Space Charge at a Junction
Introduction:
Within the transition region, electrons and holes are in transit from one side of the junction to the other. Some electrons diffuse from n to p, and some are
swept by the electric field from p to n (and conversely for holes); there are, however, very few carriers within the transition region at any given time, since the electric field serves to sweep out carriers which have wandered into W.
Space charge and electric field distribution:
- we can consider the space charge within the transition region as due only to the uncompensated donor and acceptor ions.
- The charge density within W is plotted in Fig.(b). Neglecting carriers within the space charge region, the charge density on the n side is just q times the concentration of donor ions N_{d}, and the negative charge density on the p side is -q times the concentration of acceptors N_{a.}
- The assumption of carrier depletion within W and neutrality outside W is known as the depletion approximation.
- Since the dipole about the junction must have an equal number of charges on either side,(Q_{ } = \Q_{-}\), the transition region may extend into the p and n regions unequally, depending on the relative doping of the two sides.
- For example, if the p side is more lightly doped than the n side (N_{a} < N_{d}), the space charge region must extend farther into the p material than into the n, to "uncover" an equivalent amount of charge.
For a sample of cross-sectional area A, the total uncompensated charge on either side of the junction is
where x_{p0} is the penetration of the space charge region into the p material, and x_{n0} is the penetration into n.The total width of the transition region (W) is the sum of x_{p0} and x_{n0.}
To calculate the electric field distribution within the transition region, we begin with Poisson's equation, which relates the gradient of the electric field to the local space charge at any point x:
This equation is greatly simplified within the transition region if we neglect the contribution of the carriers (p - n) to the space charge. With this approximation we have two regions of constant space charge:
The value of ξ_{0} can be found by integrating either part of the above equ with appropriate limits (see Fig. c)
Therefore, the maximum value of the electric field is