Dark Current Modeling for a Polyimide-Amorphous Lead Oxide-Based Direct Conversion X-ray Detector

Abstract

The reduction of the dark current (DC) to a tolerable level in amorphous selenium (a-Se) X-ray photoconductors was one of the key factors that led to the successful commercialization of a-Se-based direct conversion flat panel X-ray imagers (FPXIs) and their widespread clinical use. Here, we discuss the origin of DC in another X-ray photoconductive structure that utilizes amorphous lead oxide (a-PbO) as an X-ray-to-charge transducer and polyimide (PI) as a blocking layer. The transient DC in a PI/a-PbO detector is measured at different applied electric fields (5-20 V/μm). The experimental results are used to develop a theoretical model describing the electric field-dependent transient behavior of DC. The results of the DC kinetics modeling show that the DC, shortly after the bias application, is primarily controlled by the injection of holes from the positively biased electrode and gradually decays with time to a steady-state value. DC decays by the overarching mechanism of an electric field redistribution, caused by the accumulation of trapped holes in deep localized states within the bulk of PI. Thermal generation and subsequent multiple-trapping (MT) controlled transport of holes within the a-PbO layer governs the steady-state value at all the applied fields investigated here, except for the largest applied field of 20 V/μm. This suggests that a thicker layer of PI would be more optimal to suppress DC in the PI/a-PbO detector presented here. The model can be used to find an approximate optimal thickness of PI for future iterations of PI/a-PbO detectors without the need for time and labor-intensive experimental trial and error. In addition, we show that accounting for the field-induced charge carrier release from traps, enhanced by charge hopping transitions between the traps, yields an excellent fit between the experimental and simulated results, thus, clarifying the dynamic process of reaching a steady-state occupancy level of the deep localized states in the PI. Practically, the electric field redistribution causes the internal field to increase in magnitude in the a-PbO layer, thus improving charge collection efficiency and temporal performance over time, as confirmed by experimental results. The electric field redistribution can be implemented as a warm-up time for a-PbO-based detectors.

Keywords: X-ray detector; amorphous lead oxide; blocking layer; dark current; direct conversion; kinetics; mathematical model; polyimide.

Figure 1

(a) Schematic diagram (not to scale) and (b) a cross-sectional scanning electron microscopy (SEM) image of a single-pixel PI/a-PbO direct conversion X-ray detector.

Figure 2

Experimental setups for (a) modulated and continuous XPM and (b) DC kinetics.

Figure 3

The X-ray response of the PI/a-PbO detector, biased at 20 V/μm, to a continuous (black) and modulated (red) beam of X-rays. Modulated beam has a frame rate of 30 frames per second, matching that used in fluoroscopy. The photocurrent is normalized to the steady-state magnitude of the continuous response.

Figure 4

The ratios of W_± measured immediately after the application of the bias (${\mathrm{W}}_{+}^{\mathrm{inst}.}$) to W_± measured after waiting 10 min post bias application (${\mathrm{W}}_{\pm }^{\mathrm{inst}.}/{\mathrm{W}}_{\pm }$). Note that W±, measured 10 min after the bias was applied was chosen as the reference point because it is observed that after this amount of waiting, the ehp creation energy remains relatively constant, undergoing very little change over time.

Figure 5

Experimental DC kinetics data plotted in a semi-log scale corresponding to a PI/a-PbO detector biased at selected fields (5–20 V/µm) for two hours. The horizontal dashed line illustrates the operational threshold of 1 pA/mm². Data extracted from [5].

Figure 6

A simplified schematic diagram of the PI/a-PbO detector and its time-dependent spatial electric displacement field profile. The dashed line represents the displacement field at the instant of bias application. The solid line represents the displacement field profile post-bias application when holes have accumulated in PI. In addition, a schematic of MT transport of thermally generated holes through the bulk of a-PbO is illustrated.

Figure 7

Experimental (solid black) and simulated (injected (dash-dotted green), thermal (solid blue), and total (dashed red)) DC kinetics data plotted in a semi-log scale corresponding to a PI/a-PbO detector biased at fields of (a) 20 V/µm, (b) 15 V/µm, (c) 10 V/µm, and (d) 5 V/µm for two hours.

Figure 8

Electric displacement field (D(t)) at the ITO/PI interface (dashed red) and throughout the bulk of a-PbO (solid black) as functions of time for an applied field of 20 V/µm.

Figure 9

Release time (${\tau }_{r,m}$) plotted as a function of the instantaneous field at the ITO/PI interface ($F_{PI}\left(0,t\right)$). For the deepest level of traps at 1.0 eV (${\tau }_{r,3}$), a stronger field dependence, compared to the other levels, yielded a more accurate fit between experimental and simulated data.

Figure 10

Capture time (${\tau }_c$) plotted as a function of the applied nominal field (F₀). A unique constant ${\tau }_c$ was given for each applied nominal field to obtain the best fitting between experimental and simulated data.

Figure 11

Simulated (dashed lines) and experimental (solid lines) DC kinetics data plotted in a semi-log scale corresponding to a PI/a-PbO detector biased at selected fields (5–20 V/µm) for two hours. Here the model is modified by treating the release times (${\tau }_{r,m}$) and capture times (${\tau }_c$) as electric field dependent parameters in accordance with the hopping enhanced release and capture mechanisms discussed above.

Figure 12

The occupancy of trapping sites, segmented into three discrete levels, plotted as a function of time. Here, these data are obtained from the simulated kinetics corresponding to a nominal field of 20 V/μm. Note that these data are simulated from the unmodified model, where hopping-assisted release and capture is not accounted for.