Semiconductor Device Physics
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1 1 Semiconductor Device Physics Lecture
2 2 Semiconductor Device Physics Textbook: Semiconductor Device Fundamentals, Robert F. Pierret, International Edition, Addison Wesley, Textbook and Syllabus Syllabus: Chapter 1: Semiconductors: A General Introduction Chapter 2: Carrier Modeling Chapter 3: Carrier Action Chapter 5: pn Junction Electrostatics Chapter 6: pn Junction Diode: I V Characteristics Chapter 7: pn Junction Diode: Small-Signal Admittance Chapter 8: pn Junction Diode: Transient Response Chapter 14: MS Contacts and Schottky Diodes Chapter 9: Optoelectronic Diodes Chapter 10: BJT Fundamentals Chapter 11: BJT Static Characteristics Chapter 12: BJT Dynamic Response Modeling
3 3 Semiconductor Device Physics References The class materials are the Lecture note slides of the Semiconductor Device Physics course offered by Dr.-Ing. Erwin Sitompul, President University, Indonesia. semiconductor-device-physics/
4 Semiconductor Device Physics 4 Chapter 1 Semiconductors: A General Introduction
5 5 Chapter 1 Semiconductors: A General Introduction What is a Semiconductor? Low resistivity conductor High resistivity insulator Intermediate resistivity semiconductor The conductivity (and at the same time the resistivity) of semiconductors lie between that of conductors and insulators.
6 6 Chapter 1 Semiconductors: A General Introduction What is a Semiconductor? Semiconductors are some of the purest solid materials in existence, because any trace of impurity atoms called dopants can change the electrical properties of semiconductors drastically. Unintentional impurity level: 1 impurity atom per 10 9 semiconductor atom. Intentional impurity ranging from 1 per 10 8 to 1 per Completely ordered in segments No recognizable long-range order Entire solid is made up of atoms in an orderly three- dimensional array polycrystalline amorphous crystalline Most devices fabricated today employ crystalline semiconductors.
7 7 Chapter 1 Semiconductors: A General Introduction Semiconductor Materials Elemental: Si, Ge, C Compound: IV-IV SiC III-V GaAs, GaN II-VI CdSe Alloy: Si 1-x Ge x Al x Ga 1-x As As Cd Se Ga : Arsenic : Cadmium : Selenium : Gallium
8 8 Chapter 1 Semiconductors: A General Introduction From Hydrogen to Silicon # of Electrons Z Name 1s 2s 2p 3s 3p 3d Notation 1 H 1 1s 1 2 He 2 1s 2 3 Li 2 1 1s 2 2s 1 4 Be 2 2 1s 2 2s 2 5 B s 2 2s 2 2p 1 6 C s 2 2s 2 2p 2 7 N s 2 2s 2 2p 3 8 O s 2 2s 2 2p 4 9 F s 2 2s 2 2p 5 10 Ne s 2 2s 2 2p 6 11 Na s 2 2s 2 2p 6 3s 1 12 Mg s 2 2s 2 2p 6 3s 2 13 Al s 2 2s 2 2p 6 3s 2 3p 1 14 Si s 2 2s 2 2p 6 3s 2 3p 2 15 P s 2 2s 2 2p 6 3s 2 3p 3 16 S s 2 2s 2 2p 6 3s 2 3p 4 17 Cl s 2 2s 2 2p 6 3s 2 3p 5 18 Ar s 2 2s 2 2p 6 3s 2 3p 6
9 9 Chapter 1 Semiconductors: A General Introduction 14 electrons occupying the first 3 energy levels: 1s, 2s, 2p orbitals are filled by 10 electrons. 3s, 3p orbitals filled by 4 electrons. To minimize the overall energy, the 3s and 3p orbitals hybridize to form four tetrahedral 3sp orbital. Each has one electron and is capable of forming a bond with a neighboring atom. The Silicon Atom
10 10 Chapter 1 Semiconductors: A General Introduction The Si Crystal Each Si atom has 4 nearest neighbors. Atom lattice constant (length of the unit cell side) a = 5.431A, 1A=10 10 m Each cell contains: 8 corner atoms 6 face atoms 4 interior atoms a Diamond Lattice
11 11 Chapter 1 Semiconductors: A General Introduction How Many Silicon Atoms per cm 3? Number of atoms in a unit cell: 4 atoms completely inside cell Each of the 8 atoms on corners are shared among 8 cells count as 1 atom inside cell Each of the 6 atoms on the faces are shared among 2 cells count as 3 atoms inside cell Total number inside the cell = = 8 Cell volume = (.543 nm) 3 = 1.6 x cm 3 Density of silicon atom = (8 atoms) / (cell volume) = atoms/cm 3 What is density of silicon in g/cm 3?
