconductor or dielectric are stacked in a periodically, each layer with an optical thickness l /4n, the reflections from each of the boundaries will be added in phase to produce a large reflection coefficient. The number of layers required to produce a highly reflective mirror at a particular wavelength is determined by the difference in the refractive index of the contrasting materials. Also to be considered is the lattice constant of the materials, which must be matched within about one percent of the boundaries they are deposited, to avoid failure due to strain effects. Given the refractive index of the substrate n _s and surrounding material (usually air) n ₀ as well as the refractive indices of the contrasting semiconductors n ₁ , n ₂ for a given number of periods m the reflectivity is given by:

Mirrors for long-wavelength devices must be designed carefully, arranging a number of parameters. The most important considerations relate to the choice of materials used to fabricate the Bragg layers. These must be grown using materials that lattice-match to the material of the device cavity. The traditional choice of material for long wavelength devices has been GaAsInP/InP. However the contrast ratio between these two materials is very low. Therefore, a large number of alternating layers is required to achieve the high reflectivities demanded in VCSEL devices. Each layer of semiconductor increases the resistance of the device and raises the threshold current so it is important to minimise the number of layers required. Growing such Bragg reflectors puts considerable demands on the grower and makes for sporadic reliability. Highly reflective mirrors can also be fabricated from dielectric materials. Materials in common use are ZnSe/MgF and Si/SiO ₂ .While dielectrics have a high refractive index contrast and can be deposited using low-temperature techniques they do not conduct an electric current. In addition, they are, in general, poor conductors of heat, an important consideration. Britney considers calculation of the reflectivity using transfer matrices here.

Current Confinement

As well as reducing the dimensions of the cavity one can reduce the threshold current of a VCSEL device by limiting the cross-sectional area in which gain occurs. There are a number of methods currently used in VCSELs.
A simple method is to etch a pillar down to the active layer. The large difference in refractive index between the air and device material also act to guide the light emitted. The problemw with this type of structure are the loss of carriers due to surface recombination at the sidewalls and poor dissipation of heat from the laser cavity.
Another technique for current confinement is ion implantation. By selectively implanting ions into a semiconductor it can be turned into an insulating material. Protons are most often used, however other ion species including F ⁺ , O ⁺ , N ⁺ and H ⁺ have been tried.
The bombarding of semiconductor with ions tends to damages the crystal structure of the implanted material and so it must be used with caution within close proximity to the active layer.

The formation of an insulating apeture of aluminium oxide between the cavity layer and the one of the Bragg reflectors . This starts as a layer of AlGaAs. In a steam environment of 350deg C to 500deg C the AlGaAs is converted into an oxide layer. The rate of formation of the oxide layer is proportional to the content of Al in the material; thus the oxide forms first in those layers with the highest aluminium content. The oxide layer has a low refractive index compared with the semiconductor and thus also acts as a waveguide for the emitted light. Much research has concentrated on lateral oxidation for use with near infrared devices; A 1.5 m m cw VCSEL was announced by Their device consisted of a InGaAsP-InP active region and mirrors of AlGaAs/GaAs and GaAs/AlAs bonded by wafer fusion.

Optical Power and Differential Quantum Efficiency

The optical output power is

where h depends on two factors: (1) the injection current efficiency accounting for the fraction of injected carriers contributing to the emission process (some the carriers can recombine in the undoped confinement regions where the carriers do not interact with the optical field), and the (2) the optical efficiency accounting for the fraction of generated photons that are transmitted out of the cavity. Note that the threshold current depends on the injection current as well as on the junction temperature T _jct . The differential quantum efficiency is then current dependent:

We see that h (I) _ext can be negative if di _th /di>1. The light output P _out vs. the injection current will have a negative slope.