THz Science & Technology Network

By Carlo Sirtori

By applying an extremely large magnetic field to break a semiconductor’s energy bands into discrete levels, researchers have shown that it is possible for terahertz quantum cascade lasers to operate at unprecedented temperatures and wavelengths.

The terahertz (THz) part of the electromagnetic spectrum, which lies between the mid-infrared and microwave regions, is increasingly important for a wide range of applications ranging from spectroscopy and imaging through to communications1. Unfortunately, it is a region that is not yet well-served by semiconductor technology and there is a lack of convenient and efficient emitters available.

Following the report of radiation emission with a frequency of a few THz in 2002 (ref. 2), the quantum cascade laser (QCL) has generated much interest as a potential solution to this problem. As QCLs are made from well-known semiconductor compounds, such as GaAs or InP, they offer the great attraction of compact, mass-producible devices based on the same fabrication technology as diode lasers and transistors.

In many ways, QCLs can be viewed as the final part of the jigsaw, providing the photonics community with a complete suite of semiconductor radiation sources that spans the entire spectrum from UV to radiofrequency. However, even with intense research efforts the highest temperature of operation of THz quantum cascade lasers has still only reached approximately -100 °C (refs 3,4). This is, without any doubt, the most important limitation and the challenge to be overcome for making these devices a practical reality.

The big question that is often asked is: “Are there any fundamental reasons that should prevent THz quantum cascade lasers from operating at room temperature?” In my opinion there are not, and this view is now corroborated by the findings reported by Aaron Wade and co-workers on page 41 in this issue5, in which laser action has been demonstrated at a record temperature of up to -50 °C. Wade et al. report lasing between 0.68 THz and 3.33 THz including 1 THz at 215 K (-58 °C) and 3 THz at 225 K (-48 °C).

It is important to note, however, that this very significant leap in the operating temperature has only been realized with the help of an extremely strong static magnetic field of about 20 T or higher. This obviously limits the direct technological impact of the results as a continuous-wave magnetic field of 20–30 T is only available in about ten labs around the world. It is hard to imagine how in the future such fields could be applied in a practical way for the realization of a commercial QCL that is compact and affordable. Yet, the results of Wade et al. are important from a fundamental point of view because they clearly indicate that THz QCLs can operate even when their photon energy is smaller than the average energy of electrons at a given temperature ( < kT).

This may be not a surprise, as THz lasers (albeit not semiconductor-based) that can operate at room temperature have existed for almost forty years. Methane optically pumped by high-power CO2 lasers or vapour water directly excited by an electrical discharge can deliver milliwatts of output power in the THz region. This being the case, why is it more difficult for a semiconductor laser to produce gain at room temperature than a molecular laser?

The catch is in the continuum. Semiconductors, like all crystalline matter, do not have discrete energy levels but the electronic structure is described by bands of energies. This holds true even for systems in which the spatial confinement has reduced degrees of freedom, such as quantum wells or wires.

The quantum cascade laser is based on two-dimensional energy bands (called also sub-bands) arising from the quantum-well confinement in one direction. In this system, electrons are free particles in a plane and their energy has a quadratic dependence on the momentum in the plane, as shown in Fig. 1a. In this representation the emitted photons correspond to vertical transitions and are indicated by the wavy arrows that connect that energy states EU and EL, typically separated by 10 meV.

Figure 1: The effect of a magnetic field on the energy band structure of a two-dimensional semiconductor.

Under electrical injection, carriers populate the upper state, EU, and reach a temperature within the sub-band that can be significantly greater than the respective lattice temperature6. Electrons, therefore, can occupy sufficiently high-energy states in the excited sub-band (the energy of an optical phonon is LO = 36 meV) to relax directly into the lower sub-band EL by emitting optical phonons (blue arrows in Fig. 1). This is an extremely efficient process that transfers carriers from the excited to the lower state, thus hindering population inversion. In other words, due to the continuum of the sub-bands, there is a temperature-activated process for the onset of the phonon emission.

Wade et al. have now demonstrated experimentally that the situation changes drastically when an intense magnetic field is applied perpendicularly to the degree of freedom of a two-dimensional electronic system. The continuum of states in the plane breaks into a series of discrete levels (Fig. 1b; Landau quantization7, 8) similar to that of quantum boxes. This phenomenon can be appreciated with an intuitive semi-classical approach, which is to imagine the electrons rotating in orbits that become smaller and smaller as the magnetic field increases9. For a field strength of 30 T the radius of the orbit of an electron is 5 nm, much smaller than the confinement provided by a quantum well (50 nm).

The separation between the Landau levels is a linear function of the applied magnetic field and therefore for a very high magnetic field, only the lower levels have to be taken into account as the excited ones are out of the characteristic energies of the system. This has a very important consequence on the behaviour of the THz system presented by Wade et al. It means that no states are available near to the onset of the optical phonon and therefore the phonon emission process is suppressed (Fig. 1c). This is an extreme case, but it essentially explains the physical reason that makes lasing possible at higher temperature — the suppression of a non-radiative phenomenon that usually fights against the creation of a population inversion.

More subtle consequences are also probably at work. The strong magnetic field shrinks the size of the electronic wavefunction within the defect at the quantum well interface, which contributes towards trapping the carrier and therefore breaks the picture of free electrons in the plane. This extra confinement of the electrons is also at the origin of the very low emission frequency of 0.7 THz achieved by Wade and colleagues, which is the lowest achieved to date with a QCL.

The results presented by Wade et al. show that the ability to create a discrete energy spectrum of levels, as exists for molecular lasers, could also help push semiconductor THz sources to enhanced operating temperatures and longer wavelengths (lower frequencies). Although high magnetic fields are one way of quantizing the energy band structure, for more practical implementations there might be other ways to achieve the same effect. One possible approach is to use three-dimensional confining potentials arising from the intersection between the device epitaxy (growth of semiconductor layers) in the vertical direction and planar technology for the lateral confinement. THz-frequency devices might be the first to see and benefit from the convergence of these two technologies.

References

1. Tonouchi, M. Nature Photon. 1, 97–105 (2007).
2. Köhler, R et al. Nature 417, 156–159 (2002).
3. Williams, B. S., Kumar, S., Hu, Q. & Reno J. L. Opt. Express 13, 3331–3339 (2005).
4. Belkin, M. et al. Opt. Express 16, 3242–3248 (2008).
5. Wade, A. et al. Nature Photon. 3, 41–45 (2009).
6. Vitiello, M. S. et al. Appl. Phys. Lett. 86, 111115 (2005).
7. Landau, L. D. & Lifshitz, E. M. Quantum Mechanics: Non-Relativistic Theory (Pergamon, London, 1959).
8. Ando, T., Fowler, A. B. & Stern, F. Rev. Mod. Phys. 54, 437–672 (1982).
9. Smirnov, D. et al. Phys. Rev. B 66, 121305 (2002).

From: Nature Photonics 3, 13 – 15 (2009)

This was posted on Tuesday, January 27th, 2009 at 15:00 and is filed under News.