<p>The development of Thin-Film Transistors (TFTs) for modern applications requires thicker gate dielectrics to improve scalability and efficiency. However, decreased thickness leads to higher leakage currents and reducing reliability. To address this challenge, the examination of other gate dielectric materials has been explored to select a dielectric material that is more suitable for this thin thickness. A numerical simulation was performed on the a-Si: H TFT structure using Silvaco Atlas software to study the impact of different gate dielectric materials with a wide band gap energy and a high dielectric constant (<Emphasis Type="BoldItalic">k</Emphasis>) varying from 3.9 to 300 on device characteristics and electrical field distributions performance and to quantified this affect as mathematical expressions for several materials: SiO₂, Si₃N₄, Al₂O₃, Y₂O₃, Gd₂O₅, ZrO₂, CeO₂, La₂O₃, Ta₂O₅, HfO₂, TiO₂, Nb₂O₅, SrZrO₃, BaSrTiO₃, SrTiO₃. The obtained results showed that the increase in dielectric constant showed great improvement in the performance of the a-Si:H TFT, e.g., Drain current = 2.82 × 10^–5 A, capacitance per unit area = 2.65 × 10 ⁻⁹ F cm⁻², threshold voltage = 3.9 V, field-effect mobility = 0.0603 cm² V⁻¹ s ⁻¹, I_on/I_off ratio = 6.276 × 10⁷, and Subthreshold swing = 0.7691 V. These variations were quantified through curve fitting to establish mathematical expression for <Emphasis Type="BoldItalic">k</Emphasis> as a function of every investigated parameter. Moreover, it was also shown that the use of high gate dielectric materials can effectively reduce leakage currents, ensuring improved reliability and performance in thicker TFTs and leading to a suitable choice for gate dielectric materials in modern applications.</p>