The distance dependence function (DDF) of surface-enhanced Raman scattering (SERS) has been measured. A novel feature of this work is that a self-assembled monolayer (SAM) of alkanethiol is used as the spacer layer whose length is varied from 1 to 15 methylene units : In addition, an azobenzene Raman label is covalently linked to the monolayer via an amide bond. Experimental DDF curves can be modeled reasonably with an electromagnetic (EM) field enhancement theory of Gersten and Nitzan. The characteristic distance at which SERS signals decrease by half is about 7 Angstrom, 5 times shorter than previous values obtained with LB films as the spacer layer. We ascribe this discrepancy to the difference in the number of defects present in the spacer layer.