4/28/15 Electrical Properties View of an Integrated Circuit • Scanning electron micrographs of an IC: ISSUES TO ADDRESS... Al (d) • How are electrical conductance and resistance Si characterized? (What effects conductance?) (doped) 45 µm 0.5 mm • What are the physical phenomena that distinguish conductors, semiconductors, and insulators? • A dot map showing location of Si (a semiconductor): • For metals, how is conductivity affected by -- Si shows up as light regions. (b) imperfections, temperature, and deformation? & dark region is Al wiring • For semiconductors, how is conductivity affected by impurities (doping) and temperature? 2 Chapter 18 - 1 Chapter 18 - Electrical Conduction Electrical Properties • Ohm's Law: V = I R • Which will have the greater resistance? voltage drop (volts = J/C) resistance (Ohms) current (amps = C/s) C = Coulomb 2 2ρ 8ρ R D 1 = 2 = 2 !D$ πD • Resistivity, ρ: π # & " 2 % - a material property that is independent of sample size and geometry current flow € ρ ρ R 2D R = = = 1 path length 2 2 2 !2D$ πD 8 cross-sectional area π # & " 2 % of current flow € RA ρ = • Analogous to flow of cars on road • Resistance depends on sample geometry and • Conductivity, σ 1 size. σ = ρ • Resistivity of independent of sample geometry Chapter 18 - 3 Chapter 18 - 4 1 4/28/15 Conductivity: Comparison Definitions Room temperature values in (Ω - m)-1 Further definitions METALS conductors CERAMICS J = σ ε ß another way to state Ohm’s law Silver 6.8 x 10 7 Soda-lime glass 10 -10-10 -11 7 -9 current I Copper 6.0 x 10 Concrete 10 J = current density = = like a flux 7 surface area A Iron 1.0 x 10 Aluminum oxide <10-13 ε = electric field potential = V/ℓ € SEMICONDUCTORS POLYMERS J = σ (V/ℓ ) -14 Silicon 4 x 10 -4 Polystyrene <10 0 -15 -17 Electron flux conductivity voltage gradient Germanium 2 x 10 Polyethylene 10 -10 GaAs 10 -6 semiconductors insulators 6 Chapter 18 - 5 Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 9e. Chapter 18 - Electron Drift Example: Conductivity Problem What is the minimum diameter (D) of the Cu wire so that V < 1.5 V? = 100 m Cu wire - I = 2.5 A + V € Electrons are scattered and drift slowly in one direction 100 m (1.2 in./min in Cu) due to the E field. < 1.5 V V R = = 2.5 A πD2 Aσ I However electrical signal “appear” to travels at about 2/3 the speed of light. 4 6.07 x 107 (Ohm-m)-1 As one electron is pushed into “full” pipe, an electron is Solve to get D > 1.87 mm pushed out the other end. Chapter 18 - 7 Chapter 18 - 2 4/28/15 Matthiessen’s Rule: The total resistivity of a material is the sum of the contributions from thermal vibrations, impurities, and plastic deformation σ = n |e| µe ρtotal = ρt + ρi + ρd σ – Conductivity t – Thermal Vibrations n - # of free electrons/VOL i - Impurities e - 1.6 X 1019 C d - Deformation µe - Electron Mobility Chapter 18 - 9 Chapter 18 - 10 Resistance vs. temp for other metals Resistance rises linearly with temperature when T > -200 oC ρt = ρο + aΤ = + aT ρt ρ0 Chapter 18 - 11 Chapter 18 - 12 3 4/28/15 Metals: Influence of Temperature and Impurities on Resistivity Estimating Conductivity • Presence of imperfections increases resistivity • Question: -- grain boundaries -- Estimate the electrical conductivity σ of a Cu-Ni alloy Adapted from Fig. -- dislocations These act to scatter 18.9, Callister & that has a yield strength of 125 MPa. Rethwisch 9e. -- impurity atoms electrons so that they 180 ρ take a less direct path. 50 -- vacancies 160 140 40 • Resistivity 125 Ohm-m) 6 30 120 ρ -8 increases with: 5 100 20 Resistivity, Resistivity, Cu + 3.32 at%Ni 21 wt% Ni (10 4 -- temperature 80 10 Ohm-m) -- wt% impurity 0 60 3 strength (MPa) Yield 0 10 20 30 40 50 0 -8 ρ 10 20 30 40 50 deformedd Cu + 1.12 at%Ni -- %CW Cu + 1.12 at%Ni wt% Ni, (Concentration C) wt% Ni, (Concentration C) Resistivity, Resistivity, 2 (10 ρi ” Cu Adapted from Fig. 7.16(b), Callister & Rethwisch 9e. −8 1 “Pure ρ = ρ ρ = 30 x 10 Ohm − m ρ thermal From step 1: t 0 + ρ 1 6 −1 -200 -100 0 T (ºC) impurity 3.3 x 10 (Ohm m) C = 21 wt% Ni σ = = − Fig. 18.8, Callister & Rethwisch 9e. [Adapted from J. O. Linde, Ann. + ρ Ni ρ Physik, 5, 219 (1932); and C. A. Wert and R. M. Thomson, Physics of Solids, deformation 2nd edition, McGraw-Hill Book Company, New York, 1970.] Chapter 18 - 13 Chapter 18 - 14 Electron Energy Band Structures Band Structure Representation Fig. 18.3, Callister & Rethwisch 9e. Adapted from Fig. 18.2, Callister & Rethwisch 9e. Chapter 18 - 15 Chapter 18 - 16 4 4/28/15 