Terahertz sources based on semiconductor quantum devices attract great attention from many research groups as promising radiation sources for different applications in medicine and security such as terahertz spectroscopy, explosives detection, terahertz imaging, chemical and biological sensing, and other applications. Among electronic devices, quantum structures like resonant tunneling diodes (RTDs) and quantum cascade lasers (QCLs) are considered as candidates for terahertz wave generation and amplification, for signal detection and frequency mixing, hopefully at room temperature. However, at lower THz frequencies (< 4 THz) these QCL devices require cryogenic cooling that limited the area of application of these devices. In this paper we identify the conditions for room-temperature operation of 1.33 THz quantum cascade lasers based on ZnMgSe/ZnSe material systems employing both approaches of alternating quantum barriers with variable heights and n-type delta-doping of the injector well. It was found that the negative differential resistance (NDR) exists up to room temperature in the current-voltage characteristics of these QCL devices. Thus, the suggested QCL devices with variable barrier heights could be also considered as quantum cascade oscillators for practical application.