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Or negative 25 electron and hole eecve mass in

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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 (E-k) 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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