Current Noise Spectral Density and Excess Noise of a Silicon Low-Gain Avalanche Diode (LGAD)

The current noise power spectral density (NPSD) of a silicon low-gain avalanche diode (LGAD) has been measured at room temperature under different bias conditions. The device has been biased in its whole operating range up to close the junction breakdown with dark currents between 100 pA and 3 nA. The NPSDs have been measured in a bandwidth from 10 Hz up to a maximum frequency ranging from 10 kHz up to 3 MHz, depending on the noise level. The NPSDs have been found white in all the operative conditions with no evidence of a 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> component. An empirical law is proposed to describe the NPSD with high accuracy over four orders of magnitude from 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−28</sup> to 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−24</sup> A<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>/Hz. The excess noise factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\zeta $ </tex-math></inline-formula> has been experimentally determined from the NPSD and accurate measurements of the multiplication gain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>. A good agreement with McIntyre’s theory has been found only at higher gain values, but for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} \lt 30$ </tex-math></inline-formula>, the excess noise has been found to be accurately predicted by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{~\text {n}}$ </tex-math></inline-formula> law with n = 0.632 ± 0.014. An extremely low value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\zeta \,\, = \,\, 1.06~\pm ~0.01$ </tex-math></inline-formula> has been measured at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} \,\, =5$ </tex-math></inline-formula>, opening perspectives to the development of ultralow-noise radiation and particle detecting systems for both timing and spectroscopy applications.