The Tobin Coefficient: A Relevant Photodetector Performance Metric for IR Imaging

Abstract

The well-known Rule07 is a simple thus efficient way to compare available technologies for IR imaging detectors in terms of dark current. The noise is then often estimated using a shot noise approximation on the dark current. Both II–VI and III–V communities use this rule of thumb as a reference for well-performing IR photodiodes. For HOT applications, a dark current close to this rule07 is considered a necessary condition but not a sufficient one to obtain a high-performance IR imager. Indeed, when limited by shot noise, rule07 describes well the noise behavior of the considered device. However, when considering low-frequency noise, it fails to describe the expected performances. In this paper, we focus on another figure-of-merit, dedicated to detector low-frequency noise rather than dark current. Systemic 1/f noise investigation in an IR detector was first reported by Tobin et al. in 1980. There is today a relative consensus on the fact that measured 1/f noise is proportional to the dark current. The ratio between the amplitude of the 1/f noise and the dark current of the same devices may therefore be used as a figure-of-merit for a given technology. This ratio (called the Tobin factor \({\alpha }_{\text{T}}\)) therefore appears adequate to compare different technologies as a figure-of-merit qualifying 1/f noise properties. This dimensionless ratio can also be very useful for optimizing a particular technology or process. However, in order to be relevant, this figure-of-merit must be estimated carefully as it appears, for instance, pixel pitch-dependent. Different examples of Tobin coefficient extraction are presented in this paper. We show that, depending on the technologies, the values of the Tobin coefficient can spread over several orders of magnitude. However, only low values result in high-quality IR imagers. Today, the best results we obtained show that \({\alpha }_{\text{T}}={10}^{-5}\) is a state-of-art value to be compared with.