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We report our recent experimental and numerical investigation into the thermal and electrical transport in GaAs-AlGaAs semiconductor multilayer structures. Electrical and thermal conduction measurements were performed on multilayer structures to determine the temperature gradient across the sample. AuGe was used for top contact metallisation, and an InGa eutectic for bottom substrate contact. Metallisation contacts were also grown directly onto the substrate in order to compare results with and without the device included. By using a variable load resistor connected in series with the device, we can accurately determine the current-voltage characteristics of the device. Thus the power input can be obtained. The temperature distribution on the top and bottom substrate was measured with micro thermocouples. Since the cooling device is grown on an n-type semiconductor substrate the effects of joule heating in the substrate had to be considered. Treating the substrate as bulk material and calculating joule heating showed that this effect is negligible. Comparing experimental measurements of the device and of the substrate alone support this. The experimental I-V characteristics of the device differ significantly in shape from theoretical I-V characteristics. This may be due to that fact that space-charge effects are not included in the currently accepted model (Richardson's equation). Due to the small size of the devices and therefore very large electric fields, this effect may be important. Work is currently being carried out to modify the model. The devices studied so far have been made from undoped GaAs-AI0.07Ga0.03As heterostructures. For large cooling power it is a requirement that the conduction band of the layers be close to the Fermi level.