What Is the Work Function?


What is the work function?

The work function is the energy needed to remove an electron from a material. Band theory makes this concept much easier to visualize. The work function is the difference between the vacuum level and the Fermi level energies. Vacuum level energy is the energy that a stationary electron has, i.e., zero. Since a metal’s conduction band (CB) is at the same level as the Fermi level, the work function calculation doesn’t change. Semiconductors’ calculations are the same, but the variable Fermi level and band gap gives us other methods of calculating it. By taking the electron affinity (χ) and adding it to the difference between the CB energy and Fermi level energy, we can also get the work function. Or,

\phi_S =\chi_S + (E_c - E_F)

Can we change it?

Doping a semiconductor, or adding impurities to it, changes the Fermi level and makes it possible for electronic devices to work. Adding pentavalent dopants (with five valence electrons) makes an n-type semiconductor and brings the Fermi level closer to the CB. This makes sense, since adding electrons would increase the chance of conduction electrons being found. Remember though, that the Fermi level probability does not change, as the probability of finding an electron at that energy level is still 50%. Since the level itself is closer to the CB, it’s more likely to find an electron in or close to the CB.

Adding trivalent dopants (with three valence electrons) makes a p-type semiconductor and brings the Fermi level closer to the valence band (VB). This makes sense because trivalent dopants essentially take away electrons, or add positively charged holes. This makes it less likely for an electron to be found at the CB. Another way to see it is that since there are more holes, there are more vacant spots for electrons to fill. Electrons naturally diffuse into states of lower energy, so it is more likely to find electrons at lower energies when holes are added.

Photovoltaic effect

The photovoltaic effect is dependent on the work function. If the light hitting the material has enough energy to knock electrons out of it, those electrons will move around and we can harness the electricity. This is the principle behind solar power. One may expect that reducing this work function as much as possible would be the best way to harness power, but sometimes it is desirable to have solar materials with higher work functions. Higher work functions allow for more efficient power conversion of visible light, with very high work functions absorbing near ultraviolet light. Lower work functions allow for more efficient power conversion of near infrared and infrared light.

Contact potential

Putting two materials together with different work functions produces a contact potential, or a voltage right at the contact between the two surfaces. Transparent conducting oxides in solar cells produce a contact potential that helps push majority carriers (electrons or less often, holes) through the cell more easily, thus generating more power.

If a material t has a higher work function than a material s, then electrons in s will see that there are lower energy states in t and tunnel to them. This continues until the Fermi levels of s and t align. Since electrons go from s to t, s is left with a positive charge and t is left with a negative charge because it has more electrons now. This difference in charge produces an electric field and thus an electric potential equal to the difference in work functions. Contact potential is seen in electronic devices in junctions between doped semiconductors. Sometimes, it’s used to enhance light emission (LEDs) or to enhance solar power generation.

Vacuum tubes and thermionic emission

Vacuum tubes utilize thermionic emission. A filament heats an electron emitter (the cathode), giving the cathode enough energy for its electrons to overcome the work function and boil off. A tube is evacuated to a near vacuum to reduce the number of air molecules to bounce off of. A circuit is formed between the anode and cathode which aids the emission by inducing a voltage. This, in turn, induces a bias which reduces the work function and thus makes it easier for electrons to emit. The cathode could be pointed to concentrate the electric field and make it even easier. Counterintuitively, a sharp-pointed cone is not the most effective way of concentrating the electric field, but instead a thread with a rounded end. Vacuum tubes were used for computing, noise amplification, and television, to name some uses. For television, the cathodes were placed on a substrate with specific spacings and the emitted electrons struck phosphors on the screen. There were no anodes, hence the name cathode ray tubes.

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