Enhanced Carrier Mobility in Finite Versus Infinite Square Quantum Wells: A Comparative Study of GaAs/In _<i>x</i> Ga _{1− <i>x</i>} As/GaAs Heterostructures

The geometry of quantum wells (QWs) critically influences carrier mobility, yet systematic comparisons between finite and infinite square QWs remain scarce. In comparing finite and infinite square wells, we use the analytic solution of the finite square well, obtained by applying the boundary conditions and solving the transcendental equation for the subband energy; the infinite well is included as a reference case. We present a comprehensive study of GaAs/In x Ga 1− x As/GaAs heterostructures, analyzing key scattering mechanisms: remote impurities (RI), alloy disorder (AD), surface roughness (SR), acoustic (ac) and piezoelectric (PE) phonons, and longitudinal polarized optical (LO) phonons. The mobility ratio reveals distinct trends: and &lt; 1 (long‐range Coulomb/inelastic scattering), while , , , &gt; 1 (static potentials). Finite QWs achieve higher mobility at low temperatures (77 K), narrow widths (100 Å), and low densities, enhanced by high indium content. Conversely, infinite QWs outperform at 300 K due to dominant LO scattering. These findings provide actionable guidelines for optimizing QW‐based devices such as high‐electron‐mobility transistors and lasers across operational regimes.