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368                           Optoelectronics

                                                                          P in

                                                        R


                                            –
                                                                  P
                                                                   i              Quantum well
                                           V 0
                                                                   n
                                            +

     Fig. 13.29
     The device of Fig. 13.24 in a circuit in
                                                                          P out
     which it can exhibit bistability.

                                   It is grown on a GaAs substrate, which needs to be etched away, since it is not
                                   transparent at the wavelength where the mechanism is suitable for modulation.
                                     What else can we do with this device? It can be used for light detection in
                                   the same manner as an ordinary p–i–n junction. The added advantage of the
                                   multiple quantum well structure is that the resulting photocurrent is strongly
                                   dependent on the applied voltage and on the wavelength. It can therefore be
                                   used, admittedly in a very narrow range, for measuring wavelength.
                                     The most interesting application is, however, for a bistable device, shown
                                   schematically in Fig. 13.29. The wavelength of the incident light is chosen, so
                                   that decreasing reverse bias voltage gives increasing optical absorption (line
                                   A in Fig. 13.27). In the absence of optical input, no current flows, and hence
                                   all the applied voltage appears across the quantum wells. As light is incident,
                                   a photocurrent flows, hence the voltage across the quantum wells decreases,
                                   which leads to higher absorption, which in turn leads to lower voltage, etc.
                                   There is obviously positive feedback, which under certain circumstances may
                                   be shown to lead to switching to a high absorption state with low voltage across
                                   the junction.
                                     The problem can of course be solved rigorously by considering the relation-
                                   ship between the four variables, namely the input optical power, P in , the output
                                   optical power, P out , the voltage across the quantum wells, V, and the current
                                   flowing in the circuit, I. First, we need
                                                         P out = P out (P in , V, λ),      (13.23)

                                   which can be derived from experimental results like those shown in Fig. 13.27.
                                   Second, we need the current–voltage characteristics of the circuit of Fig. 13.25,
                                   which may be written simply as

                                                             V = V 0 – IR.                 (13.24)
                                   And third, we need to determine the current which flows in response to the
                                   light power incident upon the junction,

                                                           I = I(V, P in , λ).             (13.25)
                                   From eqns (13.23–13.25) we may then derive the P out versus P in curve which,
                                   in many cases, will exhibit bistability similar to that shown in Fig. 13.23.
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