8. Memory Aid “a hairpin is lighter than a frying pan”
light m*
(larger d2E/dK2)
heavy m*
(smaller d2E/dK2)

13. f(E) = 1/{1+exp[(E-EF)/kT]}EF E
T=0 oK
T1>0
T2>T1
0.5
All energy levels are filled with e-’s below the Fermi Energy at 0 oK

14. Putting the pieces together: for electrons, n(E)
f(E) 1 EF E
T=0 oK
T1>0
T2>T1
0.5 EV EC
S(E) E
n(E)=S(E)f(E)

15. Putting the pieces together:
for holes, p(E)
fp(E)
T=0 oK 1
T1>0
T2>T1
0.5
S(E) E EV EF EC
p(E)=S(E)f(E)
hole energy

16. Finding no and po the effective density of states
in the conduction band

21. NA -> NA-ND = NA’ = ppo
ND -> ND-NA = ND’ = nno

27. w=(2εV/qNB)1/2

35. Lasers

37. p n+
n++ L W
(x)
Ec(y) with VDS=0

38. Increasing VGS decreases EB
EF ~ EC y L

39. Band diagram of triode and saturation

40. Threshold Voltage Definition
VGS = VT when the carrier concentration in the channel is equal to the carrier concentration in the bulk silicon.
Mathematically, this occurs when fs=2ff ,
where fs is called the surface potential

41. Quantum Effects
on Threshold Voltage

46. (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!

51. Most Simple Model: Constant Field Scaling
E = VDD/L
after scaling becomes
E = (VDD/a)/(L/a)
…where a>1
next

52. Subthreshold Current (revisited) VDD scaling  VT scaling

53. High-K gate insulator reduces tunneling current by allowing a thicker insulator
0.8 nm

54. Junction Leakage Current Tunneling current due to highly doped Drain-Body junctionsEV W D
IJE
Recall: tunneling
T = Kexp(-2kW)

55. Total Stand-by Power Poff = VDD(Ig + IJE + Ioff)

56. Scaling Directions (I) SOI (DST, depleted substrate transistor)
Very thin body region (Tsi = L/3) makes the source and drain spreading resistance (RS) large.
Raised S/D improves ID (next)
Improves subthreshold slope, S
and decreases Ioff
Also decreases CjE
…and IJE

57. Scaling Directions (II) The “FinFET” moves from a single gate to double and triple gate structures and also multiple channels.

69. (Equation 2.111)

75. Effect of recombination currents.
High injection effects also shown.
Note: recombination does not contribute to Ic!

76. General behavior of β (hFE) 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.