Electronic Properties of Si

2. Chapter 2 Carrier 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=+1.602  10–19C • The concentration (number of atom/cm3) 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

3. Chapter 2 Carrier Modeling Si Si Si Si Si Si Si Si Si Bond Model of Electrons and Holes • 2-D Representation Hole • When an electron breaks loose and becomes a conduction electron, then a hole is created. Conductionelectron

4. 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.

5. 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≈ 1010 cm–3 at room temperature ni= intrinsic carrier concentration

6. Chapter 2 Carrier Modeling Si: From Atom to Crystal 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.

7. Chapter 2 Carrier Modeling Energy Band Diagram Energy Band Diagram Ec EG, band gap energy Electron energy Ev • For Silicon at 300 K, EG = 1.12 eV • 1 eV = 1.6 x 10–19 J • Simplified version of energy band model, indicating: • Lowest possible conduction band energy (Ec) • Highest possible valence band energy (Ev) • Ec and Ev are separated by the band gap energy EG.

8. Chapter 2 Carrier Modeling Measuring Band Gap Energy • EGcan 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 Ec Photon photon energy: hn= EG Ev Hole Band gap energies

9. 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.

10. Chapter 2 Carrier Modeling E v E c Band Gap and Material Classification E c = E ~8 eV G E c = E 1.12 eV E G c E E E v v v Metal Si SiO2 • Insulators have large band gap EG. • Semiconductors have relatively small band gap EG. • Metals have very narrow band gap EG . • Even, in some casesconduction band is partially filled,Ev > Ec.

11. Chapter 2 Carrier Modeling Carrier Numbers in Intrinsic Material • More new notations are presented now: • n : number of electrons/cm3 • p : number of holes/cm3 • ni: intrinsic carrier concentration • In a pure semiconductor, n = p = ni. • At room temperature, • ni= 2  106 /cm3 in GaAsni= 1  1010 /cm3 in Si ni= 2  1013 /cm3 in Ge

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

13. Chapter 2 Carrier Modeling Doping Silicon with Acceptors • Example: Aluminium atom is doped into the Si crystal. Al– is immobile • 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.

14. Chapter 2 Carrier Modeling Doping Silicon with Donors • Example: Phosphor atom is doped into the Si crystal. P+ is immobile • 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.

15. Chapter 2 Carrier Modeling E c ED Donor Level Donor ionization energy Acceptor ionization energy Acceptor Level E A E v Donor / Acceptor Levels (Band Model) ▬ + ▬ + Ionization energy of selected donors and acceptors in Silicon Donors Acceptors Sb P As B Al In Ionization energy of dopant EC – ED or EA – EV(meV) 39 45 54 45 67 160

16. Chapter 2 Carrier Modeling Dopant Ionization (Band Model) • Donor atoms • Acceptor atoms

17. Chapter 2 Carrier 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 = ni.Extrinsic semiconductor: doped semiconductor.

18. Chapter 2 Carrier Modeling DE Ec Ev Density of States E gc(E) Ec density of states g(E) Ev gv(E) • g(E) is the number of states per cm3 per eV. • g(E)dE is the number of states per cm3 in the energy range between E and E+dE).

19. Chapter 2 Carrier Modeling DE Ec Ev Density of States E gc(E) Ec density of states g(E) Ev gv(E) • Near the band edges: E Ec EEv mo: electron rest mass

20. Chapter 2 Carrier 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: k : Boltzmann constant T : temperature in Kelvin • EF is called the Fermi energy or the Fermi level.

21. Chapter 2 Carrier Modeling Effect of Temperature on f(E)

22. Chapter 2 Carrier Modeling Effect of Temperature on f(E)

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

24. Chapter 2 Carrier Modeling Equilibrium Distribution of Carriers • n-type semiconductor material Energy band diagram Density of States Carrier distribution Probability of occupancy

25. Chapter 2 Carrier Modeling Equilibrium Distribution of Carriers • p-type semiconductor material Energy band diagram Density of States Carrier distribution Probability of occupancy

26. Chapter 2 Carrier Modeling Important Constants • Electronic charge, q = 1.610–19 C • Permittivity of free space, εo = 8.854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, mo = 9.110–31 kg • Thermal energy, kT = 0.02586 eV (at 300 K) • Thermal voltage,kT/q = 0.02586 V (at 300 K)

27. Problem 2.5 Develop an expression for the total number of available states/cm3 in the conduction band between energies Ec and Ec+ γkT, where γis an arbitrary constant. Problem 2.6 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? If EF is positioned at Ec, determine (numerical answer required) the probability of finding electrons in states at Ec + kT. The probability a state is filled at Ec + kT is equal to the probability a state is empty at Ec + kT. Where is the Fermi level located? Chapter 2 Carrier Modeling Homework 1 Due date: Thursday, 28.01.10, 8 am.