Analysis of activity dips in quartz crystal microbalances under temperature bias fields using the Lee plate model

High-frequency quartz crystal microbalances (QCMs) operating in the thickness-shear mode exhibit pronounced frequency-temperature behavior, particularly in ultrathin plates. Since frequency-temperature stability is strongly influenced by structural dimensions, temperature variations modify the electromechanical coupling and mode interactions of quartz, thereby affecting the electrical response of QCMs. In this study, the Lee plate model incorporating temperature bias fields is developed to analyze the vibrational and electrical responses of QCMs with and without electrodes. The novelty of this work lies in establishing a mathematically consistent plate formulation that captures temperature dependent mode coupling and electrical response without empirical correction factors. Its correctness is validated through dispersion analysis of infinite quartz plates and formulated as a system of partial differential equations (PDEs) for free and forced vibration analysis. Results reveal that strong mode coupling induced by structural dimensions and intensified by temperature variations leads to significant loss of mass sensitivity over a limited temperature range. Moreover, the resonant frequency associated with the admittance peak and the electrical response amplitude become highly sensitive to the absorbed mass under temperature bias fields. These findings provide a rigorous mathematical explanation for temperature-induced activity dips and electrical anomalies in high-frequency QCMs.