domingo, 30 de mayo de 2010
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an electric field. The only elements left in the depletion region are ionized donor or acceptor impurities.
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.
The following discussion is limited to the p-n junction and the MOS capacitor, but depletion regions arise in all the devices mentioned above.
Formation of depletion region in a P-N junction
A depletion region forms instantaneously 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 migrate into the P-side and holes migrate 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 exchange 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).
Mathematically speaking, charge transfer in semiconductor devices is due both to conduction driven by the electric field (drift) and by diffusion. For a P-type region, where holes conduct with electrical conductivity σ and diffuse with diffusion constant D, the net current density is given by
j = σ E - D ∇qp
with q the elementary charge (1.6×10−19 coulomb) and p the hole density (number per unit volume). Conduction forces the holes along the direction of the electric field. Diffusion moves the carriers in the direction of decreasing concentration, so for holes a negative current results for a positive density gradient. (If the carriers are electrons, we replace the hole density p by the negative of the electron density n; in some cases, both electrons and holes must be included.) When the two current components balance, as in the pn-junction depletion region at dynamic equilibrium, the current is zero due to the Einstein relation, which relates D to σ.
(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.
A PN junction in thermal equilibrium with zero bias voltage applied. Electron and hole concentrations are reported respectively with blue and red lines. Gray regions are charge neutral. Light red zone is positively charged. Light blue zone is negatively charged. Under the junction, plots for the charge density, the electric field and the voltage are reported.
Depletion width describes the width of the depletion region in a semiconductor, particularly in geometries that are one-dimensional, like the pn-junction and MOS capacitor. The width of the depletion region is governed by the principle of charge neutrality. Two examples follow:
Depletion width in pn-junction
The principle of charge neutrality in this case relates the depletion width wP in the p-region with acceptor doping NA to the depletion width wN in the n-region with donor doping ND:
This condition ensures that the net negative acceptor charge exactly balances the net positive donor charge. The total depletion width in this case is the sum w = wN + wP. A full derivation for the depletion width is presented in reference. This derivation is based on solving the Poisson equation in one dimension – the dimension normal to the metallurgical junction. The electric field is zero outside of the depletion width (seen in above figure) and therefore Gauss's law implies that the charge density in each region balance – as shown by the first equation in this sub-section. Treating each region separately and substituting the charge density for each region into the Poisson equation eventually leads to a result for the depletion width. This result for the depletion width is:
where Ks is the semiconductor dielectric, Vbi is the built-in voltage, and V is the applied bias. The depletion region is not symmetrically split between the n and p regions - it will tend towards the lightly doped side.
The depletion-region width of germanium as a function of impurity concentration (acceptors/donors) for a range of applied bias. Hyper-pure germanium under an applied bias of 2kV has a depletion region in the order of 2cm. This thickness is suitable for detecting gamma rays (200keV - 10MeV) in nuclear spectroscopy which are highly penetrating.
Lenny Z. Perez M.
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