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This dissertation presents the recent developments and experiments performed using the third generation femtosecond electron diffractometer in Professor Jianming Cao's group as well as experiments performed using the previous second generation diffractometer now located at Shanghai Jiao Tong University. Two techniques of ultrafast electron diffraction (UED), time-resolved reflection high energy electron diffraction (Tr-RHEED) and time-resolved transmission electron diffraction (Tr-TED) were developed and applied to study the ultrafast lattice dynamics in semiconductor nanostructures. Tr-RHEED provides the ability to directly monitor the thermal transport across an interface inside a semiconductor quantum well (QW) by measuring the temperature evolution of the first few atomic layers. Tr-TED allows for a measurement of the laser-induced ultrafast structural dynamics of 5 nm PbSe quantum dots (QDs) in real time by diffracting through the entire sample thickness. In the first project, the setup of the first Tr-RHEED experiments and the first successful collection of Tr-RHEED data in our laboratory's history is discussed. The ultrafast temperature evolution of the GaAs nanofilm was measured and numerically modeled using the well known heat conduction equation and also a three-temperature model. These models were fit to the experimental data, allowing for the extraction of the thermal boundary conductance (TBC) and providing a method of measuring TBC in epitaxially grown semiconductor heterostructures. Surprisingly, the TBC was found to increase with increasing temperature even for temperatures above the Debye temperature, opening up questions about the exact mechanisms governing heat transfer at interfaces between very similar semiconductor nanoscale materials. In the second project, we directly monitored the lattice dynamics in PbSe quantum dots induced by laser excitation using Tr-TED. The energy relaxation between the carriers and the lattice took place within 10 ps, showing no evidence of any significant phonon bottleneck effect. Meanwhile, the lattice dilation exhibited some unusual features that could not be explained by the available mechanisms of photon-induced acoustic vibrations in semiconductors alone. The heat transport between the QDs and the substrate deviates significantly from Fourier's Law, which furthers studies about the heat transfer under nonequilibrium conditions in nanoscale materials. In addition to the UED projects, femtosecond transient spectroscopy (FTS) experiments were set up and tested on 20 nm gold nanofilms for various optical excitation laser fluences. The experimental data obtained agrees well with many previous published results. The well known two-temperature model (TTM) was used to describe the temperature evolution and the energy redistribution from the electronic to lattice systems. Using similar experimental and data analysis techniques to the ones developed in this dissertation will pave the way for future FTS experiments performed in conjunction to UED experiments to gain a more complete picture of the ultrafast dynamics in carriers and phonons in complex materials.