1. Chap. 41: Conduction of electricity in solids Hyun-Woo Lee

2. 41-1 What Is Physics?  Q: Why certain materials conduct electricity?  Q: Why certain materials do NOT conduct electricity?  Solid material Many many electrons and atoms Many many electrons and atoms  Solid state physics Application of quantum physics to solids Application of quantum physics to solids

3. 41-2 Electrical Properties of Solids  Crystalline solids Lattice structure Lattice structure Repetition of unit cellsRepetition of unit cells  Classification criteria Resistivity  at room temperature (  m) Resistivity  at room temperature (  m) Temperature coefficient of resistivity  (K -1 ) Temperature coefficient of resistivity  (K -1 ) Number density of charge carriers n (m -3 ) Number density of charge carriers n (m -3 ) Can be found from Hall effect measurementCan be found from Hall effect measurement  Metals, semiconductors, insulators  Metals, semiconductors, insulators

4. Insulators, semiconductors & metals  Insulators Extremely large  Extremely large  Ex: Diamond  diamond /  copper ~10 24 Ex: Diamond  diamond /  copper ~10 24  Semiconductors vs Metals  insulator >>  semiconductor >>  metal  insulator >>  semiconductor >>  metal  silicon =3  10 3  m,  copper =2  10 -8  m  silicon =3  10 3  m,  copper =2  10 -8  m  semiconductor 0  semiconductor 0  silicon = -70  10 -3 K -1,  Copper = +4  10 -3 K -1  silicon = -70  10 -3 K -1,  Copper = +4  10 -3 K -1 n semiconductor << n metal n semiconductor << n metal n silicon =1  10 16 m -3, n copper =9  10 28 m -3n silicon =1  10 16 m -3, n copper =9  10 28 m -3

5. 41-3 Energy Levels in a Crystalline Solids  Single atom (Ex: Cu Z =29) 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 10 4 s 1 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 10 4 s 1  Two atoms Tunneling between two atoms Tunneling between two atoms  Three atoms More tunneling More tunneling

6. Tunneling effects  Two wells  Level splitting into two levels  Level splitting into two levels

7. Tunneling effects in solids  N (  ) wells Energy level splitting into N levels Energy level splitting into N levels  Energy bands & energy gaps  Energy bands & energy gaps

8. 41-4 Insulators  No partially filled bands  For a current to exist, Kinetic energy must increase Kinetic energy must increase  Electrons must move to higher-energy levels  Electrons must move to higher-energy levels Pauli exclusion principle Pauli exclusion principle Transition to filled state is prohibitedTransition to filled state is prohibited Energy gap (Ex: E g =5.5 eV in diamond) Energy gap (Ex: E g =5.5 eV in diamond)  Large energy supply needed  Large energy supply needed  Current flow strongly suppressed  Current flow strongly suppressed

9. Thermal fluctuation effects  Thermal excitations Finite probability to jump E g Finite probability to jump E g  Probability P for the jump For E g =5.5 eV, T =300K For E g =5.5 eV, T =300K cf: # of electron in 1 cm 3 ~ 10 23cf: # of electron in 1 cm 3 ~ 10 23

10. 41-5 Metals  Partially filled bands Easy to induce energy “jump” Easy to induce energy “jump”  Fermi level E F Highest occupied level at T =0K Highest occupied level at T =0K Ex: E F =7.0 eV for copper Ex: E F =7.0 eV for copper  Fermi speed v F Electron speed at E F Electron speed at E F Ex: v F =1.6  10 6 m/s for copper Ex: v F =1.6  10 6 m/s for copper No relaxation of v F due to Pauli exclusion principle No relaxation of v F due to Pauli exclusion principle

11. How Many Conduction Electrons Are There?  Number density n  Ex: Magnesium w/ volume 2.00  10 -6 m 3 Bivalent Bivalent 

