The depletion region is so named because it is formed from a conducting region by removal of all free charge carriers, leaving none to carry a current. Understanding the depletion region is key to explaining modern semiconductor electronics: diodes, bipolar junction transistors, field-effect transistors, and variable capacitance diodes all rely on depletion region phenomena.
A depletion region forms spontaneously across a P-N junction. It is most easily described when the junction is in thermal equilibrium or in a steady state: in both of these cases the properties of the system do not vary in time; they have been called dynamic equilibrium. , Electrons and holes diffuse into regions with lower concentrations of electrons and holes, much as ink diffuses into water until it is uniformly distributed. By definition, N-type semiconductor has an excess of free electrons compared to the P-type region, and P-type has an excess of holes compared to the N-type region. Therefore when N-doped and P-doped pieces of semiconductor are placed together to form a junction, electrons diffuse into the P-side and holes diffuse into the N-side. Departure of an electron on the N-side for the P-side leaves a positive donor ion behind on the N-side, and likewise the hole leaves a negative acceptor ion on the P-side. Following transfer, the injected electrons come into contact with holes on the P-side and are eliminated by recombination. Likewise for the injected holes on the N-side. The net result is the injected electrons and holes are gone, leaving behind the charged ions adjacent to the interface in a region with no mobile carriers (called the depletion region). The uncompensated ions are positive on the N side and negative on the P side. This creates an electric field that provides a force opposing the continued diffusion of charge carriers. When the electric field is sufficient to arrest further transfer of holes and electrons, the depletion region has reached its equilibrium dimensions. Integrating the electric field across the depletion region determines what is called the built-in voltage (also called the junction voltage or barrier voltage or contact potential).
(1) Under reverse bias (P negative with respect to N), the potential drop (i.e., voltage) across the depletion region increases. This widens the depletion region, which increases the drift component of current and decreases the diffusion component. In this case the net current is leftward in the figure of the pn junction. The carrier density then is small and only a very small reverse saturation current flows.
(2) Forward bias (P positive with respect to N) narrows the depletion region and lowers the barrier to carrier injection. The diffusion component of the current greatly increases and the drift component decreases. In this case the net current is rightward in the figure of the pn junction. The carrier density is large (it varies exponentially with the applied bias voltage), making the junction conductive and allowing a large forward current. The mathematical description of the current is provided by the Shockley diode equation. The low current conducted under reverse bias and the large current under forward bias is an example of rectification.
Another example of a depletion region occurs in the MOS capacitor. It is shown in the figure to the right, for a P-type substrate. Suppose that the semiconductor initially is charge neutral, with the charge due to holes exactly balanced by the negative charge due to acceptor doping impurities. If a positive voltage now is applied to the gate, which is done by introducing positive charge Q to the gate, then some positively charged holes in the semiconductor nearest the gate are repelled by the positive charge on the gate, and exit the device through the bottom contact. They leave behind a depleted region that is insulating because no mobile holes remain; only the immobile, negatively charged acceptor impurities. The greater the positive charge placed on the gate, the more positive the applied gate voltage, and the more holes that leave the semiconductor surface, enlarging the depletion region. (In this device there is a limit to how wide the depletion width may become. It is set by the onset of an inversion layer of carriers in a thin layer, or channel, near the surface. The above discussion applies for positive voltages low enough that an inversion layer does not form.)
If the gate material is polysilicon of opposite type to the bulk semiconductor, then a spontaneous depletion region forms if the gate is electrically shorted to the substrate, in much the same manner as described for the pn-junction above.
This condition insures that the net negative acceptor charge exactly balances the net positive donor charge. The total depletion width in this case is the sum .
If the depletion width becomes wide enough, then electrons appear in a very thin layer at the semiconductor-oxide interface, called an inversion layer because they are oppositely charged to the holes that prevail in a P-type material. When an inversion layer forms the depletion width ceases to expand with increase in gate charge Q. In this case neutrality is achieved by attracting more electrons into the inversion layer. In the MOSFET this inversion layer is referred to as the channel.
where A is the gate area, = 8.854×10−12 F/m, F is the farad and m is the meter. This linearly-varying electric field leads to an electrical potential that varies quadratically in space. The energy levels, or energy bands, bend in response to this potential.
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