The application of the unique properties of terahertz radiation is increasingly needed in sensors, especially in those operating at room temperature without an external bias voltage. Bow-tie microwave diodes on the base of InGaAs semiconductor structures meet these requirements. These diodes operate on the basis of free-carrier heating in microwave electric fields, which allows for the use of such sensors in millimeter- and submillimeter-wavelength ranges. However, there still exists some uncertainty concerning the origin of the voltage detected across these diodes. This work provides a more detailed analysis of the detection mechanisms in InAlAs/InGaAs selectively doped bow-tie-shaped semiconductor structures. The influence of the InAs inserts in the InGaAs layer is investigated under various illumination and temperature conditions. A study of the voltage-power characteristics, the voltage sensitivity dependence on frequency in the Ka range, temperature dependence of the detected voltage and its relaxation characteristics lead to the conclusion that a photo-gradient electromotive force arises in bow-tie diodes under simultaneous light illumination and microwave radiation.