Unformatted text preview: is either par2ally ﬁlled or overlaps valence band. 20 Electrons and Holes in “Perfect” Semiconductors • When an electron is freed from the valence band where it was involved in atomic bonding, an empty state is let behind • In a perfect, undoped semiconductor, electron hole pairs can be created through thermal excita[on
or by interac[on with a photon • Once created, the electrons and holes are free to move (drit and diﬀusion) Light Heat Equa[on for a Parabola y = ax 2 ← Curvature at origin related to "a" coefficient
y = 5x2 y = x2 3.2 2.4 1.6 0.8 4.8 4 3.2 2.4 1.6 0.8 0 0.8 1.6 2.4 3.2 4 4.8 0.8 1.6 2.4 24
3.2 Electrons in Free Space • As a consequence of wave par[cle duality, the electron has a wave like nature p2
Classical Mechanics: E =
2m E ψ ( z, t ) = Ae[ i ( kz−ω t )]
2π
where k =
(wave vector); 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?
25 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 26 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 lajce, emits a phonon, and transfers to the L valley to become a higher eﬀec[ve mass electron...
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 Spring '11
 Leburton
 Atom, Electron, Energy, Electronic band structure

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