nc1d = gs*gv*((2*[Pi]*mc*kb*T)/h^2)^0.5;
n1d = 0.5*nc1d*(-PolyLog[1/2, -Exp[x]] - PolyLog[1/2, -Exp[x - vd]]);
n1d = nc1d*(-PolyLog[1/2, -Exp[y]]);
j01d = q/h*kb*T;
j1d = j01d*(-PolyLog[0, -Exp[x]] - PolyLog[0, -Exp[x - vd]]);
u0 =  l*nc1d*kb*T;
KE = u0* ((-PolyLog[3/2, -Exp[x]] - PolyLog[3/2, -Exp[x - vd]])/2 +
    PolyLog[3/2, -Exp[y]]);
L = (2*KE)/j1d^2;