Handbook of silicon based MEMS materials and technologies 2.8.4 Continuous Czochralski growth 2.9 Heavily n type doped silicon and constitutional supercooling 2.9.1 Constitutional supercooling 2.9.2 Melting point depression 2.9.3 Origin of dopant gradient in the melt 2.9.4 Path to lower resistivity 2.10 Growth of large diameter crystals 2.10.1 Neck growth for large crystals 2.10.2 Neck extension 2.10.3 Additional stresses on neck 2.10.4 Dislocations oriented in (100) direction in large diameter crystals 2.10.5 Crucible wall temperature 2.10.6 Double layered crucible structure 2.10.7 Crucible deformations 2.3 Selected issues of crystal growth 2.3.1 Diameter control 2.3.2 Doping 2.3.3 Hot zone lifetime 2.4 Improved thermal and gas flow designs 2.5 Heat transfer 2.6 Melt convection 2.6.1 Free convection 2.6.2 Crucible rotation 2.6.3 Crystal rotation 2.6.4 Marangoni convection and gas shear 2.7 Magnetic fields 2.7.1 Cusp field 2.7.2 Transverse field 2.7.3 Melt flows under transverse field 2.7.4 Time dependent fields 2.8 Hot recharging and continuous feed 2.8.1 Hot recharging 2.8.2 Charge topping 2.8.3 Crucible modifications 2.10.8 Intentional devitrification 2.10.9 Transverse or cusp field for very large crystals 2.10.10 Boosting crystal weight 2.10.11 Seed chuck 2.10.12 Additional challenges References Further reading 3 Properties of silicon crystals 3.1 Dopants and impurities 3.2 Typical impurity concentrations 3.3 Concentration of dopants and impurities in axial direction 3.4 Resistivity 3.5 Radial variation of impurities and resistivity 3.6 Thermal donors 3.7 Defects in silicon crystals Front Cover Handbook of Silicon Based MEMS Materials and Technologies Copyright Page Contents List of contributors Preface Where is silicon based MEMS heading to References I. Silicon as MEMS Material 1 Properties of silicon 1.1 Properties of silicon 1.1.1 Crystallography of silicon 1.1.1.1 Miller index (hkl) system 1.1.1.2 Stereographic projection 1.1.2 Defects in silicon lattice 1.1.3 Mechanical properties of silicon 1.1.4 Electrical properties 1.1.4.1 Introduction dopants and impurities in silicon 1.1.4.2 Piezoresistive effect in silicon General piezoresistive effect Strain Stress in anisotropic materials Strain effect on resistivity Linearity Effect of temperature and doping Example of a piezoresistive sensor design Surface effects References 2 Czochralski growth of silicon crystals 2.1 The Czochralski crystal growing furnace 2.1.1 Crucible 2.1.2 Hot zone materials 2.1.3 Hot zone structure 2.1.4 Gas flow 2.2 Stages of growth process 2.2.1 Melting 2.2.2 Neck 2.2.3 Crown 2.2.4 Body 2.2.5 Tail 2.2.6 Shut off