22 Semiconductors Gennady Sh. Gildenblat Energy Bands. Electrons and Holes. Transport Prope Hall Boris elmont Effect. Electrical Breakdown.Optical Properties and Recombination Processes.Nanostructure Engineering Disordered Semiconductors Miram ilkovic 22.2 Diodes Analog Technology Consultants pn-Junction Diode.pn-Junction with Applied Voltage. Forward Biased Diode. Ip Vo Characteristic. DC and Large-Signal Aicha elshabini-Riad Model. High Forward Current Effects. Large-Signal Piecewise irginia Polytechnic Institute and Linear Model. Small-Signal Incremental Model. Large-Signal State University Switching Behavior of a pn-Diode. Diode Reverse Breakdown Zener and avalanche diodes. varactor Diodes Tunnel F.W. Stephenson Diodes. Photodiodes and Solar Cells. Schottky Barrier Diode ginia Polytechnic Institute and 2.3 Electrical Equivalent Circuit Models and Device Simulators oran Overview of Equivalent Circuit Models. Overview of RAPP Semiconductor Device Simulators David C. look 22.4 Electrical Characterization of Semiconductors Theory. Determination of Resistivity and Hall Coefficient. Data Wright State University Analysis. Sources of Error 22.1 Physical Properties Gennady Sh. Gildenblat and Boris Elmont Electronic applications of semiconductors are based on our ability to vary their properties on a very small scale. In conventional semiconductor devices, one can easily alter charge carrier concentrations, fields, and current densities over distances of 0. 1-10 um. Even smaller characteristic lengths of 10-100 nm are feasible in materials with an engineered band structure. This section reviews the essential physics underlying modern semiconductor technology Energy Bands In crystalline semiconductors atoms are arranged in periodic arrays known as crystalline lattices. The lattice structure of silicon is shown in Fig 22. 1. Germanium and diamond have the same structure but with different interatomic distances. As a consequence of this periodic arrangement, the allowed energy levels of electrons are grouped into energy bands, as shown in Fig 22. 2. The probability that an electron will occupy an allowed quantum state with energy Eis f=[1+ exp(e- F)/kBr Here kB=1/11,606 eV/K denotes the Boltzmann constant, T is the absolute temperature, and F is a parameter known as the Fermi level. If the energy E> F+ 3kg T, then f(e)<0.05 and these states are mostly empty. Similarly, the states with E< F-3ka T are mostly occupied by electrons. In a typical metal Fig. 22. 2(a)], the c 2000 by CRC Press LLC© 2000 by CRC Press LLC 22 Semiconductors 22.1 Physical Properties Energy Bands • Electrons and Holes • Transport Properties • Hall Effect • Electrical Breakdown • Optical Properties and Recombination Processes • Nanostructure Engineering • Disordered Semiconductors 22.2 Diodes pn-Junction Diode • pn-Junction with Applied Voltage • Forward￾Biased Diode • ID-VD Characteristic • DC and Large-Signal Model • High Forward Current Effects • Large-Signal Piecewise Linear Model • Small-Signal Incremental Model • Large-Signal Switching Behavior of a pn-Diode • Diode Reverse Breakdown • Zener and Avalanche Diodes • Varactor Diodes • Tunnel Diodes • Photodiodes and Solar Cells • Schottky Barrier Diode 22.3 Electrical Equivalent Circuit Models and Device Simulators for Semiconductor Devices Overview of Equivalent Circuit Models • Overview of Semiconductor Device Simulators 22.4 Electrical Characterization of Semiconductors Theory • Determination of Resistivity and Hall Coefficient • Data Analysis • Sources of Error 22.1 Physical Properties Gennady Sh. Gildenblat and Boris Gelmont Electronic applications of semiconductors are based on our ability to vary their properties on a very small scale. In conventional semiconductor devices, one can easily alter charge carrier concentrations, fields, and current densities over distances of 0.1–10 µm. Even smaller characteristic lengths of 10–100 nm are feasible in materials with an engineered band structure. This section reviews the essential physics underlying modern semiconductor technology. Energy Bands In crystalline semiconductors atoms are arranged in periodic arrays known as crystalline lattices. The lattice structure of silicon is shown in Fig. 22.1. Germanium and diamond have the same structure but with different interatomic distances. As a consequence of this periodic arrangement, the allowed energy levels of electrons are grouped into energy bands, as shown in Fig. 22.2. The probability that an electron will occupy an allowed quantum state with energy E is (22.1) Here kB = 1/11,606 eV/K denotes the Boltzmann constant, T is the absolute temperature, and F is a parameter known as the Fermi level. If the energy E > F + 3kBT, then f(E) < 0.05 and these states are mostly empty. Similarly, the states with E < F – 3kBT are mostly occupied by electrons. In a typical metal [Fig. 22.2(a)], the f E F kT =+ − B − [ exp( ) ]1 1 / Gennady Sh. Gildenblat The Pennsylvania State University Boris Gelmont University of Virginia Miram Milkovic Analog Technology Consultants Aicha Elshabini-Riad Virginia Polytechnic Institute and State University F.W. Stephenson Virginia Polytechnic Institute and State University Imran A. Bhutta RFPP David C. Look Wright State University