Lecture 2

1. Lecture 2 OUTLINE • Semiconductor Basics Reading: Chapter 2

2. Announcement • Office Hours for tomorrow is cancelled (ONLY for this week) There will be office hours on Friday (2P-3P) (ONLY for this week) Thursday’s class will start at 4P (ONLY for this week)

3. What is a Semiconductor? • Low resistivity => “conductor” • High resistivity => “insulator” • Intermediate resistivity => “semiconductor” • conductivity lies between that of conductors and insulators • generally crystalline in structure for IC devices • In recent years, however, non-crystalline semiconductors have become commercially very important polycrystalline amorphous crystalline

4. Semiconductor Materials Phosphorus (P) Gallium (Ga)

5. Energy Band Description • For current flow, one needs to have electrons in the conduction band or holes in the valence band • Completely full or completely empty bands cannot carry current

6. Energy Band Description Current due to electron flow and hole flow will add up

7. Silicon • Atomic density: 5 x 1022 atoms/cm3 • Si has four valence electrons. Therefore, it can form covalent bonds with four of its nearest neighbors. • When temperature goes up, electrons can become free to move about the Si lattice.

8. 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 electronsare negatively charged; • Holesare positively charged.  The concentration (#/cm3) of conduction electrons & holes in a semiconductor can be modulated in several ways: • by adding special impurity atoms ( dopants ) • by applying an electric field • by changing the temperature • by irradiation

9. Electron-Hole Pair Generation • When a conduction electron is thermally generated, a “hole” is also generated. • A hole is associated with a positive charge, and is free to move about the Si lattice as well.

10. Carrier Concentrations in Intrinsic Si • The “band-gap energy” Eg is the amount of energy needed to remove an electron from a covalent bond. • The concentration of conduction electrons in intrinsic silicon, ni, depends exponentially on Egand the absolute temperature (T):

11. Doping (N type) • Si can be “doped” with other elements to change its electrical properties. • For example, if Si is doped with phosphorus (P), each P atom can donate a conduction electron, so that the Si lattice has more electrons than holes, i.e. it becomes “N type”: Notation: n = conduction electron concentration

12. Doping (P type) • If Si is doped with Boron (B), each B atom can accept an electron (creating a hole), so that the Si lattice has more holes than conduction electrons, i.e. it becomes “P type”: Notation: p = hole concentration

13. Terminology donor: impurity atom that increases n acceptor: impurity atom that increases p 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: n = p = ni extrinsic semiconductor: doped semiconductor

14. Intrinsic vs. Extrinsic Semiconductor

15. Under thermal equilibrium conditions, the product of the conduction-electron density and the hole density is ALWAYS equal to the square of ni: Electron and Hole Concentrations N-type material P-type material

16. Dopant Compensation • An N-type semiconductor can be converted into P-type material by counter-doping it with acceptors such that NA > ND. • A compensated semiconductor material has both acceptors and donors. N-type material (ND > NA) P-type material (NA > ND)

17. Doping What is the electron and hole density if you dope Si with Boron to 1018 /cm3 ?

18. Charges in a Semiconductor • Negative charges: • Conduction electrons (density = n) • Ionized acceptor atoms (density = NA) • Positive charges: • Holes (density = p) • Ionized donor atoms (density = ND) • The net charge density (C/cm3) in a semiconductor is

19. Carrier Drift • The process in which charged particles move because of an electric field is called drift. • Charged particles within a semiconductor move with an average velocity proportional to the electric field. • The proportionality constant is the carrier mobility. Hole velocity Electron velocity Notation: mp hole mobility (cm2/V·s) mn electron mobility (cm2/V·s)

20. Velocity Saturation • In reality, carrier velocities saturate at an upper limit, called the saturation velocity (vsat).

21. Drift Current • Drift current is proportional to the carrier velocity and carrier concentration: Total current Jp,drift= Q/t Q= total charge contained in the volume shown to the right t= time taken by Q to cross the volume Q=qp(in cm3)X Volume=qpAL=qpAvht  Hole current per unit area (i.e. current density) Jp,drift = qpvh

22. Conductivity and Resistivity • In a semiconductor, both electrons and holes conduct current: • The conductivity of a semiconductor is • Unit: mho/cm • The resistivity of a semiconductor is • Unit: ohm-cm

23. Resistivity Example • Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015 cm-3 and boron to a concentration of 6x1017 cm-3.