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ssp_22 - 6 Continued 6-28 6.3 Experimental methods Crystal...

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6-28 6 Continued
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6-29 6.3 Experimental methods Crystal electron in a magnetic field Fig. 6.19 Orbit of an electron in a solid ender the influence of an applied magnetic field B . The orbit is perpendicular to B and confined to surfaces of constant energy in k space (see eq. (6.3.1)). On closed orbits the period is proportional to the derivative of the cross-sectional area. A with respect to E (see eq. (6.3.2)). In metals electrons move on the Fermi surface. In semiconductors they move at surfaces of constant energy near the minimum of the conduction band. Lorentz force : F = -e ( v x B ) E grad v k h 1 = k F & h = ) ( 2 k E grad B e dt k d k × = h (6.3.1) Orbit of electron : B grad k E , i.e. on surface E = const.
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6-30 Fig. 6.20 Possible orbits of electrons in a solid in a magnetic field. For electronlike orbit the direction of motion is as for a free electron (b). For holelike orbits the filled electron states lie outside the Fermi surface (cf. Fig.5.23b)Therefore the direction of grad k E is such that the movement is opossite to that of a free electron, i.e. in the direction of a positive particle (c). In addition, there are also open orbits (a).
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