Example band structures at 0K Conduction & Electron Transport • Metals (Conductors): -- for metals empty energy states are adjacent to filled states. -- thermal energy Partially filled band Overlapping bands excites electrons Energy Energy into empty higher empty energy states. band -- two types of band GAP empty structures for metals band - partially filled band partly filled filled - empty band that overlaps filled band band band filled filled band filled states band filled states Chapter 18 - 17 Chapter 18 - 18 Energy Band Structures: Charge Carriers in Insulators and Insulators & Semiconductors Semiconductors Fig. 18.6 (b), Callister & • Insulators: • Semiconductors: Rethwisch 9e. -- wide band gap (> 2 eV) -- narrow band gap (< 2 eV) Two types of electronic charge -- few electrons excited -- more electrons excited carriers: across band gap across band gap Free Electron Energy empty Energy empty conduction conduction – negative charge band band GAP ? – in conduction band GAP Hole filled filled valence valence – positive charge band band – vacant electron state in the valence band filled filled filled states filled states band band Move at different speeds - drift velocities Chapter 18 - 19 Chapter 18 - 20 5 4/28/15 Intrinsic Semiconductors • Pure material semiconductors: e.g., silicon & germanium – Group IVA materials • Compound semiconductors – III-V compounds • Ex: GaAs & InSb – II-VI compounds • Ex: CdS & ZnTe – The wider the electronegativity difference between the elements the wider the energy gap. Chapter 18 - 21 Chapter 18 - 22 Intrinsic Semiconduction in Terms of Number of Charge Carriers Electron and Hole Migration Intrinsic Conductivity • Concept of electrons and holes: n e p e valence electron hole electron hole σ = µe + µh Si atom electron pair creation pair migration • for intrinsic semiconductor n = p = ni - + - + ∴ σ = ni|e|(µe + µh) • Ex: GaAs no applied applied applied −6 −1 electric field electric field electric field σ 10 ( ⋅m) n Ω Adapted from Fig. 18.11, i = = −19 2 • Electrical Conductivity given by: Callister & Rethwisch 9e. e (1.6 x 10 C)(0.85 0.45 m /V s) (µe + µh ) + ⋅ # holes/m3 σ = n e µ + p e µ 24 -3 e h hole mobility For GaAs ni = 4.8 x 10 m 16 -3 # electrons/m3 electron mobility For Si ni = 1.3 x 10 m Chapter 18 - 23 Chapter 18 - 24 6 4/28/15 Intrinsic Semiconductors: Conductivity vs T Thermistors as temperature sensors – devices made from semiconductor material. Their • Data for Pure Silicon: -- σ increases with T resistance decreases with increasing temperature. -- opposite to metals n e σ = i (µe + µh ) −Egap /kT ni ∝ e material band gap (eV) Si 1.11 Ge 0.67 GaP 2.25 CdS 2.40 Selected values from Table 18.3, Callister & Rethwisch 9e. Adapted from Fig. 18.16, 25 Callister & Rethwisch 9e. Chapter 18 - Chapter 18 - 26 Comparing Si to Cu at room temp. 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. If the red x still appears, you may have to delete the image and then insert it again. 2 • µcu = 30 cm /V-S 29 2 • ncu = 10 /cm 2 • µsi = 1400 cm /V-S 16 2 • nsi = 10 /cm Electrons are 50 times more mobile in Si than in Cu but there are many more free electrons in Cu, therefore table_18_03 Cu is 200,000,000,000 times less resistive compared to copper. Chapter 18 - Chapter 18 - 28 7 4/28/15 Intrinsic vs Extrinsic Conduction • Intrinsic: -- case for pure Si -- # electrons = # holes (n = p) • Extrinsic: -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n ≠ p • n-type Extrinsic: (n >> p) • p-type Extrinsic: (p >> n) Phosphorus atom Boron atom hole 4 + 4 + 4 + 4 + conduction 4 + 4 + 4 + 4 + electron σ ≈ n e µe 4 + 5+ 4 + 4 + 4 + 3 + 4 + 4 + σ ≈ p e µh valence 4 + 4 + 4 + 4 + electron 4 + 4 + 4 + 4 + no applied no applied Adapted from Figs. 18.12(a) Si atom & 18.14(a), Callister & electric field electric field Rethwisch 9e. Chapter 18 - 29 Chapter 18 - Extrinsic Semiconductors: Conductivity vs. Temperature Factors That Affect Carrier Mobility Calculate the room-temperature electrical conductivity of Data for Doped Silicon: silicon that has been doped with 2 × 1023 m–3 of arsenic σ increases with doping doped atoms. The image cannot be displayed. Your computer may not have enough memory to open the Reason: dopants donate charge image, or the image may have been corrupted. Restart your computer, and then open the file undoped again. If the red x still appears, you may have to delete the image and then insert it again. carriers. 3 ) Conduction electrons = # of dopant ions.