Chapter 12: Solid state physics 67 12.5.3 The Hall-effect If a magnetic Feld is applied ⊥ to the direction of the current the charge carriers will be pushed aside by the Lorentz force. This results in a magnetic Feld ⊥ to the ±ow direction of the current. If ± J = J ± e x and ± B = B ± e z than E y /E x = μB . The Hall coefFcient is deFned by: R H = E y /J x B , and R H =-1 /ne if J x = neμE x . The Hall voltage is given by: V H = Bvb = IB/neh where b is the width of the material and h de height. 12.5.4 Thermal heat conductivity With ² = v F τ the mean free path of the electrons follows from κ = 1 3 C ± v ² ² : κ electrons = π 2 nk 2 T τ / 3 m . ²rom this follows for the Wiedemann-Franz ratio : κ / σ = 1 3 ( π k/e ) 2 T . 12.6 Energy bands In the tight-bond approximation it is assumed that ψ =e ikna φ ( x-na ) . ²rom this follows for the energy: ± E ² = ± ψ | H | ψ ² = E at-α-2 β cos( ka ) . So this gives a cosine superimposed on the atomic energy, which can often be approximated by a harmonic oscillator. If it is assumed that the electron is nearly free one can
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