Operating Principles of Semiconductor Lasers

This is a continuation from the previous tutorial - the history of semiconductor lasers.

This tutorial provides a qualitative understanding of the physics behind the semiconductor laser. Most of the concepts introduced here are discussed in detail in subsequent tutorials.

Two things are required to operate a laser: (i) a gain medium that can amplify the electromagnetic radiation propagating inside it and provide the spontaneous-emission noise input and (ii) a feedback mechanism that can confine the electromagnetic field through the well-defined optical modes.

As the name itself implies, the gain medium for a semiconductor laser consists of a semiconductor material [refer to the history of semiconductor lasers tutorial].

The optical feedback is obtained using the cleaved facets that form a Fabry-Perot (FP) cavity, and the mode confinement is achieved through dielectric waveguiding.

To provide the optical gain, a semiconductor laser needs to be externally pumped, and both electrical and optical pumping techniques have been used for this purpose.

A simple, practical, and most commonly used method employs current injection through the use of a forward-biased p-n junction. Such semiconductor lasers are sometimes referred to as injection lasers or laser diodes.

p-n Junction

At the heart of a semiconductor injection laser is the p-n junction. A p-n junction is formed by bringing a p-type and an n-type semiconductor into contact with each other.

When they first come into contact, their quasi-Fermi levels do not match since the two are not in equilibrium. An equilibrium is, however, quickly established through diffusion of electrons from the n side to the p side, while the reverse occurs for holes.

These diffusing electrons and holes recombine in the junction region. Eventually a steady state is reached in such a way that further diffusion of electrons and holes is opposed by the built-in electric field across the p-n junction arising from the negatively charged acceptors on the p side and the positively charged donors on the n side.

The Fermi level is then continuous across the p-n junction, as shown in Figure 1-6 where the energy-band diagram of the p-n homojunction (junction between two similar semiconductors) is shown.

When a p-n junction is forward-biased by applying an external voltage, the built-in electric field is reduced, making possible a further diffusion of electrons and holes across the junction.

As Figure 1-6(b) shows, in a narrow depletion region both electrons and holes are present simultaneously and can recombine either radiatively or nonradiatively.

Photons of energy \(h\nu\approx{E}_\text{g}\) are emitted during radiative recombination. However, these photons can also be absorbed through a reverse process that generates electron-hole pairs.

When the external voltage exceeds a critical value, a condition known as population inversion is achieved, in which the rate of photon emission exceeds that of absorption. The p-n junction is then able to amplify the electromagnetic radiation, whose wavelength satisfies (1-2-1) [refer to the history of semiconductor lasers tutorial], and is said to exhibit optical gain.

However, for a homojunction the thickness of the region where gain is sufficiently high is very small (~0.01 μm) since there is no mechanism to confine the charge carriers.

The carrier-confinement problem is solved through the use of a p-n heterojunction. Figure 1-7 shows the energy-band diagram for a double-heterostructure laser wherein the thin p-type active region has a lower band gap compared to that of the two p-type and n-type cladding layers.

Electrons and holes can move freely to the active region under forward bias. However, once there, they cannot cross over to the other side because of the potential barrier resulting from the band-gap difference.

This allows for a substantial build-up of the electron and hole populations inside the active region, where they can recombine to produce optical gain. The width of the gain region is determined by the active-layer thickness, typically 0.1-0.3 μm.

As mentioned in the history of semiconductor lasers tutorial, it was the adoption of the heterostructure scheme that resulted in significantly lower threshold current densities (compared with a homojunction) and led to the room-temperature operation of semiconductor lasers.

Dielectric Waveguide

The successful operation of a laser requires that the generated optical field should remain confined in the vicinity of the gain region.

In double-heterostructure semiconductor lasers the optical confinement occurs by virtue of a fortunate coincidence.

The active layer with a smaller band gap also has a higher refractive index compared with that of the surrounding cladding layers (see Figure 1-2 [refer to the history of semiconductor lasers]).

Because of the index difference, the active layer in effect acts as a dielectric waveguide. The physical mechanism behind the confinement is total internal reflection, as illustrated in Figure 1-8.