12. Conductivity Above Absolutely Zero  Ex: T =1000 K kT =0.086 eV kT =0.086 eV cf: E F =7.0 eV in copper cf: E F =7.0 eV in copper   # of charge carriers extremely insensitive to T

13. 41-6 Semiconductors  No partially filled bands  But small energy gap Ex: E g =1.1 eV for silicon Ex: E g =1.1 eV for silicon cf: E g =5.5 eV for diamond cf: E g =5.5 eV for diamond  Valence band Highest filled band Highest filled band  Conduction band Lowest vacant band Lowest vacant band

14. Number Density of Charge Carriers  Probability P for jump  Charge carriers Electrons Electrons Conduction bandConduction band Holes Holes Valence bandValence band # of charge carriers extremely sensitive to T # of charge carriers extremely sensitive to T

15. Motion of charge carriers  Electrons in conduction band  Holes in valence band Efficient description in terms of holes Efficient description in terms of holes  Effective charge of hole: + e  Effective charge of hole: + e E E

16. Resistivity    silicon /  copper = 1.5  10 11  Classical estimation Difference between  silicon and  copper mainly from carrier density n Difference between  silicon and  copper mainly from carrier density n

17. Temperature Coefficient of Resistivity   : : : :  Temperature dependence Classical estimation Classical estimation  Semiconductor (Ex: silicon) n increases as T increases   < 0 n increases as T increases   < 0  Metal (Ex: copper)  decreases as T increases   > 0  decreases as T increases   > 0

18. More about metals

19. How Many Quantum States Are There?  Too many states to list all states  Density of states N ( E ) N ( E ) dE : # of states between E and E + dE per volume N ( E ) dE : # of states between E and E + dE per volume Near lower edge of partially filled band Near lower edge of partially filled band

20. How Many Quantum States Are There ? (continued)  Ex: Metal w/ V =2  10 -9 m 3 at E =7 eV

21. The Occupancy Probability P ( E )  Maxwell distribution Not applicable due to Pauli exclusion principle Not applicable due to Pauli exclusion principle  Fermi-Dirac statistics  At E=E F P ( E )=1/2 regardless of T P ( E )=1/2 regardless of T  Useful way to define E F at T >0  Useful way to define E F at T >0

22. How Many Occupied States Are There?  Density of occupied states N 0 ( E ) N 0 ( E )= N ( E ) P ( E ) N 0 ( E )= N ( E ) P ( E )

23. Calculating the Fermi Energy  At T =0, Due to Pauli exclusion principle Due to Pauli exclusion principle With N ( E )  E 1/2 With N ( E )  E 1/2

24. More about semiconductors

25. 41-7 Doped Semiconductors  Doping Introducing a small number of replacement atoms (impurities) into semiconductor lattice Introducing a small number of replacement atoms (impurities) into semiconductor lattice ~ 1 out of 10 7 atoms replaced ~ 1 out of 10 7 atoms replaced

26. n -Type Semiconductors  Pure silicon: Si ( Z =14) 1 s 2 2 s 2 3 p 6 3 s 2 3 p 2 Valence number: 4 Valence number: 4  Doping by P ( Z =15, valence=5) One extra el.  n(egative) -type One extra el.  n(egative) -type 5th el. in the “conduction band” 5th el. in the “conduction band”

27. Extra electron & proton  w/o extra proton  w/ extra proton Weakly bound donor levels Weakly bound donor levels

28. At room temperature  Thermal excitations E d =0.045 eV for phosphorous doping E d =0.045 eV for phosphorous doping cf: E g =1.1 eV cf: E g =1.1 eV  Excitations from donor levels to conduction band much easier  Excitations from donor levels to conduction band much easier  Majority carriers Electrons in conduction band Electrons in conduction band  Minority carriers Holes in valence band Holes in valence band

