Unformatted text preview: ); and ω = 2πυ (frequency)
λ
1 2 p2
E = mv =
(note, here v is velocity)
2
2m
but p = k
2 2
so E =
k
2m 2 2
E=
k
2m • The E(k) rela[onship is parabolic for an electron in free space k
• The curvature at the origin is 2
related to What would this look like if the
2m mass were smaller? or negative?
16 Electron and Hole Eﬀec[ve Mass • • • • •
• In a semiconductor, the E(k) rela[onship looks parabolic near the conduc[on band minima and the valence band maxima The curvature of the parabola diﬀers from the free space curvature, and depends upon which minima the electron or hole is in Near a minima, the E(k) rela[onship is: GaAs Band Structure 2
E (k ) =
k2
2 m * mo This is similar to the E(k) rela[onship for a free electron, but with a mass m*mo instead of mo The parameter m* is the eﬀec[ve mass Tabulated eﬀec[ve masses are generally expressed as a mul[ple of the free space electron mass mo http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html 17 Eﬀec[ve Mass in Si, Ge, and GaAs • In GaAs – Lower eﬀec[ve mass electron in Γ Valley – Higher eﬀec[ve mass electron in L Valley (Ek) Diagram for GaAs
L e e ΔEc=0.3eV • Applied Electrical Field: Eﬀect on Electron – Electron gains energy, increases velocity in Γ Valley – Electron collides with laqce, emits a phonon, and transfers to the L valley to become a higher eﬀec[ve mass electron...
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 Spring '11
 Leburton
 Electron, Potential Energy, Semiconductors, Condensed matter physics

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