The Biased p-n Junction

     An externally applied potential will alter the potential difference between the p- and n-regions. This in turn will modify the flow of majority carriers, so that the junction can be used as a “gate”. If the junction is forward biased by applying a positive voltage V to the p-region Fig. , its potential is increased with respect to the n-region, so that an electric field is produced in a direction opposite to that of the built-in field.

The presence of the external bias voltage causes a departure from equilibrium and a misalignment of the Fermi levels in the p- and n-regions, as well as in the depletion layer.

               The presence of the two Fermi levels in the depletion layer, Efc and Efv represents a state of quasi-equilibrium. Fig.  

 Energy band diagram and carrier concentrations for a forward-biased p-n junction. In effect, then, if one were to connect the two terminals of the p-n junction to form a closed circuit, two currents would be present. First, a small current, called reverse saturation current, is, exists because of the presence of the contact potential and the associated electric field. In addition, it also happens that holes and free electrons with sufficient thermal energy can cross the junction. This current across the junction flows opposite to the reverse saturation current and is called diffusion current. Of course, if a hole from the p side enters, it is quite likely that it will quickly recombine with one of the n-type carriers on the n side. Fig.

              The net effect of the forward bias is to reduce the height of the potential-energy hill by an amount eV. The majority carrier current turns out to increase by an exponential factor exp(eV/kT). So that the net current becomes i = isexp(eV/kT) – is, where is is nearly a constant. The excess majority carrier holes and electrons that enter the n and p regions, respectively, become minority carriers and recombine with the local majority carriers. Their concentration therefore decreases with the distance from the junction as shown in Fig.  This process is known as minority carrier injection. If the junction is reversed biased by applying a negative voltage V to the p-region, the height of the potential energy hill is augmented by eV. This impedes the flow of majority carriers. The corresponding current is multiplied by the exponential factor exp(eV/kT) where V is negative; i.e. it is reduced. The net result for the current is i = is exp(eV/kT) - is, so that a small current of magnitude ≈ is flows in the reverse direction when IVI » kT/c. A p-n junction therefore acts as a diode with a current-voltage (i-V) characteristic as illustrated.

                          

                                 I= i_s [exp( eV/kT)-1]  Ideal Diode Characteristic