Holes and electrons

The absence of an electron from a covalent bond leaves a hole and the neighboring valence electron can vacate its covalent bond to fill the hole, thereby creating a hole in a new location. The new hole can, in turn, be filled by a valence electron from another covalent bond, and so on. Hence, a mechanism is estabUshed for electrical conduction that involves the motion of valence electrons but not free electrons. Although a hole is a conceptual artifact, it can be described as a concrete physical entity to keep track of the motion of the valence electrons. Because holes and electrons move in opposite directions under the influence of an electric field, a hole has the same magnitude of charge as an electron but is opposite in sign. 

More precise coefficients are available (33). At room temperature, cii 1.12 eV and cii 1.4 x 10 ° /cm. Both hole and electron mobilities decrease as the number of carriers increase, but near room temperature and for concentrations less than about 10 there is Htde change, and the values are ca 1400cm /(V-s) for electrons and ca 475cm /(V-s) for holes. These numbers give a calculated electrical resistivity, the reciprocal of conductivity, for pure sihcon of ca 230, 000 Hem. As can be seen from equation 6, the carrier concentration increases exponentially with temperature, and at 700°C the resistivity has dropped to ca 0.1 Hem. 

The effective masses of holes and electrons in semiconductors are considerably less than that of the free electron, and die conduction equation must be modified accordingly using the effective masses to replace tire free electron mass. The conductivity of an intrinsic semiconductor is then given by... 

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

Figure 13-1. Encigy level diagrams under forward bias, (a) Single-layer device Iransports both holes and clccu ons and emits (b) iwo-layer device with hole and electron transport layers, one or both of which may emit (c) three-layer device with emitting dye doped (here) into a thin region of the electron transport layer.

Figure 13-11. (a) A diagram showing ihc spatial distribution of lire relative hole and electron currents in an OLED. The recombination efficiency h is equal to the fraction of the electron (hole) current that docs not make it to the anode (cathode) (b) cll icicncy-currcni balance diagram for OLEDs. Sec text for details. 

The use of organic polymers as conductors and semiconductors in the electronics industry has led to a huge research effort in poly(thiophenes), with a focus on the modification of their electronic properties so that they can behave as both hole and electron conductors. Casado and co-workers [60] have performed combined experimental and theoretical research using Raman spectroscopy on a variety of fluorinated molecules based on oligomers of thiophene, an example of one is shown in Figure 7. 

While zinc interstitials are possible, the formation energy for these defects is higher than that of oxygen vacancies. As in the case of NiO, continuing theoretical studies are needed to clarify the location of holes and electrons in these phases. 

Note that the effective mass of holes and electrons can differ considerably.) The l/T3/2 terms cancel in the expressions for n and p, hence ... 

---