[...]... showing how the field of semiconductor nanostructures has emerged as a special topic of solid state physics 2 Introduction Atom physics Quantum mechanics Quantum statistics Optics Material research Semiconductor Nanostructures Low temperature physics Metal physics Electronics Fig 1.2 The physics of semiconductor nanostructures is related to many other areas of physics and a lot more Quantum information... constant Gray areas represent energy bands in which allowed states (dispersion curves) exist States are occupied up to the Fermi level EF as indicated by thick dispersion curves (a) In insulators and semiconductors, all conduction band states are unoccupied at zero temperature and EF lies in the energy gap (b) In metals EF lies in the conduction band and the conduction band is partially occupied resulting... conduction band Energy Energy (a) conduction band EF EF Eg Eg valence band Wave vector 1.3 π/a valence band Wave vector π/a Semiconducting materials Semiconducting materials are numerous and versatile We distinguish elementary and compound semiconductors Elementary semiconductors Silicon (Si) and germanium (Ge), phosphorous (P), sulfur (S), selenium (Se), and tellurium (Te) are elementary semiconductors... conduction band [Fig 1.5(c)] Semiconductors can be distinguished from insulators only by the size of their band gap Typical gaps in semiconductors are between zero and 3 eV However, this range should not be seen as a strict definition of semiconductors, because, depending on the context, even materials with larger band gaps are often called semiconductors in the literature The band gaps of a selection of semiconductors... branch of solid sate physics is semiconductor physics Particular aspects of this branch are materials, electrical transport properties of semiconductors and their optical properties Other aspects include modern semiconductor devices, such as diodes, transistors and field-effect transistors Miniaturization of electronic devices in industry and research We all use modern electronics every day, sometimes... an adequate description of the band structure of solids and thereby gives a more robust criterion for the distinction between semiconductors and other material classes Resistivity and conductivity The electrical conductivity of solid materials varies over many orders of magnitude A simple measure- Fig 1.4 Summary of important quantum transport phenomena in semiconductor nanostructures (a) Schematic drawing... fundamental property that semiconductors share with insulators is their band structure In both classes of materials, the valence band is (at zero temperature) completely filled with electrons whereas the conduction band is completely empty A band gap Eg separates the conduction band from the valence band [see Fig 1.6(a)] The Fermi level EF is in the middle of the band gap 1.2 What is a semiconductor? 7 (c)... P (indium gallium phosphide), and also CuFeS2 (chalcopyrite) In this case, one talks about ternary semiconductors or semiconductor alloys They play an important role for the so-called ‘bandgap engineering’ which will be discussed in a later chapter In this book, with its focus on electronic transport in semiconductor nanostructures, the emphasis is often put on III-V semiconductors or on silicon The... and field effect in graphene 171 Further reading 173 Exercises 174 11 Ballistic electron transport in quantum point contacts 11.1 Experimental observation of conductance quantization 11.2 Current and conductance in an ideal quantum wire 11.3 Current and transmission: adiabatic approximation 11.4 Saddle point model for the quantum point contact 11.5 Conductance in the nonadiabatic case 11.6 Nonideal quantum. .. resistivity (a) of a metal, (b) of a semiconductor Right: Characteristic optical absorption as a function of photon energy (c) of a metal, (d) of a semiconductor This property distinguishes semiconductors and insulators from metals, in which a band gap may exist, but the conduction band is partially filled with electrons up to the Fermi energy EF and the lowest electronic excitations have an arbitrarily .