Write a concise description of the operation of a p-n diode in terms that a high

Question

Write a concise description of the operation of a p-n diode in terms that a high school student could understand. Assume the student is blight, having recently been admitted to Rice, and already understands E&M; concepts at the level of a college freshman. You can also assume the student understands the concepts of electrons and holes and of n- and p-type semiconductors. You are not allowed to refer to the conduction or valence bands or to Fermi levels, or use calculus or differential equations in your explanation. In particular you should explain the following concepts: Diffusion and drift of electrons and holes; recombination The depletion region between n & p regions - why it forms What physically happens when forward and reverse bias are applied to a p-n junction - where do the electrons & holes go and how do they contribute to the observed terminal current? The description can be qualitative with few or no equations, and need not mention the exponential I vs. V behavior. Use at least 1 sketch for each of the 3 points above to illustrate your explanation.

Explanation / Answer

a. The difference between drift current and diffusion current is that drift current depends on the electric field applied: if there's no electric field, there's no drift current. Diffusion current occurs even though there isn't an electric field applied to the semiconductor. It does not have E as one of its parameters. The constants it does depend on are Dp and Dn, and +q and -q, for holes and electrons respectively. The first constants are called the diffusion coefficients, a proportionality factor. We don't worry too much about these because they are constants. We do worry about the gradient of the concentration of p and/or n, though. But, since we are talking about a one dimensional situation when we are solving for current densities, we only worry about the gradient (or derivative) with respect to the x-plane. The other difference between drift current and diffusion current, is that the direction of the diffusion current depends on the change in the carrier concentrations, not the concentrations themselves. In the equation, the signs are reversed as we are used to seeing them. We usually assign a +q to holes and -q to electrons. In the case of diffusion current, they are reversed to be opposite of the derivative of the concentrations. This occurs because the carriers are diffusing from areas of high concentrations to areas of low concentrations. For example, if the derivative of p with respect to x is positive, then the concentration of holes is growing as you move towards the +x direction. Diffusion current will be the opposite of that, the holes will be diffusing in the -x direction to where there's a lower concentration of holes. If the derivative is negative, the opposite will occur. The concentration of holes is decreasing as you go from the -x to +x direction. Therefore, holes will diffuse to the +x direction where there's a lower concentration of holes. This is why the negative sign is needed in the equation for the hole diffusion current. The same goes for electrons, but in this case, the signs cancel for a positive derivative because the electrons, carrying -q, diffuse to the -x direction where there's less electrons. The sign remains if the derivative is negative, because electrons will be diffusing to the +x direction carrying a -q charge. For these reasons it's not included in the equation for the electron diffusion current. b. 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 instantaneously across a P-N junction. It is most easily described when the junction is in thermal equilibrium or in asteady state: in both of these cases the properties of the system do not vary in time; they have been called dynamic equilibrium.[1] [2] 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 from the N-side to 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 diffused electrons come into contact with holes on the P-side and are eliminated by recombination. Likewise for the diffused holes on the N-side. The net result is the diffused 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 s and diffuse with diffusion constant D, the net current density is given by j = s 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 s. (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.[3] 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. c. Forward Biased Conduction When the p-n junction is forward biased, the electrons in the n-type material which have been elevated to the conduction band and which have diffused across the junction find themselves at a higher energy than the holes in the p-type material. They readily combine with those holes, making possible a continuous forward current through the junction.

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