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light m * (larger d 2 E/dK 2 ). heavy m * (smaller d 2 E/dK 2 ). Memory Aid “a hairpin is lighter than a frying pan”. 1. T=0 o K. T 1 >0. f (E). T 2 >T 1. 0.5. 0. E. E F. 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.
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light m* (larger d2E/dK2) heavy m* (smaller d2E/dK2) Memory Aid“a hairpin is lighter than a frying pan”
1 T=0 oK T1>0 f(E) T2>T1 0.5 0 E EF f(E) = 1/{1+exp[(E-EF)/kT]} All energy levels are filled with e-’s below the Fermi Energy at 0 oK
f(E) 1 T=0 oK T1>0 T2>T1 S(E) 0.5 0 E EV EF EC n(E)=S(E)f(E) E Putting the pieces together:for electrons, n(E)
S(E) Putting the pieces together: for holes, p(E) fp(E) T=0 oK 1 T1>0 T2>T1 0.5 0 E EV EF EC p(E)=S(E)f(E) hole energy
Finding no and po the effective density of states in the conduction band
NA -> NA-ND = NA’ = ppo ND -> ND-NA = ND’ = nno
n++ p n+ n+ W L (x) Ec(y) with VDS=0
Increasing VGS decreases EB EB EF ~ EC y 0 L
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 fsis called the surface potential
Quantum Effects on Threshold Voltage
(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!