8. Memory Aid “a hairpin is lighter than a frying pan” light m * (larger d 2 E/dK 2 ) heavy m * (smaller d 2 E/dK 2 )

13. f(E) = 1/{1+exp[(E-E F )/kT]} All energy levels are filled with e - ’s below the Fermi Energy at 0 o K f(E) 1 0 EFEF E T=0 o K T 1 >0 T 2 >T 1 0.5

14. Putting the pieces together: for electrons, n(E) f(E) 1 0 EFEF E T=0 o K T 1 >0 T 2 >T 1 0.5 EVEV ECEC S(E) E n(E)=S(E)f(E)

15. Putting the pieces together: for holes, p(E) f p (E) 1 0 EFEF E T=0 o K T 1 >0 T 2 >T 1 0.5 EVEV ECEC S(E) p(E)=S(E)f(E) hole energy

16. Finding n o and p o the effective density of states in the conduction band

21. N A -> N A -N D = N A ’ = p po N D -> N D -N A = N D ’ = n no

27. w=(2εV/qN B ) 1/2

34. Lasers

36. p n+ n++ L W E c (y) with V DS =0 (x)

37. Increasing V GS decreases E B EBEB y 0L E F ~ E C

38. Band diagram of triode and saturation

39. Threshold Voltage Definition V GS = V T when the carrier concentration in the channel is equal to the carrier concentration in the bulk silicon. Mathematically, this occurs when  s =2  f, where  s is called the surface potential

40. Quantum Effects on Threshold Voltage

45. (Maybe not so good for GaAs!) This is very confusing, because this effective mobility is being used to describe the velocity of carriers when the concept of mobility is not applicable!

53. Most Simple Model: Constant Field Scaling E = V DD /L after scaling becomes E = (V DD /  )/(L/  ) …where  >1 next

54. Subthreshold Current (revisited) V DD scaling  V T scaling

55. Total Stand-by Power P off = V DD (I g + I JE + I off )

68. (Equation 2.111)

74. Effect of recombination currents. High injection effects also shown. Note: recombination does not contribute to I c !

75. General behavior of β (h FE ) as a function of collector current (from Sze). Low currents: Recombination currents dominate (just as in diode). High currents: High injection effects (increases effective base doping) and series resistance effects increase.