Mobility of electrons in bulk GaN and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi>−</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">GaN</mml:mi></mml:math>heterostructures

The room-temperature drift mobility of electrons in the channel of a ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ field-effect transistor associated with scattering by optical and acoustic phonons is calculated as a function of areal density taking into account the two-mode nature of the alloy and half-space and interface modes. It is found that the two-dimensional (2D) mobility is significantly greater than the bulk mobility and this means that the mobility goes through a maximum as a function of density corresponding to a transition from bulk to 2D transport. A simple model is used to describe the transition from bulk to 2D transport as the electron density increased. It is shown that for the structure considered the mobility at 300 K goes through a weak maximum at about 2000 ${\mathrm{cm}}^{2}$/V s at a density of about $2\ifmmode\times\else\texttimes\fi{}{10}^{12} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ dropping to about 1300 ${\mathrm{cm}}^{2}$/V s at ${10}^{13} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}.$ Results for the Hall factor and for the temperatures 77 and 600 K are also obtained. The contribution made by interface-roughness scattering is also discussed.