In the plot below, I use the energy of the single tower (tower with max energy) presumably the tower the photon hit. The nonlinearity seems to disappear.
In the plot below, I use the energy of the 3x3 cluster of tower centered around the tower with the max energy. The nonlinearity is restored.
The plot below shows Etower/Ecluster vs. eta where the cluster consists of 3x3 towers centered around the max energy tower.
Below is the profile of E_tower/E_cluster vs. eta.
The plot below shows the energy sampled by the entire calorimeter as a function of eta, i.e. sampling fraction as a function of eta.
Sampling fraction integrated over all eta's.