Theory of carrier multiplication and noise in avalanche devices—Part II: Two-carrier processes

Abstract

It is shown that the standard theories of avalanche statistics for two-carrier impact ionization by Tager, McIntyre, and Personick only deal with processes for which the number of possible ionizations is very large. On the contrary, it is believed that in many modern devices the number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> of possible ionizations is finite and perhaps even very small ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 1-5</tex> ). A complete theory for this case is developed, using a new statistical approach, referred to as the "method of recurrent generating functions." The rather complex detailed expressions so obtained contain as special cases the result for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 1</tex> given by Lukaszek et al., and the results of the above mentioned standard theories for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = \infin</tex> these theories thus retain asymptotic validity. Computer plots of the new results indicate that the standard theories overestimate the noise of the avalanche process; this may explain exceedingly low noise data, as reported recently by Goedbloed and Smeets. Finally, for the asymptotic case a complete evaluation is made of the distribution for the output particle population. Previous results by McIntyre are fully corroborated.