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P. 164

Lasers

          158   Photonic Devices

            Laser diodes operate normally at higher forward bias voltages than
          that shown in Fig. 7.8. Of course, the appropriate variable is not volt-
          age, but current. This situation is shown schematically in Fig. 7.9.
          There are some important features to note in this diagram. The most
          important is that the physical overlap of occupied conduction and va-
          lence band states is even more complete. This improves optical gain.
          There is now a perceptible electric field in the contact regions, which
          we have up to now presumed to have negligible resistance. The width
          of the space–charge region does not go to zero when the bias voltage
          equals the built-in voltage as implied by Eq. 4.5. This indicates that
          the depletion model breaks down in forward bias. On the other hand,
          the only region where the electric field remains zero is at the edges of
          the depletion region (where the slope of the energy level versus dis-
          tance is zero). That is, at the edges of the depletion region, the current
          is carried entirely by diffusion, justifying the all-important boundary
          conditions we used to develop the I–V model for the p-n junction diode
          even in strong forward bias.
            To summarize, a laser is an amplifier with positive feedback. We
          have determined that the condition necessary for amplification to oc-
          cur is a population inversion, and we have described how this can be



                                          Electrons


                             C B



                                   w
               ENERGY       V B





                                              Region of
                                 Holes
                                              Population Inversion







                                        DISTANCE
          Figure 7.9. Energy level diagram in a degenerately doped p-n junction diode in strong
          forward bias (V > V BI ). The depletion region is increasingly more narrow but does not
          decrease to zero.

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