Page 311 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers
P. 311

Interacting Subsystems
                             fusion current, to give a net current of zero. Thus the following current
                             relations hold in thermal equilibrium
                               j =  j +  j =  j (  +  j  ) +  j (  +  j  ) =  0  (7.166a)
                                                                      ,
                                                              ,
                                              ,
                                                      ,
                                    n   p     n Drift  n Diff  p Drift  p Diff
                               j =  j  n Drift  +  j n Diff  =  0  j =  j  p Drift  +  j  p Diff  =  0  (7.166b)
                                             ,
                                                               ,
                                                                       ,
                                     ,
                                                          p
                                n
                                               n
                             j =  qµ nE +  qD ∇ =  0     j =  qµ pE qD ∇   p =  0  (7.166c)
                                                                    –
                                            n
                                                                p
                              n
                                                                        p
                                    n
                                                          p
                Biased       When the thermally equilibrated junction is biased, i.e., a voltage is
                Junction     applied across the junction, it either adds to or subtracts from the built-in
                             voltage. This has the effect of either raising or lowering the band edges
                             on one side of the junction w.r.t. the other:
                             • When the band edges on the N side of the junction are lowered w.r.t
                               the P side, we say that the junction is reverse biased; calculations sug-
                               gest that a small limiting leakage current, due mainly to drift, flows
                               through the diode for all reverse bias voltages. In this mode the diode
                               appears to have a very high series resistance.
                             • When the band edges on the N side of the junction are raised w.r.t the
                               P side, we say that the junction is forward biased; calculations sug-
                               gest that the current through the diode, now mainly due to diffusion,
                               grows as an exponential function of the forward bias voltage. In this
                               mode the diode appears to have a very low series resistance.
                             It is the above asymmetry makes the PN-junction diode so very useful
                             technologically, because, used alone and even better in pairs, these
                             diodes can be used to rectify the current flow through a particular circuit
                             branch, as illustrated in Figure 7.20. To simplify the bookkeeping, we
                             now introduce further notation. Since the diode has a P and an N doped
                             side, and in the vicinity of the junction we expect to find both holes and
                             electrons on both sides, we will term the P side holes  p  p   and the N side
                             electrons n n  the majority carriers, and the P side electrons n  p   and the N
                             side holes  p n   the  minority  carriers.  The derivation is straightforward
                             [7.16] if we remember the following:




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