Real-time monitoring of plasma parameters at the wafer plane is important because it significantly affects the processing results, yield enhancement, and device integrity of plasma processing. Various plasma diagnostic sensors, including those embedded in a chamber wall and on-wafer sensors, such as flat-cutoff sensors, have been developed for plasma measurements. However, to measure the plasma density on the wafer surface in real-time when processing plasma with bias power, such as in the semiconductor etching process, one must analyze the transmission spectrum of the flat-cutoff sensor in an environment with bias power applied. In this study, the transmission-spectrum and measured plasma-density characteristics of an electrode-embedded flat-cutoff sensor are analyzed via electromagnetic simulations and experiments under applied bias power. Our findings indicate that the flat-cutoff sensor accurately measures the plasma density, which is equivalent to the input plasma density under low bias power. Conversely, under high bias power, the plasma density measured by the sensor is lower than the input plasma density. Also, a thick-sheath layer is formed owing to the high bias power, which may complicate the measurement of plasma parameters using the flat-cutoff sensor. Plasma diagnostics using a flat-cutoff sensor in thick-sheath environments can be achieved by optimizing the flat-cutoff sensor structure. Our findings can enhance the analysis of plasma parameters on-wafer surfaces in processing environments with bias power applied.