Very high thermal to electric conversion efficiencies have been reported previously with thermal diode structures in which a thin n-type emitter layer is formed on the hot side of a thick near-intrinsic thermoelectric semiconductor. The figure of merit derived from direct measurements of electrical parameters and heat flow is increased by as much as a factor of eight. The question of what physical mechanisms are involved has been of interest since the initial observations of the effect. We have conjectured that the short-circuit current injection in these experiments is due to a second-order thermionic injection mechanism. More recently, we proposed that the open-circuit voltage comes about due to the presence of a p-type blocking layer between the emitter and the near-intrinsic bulk region. The experiments reported here show that a p-type blocking layer is required for the effect, and the dependence of conversion efficiency on the blocking layer concentration and width is studied. The results are generally consistent with calculations done so far based on a nonlocal generalized Onsager-type transport model.