The Electromagnetic Properties of Materials

Transcription

1 The lectromagnetic Properties of Materials lectrical conduction Metals Semiconductors Insulators (dielectrics) Superconductors Magnetic materials Ferromagnetic materials Others Photonic Materials (optical) Transmission of light Photoactive materials Photodetectors and photoconductors Light emitters: LD, lasers

2 Ohm s Law V V = IR L = (ja)r + - I L e - ρ j = σ = jρ σ = conductivity ρ = 1/σ = resistivity Ohm s Law: V = IR Describes macroscopic conductivity Note current is opposite electron flow Material properties Separate geometry from inherent material behavior Material properties relate current density, j, to local field, If material is cubic or isotropic, σ is scalar

3 Conduction by electrons v F = q = e v v = v + δv = v + Ft m = v et m δv = eτ m = e l mv v In an electron field lectrons accelerated by field lectrons scattered by collisions Acquire net drift velocity <δv> Collisions characterized by τ = mean time between collisions <l> = mean free path δv = µ µ = mobility = eτ m = e l mv

4 Current Density <δv> j = ne δv = neµ σ = ne2 τ m = ne2 l mv ρ = mv ne 2 l j = - ne<δv> lectron current is by diffusion n = conduction electrons/unit vol µ = mobility Quality of metallic conductor n = bonding and crystal structure µ = microstructure sensitive σ = neµ

5 Conductor Type and Quality F G F G conduction band valence band F The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. F If the red still appears, you may have to delete the image and then insert it again. The image cannot be G G F For metallic conduction F in valence band Three types Natural metals Odd valence High σ (Al, Cu. Au ) Band overlap metals ven valence Lower σ (Zn, Ca, Mg ) Transition metals F in d-band Poor σ (Fe, Ni, )

6 Resistivity Scattering from imperfections Impurities strain or charge) Phonons Vibrations displace atom cores /2 a Contributions to resistivity add N =# collisions = L l = L l 1 + L l ρ = mv ne 2 l = ρ 1 + ρ

7 Resistivity T ρ = ρ 0 + AT impurity increasing purity phonon Resistivity Impurities and phonons add Phonon linear in T Impurity independent of T Use residual resistivity to measure purity

8 Semiconductors: The Bottom Line Semiconductors are poor conductors of electricity Semiconductors are useful because they are controllable Can adjust conductivity Can choose type of conductor: electrons or positive holes Most microelectronic devices use semiconductor junctions Diodes (n p) Transistors (n p n or p n p) Other devices are based on controlling band gap specially photonic materials (optical properties) We shall cover these later

9 Semiconductors Semiconductor type and conductivity Conductivity dominated by carrier density Intrinsic semiconductors (ecitation across band gap) trinsic semiconductors n-type (donors) or p-type (acceptors) Permit precise control over σ and type of carrier Semiconductor junctions n p diode n p n bipolar transistor Field effect transistor (mosfet) Manufacturing semiconductor devices Lithography Doping Packaging

10 Intrinsic Semiconductor e - conduction band Filled bands separated by a gap F approimately in center of the gap F G valence band citation creates two carriers: Free electron in conduction band Hole in valence band Conductivity controlled by carrier density σ = n e eµ e + n p eµ p

11 Conduction lectron Density Probability an electron state is filled Fermi-Dirac function for energy, : P() = For F at midpoint of band gap: 1 ep ep F F +1 kt P() ep c ep c F ep c ep G 2kT n = c F P()N()d ep G 2kT c G conduction band valence band ep c N()d n = N c ep G 2kT (N c N 0 )

12 Density of Holes Probability of hole at : 1 p() =1 P() = ep F +1 ep F = ep F v ep v p() ep v ep G 2kT p = F v G p()n()d p N 0 ep G 2kT conduction band valence band (= n)

13 Carrier Density in an Intrinsic Semiconductor lectrons (n) n N 0 ep G 2kT F G conduction band valence band Holes (p) p N 0 ep G 2kT (= n) n = p = c v P()N()d p()n()d

14 Conductivity of an Intrinsic Semiconductor σ sums electrons and holes: σ = neµ e + peµ p N 0 e(µ e + µ p )ep G 2kT σ N 0 eµ e ep G 2kT (µ e >> µ p ) Plot ln(σ) vs. 1/kT: Straight line Slope is ( G /2)

15 Semiconductors Semiconductor type and conductivity Conductivity dominated by carrier density Intrinsic semiconductors (ecitation across band gap) trinsic semiconductors n-type (donors) or p-type (acceptors) Permit precise control over σ and type of carrier Semiconductor junctions n p diode n p n bipolar transistor Field effect transistor (mosfet) Manufacturing semiconductor devices Lithography Doping Packaging

16 trinsic Semiconductors: n-type e Si Si P Si Si Î G Conduction band Valence band } ÎD donor levels n-type semiconductors are doped with donors Common donor has 1 etra valence electron (e.g., P in Si) Donor electron in ecited state weakly bound to etra + on donor Corresponds to localized donor levels just below conduction band lectrons are ecited from donor levels to produce carriers Conduction is by electrons

17 trinsic Semiconductors: p-type Si Si B Si Si Î G Conduction band Valence band acceptor levels } ÎA p-type semiconductors are doped with acceptors Common acceptor has 1 less valence electron (e.g., B in Si) Hole in valence state weakly bound to effective - on acceptor Corresponds to localized acceptor levels just above valence band lectrons are ecited to acceptor levels to produce free holes Conduction is by holes

18 trinsic Semiconductors: Conductivity of an n-type Semiconductor Fermi level and carrier density F (T) n N 0 ep c F T p N 0 ep F V 2kT D + 1 F = 2 c D V + G 2 2N 0 ( ) + kt 2 ln N D (low T) (high T) n = N D + + p F ~ D + Δ D /2 at low T, ~ V + G /2 at high T

19 trinsic Semiconductors: Conductivity of an n-type Semiconductor intrinsic Carrier density determines σ σ = neµ e ln(n) G /2kT D /2kT saturation etrinsic higher N n N 0 ep c F p N 0 ep F V 2 n = N + D + p 1/kT n = N 0 N D 2 ep Δ D 2 N D N 0 ep G 2kT (low T) (saturation) (high T)

20 trinsic Semiconductors: Conductivity of a p-type Semiconductor Carrier density determines σ F sits near V + Δ A /2 at low T F rises to V + G /2 at high T F (T) p N 0 ep F V 2kT p = N A + n T p = N 0 N A 2 ep Δ A 2 N A N 0 ep G 2kT (low T) (saturation) (high T) ln (p) G 2 σ = peµ p Δ A 2 1/ kt

21 trinsic Semiconductors: Degeneracy Conduction band donor band acceptor levels Valence band At a critical concentration, donor states overlap Donor band = continuous band of donor states Degenerate semiconductor is a metallic conductor Overpopulation of acceptors also creates degeneracy

22 trinsic Semiconductors: Titration Conduction band donor levels acceptor levels Valence band Donor electrons fill acceptor levels n-type behavior is not achieved until acceptors filled Acceptors must be titrated before donor states overlap Semiconductors must have high purity prior to doping Converse applies: acceptors titrate donors Can convert n-type to p-type if donor concentration is small

23 Semiconductor Junctions Join n- and p-type regions to create a junction Junctions have asymmetric electrical properties Can be done by doping adjacent regions Write junction devices onto a single crystal (chip) This is the basis of all microelectronics