We present the experimental methodology to estimate the inhomogeneity of interface energy barrier in heterojunction by using the solid-state device version of ballistic electron emission spectroscopy (BEES). As a prototype of the device version BEES, which can be considered to be a collection of numerous STM tips connected in parallel, a Pt/Al2O3/Pt/4H-SiC vertical metal-base transistor structure was fabricated. We observed that the threshold voltage Vth of BEES spectrum, extracted by fitting the measured data to the Bell-Kaiser theory, decreases noticeably as the Pt/4H-SiC was reverse-biased at ~40 K. In order to address the sharp dependence of Vth on the reversewise collector-base voltage VCB, a modified Bell-Kaiser theory adopting the Tung model for inhomogeneous distribution of Schottky barrier at the interface was developed. The modified theory predicts two crucial features: (1) The barrier inhomogeneity renders the 1/3 power-law dependence of Vth on VCB in the limit of low inhomogeneity while the image force lowering leads to 1/4 power-law dependence. (2) The square-law dependence of BEES spectrum on the emitter-base voltage VEB is still valid in the low inhomogeneity limit. The VCB dependence of extracted Vth agrees well with the modified theory, leading to the conclusion that the observed decrease of Vth stems mainly from the barrier inhomogeneity.