Molecular electronicsis an emerging field associated

Chapter 5, Problem 5.21

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Molecular electronicsis an emerging field associated withcomputing and data storage utilizing energy transfer at themolecular scale. At this scale, thermal energy is associ-ated exclusively with the vibration of molecular chains.The primary resistance to energy transfer in these pro-posed devices is the contact resistance at metal-moleculeinterfaces. To measure the contact resistance, individualmolecules are self-assembledin a regular pattern onto avery thin gold substrate. The substrate is suddenly heatedby a short pulse of laser irradiation, simultaneously trans-ferring thermal energy to the molecules. The moleculesvibrate rapidly in their hot state, and their vibrationalintensity can be measured by detecting the randomness ofthe electric field produced by the molecule tips, as indi-cated by the dashed, circular lines in the schematic. Molecules that are of density ??180 kg/m3and spe-cific heat cp?3000 J/kg?K have an initial, relaxedlength of L?2 nm. The intensity of the molecularvibration increases exponentially from an initial value ofIito a steady-state value of Iss?Iiwith the time constantassociated with the exponential response being?I?5 ps. Assuming the intensity of the molecularvibration represents temperature on the molecular scaleand that each molecule can be viewed as a cylinder ofinitial length Land cross-sectional area Ac, determine thethermal contact resistance, , at the metalmoleculeinterface.