12 13 Miller Indices Chapter 1 Semiconductors: A General Introduction Crystallographic Notation Notation Interpretation ( h k l ) crystal plane { h k l } equivalent planes [ h k l ] crystal direction < h k l > equivalent directions h: inverse x-intercept of plane k: inverse y-intercept of plane l: inverse z-intercept of plane (h, k and l are reduced to 3 integers having the same ratio.)
13 14 Chapter 1 Semiconductors: A General Introduction Crystallographic Planes _ (123) plane (001) plane (112) plane
14 15 Chapter 1 Semiconductors: A General Introduction Crystallographic Planes
15 16 Chapter 1 Semiconductors: A General Introduction Crystallographic Planes of Si Wafers Silicon wafers are usually cut along a {100} plane with a flat or notch to orient the wafer during integrated-circuit fabrication. The facing surface is polished and etched yielding mirror-like finish.
16 Chapter 1 Semiconductors: A General Introduction Crystal Growth Until Device Fabrication 17
17 18 Chapter 1 Semiconductors: A General Introduction Crystallographic Planes of Si Unit cell: View in <111> direction View in <100> direction View in <110> direction
18 Chapter 2 Carrier Modeling 19
19 Chapter 2 Carrier Modeling Electronic Properties of Si 20 Silicon is a semiconductor material. Pure Si has a relatively high electrical resistivity at room temperature. There are 2 types of mobile charge-carriers in Si: Conduction electrons are negatively charged, e = C Holes are positively charged, p = C The concentration (number of atoms/cm 3 ) of conduction electrons & holes in a semiconductor can be influenced in several ways: Adding special impurity atoms (dopants) Applying an electric field Changing the temperature Irradiation
20 21 Chapter 2 2-D Representation Carrier Modeling Bond Model of Electrons and Holes Si Si Si Si Si Si Si Si Si When an electron breaks loose and becomes a conduction electron, then a hole is created. Hole Si Si Si Si Si Si Si Si Si Conduction electron
21 22 Chapter 2 Carrier Modeling What is a Hole? A hole is a positive charge associated with a half-filled covalent bond. A hole is treated as a positively charged mobile particle in the semiconductor.
22 23 Chapter 2 Carrier Modeling Conduction Electron and Hole of Pure Si Covalent (shared e ) bonds exists between Si atoms in a crystal. Since the e are loosely bound, some will be free at any T, creating hole-electron pairs. n i = intrinsic carrier concentration n i cm 3 at room temperature
23 Chapter 2 Carrier Modeling Si: From Atom to Crystal 24 Energy states (in Si atom) Energy bands (in Si crystal) The highest mostly-filled band is the valence band. The lowest mostly-empty band is the conduction band.
24 Electron energy 25 Chapter 2 Carrier Modeling Energy Band Diagram E c E G, band gap energy E v For Silicon at 300 K, E G = 1.12 ev 1 ev = 1.6 x J Simplified version of energy band model, indicating: Lowest possible conduction band energy (E c ) Highest possible valence band energy (E v ) E c and E v are separated by the band gap energy E G.
25 26 Chapter 2 Carrier Modeling Measuring Band Gap Energy E G can be determined from the minimum energy (hn) of photons that can be absorbed by the semiconductor. This amount of energy equals the energy required to move a single electron from valence band to conduction band. Electron Photon E c photon energy: hn = E G E v Hole Band gap energies Semiconductor Ge Si GaAs Diamond Band gap (ev)
26 27 Chapter 2 Carrier Modeling Carriers Completely filled or empty bands do not allow current flow, because no carriers available. Broken covalent bonds produce carriers (electrons and holes) and make current flow possible. The excited electron moves from valence band to conduction band. Conduction band is not completely empty anymore. Valence band is not completely filled anymore.
27 28 Chapter 2 Carrier Modeling Band Gap and Material Classification E c E v E c E G = ~8 ev E v E G =1.12 ev Ec Ev E c E v SiO 2 Si Metal Insulators have large band gap E G. Semiconductors have relatively small band gap E G. Metals have very narrow band gap E G. Even, in some cases conduction band is partially filled, E v > E c.
28 29 Chapter 2 Carrier Modeling Carrier Numbers in Intrinsic Material More new notations are presented now: n : number of electrons/cm 3 p : number of holes/cm 3 n i : intrinsic carrier concentration In a pure semiconductor, n = p = n i. At room temperature, n i = /cm 3 in GaAs n i = /cm 3 in Si n i = /cm 3 in Ge
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