Scanning tunneling microscope as a probe of the local transport field in mesoscopic systems

A theoretical analysis of the local electric field associated with dc conduction in mesoscopic systems is presented, and the possibility of probing this field with the scanning tunneling microscope (STM) as in the measurements of Kirtley et al. is theoretically investigated. The theory is based on a Landauer-type analysis in which a given distribution of electrons is incident upon a disordered mesoscopic system. Results are presented for a thin film containing grain boundaries within the jellium model. In the case of an ultrathin film with only one occupied transverse subband and in the case of a random distribution of parallel grain boundaries modeled as semiclassical barriers, the voltage drop measured by the STM (δ$V_{\mathrm{STM}}$) does equal the voltage drop in the local transport field (δ$V_{\mathrm{LTF}}$) across a grain boundary. In the more general case, δ$V_{\mathrm{STM}}$ does not equal δ$V_{\mathrm{LTF}}$, but they are of the same order of magnitude. It is also found that δ$V_{\mathrm{STM}}$ exhibits larger quantum-size effects than δ$V_{\mathrm{LTF}}$. .AE