Semiconductor Electrodes docx

Semiconductor Electrodes S Cattarin, Institute for Energetics and Interphases – CNR, Padova, Italy F Decker, Universita ` di Roma ‘‘La Sapienza’’, Rome, Italy & 2009 Elsevier B.V. All rights reserved. Introduction The modern interest for phenomena at the semi- conductor–electrolyte interface dates back to experi- ments performed in the 1950s with germanium, and has extended to most semiconducting materials for reasons of fundamental knowledge or potential application, going from semiconductor processing technology to hetero- geneous photocatalysis to sensors. The subject is highly interdisciplinary and involves fields like electrochemistry, solid-state physics, and surface science. The aim of this article is to provide a concise survey of the basic concepts involved in the formation and op- eration of a semiconductor–electrolyte junction, both in the dark and under illumination. In most cases, ter- minologies and symbols recommended by IUPAC are used. Some important equations are reported but not derived. Energy Levels in Semiconductors and in Solution The electronic states in semiconductors are described by the quantum theory of crystalline solids, developed tak- ing advantage of the properties of periodicity of their structures. The peculiar characteristic of semiconductors is that for a given interval of energies there are no electronic states available: an interval of prohibited en- ergies E g , called the energy gap, separates a band of filled energy states, the valence band with upper edge E v , from a band of empty energy states, the conduction band with lower edge E c . The conductivity of semiconductors at room tem- perature is because of the presence of mobile charge carriers, electrons in the conduction band, or holes in the valence band. In intrinsic semiconductors these carriers result from interband thermal excitation and the density n i of electrons in the conduction band equals that of holes p i in the valence band (n i ¼ p i ). In semiconductors doped with a controlled concentration of donor or acceptor atoms that may be easily ionized, one carrier type is dominant. The relations between carrier densities at equilibrium (n 0 or p 0 ) and Fermi levels of electrons n E F and holes p E F are n 0 ¼ N c exp À ðE c À n E F Þ kT  ½1 p 0 ¼ N v exp À ð p E F À E v Þ kT  ½2 where N c and N v are the effective density of states per unit volume at the bottom of the conduction band and at the top of the valence band, respectively, and are a function of temperature T and the effective masses of electrons or holes. Typical values of N c and N v are in the range 10 18 –10 19 cm À3 , to be compared with a density of atoms on the order of 10 22 cm À3 . At equilibrium electrons and holes have the same Fermi level n E F ¼ p E F ¼ E F and the product between the densities is constant at a given temperature analogous to the law of mass action in chemistry. n 0 p 0 ¼ N c N v exp À E g kT  ¼ n i 2 ½3 Following eqns [1]–[3], the Fermi level E i of intrinsic semiconductors is located essentially at midgap. In ma- terials doped with donor atoms (n-type), the majority carriers are electrons (n 0 cp 0 ) and the Fermi level is close to the conduction band edge; materials doped with acceptor atoms are known as p-type, the majority carriers are holes (p 0 cn 0 ), and the Fermi level is close to the valence band edge (Figure 1 ). Materials with typical dopant concentrations in the range 10 15 –5 Â 10 18 cm À3 have a Fermi level located some 0.25–0.04 eV from the band edge. For reasons of conciseness mostly the case of n-type semiconductors is considered; a similar treatment is valid for p-type materials. In order to discuss the formation of a solid–liquid junction, it is necessary to correlate the scale of absolute E C E F E V −−− E E E C E F E V p-type semiconductorn-type semiconductor + + + Figure 1 Energy schemes of n-type and p-type semiconductors with the indicated valence band edge E v , the conduction band edge E c , and the Fermi levels E F . 121 . scale of absolute E C E F E V −−− E E E C E F E V p-type semiconductorn-type semiconductor + + + Figure 1 Energy schemes of n-type and p-type semiconductors with the indicated valence band edge E v ,. important equations are reported but not derived. Energy Levels in Semiconductors and in Solution The electronic states in semiconductors are described by the quantum theory of crystalline solids,. conductivity of semiconductors at room tem- perature is because of the presence of mobile charge carriers, electrons in the conduction band, or holes in the valence band. In intrinsic semiconductors