ECE 474: Principles of Electronic Devices. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University
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1 ECE 474: Principles of Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University
2 Lecture 14: Chp. 03 Introducing a new way to understand current I N(E) and f
3 Lecture 14: Chp. 03 Introducing a new way to understand current I N(E) and f
4 Lecture 12, slide 7: The PE physical situation of an electron ψ inside a semiconductor (GaAs): e- PE (ev) Energy in ev Chp. 03 <100> <111>
5 Compare this to a road through the Rocky mountains. Analyze what is involved: Barrier Road along valley floor: best Road along upper valley: OK Google: rocky mountains facts pictures
6 Compare this to a road through the Rocky mountains. Analyze what is involved: Some paths through this would require immense energy Road along valley floor: requires least energy Road along upper valley: OK energy requirement after you get into it. Google: rocky mountains facts pictures
7 Compare this to a road through the Rocky mountains. Analyze what is involved: When are you most likely to find cars on these roads, daytime or night time? Google: rocky mountains facts pictures
8 Compare this to a road through the Rocky mountains. Analyze what is involved: Probability of cars occupying these roads is greater during the day time. Daytime sun energy time. Could even relate sun radiant energy to temperature ~ kbt = (1.38 x J/K) Temp Google: rocky mountains facts pictures
9 Compare this to a road through the Rocky mountains. Analyze what is involved: Do these roads exist even when cars are not on them? Google: rocky mountains facts pictures
10 Compare this to a road through the Rocky mountains. Analyze what is involved: Do these roads exist even when cars are not on them? Yes, of course. Google: rocky mountains facts pictures
11 Compare this to a road through the Rocky mountains. Analyze what is involved: If there are any settlements, with cars making local drives, where are they likely to be found? Google: rocky mountains facts pictures
12 Compare this to a road through the Rocky mountains. Analyze what is involved: If there are any settlements, with cars making local drives, where are they likely to be found? In the lower and upper valleys of course. Google: rocky mountains facts pictures
13 Cars electrons in a current I Concentration of carriers: electrons and holes n 0 and p 0 : topenergy n = f ( E, E ) N( E) de Units: 0 F 0 3 bottomenergy cm n # electrons : Concentration of holes p 0 is related. Can also have increased concentrations of electrons n or holes p when you add dopants. Use n and p to get current I drift : I drift = q( n μ n + p μ h )E, E = electric field (V/cm), μ = mobility (cm cm) s V Chp 04: I = I drift + I diffusion
14 Cars electrons in a current I Concentration of electrons n 0 : top energy n = f(e,e )N(E)dE 0 F least energy N: The road f: The probability that the road is occupied E: the energy needed to occupy the road.
15 N(E)dE is the energy density of states. How many different roads (energy levels) there are through a given territory and how much energy it takes to use each one. N 3D (E)dE = # energy levels [ Volume][ available energy : de] f is the Fermi distribution probability function. It is the probability that a given road (energy level) is occupied.:
16 N(E, de) is the energy density of states. How many different roads (energy levels) there are through a given territory and how much energy it takes to use each one. Important: N(E)dE changes form when any momentum(s) are quantized: N 3D (E)dE = N 2D (E)dE = N 1D (E)dE = # energy levels [ Volume][ available energy : de] # energy levels [ Area][ available energy : de] # energy levels [ Line][ available energy : de] This changes the expressions for the current I and the resistance R. V =IR only applies for N 3D (E, de)
17 Lecture 14: Chp. 03 Introducing a new way to understand current I N(E) and f
18 3-Deg N(E,dE) = Energy Density of States (DOS) topenergy n = f ( E, E ) N( E) de 0 bottomenergy F n 0 : # electrons 3 cm N 3D (E)dE 2 = π 2 m * 2 hbar 3/2 E 1/2 de
19
20
21 Probability f(e) = Fermi distribution function topenergy n = f ( E, E ) N( E, de) de Units: # electrons : 0 F 0 3 bottomenergy cm n # between 0 and 100%
22 Pr. 3.2: Probability f(e) E (ev)
23 Probability f(e) Invert the axes E (ev)
24 About the plot: same
25 Probability f(e) = Fermi distribution function
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