The photovoltage developed along the plane of the layers, due to illumination with a broad-band white-light source, was investigated in five different GaAs/AlGaAs MQW structures. Four of the samples were undoped, and the other was doped with silicon (n approximately 1017 cm-3). In perfect material there should be no photovoltage, so an indication of material quality can be obtained from photovoltage measurements. Measurements of photovoltage were made either: (i) as a function of illumination intensity, with the temperature held constant, or (ii) as a function of temperature with the illumination intensity held constant. The temperature range was 1.3 to 300 K, and the illumination intensity could be varied over nine orders of magnitude. A theory of random doping fluctuations is used to explain the origin of the photovoltage in terms of n-i (or p-i) junctions. Barrier heights, in the range 20 to 200 meV, were obtained from the photovoltage data. This barrier height can be related to the compensation ratio and is, therefore, a measure of the electrical quality of the material.