Chapter 5, Problem 5.21P

Molecular electronics is an emerging field associated with computing and data storage utilizing energy transfer at the molecular scale. At this scale, thermal energy is associated exclusively with the vibration of molecular chains. The primary resistance to energy transfer in these proposed devices is the contact resistance at metal-molecule interfaces. To measure the contact resistance, individual molecules are self-assembled in a regular pattern onto a very thin gold substrate. The substrate is suddenly heated by a short pulse of laser irradiation, simultaneously transferring thermal energy to the molecules. 11te molecules vibrate rapidly in their state, and their vibrational intensity can be measured by detecting the randomness of the electric field produced by the molecule tips, as indicated by the dashed. circular lines in the schematic.

Molecules that are of density $\rho =180\text{}{\text{kg/m}}^{\text{3}}$ and specific heat $c_p=3000\text{J/kg}\cdot \text{K}$ have an initial, relaxed length of $L=2\text{nm}\text{.}$ The intensity of the molecular vibration increases exponentially from an initial value of $I_i$ to a steady-state value of $I_{ss}>I_i$ with the time constant associated with the exponential response being ${\tau }_i=5\text{ps}\text{.}$ Assuming the intensity of the molecular vibration represents temperature on the molecular scale and that each molecule can be viewed a cylinder of initial length L and cross-sectionalarea $A_c,$ determine the thermal contact resistance, $R_{t,c}^{"}$ at the metal—molecule interface.