The authors examine the electrical properties of ultrathin MgO barriers grown on (001) InAs epilayers and the dependence on InAs surface pretreatment and growth conditions. Pretreatment improves the yield of tunnel junctions and changes the roughness of the interface between oxide and semiconductor. Electrical characterization confirms that tunnel barriers with appropriate values of interface resistance for efficient spin injection/detection have been achieved. Using the Rowell criteria and various tunneling models, the authors show that single step tunneling occurs above 150K. Incorporating a thermal smearing model suggests that tunneling is the dominant transport process down to 10K.