[en] We show that I-V characteristics of thermionic current from a semiconductor with the Fermi energy E_fl into a semiconductor with the Fermi energy E_f2 over a ballistic barrier. exhibits strong maximum in dI/dV at eV=ΔE_f≡ E_f2-E_f1. It could be a simple method for Fermi energy measurement in one of the semiconductors provided that the Fermi energy of the second one is known. However, in order to meet the ballistics requirement the barrier has to be so thin that tunneling contribution could not be ignored. We demonstrate that even for thick non-ballistic barrier with build-in positive charge dI/dV has a well pronounced maximum at the same point, namely at eV=ΔE_f. Our calculations were successfully tested in n-GaAs/AlGaAs/n-GaAs sandwich where AlGaAs barrier was artificially charged by introducing Si δ-doping in the middle of the barrier. In heavily Sn doped sandwiches there is no need to charge the barrier artificially since the diffusion of a small amount of Sn into the barrier during a growth provides charge sufficient to observe the above described feature. We grew by molecular-beam epitaxy (MBE) a set of n-InGaAs/AlInAs/n-InGaAs heterojunctions with fixed low n₁≅ 5 x 10¹⁷ cm^-3 carrier concentration in tile first InGaAs, fixed chemical composition of the barrier and a variable doping concentration n₂ in the second InGaAs layer in the range n₂ : 10¹⁸ -: 4 x 10¹⁹ cm^-3. Tile carrier densities in each layer were measured by standard Hall effect technique and were found to be consistent with the doping levels confirmed by SIMS measurements. The dI/dV of the I-V characteristics of the junctions exhibit sharp peak for all samples. It's position on the voltage axes, being interpreted as ΔE_f allow us to extract the dependence of E_f2 on carrier density, n₂. This dependence strongly deviates from standard theoretical predictions. The most striking observed anomaly is the near saturation of the Fermi level at a value E_f ≅ 130 MeV when the mobile carrier concentration exceeds 10¹⁹ cm^-3. Photoluminescence measurements on the same set of samples allow independent evaluation of E_f2, which is consistent with tile data obtained from the transport experiments. In addition a pronounced discrete peak appears in the photoluminescence spectrum just above E_f2 in the heavily doped samples which show the saturation behaviour. Our results call for a thorough re-examination of the existing theory