1. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) These PowerPoint color diagrams can only be used by instructors if the 3 rd Edition has been adopted for his/her course. Permission is given to individuals who have purchased a copy of the third edition with CD-ROM Electronic Materials and Devices to use these slides in seminar, symposium and conference presentations provided that the book title, author and © McGraw-Hill are displayed under each diagram.

2. Homework #2 – Due 09/16/14 2.11 2.12 2.17 Plus one more on Thursday

3. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Thermal conduction in a metal involves transferring energy from the hot region to the cold region by conduction electrons. More energetic electrons (shown with longer velocity vectors) from the hotter regions arrive at cooler regions and collide there with lattice vibrations and transfer their energy. Lengths of arrowed lines on atoms represent the magnitudes of atomic vibrations. Fig 2.19 Metals: Heat transport/conduction is accomplished by the electron gas Nonmetals: conduction is due to lattice vibrations

4. Fig 2.20 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Heat flow in a metal rod heated at one end. Consider the rate of heat flow, dQ/dt, across a thin section δx of the rod. The rate of Heat flow is proportional to the temperature gradient δT/δx and the cross-sectional area A.

5. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Fourier ’ s Law of Thermal Conduction Q = rate of heat flow, Q = heat, t = time,  = thermal conductivity, A = area through which heat flows, dT/dx = temperature gradient I = electric current, A = cross-sectional area,  = electrical conductivity, dV/dx = potential gradient (represents an electric field),  V = change in voltage across  x,  x = thickness of a thin layer at x Ohm ’ s Law of Electrical Conduction , aka thermal conductivity, is material dependent;

6. “Driving Forces” The driving force for heat flow is the temperature gradient The driving force for electric current is the potential gradient, i.e., electric field In metals, electrons engage in charge and heat transport, which are described by  and , respectively From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

7. Wiedemann-Franz-Lorenz Law  = thermal conductivity  = electrical conductivity T = temperature in Kelvins C WFL = Lorenz number Charge and heat transport described by  and , are related through this expression

8. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Thermal conductivity  versus electrical conductivity  for various metals (elements and alloys) at 20 ˚C. The solid line represents the WFL law with C WFL ≈ 2.44  10 8 W  K -2. Fig 2.21 Experiments on a wide variety of metals – includes pure metals and alloys WFL Law is reasonable obeyed from around room temp and above Since electrical conductivity of pure metals is inversely proportional to the temperature, we can immediately conclude that thermal conductivity must be relatively temperature independent at room temp and above

9. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Thermal conductivity versus temperature for two pure metals (Cu and Al) and two Alloys (brass and Al-14% Mg). SOURCE: Data extracted form I.S. Touloukian, et al., Thermophysical Properties of Matter, vol. 1: “ Thermal Conductivity, Metallic Elements and Alloys, “ New York: Plenum, 1970. Fig 2.22 Thermal Conductivity v. Temperature: Respective  for Cu and Al become temperature independent above ~100 K Heat conduction depends primarily on the rate at which the electrons transfers energy from one atomic vibration to another as it collides with them The mean speed, u, of the electron determines the rate o energy transfer u increases only fractionally with temperature in this range Moreover, this fractional increase is easily enough to carry the energy from one collision to another, thereby exciting more energetic lattice vibrations in colder regions

10. More on Thermal Conductivity Nonmetals do not have any free conduction electrons; therefore, the energy transfer involves lattice vibrations Recall: the “ball and spring” model Kinetic molecular theory dictates that all atoms will be vibrating and the average vibrational kinetic energy would be proportional to the temp The springs couple the vibrations to neighboring atoms thereby allowing large amplitude vibrations to propagate as a vibrational wave to cooler regions of the crystal The efficiency of heat transfer is not solely a function of the efficiency of interatomic bonding (coupling between atoms), but also on how the vibrational waves propagate in the crystal which is determined by: Scattering by crystal imperfections, and Interactions with other vibrational waves From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) The stronger the coupling, the greater will be the thermal conductivity

11. Vibrational Wave Fig 2.23 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Conduction of heat in insulators involves the generation and propagation of atomic Vibrations through the bonds that couple the atoms (an intuitive figure). If left-end atom vibrates violently (due to heat), then vibrational waves propogate down the ball-spring-ball chain

12. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Thermal conductivity, in general, depends on temperature Different types of materials exhibit different  values and also different  versus T behavior

13. Thermal Resistance Fig 2.24 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Conduction of heat through a component in (a) can be modeled as a thermal resistance  shown in (b) where =  T/ 

14. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Fourier ’ s Law Q = rate of heat flow or the heat current, A = cross-sectional area,  = thermal conductivity (material-dependent constant),  T = temperature difference between ends of component, L = length of component Ohm ’ s Law I = electric current,  V = voltage difference across the conductor, R = resistance, L = length,  = conductivity, A = cross-sectional area

15. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Definition of Thermal Resistance Q = rate of heat flow,  T = temperature difference,  = thermal resistance Thermal Resistance  = thermal resistance, L = length, A = cross-sectional area,  = thermal conductivity

16. Electrical Conductivity in Nonmetals It is possible to empirically classify various materials into conductors, semiconductors, and insulators Obviously, nonmetals are not necessarily perfect insulators with zero conductivity Also, there is no well-defined, sharp boundary between insulators and semiconductors Typically, current conduction is due to drift of mobile charge carriers through a solid by the application of an electric field Each of the drifting species of charge carriers contributes to the observed current –Drifting species of charge carriers contribute to the observed current –Metals only have free electrons From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

17. Fig 2.25 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

18. Fig 2.26 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) (a) Thermal vibrations of the atoms rupture a bond and release a free electron into the crystal. A hole is left in the broken bond which has an effective positive charge. (b) An electron in a neighboring bond can jump and repair this bond and thereby create a hole in its original site; the hole has been displaced. (c) When a field is applied both holes and electrons contribute to electrical conduction.

19. Si Silicon atoms share valence electrons to form insulator-like bonds Covalent Bonds in Silicon Crystal 19

20. Donor atoms provide excess electrons to form N-type silicon. Phosphorus atom serves as N-type dopant Excess electron (- ) P P P Free Electrons in N-type Silicon 20

21. Acceptor atoms provide a deficiency of electrons to form P-type silicon. Hole (+) Boron atom serves as P-type dopant Si B B B Holes in P-type Silicon 21

22. Valence electron freed from copper atom Negative terminal from voltage supply Positive terminal from voltage supply e - Flow of Electrons in Copper Wire 22

23. Free electrons flow toward positive charge Positive terminal from voltage supply Negative terminal from voltage supply e - Flow of Free Electrons in N-type Silicon 23

24. Positive terminal from voltage supply Negative terminal from voltage supply +Holes flow toward negative terminal -Electrons are supplied by the voltage source e - h + Flow of +Holes in P-type Silicon 24

25. Importance of Diffusion Introduce impurities Control majority carrier type Control resistivity of Si Si substrate Ion implantation Diffusion to drive impurity in to Si IC Technology -Dr. W. Hu

26. Impurity Diffusion Diffusion Mechanisms Substitutional Interstitial IC Technology -Dr. W. Hu

27. Substitutional Diffusion Figure 3.6 The kick-out (left) and Frank–Turnbull mechanisms (right). Fabrication Engineering at the Micro and Nanoscale, 4/e Stephen A. Campbell Copyright © 2014 by Oxford University Press

28. Impurity Exchange Figure 3.3 Diffusion of an impurity atom by direct exchange (A) and by vacancy exchange (B). The latter is much more likely owing to the lower energy required. Fabrication Engineering at the Micro and Nanoscale, 4/e Stephen A. Campbell Copyright © 2014 by Oxford University Press

29. Interstitial Diffusion Figure 3.5 In interstitialcy diffusion, an interstitial silicon atom displaces a substitutional impurity, driving it to an interstitial site, here it diffuses some distance before it returns to a substitutional site. Fabrication Engineering at the Micro and Nanoscale, 4/e Stephen A. Campbell Copyright © 2014 by Oxford University Press

30. Intrinsic Carrier Concentration Figure 3.4 Intrinsic carrier concentration of silicon, GaAs, and GaN as a function of temperature Fabrication Engineering at the Micro and Nanoscale, 4/e Stephen A. Campbell Copyright © 2014 by Oxford University Press

31. Resistivity vs. Doping IC Technology -Dr. W. Hu

32. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Conductivity of a Semiconductor  = conductivity, e = electronic charge, n = electron concentration,  e = electron drift mobility, p = hole concentration,  h = hole drift mobility  = en  e + ep  h v e = drift velocity of the electrons,  e = drift mobility of the electrons, e = electronic charge, F net = net force Drift Velocity and Net Force n and p are concentrations of electrons and holes in a semiconductor crystal Electrons and holes have drift mobilities, so overall conductivity of the crystal can be given by:

33. Ionic Crystals and Glasses All crystalline solids possess vacancies and interstitial atoms to satisfy thermal equilibrium Many solids have interstitial impurities that are ionized or charged These interstitial ions can diffuse from one interstitial site to another, and therefore ‘drift’ by diffusion in the presence of a field From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

34. Ionic Crystals and Glasses From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Possible contribution to the conductivity of ceramic and glass insulators. (a)Possible mobile charges in a ceramic. (b)An Na + ion in the glass structure diffuses and therefore drifts in the direction of the field. Fig 2.28