Lecture 2 OUTLINE Semiconductor Basics Reading: Chapter 2

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

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

Semiconductor Materials Phosphorus (P) Gallium (Ga)

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

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

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.

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; Holes are 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

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.

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 Eg and the absolute temperature (T):

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

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

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

Intrinsic vs. Extrinsic Semiconductor

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

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)

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

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

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)

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

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 = q p vh

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

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.