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Single-Crystal 21. Single-Crystal Silicon: Electrical and Optical Properties 21.1

Silicon Basics....................................... 21.1.1 Structure and Energy Bands........ 21.1.2 Impurity Levels and Charge-Carrier Population ... 21.1.3 Carrier Concentration, Electrical and Optical Properties ............... 21.1.4 Theory of Electrical and Optical Properties ...............

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21.2

Electrical Properties ............................. 21.2.1 Ohm’s Law Regime .................... 21.2.2 High-Electric-Field Effects .......... 21.2.3 Review Material ........................

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21.3

Optical Properties ................................ 21.3.1 Diversity of Silicon as an Optical Material ................ 21.3.2 Measurements of Optical Constants................... 21.3.3 Modeling of Optical Constants..... 21.3.4 Electric-Field and Temperature Effects on Optical Constants ........

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References .................................................. 478 We realize how formidable our task is – publications on electrical and optical properties of silicon amount to a huge number of titles, most dating back to the 1980s and 1990s – so any review of this subject will inevitably be incomplete. Nevertheless, we hope that our work will serve as a useful shortcut into the silicon world for a wide audience of applied physics, electrical and optical engineering students.

21.1 Silicon Basics 21.1.1 Structure and Energy Bands Normally silicon (Si) crystallizes in a diamond structure on a face-centered cubic (f.c.c.) lattice, with a lattice constant of a0 = 5.43 Å. The basis of the diamond structure consists of two atoms with coordinates (0, 0, 0) and a0 /4(1, 1, 1), as seen in Fig. 21.1. Other solids that can

crystallize in the diamond structure are C, Ge and Sn. The important notion for the electronic band structure is the Brillouin zone (BZ). The BZ is a primitive cell in the reciprocal-space lattice, which proves to be a bodycentered cubic (b.c.c.) lattice for an f.c.c. real-space lattice. For this case, the BZ with important reference points and directions within it is shown in Fig. 21.2.

Part C 21

Electrical and optical properties of crystalline semiconductors are important parts of pure physics and material science research. In addition, knowledge of parameters related to these properties, primarily for silicon and III–V semiconductors, has received a high priority in microelectronics and optoelectronics since the establishment of these industries. For control protocols, emphasis has recently been placed on novel optical measurement techniques, which have proved very promising as nondestructive and even non-contact methods. Earlier they required knowledge of the free-carrier-derived optical constants, related to the electrical conductivity at infrared frequencies, but interest in the optical constants of silicon in the visible, ultraviolet (UV) and soft-X-ray ranges has been revived since the critical dimensions in devices have become smaller. This chapter surveys the elec