Quantum dots (QDs) are a semiconductor nanostructure in which a small island of one type of semiconductor material is contained within a larger bulk of a different one. These structure are interesting for a wide range of applications, including highly efficient LASERs, high-density novel memory devices, quantum computing and more. In order to understand the nature of QDs, electrical characterisation techniques such as capacitance-voltage (CV) profiling and deep-level transient spectroscopy (DLTS) are used to probe the nature of the carrier capture and emission processes. This is limited, however, by the nature of QD formation which results in a spread of sizes which directly affects the energy structure of the QDs. In this work, I sought to overcome this by using Si substrates patterned with a focused ion beam (FIB) to grow an array of identically-sized Ge dots. Although I was ultimately unsuccessful, I feel this approach has great merit for future applications.In addition, this thesis describes several unusual characteristics observed in InAs QDs in a GaAs bulk (grown by molecular beam epitaxy-MBE). Using conventional and Laplace DLTS, I have been able to isolate a single emission transient. I further show an inverted relation between the emission rate and the temperature under high field (emissions increase at lower temperatures). I attribute this to a rapid capture to and emission from excited states in the QD. In addition, I examine a metastable charging effect that results from the application of a sustained reverse bias and decreases the apparent emission rate from the dots. I believe this to be the result of a GaAs defect with a metastable state which acts as a screen, inhibiting emission from the dots due to an accumulation of charge in the metastable state. These unusual characteristics of QDs require further intensive work to fully understand. In this work I have sought to describe the phenomena fully and to provide hypotheses as to their origin.