Today's lecture deals with a fundamental concept in all kinds of electronic devices, that is energy levels in solids. We have seen in our first lecture that the potential energy of electrons in a solid can be approximated to constant value all over the solid. This approximation is called electron in a box. The constant value is of course lower than outside the solid, otherwise, electrons would escape. We can define the energy level just outside the solid as the energy of vacuum. The difference between the energy of the electrons in the solid and that of vacuum is called a work function. It corresponds to the energy required to extract an electron from the solid. In a metal, the electrons with highest energy are those located at the Fermi level. So the work function corresponds to the difference between the Fermi level and the vacuum level. In semiconductors the valence or HOMO band is full and the conduction or LUMO band is empty. So now we have to define two energy barriers, one for extracting electrons from the HOMO level called ionisation potential, and one for capturing electrons in the LUMO level called electron affinity. If we put a metal and an organic semiconductor into contact, we see that the energy E sub bn required to inject an electron from the metal into the LUMO band is equal to the work function, W sub m minus the electron affinity of the semiconductor. Similarly the injection barrier E sub bp to inject holes in the HOMO band equals the ionisation potential of the semiconductor minus the work function of the metal. Determining the energy level is therefore of primary importance in the design of organic electronic devices. A very useful tool for that is photoelectron spectroscopy. Photoelectron spectroscopy consists of impinging a solid with very high energy photons, either ultraviolet or x-ray. Because they are highly energetic, these photons can extract electrons from the solid. More precisely electrons in the shallow valence states are extracted by UV photons, while electrons deep in the core levels require X-ray photons. The two techniques are called UV photoelectron spectroscopy, or UPS, and X-ray photoelectron spectroscopy, or XPS. Note that electrons can only be extracted from filled states, so the empty states above the Fermi level, are not accessible to UPS. When an electron is extracted, its kinetic energy corresponds to the energy above the vacuum level. So the kinetic energy is equal to the energy of the incident photon, h nu Minus the binding energy E sub L of the electron. In practice, a UPS setup use a single photon energy and counts the ejected electrons as a function of their kinetic energy. The spectrum shown here is that of a metal. Note that the x-axis points to increasing kinetic energy, which from the equation established earlier, correspond to decreasing binding energy. The onset of the signal at right hand side, correspond to the Fermi level. Moving to higher binding energy to the left of the spectrum, we find structural features corresponding to electrons directly ejected by the incident photon, or primary electrons. The features mirror the density of the occupied states. The unstructured massif at right hand side corresponds to secondary electrons; that is, electrons indirectly ejected by other electrons. The signal abruptly falls to zero at the cutoff energy, which corresponds to electrons ejected with zero kinetic energy. The binding energy of these electrons is equal to that of the incident photons, so by shifting the cutoff energy by the value of the photon energy, gives the vacuum level. Now, the metal work function can be estimated as the difference between the Fermi level and the vacuum level. UPS spectroscopy is not well suited to insulators of semiconductors because these materials tend to accumulate charges when illuminated by high energy photons. To avoid this, the semiconductor is used as a very thin film deposited on a metal substrate. The UPS spectrum of a semiconductor presents several similarities with that of a metal. The main difference resides in the fact that the onset at low binding energy does not correspond to the Fermi level, because there are no, or very few electrons at the Fermi level. Instead, it correlates with the onset of the HOMO band. For the rest, the two spectra have identical features, that is, primary and secondary electrons, and cutoff energy, thus allowing for estimating the vacuum level. The difference between the vacuum level and the HOMO onset gives the ionization potential of the semiconductor. UPS can only give access to occupied levels. To analyze the unoccupied levels, one can use Inverse Photo-Electron Spectroscopy, IPES, which consists of measuring the light emitted by a solid irradiated by an electron beam with constant energy. This is the reverse process of Photo-Electron Spectroscopy. The energy, E, of the unoccupied states is related to that of the incident electron beam, E sub i, and the energy of the emitted light by E = E_i - h nu. IPES can be used in two modes. In the isochromatic mode the energy of the detected light is constant, and one scans the incident electron energy. In the spectrographic mode, the energy of the electron beam is fixed and one measure of the energy distribution of the emitted light. This slide shows a UPS spectrum in black, and IPES spectrum in red of an organic molecule. The spectrum come from the group of Professor Kahn at Princeton University. We see here all the features we have described earlier, in particular the cut off, from which we can establish the vacuum level. Combining this value with the HOMO edge and the LUMO edge, we can estimate the ionization potential and electron affinity of the semiconductor. UPS and IPS measurements have been performed on many organic semiconductors. Remarkably, the position of the frontier orbitals varies over a wide energy range. The lines on the left show the Fermi level of various metals. Gold is rated as high function metal, while aluminum, magnesium and calcium are low work function metals. We can sort these organic molecules into two families. On the left hand side we have molecules with deep LUMO level, so electrons are easily injected because the electron barrier height is low, while holes are very difficult to inject because of a very high barrier. Conversely, on the right of the figure the HOMO level is shallow, so holes are easily injected, while electrons are difficult to inject. Semiconductors with easy electron injection are often called n-type, where n stands for negative because electrons bare a negative charge. Similarly, semiconductors with easy hole injection are called p-type, where p stands for a positive because holes bare a positive charge. In n-type semiconductors, electrical current is almost exclusively carried by electrons, while p-type semiconductors essentially conduct via holes. The situation is more complex with the semiconductors between these two extremes. Here the nature of the injected charge-carriers also depends on the nature of the metal. These semiconductors are sometimes called ambipolar. Up to now, we've assumed that the vacuum level is aligned at both sides of the interface between the metal and the semiconductor. This is known as Mott-Schottky's, or vacuum level alignment, rule. However, things are not that simple in real life. Many things can happen at the interface that will lead to accumulation of electrical charges there, and a shift of energy levels. The effect of interface charges is illustrated here. We start with an ideal metal semiconductor junction, and assume that a positive charge appears at the metal side. For the sake of electrical neutrality an equivalent negative charge is induced at the semiconductor side thus forming a dipole. This induces a shift downward of the vacuum level, leading to an increase of the electron barrier and a decrease of the hole barrier. The value of the energy shift is called interface dipole, delta. Conversely, if a negative charge appears at the metal side, and a positive charge at the semiconductor side, the direction of the dipole is now reversed. The electron barrier is now reduced and the hole barrier increased. A frequently encountered situation is depicted here, when vacuum level alignment is fulfilled as long as the Fermi level of the metal is far from the band edges. However, when the Fermi level approaches one of the band edge, it is pinned at this position, which is compensated by an equivalent shift of the vacuum level. This phenomenon is called Fermi level pinning. In summary, the barrier height for electron and hole ejection depends on the respective value of the work function of the metal, the electron affinity and ionization potential of the semiconductor. In the simpler case the barrier height follows Mott-Schottky's rule, which assumes vacuum level alignment at both sides of the metal semiconductor interface. Electron injection is easy in semiconductors with deep HOMO and LUMO levels, while hole are easy to inject, in semiconductors where HOMO and LUMO levels are close to the vacuum level. We have also seen that Mott-Schottky's rule is not always fulfilled. This is the case when there are charge at the interface, which induces an electrical dipole. We have finally described the phenomenon of Fermi level pinning, when barrier height tends to level off when the Fermi level of the metal approaches the band edges of the semiconductors. Thank you for your attention.
