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46 polymer/semiconductor interfaceas a good approximation for the quantum-mechanical J αβdependence on y shifts.By combining the above results, J αβ can be calculated forany relative position and orientation of the two moleculeswithout quantum-mechanical calculations. The local contributionfor the mobility in the direction normal to theinterface µ ⊥ can be calculated from the knowledge of theoverlap Θ ⊥ :µ ∼ k k ∼ J 2 J ∼ Θ ⊥ (3.1)µ ⊥µ ⊥ 0(= e −2γ d−d0d 0) ( )Θ ⊥ 2(3.2)Θ ⊥ 0where µ0 ⊥ and Θ⊥ 0are respectively the mobility and theeffective overlap in the perfect P3HT crystal.Equation 3.2 can be used to calculate the average normalmobility within polymer layers as a function of the distancefrom the interface, as shown in Figure 3.16 and Figure3.17, where in the x-axis we report the distance fromthe interface in terms of the s-foils considered for the analysisin that point. As for the HDR interfaces, we choose tofocus only on the 010 one due to its more favourable formationenergy with respect to the 100 one. In this way, wecan compare the results of two 010-like interfaces (the LDRand the HDR).Figure 3.16.: Normal mobility obtained at 1 K by approximating thethiophene rings with ellipses of eccentricity ɛ = 1.15.