Chapter 18 Electrical Properties ISSUES TO ADDRESS How

Chapter 18: Electrical Properties ISSUES TO ADDRESS. . . • How are electrical conductance and resistance characterized? • What are the physical phenomena that distinguish conductors, semiconductors, and insulators? • For metals, how is conductivity affected by imperfections, temperature, and deformation? • For semiconductors, how is conductivity affected by impurities (doping) and temperature? Chapter 18 - 1

Ohm’s Law Chapter 18 -

Electrical Conduction • Ohm's Law: V=IR voltage drop (volts = J/C) resistance (Ohms) current (amps = C/s) C = Coulomb • Resistivity, : -- a material property that is independent of sample size and geometry • Conductivity, surface area of current flow path length Chapter 18 - 3

Electrical Properties • Which will have the greater resistance? 2 D 2 D • Analogous to flow of water in a pipe • Resistance depends on sample geometry and size. Chapter 18 - 4

Definitions Further definitions J= <= another way to state Ohm’s law J current density electric field potential = V/ J = (V/ ) Electron flux conductivity voltage gradient Chapter 18 - 5

Conductivity: Comparison • Room temperature values (Ohm-m)-1 = ( - m)-1 METALS CERAMICS conductors -10 Silver 6. 8 x 10 7 Soda-lime glass 10 -10 -11 Copper 6. 0 x 10 7 Concrete 10 -9 Iron 1. 0 x 10 7 Aluminum oxide <10 -13 SEMICONDUCTORS POLYMERS Polystyrene Silicon 4 x 10 -4 Polyethylene Germanium 2 x 10 0 Ga. As 10 -6 semiconductors -14 <10 10 -15 -10 -17 insulators Selected values from Tables 18. 1, 18. 3, and 18. 4, Callister & Rethwisch 8 e. Chapter 18 - 6

Example: Conductivity Problem What is the minimum diameter (D) of the wire so that V < 1. 5 V? I = 2. 5 A Cu wire - + V 100 m < 1. 5 V 2. 5 A 6. 07 x 107 (Ohm-m)-1 Solve to get D > 1. 87 mm Chapter 18 - 7

Chapter 18 - 8

18. 2 An aluminum wire 10 m long must experience a voltage drop of less than 1. 0 V when a current of 5 A passes through it. Using the data in Table 18. 1, compute the minimum diameter of the wire. Chapter 18 - 9

Electron Energy Band Structures Adapted from Fig. 18. 2, Callister & Rethwisch 8 e. Chapter 18 - 10

Band Structure Representation Adapted from Fig. 18. 3, Callister & Rethwisch 8 e. Chapter 18 - 11

Conduction & Electron Transport • Metals (Conductors): partly filled band filled states - partially filled band - empty band that overlaps filled band filled states -- for metals empty energy states are adjacent to filled states. -- thermal energy Partially filled band Overlapping bands excites electrons Energy into empty higher empty energy states. band empty -- two types of band GAP band structures for metals filled band Chapter 18 - 12

Energy Band Structures: Insulators & Semiconductors • Semiconductors: -- wide band gap (> 2 e. V) -- few electrons excited across band gap empty Energy conduction band filled states GAP filled valence band filled band -- narrow band gap (< 2 e. V) -- more electrons excited across band gap Energy empty conduction band ? GAP filled states • Insulators: filled valence band filled band Chapter 18 - 13

Chapter 18 -

Electron Mobility Chapter 18 -

Metals: Influence of Temperature and Impurities on Resistivity • Presence of imperfections increases resistivity (10 -8 Ohm-m) Resistivity, -- grain boundaries -- dislocations -- impurity atoms -- vacancies 6 5 4 3 2 Cu i %N t a 2 . 3 +3 u C d e form de d i 1 0 These act to scatter electrons so that they take a less direct path. t -200 12 + 1. Cu i t%N a 12 + 1. i t%N a u C ” e ur “P -100 0 T (ºC) Adapted from Fig. 18. 8, Callister & Rethwisch 8 e. (Fig. 18. 8 adapted from J. O. Linde, Ann. Physik 5, p. 219 (1932); and C. A. Wert and R. M. Thomson, Physics of Solids, 2 nd ed. , Mc. Graw-Hill Book Company, New York, 1970. ) • Resistivity increases with: -- temperature -- wt% impurity -- %CW = thermal + impurity + deformation Chapter 18 - 16

Estimating Conductivity • Question: 180 160 140 125 120 100 21 wt% Ni 80 60 0 10 20 30 40 50 Resistivity, (10 -8 Ohm-m) Yield strength (MPa) -- Estimate the electrical conductivity of a Cu-Ni alloy that has a yield strength of 125 MPa. wt% Ni, (Concentration C) Adapted from Fig. 18. 9, Callister & Rethwisch 8 e. 50 40 30 20 10 0 0 10 20 30 40 50 wt% Ni, (Concentration C) Adapted from Fig. 7. 16(b), Callister & Rethwisch 8 e. From step 1: CNi = 21 wt% Ni Chapter 18 - 17

Charge Carriers in Insulators and Semiconductors Adapted from Fig. 18. 6(b), Callister & Rethwisch 8 e. Two types of electronic charge carriers: Free Electron – negative charge – in conduction band Hole – positive charge – vacant electron state in the valence band Move at different speeds - drift velocities Chapter 18 - 18

Intrinsic Semiconductors • Pure material semiconductors: e. g. , silicon & germanium – Group IVA materials • Compound semiconductors – III-V compounds • Ex: Ga. As & In. Sb – II-VI compounds • Ex: Cd. S & Zn. Te – The wider the electronegativity difference between the elements the wider the energy gap. Chapter 18 - 19

Intrinsic Semiconduction in Terms of Electron and Hole Migration • Electrical Conductivity given by: # holes/m 3 hole mobility # electrons/m 3 electron mobility Chapter 18 -

Room Temperature Values Chapter 18 -

Number of Charge Carriers Intrinsic Conductivity • for intrinsic semiconductor n = p = ni|e|( e + h) • Ex: Ga. As For Si ni = 4. 8 x 1024 m-3 ni = 1. 3 x 1016 m-3 Chapter 18 - 22

Intrinsic Semiconductors: Conductivity vs T • Data for Pure Silicon: -- increases with T -- opposite to metals material Si Ge Ga. P Cd. S band gap (e. V) 1. 11 0. 67 2. 25 2. 40 Selected values from Table 18. 3, Callister & Rethwisch 8 e. Adapted from Fig. 18. 16, Callister & Rethwisch 8 e. Chapter 18 - 23

18. 21 At room temperature the electrical conductivity of Pb. Te is 500 (Ω-m)– 1, whereas the electron and hole mobilities are 0. 16 and 0. 075 m 2/V-s, respectively. Compute the intrinsic carrier concentration for Pb. Te at room temperature. Chapter 18 - 24