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318                           Lasers

                                   The active layer still consists of multiple quantum wells. The main difference
                                   is that the Bragg reflectors are at the top and bottom. They can be produced
                                   by the same techniques as the wells, and they can be made highly reflective. In
              λ   λ 0,0            the realization of Fig. 12.17, the reflector at the top has a reflection coefficient
           λ   0,1   λ 1,0
            0,2         λ          very near to unity, whereas the reflection coefficient of the bottom reflector
                        2,0
                                   is somewhat smaller, allowing the radiation to come through the transparent
                                   substrate. The area of the laser can now be made very small leading to even
                                   smaller threshold currents (  0.1 mA). A further advantage is the ease with
                                   which arrays can be made. A two-dimensional array is shown in Fig. 12.18,
                                   where each microlaser may work at the same wavelength (to produce a high
                                   output) or may be tuned to different wavelengths.


                                   12.7.4  Quantum cascade lasers
     Fig. 12.18
     An array of VCSEL lasers.     Before concluding the story of semiconductor lasers, it may be worth men-
                                   tioning a relative, the quantum cascade laser, that does not quite belong to
                                   the family. The family trait, as repeated many times, is the descent of the
                                   electron from the conduction band to the valence band and the subsequent
                                   emission of a photon, of one single photon. The quantum cascade laser, con-
                                   ceived in the early 1970s, is an exception. All the things that matter happen in
                                   the conduction band.
                                     The basic principle of operation of the quantum cascade laser is shown in
                                   Fig. 12.19. There are two semiconductor materials, A and B, which are altern-
                                   ately deposited upon each other (say, one hundred of them) by molecular beam
                                   epitaxy (Fig. 12.19). A is the active material which has a conduction band edge
                                   much below that of semiconductor B. Lasing action takes place between en-
                                   ergy levels 1 and 2. The wavelength of the emitted light depends on  E,the
                                   difference between the two energy levels. There is also a voltage applied across
                                   the whole sandwich. For simplicity let us assume that there is a voltage drop,
                                   V B across each piece of semiconductor B but none across semiconductor A,
                                   and choose this voltage to be eV B .
                                     Let’s start with an electron, on the left-hand end of Fig. 12.19, just enter-
                                   ing from semiconductor B into semiconductor A at the energy level 2. It sees
                                   energy level 1 to be empty. Hence it descends from level 2 to level 1 by emit-
                                   ting a photon of frequency f =  E/h. But semiconductor B is designed to be
                                   thin enough so that electrons can tunnel through it if they find a convenient



                                                    B
                                                         A
                                                              B
                                                                   A
                                                Level 2
                                                                        B
                                                                             A
                                                                                  B
                                                 ΔE
                                                Level 1
     Fig. 12.19
     Energy diagram for a quantum
     cascade laser.
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