= mv = h / λ ▁such ▁that ▁ ▁resulting ▁in ▁ ▁and ▁. ▁This ▁treatment ▁los es ▁accuracy ▁as ▁the ▁defect s ▁tend ▁away ▁from ▁either ▁band ▁edge . ▁ ▁De fect ▁Sc atter ing ▁The ▁d ang ling ▁bond ▁energy ▁levels ▁are ▁eigenvalues ▁of ▁wave functions ▁that ▁describe ▁electrons ▁in ▁the ▁vic inity ▁of ▁the ▁defect s . ▁In ▁the ▁typical ▁consideration ▁of ▁car rier ▁scatter ing , ▁this ▁corresponds ▁to ▁the ▁final ▁state ▁in ▁F erm i ' s ▁golden ▁rule ▁of ▁scatter ing ▁frequency : ▁ ▁with ▁H ' ▁being ▁the ▁interaction ▁parameter ▁and ▁the ▁Di rac ▁delta ▁function , ▁ δ ( E f - E i ), ▁indicating ▁el astic ▁scatter ing . ▁The ▁simple ▁relation ▁ 1 / τ = ▁ Σ k ', k ▁Sk ' k ▁makes ▁this ▁a ▁useful ▁equation ▁for ▁character izing ▁material ▁transport ▁properties ▁when ▁used ▁in ▁conj unction ▁with ▁ σ ▁= ▁ne 2 τ ▁/ m * ▁and ▁Matth i essen ' s ▁rule ▁to ▁incorpor ate ▁other ▁scatter ing ▁processes . ▁ ▁The ▁value ▁of ▁Sk ' k ▁is ▁primarily ▁determined ▁by ▁the ▁interaction ▁parameter , ▁H '. ▁This ▁term ▁is ▁different ▁depending ▁on ▁whether ▁shall ow ▁or ▁deep ▁states ▁are ▁considered . ▁For ▁shall ow ▁states , ▁H ' ▁is ▁the ▁perturb ation ▁term ▁of ▁the ▁re defined ▁Hamiltonian ▁H = H o + H ', ▁with ▁Ho ▁having ▁an ▁eigen value ▁energy ▁of ▁E i . ▁The ▁matrix ▁for ▁this ▁case ▁is ▁▁▁ ▁where ▁k '