# Barrier Height imaging

The Local Barrier Height (LBH) spectroscopy provides an information about the spatial distribution of the microscopic work function of the surface, as described below.

The tunneling current I_{T} in STM exponentially decays with the tip-sample separation z as

I_{T} ~ exp(-2kz),

where the decay constant is given by

2k = 2(2mU/h2)^{1/2}.

In the LBH imaging, we measure the sensitivity of tunnel current to the tip-sample separation at each pixel of an STM image. The LBH obtained in this method is the so-called apparent barrier height U defined by

U= 0,95(1/I_{T})2 (dI_{T}/dz)2

This U is customarily compared to an average work function U_{av} = (U_{s} + U_{t})/2, where U_{t} and U_{s} are the tip and sample work functions, respectively. In many cases, experimental U does not precisely agree with U_{av} but tends to be slightly smaller. Nevertheless, it is known that U is closely related to the local surface potential (local work function) and is a good measure of it.

The LBH image is obtained by measuring point by point the logarithmic change in the tunneling current with respect to the change in the gap separation, that is, the slope of log I vs. z. In the LBH measurement, the tip-sample distance is modulated sinusoidally by an additional AC voltage applied to the feedback signal for the z-axis piezodevice attached to the tip. The modulation period is chosen to be much shorter than the time constant of the feedback loop in the STM.

**References**

- G. Binnig and H. Rohrer: Surf. Sci. 126 (1983) 236. Rep. Prog. Phys. 55, 1165-1240 (1992).