Theory of carrier multiplication and noise in avalanche devices—Part I: One-carrier processes

Abstract

A new general theory is given for the carrier multiplication factor M and for the noise in devices in which avalanching occurs due to impact ionization by one type of carriers, such as in the channel of JFET's at sufficiently high channel fields. The theory involves the consideration of the discrete statistical process that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> ionizations can occur per carrier transit in an avalanche region of finite length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</tex> . For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \rarr \infin</tex> , the known results of the various continuous type theories, due to Tager, van der Ziel, and Chenette (also McIntyre, and Personick if the ionization coefficient of one type of carriers is set equal to zero) are recovered; these formulations are thus shown to be asymptotic theories. For finite <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> , the results show a continuous transition from the onset of avalanche ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 1</tex> ), as recently measured by Rucker and van der Ziel, to the asymptotic case. Curves covering the entire region are presented.