Electron power loss in the (100) n channel of a Si metal-oxide-semiconductor field-effect transistor. II. Intersubband phonon scattering

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Abstract
A simple matrix element is used to approximate electron‐acoustic phonon scattering between different electron subbands i in the n channel of a (100) surface silicon MOSFET (metal‐oxide‐semiconductor field‐effect transistor) device. This matrix element is used to determine the form of the electron power loss Pij in a i→j intersubband transition. P10 is calculated for TL =4.2 °K lattice temperature and electron temperatures Te between 4.4 °K and 18 °K when the electron inversion density Ninv =(3.76–10.0)×1011 cm−2 and an acceptor density NA =1014/cm3, and compared to Fang and Fowler’s experimental data (which is put into the form of an experimental power loss Pexp). This is justified since the total power loss P due to intrasubband scattering as well as other Pij terms besides P10 is small. It is found that good to excellent fits between P10 and Pexp occur by adjusting the separation Δε10 between the lowest two circular subband edges. Δε10 is between 5.2 and 9.4 meV, and the electron‐phonon deformation coupling constant D≊3.5 eV. The values of Δε10 obtained in such a manner roughly agree with Stern’s theoretical self‐consistent results. P10 is very sensitive to both Δε10 and to the effective mass for motion parallel to the surface m1 with the results implying that m1≊0.19m0 (m0=free electron rest mass). If one wants to find the contribution of intersubband scattering to P at higher TL, the formalism should still be applicable, although the approach could be much more complicated due to the addition of new Pij terms coming from both higher subbands and new scattering agents such as optical modes.