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Home , Extrinsic semiconductor

4/28/15

Electrical Properties View of an • Scanning 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, , and insulators? • A dot map showing location of Si (a ): • For , 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 () and temperature?

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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

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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 4 x 10 -4 Polystyrene <10 0 -15 -17 Electron flux conductivity voltage gradient 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 € 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 -

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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

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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 50 -- vacancies take a less direct path. 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

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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 filledstates band filledstates

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 filledstates filledstates band band Move at different speeds - drift velocities

Chapter 18 - 19 Chapter 18 - 20

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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 σ = µe + µh Si atom electron pair creation pair migration

• for 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

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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

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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 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 σ increases with doping doped atoms. The image cannot be displayed. Your computer may not have enough memory to open the Reason: 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.

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)

Conduction electrons = # of ions. 3

/m 21

2 • Comparison: intrinsic vs extrinsic intrinsic extrinsic conduction... 1 freeze-out

Conductionelectron -- extrinsic doping level: concentration(10 0 1021/m3 of a n-type impurity (such as P). 0 200 400 600 T (K) -- for T < 100 K: "freeze-out“, Adapted from Fig. 18.17, Callister & Rethwisch thermal energy insufficient to 9e. (From S. M. Sze, Semiconductor Devices, Physics and Technology. Copyright © 1985 by Bell Telephone excite electrons. Laboratories, Inc. Reprinted by permission of John Wiley -- for 150 K < T < 450 K: "extrinsic" & Sons, Inc.) 23 −3 −19 2 −1 -- for T >> 450 K: "intrinsic" σ = n| e |µe = (2 × 10 m )(1.602 × 10 C)(0.05 m /V−s) = 1600 (Ω− m)

Chapter 18 - 31 Chapter 18 -

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p-n Rectifying Junction Properties of Rectifying Junction • Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current). • Processing: diffuse P into one side of a B-doped crystal. p-type n-type -- No applied potential: + + - Adapted from + - Fig. 18.21, no net current flow. + - - Callister & + - Rethwisch 9e. -- Forward bias: carriers flow through p-type and p-type + - n-type + + - n-type regions; holes and + + - - - electrons recombine at + - p-n junction; current flows.

-- Reverse bias: carriers p-type n-type - + + flow away from p-n junction; - + - - + junction region depleted of + + - - carriers; little current flow. Fig. 18.22, Callister & Rethwisch 9e. Fig. 18.23, Callister & Rethwisch 9e. Chapter 18 - 33 Chapter 18 - 34

Junction

Fig. 18.24, Callister & Rethwisch 9e. 35

Chapter 18 - Chapter 18 - 36

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MOSFET Transistor CMOS à nMOS + pMOS Integrated Circuit Device

Fig. 18.26, Callister & Rethwisch 9e.

• MOSFET ( oxide semiconductor field effect transistor) • Integrated circuits – “state of the art” 50 nm channel width – ~ 5,000,000,000 on chip – chips formed one layer at a time

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Chapter 18 - 37 Chapter 18 -

Building simple devices – The Inverter The NAND Gate

Chapter 18 - 39 Chapter 18 - 40

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NAND gate layout NOR gate

Chapter 18 - 41 Chapter 18 - 42

What can be done with these devices?

Add numbers together!

Chapter 18 - 43 Chapter 18 - 44

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Chapter 18 - 45 Chapter 18 - 46

Why can we build devices with semiconductors?

• Semiconductors are neither good • The number of charge carriers in an insulators or good conductors. extrinsic semiconductor (n) is controlled • We can select specific, small regions to be by the number of dopants when electrically conductive for either holes or temperature is between 150- 450 K. electrons. • Using dopants we can create regions • Other regions can be made insulating by within si that have an engineered value for growing an oxide film conductivity. • The electrical properties of the conductive • Certain regions can be made conductive regions can be altered by applying a for certain types of charge carriers by positive or negative voltage. applying a voltage. 47

Chapter 18 - Chapter 18 - 48

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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)]

Chapter 18 - 49

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