Negative differential mobility of electrons in germanium: A Monte Carlo calculation of the distribution function, drift velocity and carrier population in the (111) and (100) minima

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Abstract
Hot electron transport properties in germanium have been investigated using a Monte Carlo method with the principal objective of elucidating the origin of the negative differential mobility observed at low temperatures and high electric fields. The model takes full account of electron transfer from the (111) to the (100) valleys and incorporates the ellipsoidal constant energy surfaces associated with both these sets of minima. The scattering rates within the (111) valleys are determined from low field data, while constraints are placed on the strength of the scattering to and within the (100) valleys by recent data on the variation of low field resistivity with pressure. It is demonstrated that this model can give a consistent explanation of the magnitude of the negative differential mobility and its threshold field as functions of temperature orientation, uniaxial stress and hydrostatic pressure. The relative importance of f((100) from or to (010)) and g((100) from or to (100)) scattering in the (100) valleys is discussed in relation to uniaxial stress experiments and it is concluded that g scattering must be an important process.