See the following two images.

The image on the left is a longitudinal shower profile for a sampling calorimeter with the configuration of the STAR BEMC. There are 20 curves corresponding to the incident particle energies {1,2,3,...,20}. The three vertical lines represent the SMD depth at eta = {0,0.5,1.0}. 

The image on the right is the intercept of those vertical lines in the left plot with the 20 curves. You can see that at eta~0 you get a slight logarithmic dependence of the deposited energy versus incident particle energy. This behavior becomes more linear as you move out towards eta=1.