Variance and skewness of the multiplication gain distribution in uniform avalanche diodes

We derived exact analytical expressions for the variance, the third central moment, and the skewness of the multiplication gain distribution in uniform avalanche structures. The model assumes Poissonianity and locality of the ionization process and is valid for arbitrary values of the electron and hole ionization coefficients, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mi>α</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mi>β</mml:mi></mml:math> , respectively, as functions of the space coordinate. Expressions are also provided for the particular case where the ionization coefficients are related by a constant ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mi>β</mml:mi><mml:mo>/</mml:mo><mml:mi>α</mml:mi></mml:math> . The skewness is found to be always positive and greater than 2, indicating statistically relevant. Finally, the implications for spectral measurements of ionizing radiation are reviewed.