Quantum-cascade lasers (QCLs) are semiconductor lasers that emit in the mid- to far-infrared portion of the electromagnetic spectrum and were first demonstrated by Jérôme Faist, Federico Capasso, Deborah Sivco, Carlo Sirtori, Albert Hutchinson, and Alfred Cho at Bell Laboratories in 1994. Unlike typical interband semiconductor lasers that emit electromagnetic radiation through the recombination of electron–hole pairs across the material band gap, QCLs are unipolar, and laser emission is achieved through the use of intersubband transitions in a repeated stack of semiconductor multiple quantum well heterostructures, an idea first proposed in the article "Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice" by R. F. Kazarinov and R. A. Suris in 1971.
Intersubband vs. interband transitions
Within a bulk semiconductor crystal, electrons may occupy states in one of two continuous energy bands — the valence band, which is heavily populated with low energy electrons and the conduction band, which is sparsely populated with high energy electrons. The two energy bands are separated by an energy band gap in which there are no permitted states available for electrons to occupy. Conventional semiconductor laser diodes generate light by a single photon being emitted when a high energy electron in the conduction band recombines with a hole in the valence band. The energy of the photon and hence the emission wavelength of laser diodes is therefore determined by the band gap of the material system used. A QCL however does not use bulk semiconductor materials in its optically active region. Instead, it consists of a periodic series of thin layers of varying material composition forming a superlattice. The superlattice introduces a varying electric potential across the length of the device, leading to spatially confined electron wavefunctions in quantum wells over the length of the device. This is referred to as multiple quantum well confinement and leads to the splitting of the band of permitted energies into a number of discrete electronic subbands. By suitable design of the layer thicknesses it is possible to engineer a population inversion between two subbands in the system which is required in order to achieve laser emission. Because the position of the energy levels in the system is primarily determined by the layer thicknesses and not the material, it is possible to tune the emission wavelength of QCLs over a wide range in the same material system.
Additionally, in semiconductor laser diodes, electrons and holes are annihilated after recombining across the band gap and can play no further part in photon generation. However, in a unipolar QCL, once an electron has undergone an intersubband transition and emitted a photon in one period of the superlattice, it can tunnel into the next period of the structure where another photon can be emitted. This process of a single electron causing the emission of multiple photons as it traverses through the QCL structure gives rise to the name cascade and makes a quantum efficiency of greater than unity possible which leads to higher output powers than semiconductor laser diodes.
Operating principles
Rate equations
QCLs are typically based upon a three-level system. Assuming the formation of the wavefunctions is a fast process compared to the scattering between states, the time independent solutions to the Schrödinger equation may be applied and the system can be modelled using rate equations. Each subband contains a number of electrons n i {\displaystyle n_{i}} (where i {\displaystyle i} is the subband index) which scatter between levels with a lifetime τ i f {\displaystyle \tau _{if}} (reciprocal of the average intersubband scattering rate W i f {\displaystyle W_{if}} ), where i {\displaystyle i} and f {\displaystyle f} are the initial and final subband indices. Assuming that no other subbands are populated, the rate equations for the three level lasers are given by:
d n 3 d t = I i n + n 1 τ 13 + n 2 τ 23 − n 3 τ 31 − n 3 τ 32 {\displaystyle {\frac {\mathrm {d} n_{3}}{\mathrm {d} t}}=I_{\mathrm {in} }+{\frac {n_{1}}{\tau _{13}}}+{\frac {n_{2}}{\tau _{23}}}-{\frac {n_{3}}{\tau _{31}}}-{\frac {n_{3}}{\tau _{32}}}}
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