NNSE618-L9-Kinetics

NNSE618-L9-Kinetics - 1 Lecture contents Electron transport...

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NNSE 618 Lecture #9 1 Lecture contents Electron transport in high fields Diffusion of carriers Einstein relation Non-equilibrium distribution function
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NNSE 618 Lecture #9 2 High field electron transport Hot electrons transfer energy into thermal vibrations of the crystal lattice (phonons). Such vibrations can be modeled as harmonic oscillations with a certain frequency, w ph . The energy levels of a harmonic oscillator are equidistant with the energy difference between the levels equal to Two types of phonons scatter electrons differently: acoustical (slow) and optical (fast): Hence, process for a hot electron can be represented as follows. The electron accelerates in the electric field until it gains enough energy to excite optical phonon: ph ph E w meV E opt opt 40 w kT E ac ac w
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NNSE 618 Lecture #9 3 Saturation velocity due to optical phonon scattering If the energy relaxation occur through optical phonons, the energy-loss rate equation can be written as: A corresponding rate equation for momentum relaxation ( v s saturation velocity): Assuming the scattering by optical phonons as a dominant mechanism, in a steady state For typical values 0 1 . 0 * m m m s s v m e dt dv m * * op op s E e v dt E d 2 1 * m E v opt s meV E opt opt 40 w s cm v s / 10 2 7
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