Thermal Behavior and Bandgap Tuning of AlGaN Alloys for High Electron Mobility Transistors

The temperature-dependent energy bandgap <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{T}))$</tex> of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{Al}_{\boldsymbol{x}}\boldsymbol{Ga}_{\boldsymbol{1-x}}\boldsymbol{N}$</tex> for High Electron Mobility Transistors (HEMT) is modeled using the Manogé model, which incorporates electron-phonon interactions via the average phonon energy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{(\langle\hbar \omega\rangle)}$</tex> and a dimensionless coupling constant (S). This study investigates the effects of varying aluminum composition (x) in AlGaN from 0.1 to 0.9, different coupling constants (S=1.5,2.0,2.5), Electron-Phonon Energy and temperatures ranging from 0 K to 600 K. The bowing parameter b=0.53 is fixed to account for the compositional nonlinearity in the bandgap energy. Results reveal that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{T})$</tex> decreases with increasing temperature due to enhanced phonon interactions, and this effect becomes more pronounced at higher values of S. The analysis also explores the rate of change of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{T})$</tex>, providing insights into the thermal behavior of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{Al}_{\boldsymbol{x}}\boldsymbol{Ga}_{\boldsymbol{1-x}}\boldsymbol{N}$</tex>. This study highlights the critical role of material composition and thermal effects in the design of AlGaN-based HEMT for optoelectronic devices.