Semiconductor Device Physics Lecture 2 Dr Ing Erwin

Semiconductor Device Physics Lecture 2 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com President University Erwin Sitompul SDP 2/1

Chapter 2 Carrier Modeling Electronic Properties of Si n Silicon is a semiconductor material. n Pure Si has a relatively high electrical resistivity at room temperature. n There are 2 types of mobile charge-carriers in Si: n Conduction electrons are negatively charged, e = – 1. 602 10– 19 C n Holes are positively charged, p = +1. 602 10– 19 C n The concentration (number of atom/cm 3) of conduction electrons & holes in a semiconductor can be influenced in several ways: n Adding special impurity atoms (dopants) n Applying an electric field n Changing the temperature n Irradiation President University Erwin Sitompul SDP 2/2

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

Chapter 2 Carrier Modeling What is a Hole? n A hole is a positive charge associated with a half-filled covalent bond. n A hole is treated as a positively charged mobile particle in the semiconductor. President University Erwin Sitompul SDP 2/4

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. ni = intrinsic carrier concentration President University ni ≈ 1010 cm– 3 at room temperature Erwin Sitompul SDP 2/5

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

Chapter 2 Carrier Modeling Energy Band Diagram Electron energy Ec EG, band gap energy Ev • For Silicon at 300 K, EG = 1. 12 e. V • 1 e. V = 1. 6 x 10– 19 J n Simplified version of energy band model, indicating: n Lowest possible conduction band energy (Ec) n Highest possible valence band energy (Ev) n Ec and Ev are separated by the band gap energy EG. President University Erwin Sitompul SDP 2/7

Chapter 2 Carrier Modeling Measuring Band Gap Energy n EG can be determined from the minimum energy (hn) of photons that can be absorbed by the semiconductor. n This amount of energy equals the energy required to move a single electron from valence band to conduction band. Electron Ec Photon photon energy: hn = EG Ev Hole Band gap energies President University Erwin Sitompul SDP 2/8

Chapter 2 Carrier Modeling Carriers n Completely filled or empty bands do not allow current flow, because no carriers available. n Broken covalent bonds produce carriers (electrons and holes) and make current flow possible. n The excited electron moves from valence band to conduction band. n Conduction band is not completely empty anymore. n Valence band is not completely filled anymore. President University Erwin Sitompul SDP 2/9

Chapter 2 Carrier Modeling Band Gap and Material Classification Ec Ev Ec EG= ~8 e. V Ev Si. O 2 EG = 1. 12 e. V Si Ec Ec Ev Ev Metal n Insulators have large band gap EG. n Semiconductors have relatively small band gap EG. n Metals have very narrow band gap EG. n Even, in some cases conduction band is partially filled, Ev > Ec. President University Erwin Sitompul SDP 2/10

Chapter 2 Carrier Modeling Carrier Numbers in Intrinsic Material n More new notations are presented now: nn : number of electrons/cm 3 np : number of holes/cm 3 n ni : intrinsic carrier concentration n In a pure semiconductor, n = p = ni. n At room temperature, ni = 2 106 /cm 3 in Ga. As ni = 1 1010 /cm 3 in Si ni = 2 1013 /cm 3 in Ge President University Erwin Sitompul SDP 2/11

Chapter 2 Carrier Modeling Manipulation of Carrier Numbers – Doping n 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. Acceptors: B, Ga, In, Al President University Erwin Sitompul Donors: P, As, Sb SDP 2/12

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

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

Chapter 2 Carrier Modeling Donor / Acceptor Levels (Band Model) ▬ + ▬ ED Donor Level Ec Donor ionization energy Acceptor Level EA Ev + Ionization energy of selected donors and acceptors in Silicon Donors Ionization energy of dopant EC – ED or EA – EV (me. V) President University Sb P 39 45 Erwin Sitompul Acceptors As B 54 45 Al In 67 160 SDP 2/15

Chapter 2 Carrier Modeling Dopant Ionization (Band Model) n Donor atoms n Acceptor atoms President University Erwin Sitompul SDP 2/16

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

Chapter 2 Carrier Modeling Density of States Ec Ev DE E Ec Ev gc(E) density of states g(E) gv(E) n g(E) is the number of states per cm 3 per e. V. n g(E)d. E is the number of states per cm 3 in the energy range between E and E+d. E). President University Erwin Sitompul SDP 2/18

Chapter 2 Carrier Modeling Density of States Ec E DE Ec Ev Ev gc(E) density of states g(E) gv(E) n Near the band edges: E Ec E Ev mo: electron rest mass President University Erwin Sitompul SDP 2/19

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

Chapter 2 Carrier Modeling Effect of Temperature on f(E) President University Erwin Sitompul SDP 2/21

Chapter 2 Carrier Modeling Effect of Temperature on f(E) President University Erwin Sitompul SDP 2/22

Chapter 2 Carrier Modeling Equilibrium Distribution of Carriers n n(E) is obtained by multiplying gc(E) and f(E), p(E) is obtained by multiplying gv(E) and 1–f(E). n Intrinsic semiconductor material Energy band diagram President University Density of states Probability of occupancy Erwin Sitompul Carrier distribution SDP 2/23

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

Chapter 2 Carrier Modeling Equilibrium Distribution of Carriers n p-type semiconductor material Energy band diagram President University Density of States Probability of occupancy Erwin Sitompul Carrier distribution SDP 2/25

Chapter 2 Carrier Modeling Important Constants n Electronic charge, q = 1. 6 10– 19 C n Permittivity of free space, εo = 8. 854 10– 12 F/m n Boltzmann constant, k = 8. 62 10– 5 e. V/K n Planck constant, h = 4. 14 10– 15 e. V s n Free electron mass, mo = 9. 1 10– 31 kg n Thermal energy, k. T = 0. 02586 e. V (at 300 K) n Thermal voltage, k. T/q = 0. 02586 V (at 300 K) President University Erwin Sitompul SDP 2/26

Chapter 2 Carrier Modeling Homework 1 Problem 2. 5 Develop an expression for the total number of available states/cm 3 in the conduction band between energies Ec and Ec+ γk. T, 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 EF is positioned at Ec, determine (numerical answer required) the probability of finding electrons in states at Ec + k. T. (c) The probability a state is filled at Ec + k. T is equal to the probability a state is empty at Ec + k. T. Where is the Fermi level located? Due date: Thursday, 28. 01. 10, 8 am. President University Erwin Sitompul SDP 2/27