GaN HEMT 2DEG: I-V, Velocity-Field & Band Diagram

This is the 2D counterpart to the 3D GaN HEMT particle-swarm model, computing the exact same AlGaN/GaN 2DEG transport physics through four analytic plots instead of a rendered channel: an output-characteristic family I_DS-V_DS, the Caughey-Thomas velocity-field curve that bends into saturation, a conduction-band cross-section showing the triangular quantum well depleting under the gate at pinch-off, and the local field-crowding profile along the channel that a real short-gate, long-drain-access HEMT layout produces. Every curve reacts live to the same gate voltage, drain voltage and lattice-temperature sliders, and the live readouts (μ₀(T), drift velocity, drain current density in mA/mm) are computed from the identical formulas driving the plots.