### 2.4:  Selective contacts

Figure 1: Selective contacts to a semiconductor.

As stated on the PV principle page, the PV effect requires two different contacts: one for the excited carriers (in the conduction band), and one for the relaxed carriers (in the valence band). How can it be achieved that mainly one type of carriers flows through a contact? By having mainly electrons near one contact, and having mainly holes near the other contact. This selectivity is achieved by doping, see figure. If you don't know what doping is, learn it from somewhere else before continuing with this course.

In the n-type region, there are mainly electrons, which move freely across the semiconductor–metal interface. There are only very few holes (which recombine at the metal interface, i.e. get "filled" by electrons that come, for example, from the metal).

In the p-type region, there are mostly holes, so it is mainly the holes in the valence band that move across the contact. What happens to the holes in the metal? The metal does not have a band gap with a valence and conduction band, so the notion of holes does not exist in metals. Only electrons exist in metals. When a hole leaves the semiconductor and goes into the contact, it is equivalent to saying that the electrons in the metal come into the semiconductor and "fill" the holes.

This behaviour of electrons and holes makes the contacts selective.

Now we have a closer look at the energy of the free carriers. When the electrons move from the n-type semiconductor to the metal, as shown in the figure, their energy seems to drop from the conduction band edge to the Fermi energy. This drop appears because within the semiconductor it is the custom to plot the total energy of an electron, while in the metal it is the custom to plot only the energy of the electron that is available in the external circuit. The drop appears because the electrons cannot carry all their energy with them when they leave the semiconductor.

This is analagous to a piston filled with steam: it is not possible to transfer all the steam's energy to the mechanical energy of the piston; part of the energy stays in the steam. This is so by fundamental principles of thermodynamics. If you want to know more about this, Peter Würfel will explain in he interview that, when electrons leave the semiconductor, they cause not only an energy flow, but also an entropy flow.

This poses the question, what the Fermi energy means in the semiconductor. The Fermi energy of the free carriers is the energy available to the external circuit. This is why the Fermi emergy lies usually below the conduction band edge.

If you plot only the energy available to the external circuit, the electrons near a contact go in and out of the metal indeed very easily without requiring or losing any energy, so the electrons have the same energy in silicon as in the metal [14]. This is why we can draw the Fermi level as a horizontal line. This means that the Fermi level is the same in the metal contact as in its neighboring region in silicon.

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