viii
Contents
2.2.5.5 Diffusion of Carriers .............................................. 36
2.2.5.6 Nonuniformly Doped Semiconductors
and Built-In Electric Field...................................... 38
2.2.6 Generation–Recombination .................................................. 39
2.2.6.1 Injection Level ......................................................... 40
2.2.6.2 Recombination Processes ...................................... 41
2.2.7 Basic Semiconductor Equations ...........................................44
2.2.7.1 Poisson’s Equation ..................................................44
2.2.7.2 Carrier Concentration in Terms
of Electrostatic Potential ........................................ 46
2.2.7.3 Quasi-Fermi Level .................................................. 48
2.2.7.4 Transport Equations .............................................. 49
2.2.7.5 Continuity Equations ............................................. 49
2.3 Theory of n-Type and p-Type Semiconductors in Contact ............ 51
2.3.1 Basic Features of pn-Junctions .............................................. 51
2.3.2 Built-In Potential .................................................................... 53
2.3.3 Step Junctions .........................................................................54
2.3.3.1 Junction Potential and Electric Field ................... 55
2.3.4 pn-Junctions under External Bias ........................................ 58
2.3.4.1 One-Sided Step Junctions ...................................... 59
2.3.5 pn-Junction Equations ........................................................... 60
2.3.5.1 Relationship between Minority Carrier
Density and Junction Voltage ............................... 61
2.3.6 pn-Junctions I–V Characteristics ..........................................65
2.3.6.1 Temperature Dependence of pn-Junction
Leakage Current ..................................................... 67
2.3.6.2 Limitations of pn-Junction Current Equation ..... 67
2.3.6.3 Bulk Resistance ....................................................... 71
2.3.6.4 Junction Breakdown Voltage ................................ 71
2.3.7 pn-Junction Dynamic Behavior ............................................ 73
2.3.7.1 Junction Capacitance.............................................. 73
2.3.7.2 Diffusion Capacitance ........................................... 76
2.3.7.3 Small Signal Conductance ....................................77
2.3.8 Diode Equivalent Circuit for Circuit CAD .........................77
2.4 Summary .............................................................................................. 78
Exercises .......................................................................................................... 79
3. Metal-Oxide-Semiconductor System ........................................................83
3.1 Introduction .........................................................................................83
3.2 MOS Capacitor at Equilibrium ..........................................................83
3.2.1 Work Function ........................................................................85
3.2.2 Oxide Charges ........................................................................ 89
3.2.2.1 Interface-Trapped Charge ..................................... 90
3.2.2.2 Fixed-Oxide Charge ...............................................90
Contents
2.2.5.5 Diffusion of Carriers .............................................. 36
2.2.5.6 Nonuniformly Doped Semiconductors
and Built-In Electric Field...................................... 38
2.2.6 Generation–Recombination .................................................. 39
2.2.6.1 Injection Level ......................................................... 40
2.2.6.2 Recombination Processes ...................................... 41
2.2.7 Basic Semiconductor Equations ...........................................44
2.2.7.1 Poisson’s Equation ..................................................44
2.2.7.2 Carrier Concentration in Terms
of Electrostatic Potential ........................................ 46
2.2.7.3 Quasi-Fermi Level .................................................. 48
2.2.7.4 Transport Equations .............................................. 49
2.2.7.5 Continuity Equations ............................................. 49
2.3 Theory of n-Type and p-Type Semiconductors in Contact ............ 51
2.3.1 Basic Features of pn-Junctions .............................................. 51
2.3.2 Built-In Potential .................................................................... 53
2.3.3 Step Junctions .........................................................................54
2.3.3.1 Junction Potential and Electric Field ................... 55
2.3.4 pn-Junctions under External Bias ........................................ 58
2.3.4.1 One-Sided Step Junctions ...................................... 59
2.3.5 pn-Junction Equations ........................................................... 60
2.3.5.1 Relationship between Minority Carrier
Density and Junction Voltage ............................... 61
2.3.6 pn-Junctions I–V Characteristics ..........................................65
2.3.6.1 Temperature Dependence of pn-Junction
Leakage Current ..................................................... 67
2.3.6.2 Limitations of pn-Junction Current Equation ..... 67
2.3.6.3 Bulk Resistance ....................................................... 71
2.3.6.4 Junction Breakdown Voltage ................................ 71
2.3.7 pn-Junction Dynamic Behavior ............................................ 73
2.3.7.1 Junction Capacitance.............................................. 73
2.3.7.2 Diffusion Capacitance ........................................... 76
2.3.7.3 Small Signal Conductance ....................................77
2.3.8 Diode Equivalent Circuit for Circuit CAD .........................77
2.4 Summary .............................................................................................. 78
Exercises .......................................................................................................... 79
3. Metal-Oxide-Semiconductor System ........................................................83
3.1 Introduction .........................................................................................83
3.2 MOS Capacitor at Equilibrium ..........................................................83
3.2.1 Work Function ........................................................................85
3.2.2 Oxide Charges ........................................................................ 89
3.2.2.1 Interface-Trapped Charge ..................................... 90
3.2.2.2 Fixed-Oxide Charge ...............................................90