Work function of titanium thin layers

The dependence of electron work function, Φ, on the thickness of Ti layers was investigated by making use of the Kelvin method under ambient conditions. Layers were produced by vacuum phase deposition and were analyzed by x-ray photoelectron spectroscopy and transmission electron microscopy. A quantum size effect was revealed finding work function to increase as the layer thickness, z, decreased below 4 nm. The extent of increase, ΔΦ, was understood in terms of a simple particle-in-a-box model arriving at the function ΔΦ=ℏ2π2/2mez2. This equation being free of any adjustable parameter, consisting only of the Planck constant and electron mass, seems to be a reasonable first approximation.