We combine nanolaminate bilayer insulator tunnel barriers (Al2O3/HfO2, HfO2/Al2O3, Al2O3/ZrO2) deposited via atomic layer deposition (ALD) with asymmetric work function metal electrodes to produce MIIM diodes with enhanced I-V asymmetry and non-linearity. We show that the improvements in MIIM devices are due to step tunneling rather than resonant tunneling. We also investigate conduction processes as a function of temperature in MIM devices with Nb2O5 and Ta2O5 high electron affinity insulators. For both Nb2O5 and Ta2O5 insulators, the dominant conduction process is established as Schottky emission at small biases and Frenkel-Poole emission at large biases. The energy depth of the traps that dominate Frenkel-Poole emission in each material are estimated.