Growth of graded quantum wells for THz polaritonics

Abstract

Rectangular quantum wells have long dominated the landscape of layered nanostructures. They exhibit a rich variety of physics and can be reliably grown with techniques such as molecular beam epitaxy. Rectangular wells represent only a fraction of the possible design space, however: much less explored have been alternative structures with continuously varying potential profiles. This is not for want of applications. Parabolic quantum wells (PQWs), wells with a quadratically varying profile, have been recently identified as a potential key ingredient for terahertz (THz) polaritonic devices. The development of THz devices remains an important challenge with myriad applications that are only just beginning to be unlocked. We aim toward this important challenge by developing THz polaritonics based on PQW active regions, bringing to bear the fascinating physics of polariton quasiparticles – part light, part matter – and one of the most ubiquitous elements in physics, the harmonic oscillator.

Using non-square quantum wells comes with challenges, however. Growing these structures with molecular beam epitaxy requires time-varying flux from the effusion cells, which is difficult to produce reliably due to the slow thermal response of the cells. While this problem can sometimes be bypassed through the use of digital alloys, there are limits on the quality of material that can be produced in this way. We develop an approach for growing smoothly graded quantum wells with molecular beam epitaxy, compensating for the effusion cell’s thermal behaviour via a simple linear dynamical model. We further provide an iterative scheme to correct for any lingering errors. With this technique, we demonstrate the ability to grow smoothly graded Al(x)Ga(1−x)As PQWs for THz polaritonics, with a root-mean-square Al composition (x) error of just ±0.0018. This accuracy is achieved at the standard growth rates (0.15-0.25 nm/s) necessary for thick structures of several micrometres or more. The approach is quite generally applicable beyond Al(x)Ga(1−x)As PQWs, and could be used for other materials or composition profiles, or for other situations where precise time-dependent flux control is required.

We further study the properties of continuously graded Al(x)Ga(1−x)As PQWs grown in this manner, both theoretically and experimentally. Theoretically, we pull together existing work in the literature to build a numerical semiclassical model of quantum well absorption, which includes the multi-subband plasmonic interactions that appear at the doping levels required for THz polaritonics. This, combined with electromagnetic modelling allows us to study the design aspects of THz quantum wells relevant to polaritonic devices. We explore the possibility of studies on polariton-polariton scattering, and examine the quality of quantum well active region necessary for such studies. We further explore the possibility of new active region designs incorporating half parabolic quantum wells.

Experimentally, we probe PQWs grown with the continuous grading method, using reflection measurements in a metal-insulator-metal cavity and absorption measurements in a multipass geometry. We demonstrate robust oscillation at 2.1 THz and 3 THz for structures containing 8, 18, and 54 PQWs. Absorption at room temperature is achieved, which is as expected from a parabolic potential but would typically be impossible with square quantum wells in the THz. Linewidths below 12% of the central frequency are obtained up to 150 K in two of the samples, with a very small 3.9% linewidth obtained in one sample at 4 K. Furthermore, we show that the system correctly displays an absence of nonlinearity despite electron-electron interactions – analogous to the Kohn theorem. The high quality of these structures already opens up several new experimental vistas.