When a ray traveling at an angle \(\theta\) (measured from the interface normal) hits the interface, it is reflected back if the angle \(\theta\) exceeds the critical angle given by

\[\tag{1-3-1}\theta=\sin^{-1}\frac{\mu_1}{\mu_2}\]

where \(\mu_1\) and \(\mu_2\) are the refractive indices of the cladding and active layers, respectively.

Thus, rays traveling nearly parallel to the interface are trapped and constitute the waveguide mode. A more detailed discussion of waveguide mode requires the use of Maxell's equations and will be given in later tutorials.

Recombination Mechanisms

When the current flowing through a semiconductor laser is increased, charge carriers (electrons and holes) are injected into the thin active region, where they recombine through radiative and nonradiative mechanisms.

As one may expect, nonradiative recombinations are not helpful for laser operation, and attempts are made to minimize their occurrence by controlling point defects and dislocations.

However, a nonradiative recombination mechanism, known as the Auger process, is intrinsic and becomes particularly important for long-wavelength semiconductor lasers operating at room temperature and above.

Physically speaking, during the Auger process the energy released by the electron-hole recombination is taken by a third charge carrier and is eventually lost to lattice phonons.

During a radiative recombination, the energy \(E_\text{g}\) released by the electron-hole pair appear in the form of a photon whose frequency \(\nu\) or wavelength \(\lambda\) satisfies the energy conservation relation \(E_\text{g}=h\nu=hc/\lambda\).

This can happen through two optical processes known as spontaneous emission and stimulated emission. These are shown schematically in Figure 1-9.

In the case of spontaneous emission, photons are emitted in random directions with no phase relationship among them.

Stimulated emission, by contrast, is initiated by an already existing photon. The remarkable feature is that the emitted photon matches the original photon not only in its wavelength but also in direction of propagation. It is this relationship between the incident and emitted photons that renders the light emitted by a laser coherent.

Laser Threshold

Although stimulated emission can occur as soon as current is applied to the semiconductor laser, the laser does not emit coherent light until the current exceeds a critical value, known as the threshold current (\(I_\text{th}\)).

This is so because stimulated emission has to compete against the absorption processes during which an electron-hole pair is generated at the expense of an absorbed photon. Since the electron population in the valence band generally far exceeds that of the conduction band, absorption dominates.

At a certain value of the external current, a sufficient number of electrons are present in the conduction band to make the semiconductor optically transparent. With a further increase in current, the active region of the semiconductor laser exhibits optical gain and can amplify the electromagnetic radiation passing through it.

Spontaneous emitted photons serve as the noise input for the amplification process.

However, optical gain alone is not enough to operate a laser. The other necessary ingredient is optical feedback. In semiconductor lasers it is provided by the cleaved facets that form an FP cavity.

The role of the FP cavity is twofold. First, it provides a direction selectivity for the process of stimulated emission, since only photons traveling along its axis are reflected back and forth. Second, it provides a wavelength selectivity since the feedback is strongest for wavelengths corresponding to the longitudinal modes of the FP cavity.

Because of the optical feedback, the number of photons traveling perpendicular to the facets increases when the current is large enough to satisfy the condition of net stimulated emission.

However, some photons are lost through the partially transmitting facets and some get scattered or absorbed inside the cavity. If the loss exceeds the gain, stimulated emission cannot sustain a steady supply of photons. This is precisely what happens below threshold, when the laser output consists of mainly spontaneously emitted photons.

At threshold, gain equals loss and stimulated emission begins to dominate. Over a narrow current range in the vicinity of the threshold current, the output power jumps by several orders of magnitude and the spectral width of the emitted radiation narrows considerably because of the coherent nature of stimulated emission.

In the above-threshold regime, laser output increases almost linearly with the current. Almost all electrons and holes injected into the active region now recombine through stimulated emission, and the internal quantum efficiency approaches 100%.

The performance of a semiconductor laser is governed by a large number of emission characteristics related to the static, dynamic, and spectral behavior of the light output. These are discussed in later tutorials.

The next tutorial discusses about Maxwell's equations for semiconductor lasers.