President UniversityErwin SitompulSDP 2/1 Dr.-Ing. Erwin Sitompul President University Lecture 2 Semiconductor Device Physics

President UniversityErwin SitompulSDP 2/2 Chapter 2Carrier Modeling Electronic Properties of Si 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 = –1.602  10 –19 C Holes are positively charged, p =  10 –19 C The concentration (number of atom/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

President UniversityErwin SitompulSDP 2/3 Hole Conduction electron Chapter 2Carrier Modeling Bond Model of Electrons and Holes When an electron breaks loose and becomes a conduction electron, then a hole is created. 2-D Representation

President UniversityErwin SitompulSDP 2/4 Chapter 2Carrier 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.

President UniversityErwin SitompulSDP 2/5 Chapter 2Carrier Modeling Conduction Electron and Hole of Pure Si n i = intrinsic carrier concentration n i ≈ cm –3 at room temperature 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.

President UniversityErwin SitompulSDP 2/6 Energy states (in Si atom) Chapter 2Carrier Modeling Si: From Atom to Crystal The highest mostly-filled band is the valence band. The lowest mostly-empty band is the conduction band. Energy bands (in Si crystal)

President UniversityErwin SitompulSDP 2/7 EcEc EvEv Electron energy For Silicon at 300 K, E G = 1.12 eV 1 eV = 1.6 x 10 –19 J E G, band gap energy Chapter 2Carrier Modeling Energy Band Diagram 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.

President UniversityErwin SitompulSDP 2/8 Band gap energies Chapter 2Carrier Modeling Measuring Band Gap Energy E G can be determined from the minimum energy (h ) 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. Photon photon energy: h  = E G EcEc EvEv Electron Hole

President UniversityErwin SitompulSDP 2/9 Carriers Chapter 2Carrier Modeling 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.

President UniversityErwin SitompulSDP 2/10 Band Gap and Material Classification E c E v E G = 1.12 eV Si Metal E v E c E E c v E c E G = ~8 eV SiO 2 E v Chapter 2Carrier Modeling 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.

President UniversityErwin SitompulSDP 2/11 Carrier Numbers in Intrinsic Material Chapter 2Carrier Modeling 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 = 2  10 6 /cm 3 in GaAs n i = 1  /cm 3 in Si n i = 2  /cm 3 in Ge

President UniversityErwin SitompulSDP 2/12 Manipulation of Carrier Numbers – Doping Donors: P, As, SbAcceptors: B, Ga, In, Al Chapter 2Carrier Modeling By substituting a Si atom with a special impurity atom (elements from Group III or Group V), a hole or conduction electron can be created.

President UniversityErwin SitompulSDP 2/13 Doping Silicon with Acceptors Al – is immobile Chapter 2Carrier Modeling Example: Aluminium atom is doped into the Si crystal. The Al atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, and as a moving positive charge, the hole carries current.

President UniversityErwin SitompulSDP 2/14 Doping Silicon with Donors P  is immobile Chapter 2Carrier Modeling Example: Phosphor atom is doped into the Si crystal. The loosely bounded fifth valence electron of the P atom can “break free” easily and becomes a mobile conducting electron. This electron contributes in current conduction.

President UniversityErwin SitompulSDP 2/15 E c Donor Level EDED Donor ionization energy E v Acceptor Level E A Acceptor ionization energy + ▬ ▬ + Ionization energy of selected donors and acceptors in Silicon Acceptors Ionization energy of dopant SbPAsBAlIn E C – E D or E A – E V (meV) Donors Chapter 2Carrier Modeling Donor / Acceptor Levels (Band Model)

President UniversityErwin SitompulSDP 2/16 Chapter 2Carrier Modeling Dopant Ionization (Band Model) Donor atoms Acceptor atoms

President UniversityErwin SitompulSDP 2/17 Chapter 2Carrier Modeling Carrier-Related Terminology Donor: impurity atom that increases n (conducting electron). Acceptor: impurity atom that increases p (hole). n-type material: contains more electrons than holes. p-type material: contains more holes than electrons. Majority carrier: the most abundant carrier. Minority carrier: the least abundant carrier. Intrinsic semiconductor: undoped semiconductor n = p = n i. Extrinsic semiconductor: doped semiconductor.

President UniversityErwin SitompulSDP 2/18 EcEc EvEv EE Chapter 2Carrier Modeling Density of States E EcEc EvEv gc(E)gc(E) gv(E)gv(E) density of states g(E) g(E) is the number of states per cm 3 per eV. g(E)dE is the number of states per cm 3 in the energy range between E and E+dE).

President UniversityErwin SitompulSDP 2/19 EcEc EvEv EE E  E c E  EvE  Ev m o : electron rest mass Chapter 2Carrier Modeling Density of States Near the band edges: E EcEc EvEv gc(E)gc(E) gv(E)gv(E) density of states g(E)

President UniversityErwin SitompulSDP 2/20 k: Boltzmann constant T: temperature in Kelvin Chapter 2Carrier Modeling Fermi Function The probability that an available state at an energy E will be occupied by an electron is specified by the following probability distribution function: E F is called the Fermi energy or the Fermi level.

President UniversityErwin SitompulSDP 2/21 Chapter 2Carrier Modeling Effect of Temperature on f(E)

President UniversityErwin SitompulSDP 2/22 Chapter 2Carrier Modeling Effect of Temperature on f(E)

President UniversityErwin SitompulSDP 2/23 Energy band diagram Density of states Probability of occupancy Carrier distribution Chapter 2Carrier Modeling Equilibrium Distribution of Carriers n(E) is obtained by multiplying g c (E) and f(E), p(E) is obtained by multiplying g v (E) and 1–f(E). Intrinsic semiconductor material

President UniversityErwin SitompulSDP 2/24 Energy band diagram Density of States Probability of occupancy Carrier distribution Chapter 2Carrier Modeling Equilibrium Distribution of Carriers n-type semiconductor material

President UniversityErwin SitompulSDP 2/25 Energy band diagram Density of States Probability of occupancy Carrier distribution Chapter 2Carrier Modeling Equilibrium Distribution of Carriers p-type semiconductor material

President UniversityErwin SitompulSDP 2/26 Chapter 2Carrier Modeling Important Constants Electronic charge, q = 1.6  10 –19 C Permittivity of free space, ε o =  10 –12 F/m Boltzmann constant, k = 8.62  10 –5 eV/K Planck constant, h = 4.14  10 –15 eV  s Free electron mass, m o = 9.1  10 –31 kg Thermal energy, kT = eV (at 300 K) Thermal voltage, kT/q = V (at 300 K)

President UniversityErwin SitompulSDP 2/27 Problem 2.5 Develop an expression for the total number of available states/cm3 in the conduction band between energies E c and E c + γ kT, where γ is an arbitrary constant. Problem 2.6 (a)Under equilibrium condition at T > 0 K, what is the probability of an electron state being occupied if it is located at the Fermi level? (b)If E F is positioned at E c, determine (numerical answer required) the probability of finding electrons in states at E c + kT. (c)The probability a state is filled at E c + kT is equal to the probability a state is empty at E c + kT. Where is the Fermi level located? Chapter 2Carrier Modeling Homework 1 Due date: Thursday, , 8 am.