the possibility of electron temperature decreasing below the lattice temperature in the presence of an external electric field (electron cooling) has been pointed out by paranjape and ambrose (1964). in the present works we show that under suitable conditions an external sound wave may produce the phenomenon of electron cooling in a semiconductor. we have shown that a decrease in electron temperature may occur when (1) the electrons are predominantly scattered by optical polar or non-polar optical modes of the lattice vibrations and (2) when the incident sound wave energy flux is greater than a certain critical value wq (which depends on the type of semiconductor). chapter i consists of a description of the model and a brief outline,of the calculations. in chapter ii, using a displaced maxwellian function, we have calculated the rates of energy and momentum transfer from the electrons to the lattice for acoustical, optical polar and non-polar optical types of scattering. the rates of energy and momentum transfer from the sound wave to the electrons are calculated in chapter ii, section (2.b,l). using these rates in conservation conditions (1.11) and (1.12), we obtain the expression for the electron temperature t as a function of the energy flux w (eqn. (3.6)). inequality conditions (3.7) and (3.8) are the main results of our calculations. condition (3.7) is equivalent to the electron cooling condition obtained by paranjape and de alba (1965) in the case of an electric field, while (3.8) gives the minimum sound wave energy flux p/q required to produce electron cooling. in non-polar and polar substances, the required predominance of optical scattering over acoustical scattering is expressed by the ratios (see document for formula) in eqns. (3.24) and (3.30), respectively. in sections (s.b.l) and (3.b.2), v/e have obtained the expressions for the sound absorption coefficient a and acoustoelectric current in terms of the energy flux w.