I am considering the integral of $z^{s-1}e^{iz}$ (where $0<s<1$) around a contour that is a triangle with vertices at 0, $R$, and $iR$, except for a circular cutout around the origin (i.e. after going down the positive imaginary axis from $iR$ to $i\delta$, go along an arc counterclockwise to $\delta$ on the positive real axis). I am trying to show that the integral along the slanted line (from $R$ to $iR$) approaches 0 as $R\rightarrow\infty$.

I used the usual approximation of the modulus of the integral by the maximum modulus of the integrand on the path times the length of the path but it wasn't giving me an upper bound that was approaching 0. I am wondering what other method I should be using or whether the integral does approach 0?