Lecture 25: Semiconductors ENGR-1600 Materials Science for Engineers Lecture 25: Semiconductors

Electron Energy Band Structures Pauli Exclusion Principle: no two e- in an interacting system can have exactly same energy When N atoms are far apart, they do not interact, so electrons in a given shell in different atoms have same energy As atoms come closer together, they do interact, perturbing electron energy levels Electrons from each atom then have slightly different energies, producing a “band” of allowed energies

Band Theory for Metals and Semiconductors @ 0 K @ room temp Metals: very large n Semiconductors: modest n

Microscopic Electric Conductivity vd = eE  = n e e each line between scatter events is very slightly curved under bias vd drift velocity [m/s] μ e- mobility [m2/Vs] n # of free electrons |e| charge of an e- [C] When an electric field E is applied, e- experience a force. Hence, they accelerate. This force is counteracted by scattering events (analogy to friction). When the forces balance out, there is a constant mean value of e- velocity vd. The vd is proportional to E by the factor μ, the “electron mobility”

Conductivity of Metals and Semiconductors metal >> semi

The Silicon Age

image from Wikipedia

Charge Carriers in Semiconductors Two types of electronic charge carriers: negative charge in conduction band positive charge of a vacant electron state in the valence band 1. Free Electron: 2. Hole: Move at different speeds - drift velocities

p = # of holes h+ left behind Intrinsic Semiconductors (for pure substances only) n = # of free electrons e- Si Si Si Si p = # of holes h+ left behind Si Si Si Si Si Si Si Si E field At a given temperature, intrinsic semiconductors have some electrons with enough energy to excite through the bandgap. What they leave behind is a “hole” Both e- and h+ are charge carriers, they move in opposite directions.

n = p Intrinsic Semiconductors: Conductivity vs T • Pure Silicon: - σ increases with T - opposite to metals n = p material Si Ge GaP CdS GaAs SiC band gap Egap (eV) 1.11 0.67 2.25 2.40 1.43 2.86 Larger electronegativity difference  larger bandgap.

Team Problem

Team Problem 1. Which of ZnSe and CdTe will have the larger band gap energy Eg ? 2. Which of ZnSe and CdTe will have the higher intrinsic carrier concentration at room temperature?

Extrinsic Semiconductors: the role of impurity 3 5 These elements have one less valence e- relative to Si When present as impurities, they will create lots of extra holes called “p-type” These elements have one more valence e- relative to Si When present as impurities, they will create lots of extra mobile e- called “n-type” 4

Extrinsic Semiconductors: n-type -- electrical behavior is determined by impurities that introduce excess electrons or holes -- n ≠ p • n-type Extrinsic: (n >> p)

Extrinsic Semiconductors: n-type

Extrinsic Semiconductors: p-type • p-type Extrinsic: (p >> n)

Extrinsic Semiconductors: p-type

Intrinsic vs. Extrinsic Semiconductors Extrinsic n-type Extrinsic p-type n for “negative” p for “positive”

What’s the difference between intrinsic and extrinsic semiconductors? Team Problem What’s the difference between intrinsic and extrinsic semiconductors? Which do you think would be more useful in modern technology?

T1 T2 Extrinsic Semiconductors: Conductivity vs. Temperature T<T1: Freeze-out region, thermal energy is not high enough to excite electron from donor state to CB T1<T<T2: Extrinsic region, thermal energy is high enough to excite electron from donor state to CB T>T2: Intrinsic region, thermal energy is high enough to excite electron from VB to CB T1 T2

Mobility vs. Impurity concentration @ room temp

Mobility vs. Temperature

So, the As is present at about 0.001 atomic %. That’s a tiny bit Team Problem Si is doped with As at a concentration of 1022 As atoms 1/m3. Is this a lot or a little bit of doping? MW [g/mol] ρ [g/cm3] So, the As is present at about 0.001 atomic %. That’s a tiny bit

p-n Rectifying Junction • Allows flow of electrons in one direction only (e.g., AC/DC). -- No applied potential: no net current flow. -- Forward bias: carriers flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. + - -- Reverse bias: carriers flow away from p-n junction; junction region depleted of carriers; little current flow. - +

Properties of Rectifying Junction

p-n-p junction Voltage amplifier

M.O.S.F.E.T. device Positive electric field at the gate: drives holes out of the p-type channel This reduces conductivity to the drain (ON/OFF, a binary communication device) Tiny change in gate voltage = big change in conductivity across the channel