Determination of X-ray detection limit and applications in perovskite X-ray detectors

Abstract

X-ray detection limit and sensitivity are important figure of merits for perovskite X-ray detectors, but literatures lack a valid mathematic expression for determining the lower limit of detection for a perovskite X-ray detector. In this work, we present a thorough analysis and new method for X-ray detection limit determination based on a statistical model that correlates the dark current and the X-ray induced photocurrent with the detection limit. The detection limit can be calculated through the measurement of dark current and sensitivity with an easy-to-follow practice. Alternatively, the detection limit may also be obtained by the measurement of dark current and photocurrent when repeatedly lowering the X-ray dose rate. While the material quality is critical, we show that the device architecture and working mode also have a significant influence on the sensitivity and the detection limit. Our work establishes a fair comparison metrics for material and detector development.

Fig. 1. Detection limit and sensitivity of various perovskite X-ray detectors.

a Perovskite X-ray detectors with sensitivity and detection limit reported in the literatures with comparison to amorphous Selenium and Cadmium Zinc Telluride (CZT). b Sensitivity of MAPbI₃ and all-inorganic CsPbBr₃ X-ray detectors prepared with different material synthesizing methods and device structures where no detection limits are reported. The superscripts stand for the reference number.

Fig. 2. Review and comparison of different methods for detection limit determination.

a The “Well-known” blank in the Currie method and the IUPAC definition. L_C, critical level; L_D, detection limit; σ_B, blank signal standard deviation; α and β, type I and type II error; X_D, smallest detectable gross signal; $\overline{X_B}$, mean of the blank signal. b The practiced way^– for perovskite detector dose rate detection limit determination. N is the total number of digitized electric current data points and I_i is the i^th point. c The method proposed in this work, which is reduced to the Currie method with certain pre-assumptions. (μ₁, $n_1,{\sigma }_1^2$), (μ₂, $n_2,{\sigma }_2^2$) are the means, sample sizes, and variances of the two respective groups following Normal distribution.

Fig. 3. Sensitivity comparison of MAPbI₃ single crystal devices in different working mode.

a Experiment setup for reverse bias operation of the Pb/Au devices and the hole dominantly induced signal collection. b Dark I–V characterization of the devices. c Sensitivity of the reversely biased Pb/Au photodiode. d Sensitivity of the forward biased #2 Pb/Au photodiode. e Sensitivity of the Au/Au photoconductor.

Fig. 4. Detection limit obtained by the dark current method for MAPbI₃ detectors working in different mode.

a Experimentally measured current response of reversely biased #2 Pb/Au photodiode to X-ray dose rates approaching the detection limit. Calculated detection limit of net current I_limit and X-ray dose rate detection limit ${\dot{D}}_{limit}$ for the b reversely biased #2 Pb/Au photodiode, and for the c #1 Au/Au photoconductor and forward biased #2 Pb/Au photodiode. d qualitative comparison of sensitivity (slope of the linear fitting) and dark current for photodiode under forward vs reverse bias mode. The subscripted F and R stands for forward and reverse bias mode, respectively.

Fig. 5. A practical procedure for detection limit determination.

a The dark current I_dark & s method. N is the number of digitized current points of dark current and I_i is the i^th point. b The X-ray photocurrent I_dark & I_X–ray method. ${\sigma }_{I_{X-ray}}$ is the standard deviation of the photocurrent under X-ray irradiation I_X–ray. $n_{I_{X-ray}}$ and $n_{I_{dark}}$ are the number of digitized current points of I_X–ray and I_dark, respectively. ${\mu }_{I_{X-ray}}$ and ${\mu }_{I_{dark}}$ are the measured mean value of I_X–ray and I_dark, respectively.