12/10/09. Chapter 18: Electrical Properties. View of an Integrated Circuit. Electrical Conduction ISSUES TO ADDRESS...

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1 Chapter 18: Electrical Properties ISSUES TO ADDRESS... How are electrical conductance and resistance characterized? What are the physical phenomena that distinguish? For metals, how is affected by and deformation? For semiconductors, how is conductivity affected by impurities (doping) and temperature? Chapter 18-1 View of an Integrated Circuit Scanning micrographs of an IC: Al Si (doped) (d) (d) 45 µm 0.5 mm A dot map showing location of Si (a semiconductor): -- Si shows up as regions. (b) (a) A dot map showing location of Al (a conductor): -- Al shows up as regions. (c) Fig. (d) from Fig (a), Callister & Rethwisch 3e. (Fig is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) Figs. (a), (b), (c) from Fig , Callister & Rethwisch 8e. Chapter 18-2 Law: Electrical Conduction voltage drop (volts = J/C) C = V = I R resistance (Ohms) current (amps = C/s), ρ: -- a material property that is independent of sample size and geometry ρ = RA surface area of current flow, σ σ = 1 ρ current flow path length Chapter

2 Electrical Properties Which will have the greater? 2 D 2D Analogous to flow of water in a pipe depends on sample geometry and size. Chapter 18-4 Definitions Further definitions <= another way to state Ohm s law J current density ε J = σ (V/ ) Electron flux conductivity Chapter 18-5 Conductivity: Comparison Room temperature values (Ohm-m) -1 = (Ω - m) -1 METALS conductors Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x Soda-lime glass Concrete 10-9 Aluminum oxide <10-13 Silicon 4 x 10-4 Germanium 2 x 10 0 GaAs 10-6 semiconductors Selected values from Tables 18.1, 18.3, and 18.4, POLYMERS Polystyrene <10-14 Polyethylene Chapter

3 Example: Conductivity Problem What is the minimum diameter (D) of the wire so that V < 1.5 V? Cu wire - I = 2.5 A + V 100 m < 1.5 V 2.5 A Solve to get D > Chapter 18-7 Electron Energy Band Structures Adapted from Fig. 18.2, Chapter 18-8 Band Structure Representation Adapted from Fig. 18.3, Chapter

4 Conduction & Electron Transport Metals ( ): -- for metals are adjacent to states. -- thermal energy excites into empty higher energy states. -- two types of structures for metals - - empty that overlaps Partially Overlapping s Energy Energy empty GAP empty partly states states Chapter Energy Band Structures: Insulators & Semiconductors : -- wide gap ( ev) -- few electrons excited across gap Energy empty conduction GAP : -- narrow gap ( ev) -- more electrons excited across gap Energy? empty conduction GAP states valence states valence Chapter Metals: Influence of Temperature and Impurities on Resistivity increases resistivity -- grain boundaries impurity atoms -- 6 Resistivity, ρ (10-8 Ohm-m) Cu at%ni deformed Cu at%ni ρ t These act to scatter electrons so that they take a less direct path. Cu at%ni Pure Cu T (ºC) Adapted from Fig. 18.8, (Fig adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill Book Company, New York, 1970.) ρ d ρ i Resistivity with: -- temperature -- wt% impurity -- %CW ρ = ρ thermal + ρ impurity + ρ deformation Chapter

5 Estimating Conductivity Question: -- Estimate the electrical conductivity σ of a Cu-Ni alloy that has a yield strength of 125 MPa. Yield strength (MPa) wt% Ni wt% Ni, (Concentration C) Adapted from Fig. 7.16(b), From step 1: C Ni = Ni Resistivity, ρ (10-8 Ohm-m) Adapted from Fig. 18.9, Callister & Rethwisch 8e wt% Ni, (Concentration C) ρ = 30 x 10 8 Ohm m Chapter Charge Carriers in Insulators and Semiconductors Adapted from Fig. 18.6(b), Two carriers: charge in conduction charge vacant electron state in the valence Move at different speeds - drift velocities Chapter Intrinsic Semiconductors Pure material : e.g., silicon & germanium Group IVA materials Compound semiconductors compounds Ex: GaAs & InSb compounds Ex: CdS & ZnTe The wider the electronegativity difference between the elements the wider the energy gap. Chapter

6 Intrinsic Semiconduction in Terms of Migration Concept of : valence electron hole electron Si atom pair creation electron hole pair migration no applied applied applied electric field electric field electric field Electrical given by: # holes/m 3 Adapted from Fig , # electrons/m 3 electron mobility hole mobility Chapter Number of Charge Carriers Conductivity for semiconductor n = p = n i σ = n i e (µ e + µ h ) Ex: GaAs For GaAs n i = For Si n i = 1.3 x m -3 Chapter Intrinsic Semiconductors: Conductivity vs T Data for : -- σ increases with T -- opposite to metals material Si Ge GaP CdS gap (ev) Selected values from Table 18.3, Adapted from Fig , Chapter

7 Intrinsic vs Extrinsic Conduction : -- case for pure Si -- # electrons = # (n = p) : -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n-type : (n >> p) Phosphorus atom no applied Adapted from Figs (a) & 18.14(a), Callister & electric field Rethwisch 8e. conduction electron valence electron Si atom p-type Extrinsic: (p >> n) Boron atom no applied electric field Chapter Extrinsic Semiconductors: Conductivity vs. Temperature Data for : reason: imperfection sites lower the activation energy to produce mobile electrons. Comparison: vs extrinsic conduction doping level: /m 3 of a n-type donor impurity (such as P). -- for T < 100 K: "freeze-out, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic" Conduction electron concentration (10 21 /m 3 ) freeze-out 200 doped undoped extrinsic 400 intrinsic 600 Adapted from Fig , Callister & Rethwisch 8e. (Fig from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.) T (K) Chapter p-n Rectifying Junction Allows flow of in one direction only (e.g., useful to convert current to current). Processing: diffuse P into one side of a B-doped crystal. -- No applied :. -- bias: carriers flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. p-type n-type p-type + - n-type Adapted from Fig Callister & Rethwisch 8e. -- bias: carriers flow away from p-n junction; junction region depleted of carriers; little current flow. + p-type n-type Chapter

8 Properties of Rectifying Junction Fig , Fig , Chapter Junction Transistor Fig , Chapter MOSFET Transistor Integrated Circuit Device Fig , Callister & Rethwisch 8e. MOSFET ( ) Integrated circuits - state of the art ca. nm line width ~ 1,000,000,000 components on chip chips formed one layer at a time Chapter

9 Ferroelectric Ceramics Experience polarization BaTiO 3 -- ferroelectric below its temperature (120ºC) Fig , Callister & Rethwisch 8e. Chapter Piezoelectric Materials application of stress induces application of voltage induces dimensional change stress-free with applied stress Adapted from Fig , (Fig from Van Vlack, Lawrence H., Elements of Materials Science and Engineering, 1989, p.482, Adapted by permission of Pearson Education, Inc., Upper Saddle River, New Jersey.) Chapter Summary Electrical conductivity and resistivity are: -- material parameters -- geometry independent Conductors, semiconductors, and insulators differ in range of conductivity values -- differ in availability of electron excitation states For metals, resistivity is increased by -- increasing temperature -- addition of imperfections -- plastic deformation For pure semiconductors, conductivity is increased by -- increasing temperature -- doping [e.g., adding B to Si (p-type) or P to Si (n-type)] Other electrical characteristics -- ferroelectricity -- piezoelectricity Chapter