29. Doping level  Pure silicon # density of conduction el. at room temp # density of conduction el. at room temp (n 0 ) no-doping ~ 10 16 m -3(n 0 ) no-doping ~ 10 16 m -3  Q: Doping for ( n 0 ) doping =10 6  (n 0 ) no-doping ( n 0 ) doping = (n 0 ) no-doping + n P ( n 0 ) doping = (n 0 ) no-doping + n P  n P  10 22 m -3  n P  10 22 m -3 cf: n Si  5  10 28 m -3 cf: n Si  5  10 28 m -3 

30. p -Type Semiconductors  Doping by Al ( Z =13) One missing el  p (ositive)-type One missing el  p (ositive)-type Missing el in “valence band” Missing el in “valence band”  w/ missing proton Weakly bound acceptor levels Weakly bound acceptor levels

31. At room temperature  Thermal excitations E d =0.067 eV for aluminium doping E d =0.067 eV for aluminium doping cf: E g =1.1 eV cf: E g =1.1 eV  Excitations from valence band to acceptor levels much easier  Excitations from valence band to acceptor levels much easier  Majority carriers Holes in valence band Holes in valence band  Minority carriers Electrons in conduction band Electrons in conduction band

32. 41-8 The p - n Junction  Junction of p -type and n -type semicond.  Upon contact, …(no bias yet) Junction plane

33. Motions of the Majority Carriers  Diffusion Diffusion current I diff Diffusion current I diff  Space charge -e-e +e+e Depletion zone Contact potential difference V 0 I diff  I diff = 0

34. Motions of the Minority Carriers  Minority carriers Drift current I drift Drift current I drift Space charge somewhat relaxed Space charge somewhat relaxed  Majority & minority carriers Balance of I diff & I drift Balance of I diff & I drift I drift

35. 41-9 The Junction Rectifier  I vs. V  p - n junction as a rectifier AC  DC conversion AC  DC conversion

36. Forward bias  Reduce V 0 Reduce V 0 Narrower depletion zone

37. Backward bias  Enhance V 0 Enhance V 0 Wider depletion zone

38. 41-10 The Light-Emitting Diode (LED)  LED  Light emission from p - n junction Photon or lattice vibration Forward bias

39. p - n junction as LED  Forward biased p - n junction Photon wavelength Photon wavelength  Commercial LEDs in visible range in visible range Ex: Gallium (valence 3) doped with arsenic (valence 5, 60%) and phosphorous (valence 5, 40%) atoms Ex: Gallium (valence 3) doped with arsenic (valence 5, 60%) and phosphorous (valence 5, 40%) atoms E g =1.8 eV (red color)E g =1.8 eV (red color)

40. The Photo-Diode  Photo-diode = (LED) -1 Photon  Current Photon  Current Ex: TV remote control Ex: TV remote control Remote control : LEDRemote control : LED Generate a certain sequence of infrared photons Generate a certain sequence of infrared photons TV : Photo-diodeTV : Photo-diode Photon detection  Electric signal Photon detection  Electric signal Photon-induced transition

41. The Junction Laser  Stimulated emission in p - n junction  Junction laser  Junction laser Ex: Laser head in compact disc (CD) playersEx: Laser head in compact disc (CD) players Mirror

42. 41-11 The Transistor  Transistor Intentional control of on-off Intentional control of on-off Application: Amplifier Application: Amplifier  FET (Field Effect Transistor)  Integrated circuits Transistors Transistors Capacitors Capacitors Resistors etc. Resistors etc. Intel Pentium chip (w/ ~7 million transistors)

43. MOSFET (Metal-Oxide-Semiconductor-FET)  MOSFET High speed on-off High speed on-off ~500 nm in length ~500 nm in length  Gate voltage V GS Negatively charge gate Negatively charge gate  Repel el. in n -channel down into substrate  Repel el. in n -channel down into substrate  Wider depletion zone between p and n  Wider depletion zone between p and n  n -channel width reduced  n -channel width reduced  Larger resistance (off realized)  Larger resistance (off realized)

44. The End