Pra.Ma.

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

U is the 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 the I(z) Spectroscopy, we measure the tunnel current versus tip-sample separation at each pixel of an STM image. For U_av = 1 eV 2k = 1.025 A^-1eV^-1.
Sharp I(z) dependence helps in determining of tip quality. As is empirically established if tunnel current I_T drop to one-half with Z < 3 A the tip is considered to be very good, if with Z < 10 A, then using this tip it is possible to have an atomic resolution on HOPG. If this takes place with Z > 20 A this tip should not be used and must be replaced.

References

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