AlInP photodiode x-ray detectors

3.1.1. Capacitance-voltage measurements.

The capacitances of the two 217 μm  ±  15 μm diameter (D1 and D2) and the two 409 μm  ±  28 μm diameter (D3 and D4) packaged Al_0.52In_0.48P photodiodes were measured in a dry N₂ environment (relative humidity  <5%) at room temperature (24 °C) using an HP 4275A Multi Frequency LCR meter and a Keithley 6487 Picoammeter/Voltage Source as the external voltage supply. The LCR meter was set with a 60 mV r.m.s AC test voltage signal magnitude and a 1 MHz frequency. National Instruments Labview software was used to automate the capacitance measurements. Each photodiode was reverse biased up to 100 V, with increments of 1 V. The capacitance of the device's package was estimated by measuring the capacitances between the empty pins on the package (pins without photodiodes connected to them) and the common pin of the package, it was found to be 0.84 pF  ±  0.05 pF. In order to find the capacitance of the device itself, the capacitance of the device's package was subtracted from the measured capacitance of the packaged device.

The depletion width (W) of each photodiode was considered to be given by,

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle W=~\frac{{{\epsilon }_{0}}{{\epsilon }_{r}}A}{C}\nonumber \end{align} \tag{ 1 }$$

where ₀ is the permittivity of the vacuum, _r is the relative permittivity of Al_0.52In_0.48P (11.25 [20]), A is the area of the photodiode, and C is the capacitance of the photodiode.

The capacitances and the associated depletion widths of the photodiodes as functions of applied reverse bias are shown in figures 3 and 4, respectively. The capacitance densities of these photodiodes were found to be similar across the investigated biases and become relative constant (5 pF mm⁻²  ±  1 pF mm⁻²) at high reverse biases (>80 V). At 100 V reverse bias, the capacitances of the 217 μm diameter photodiodes (D1 and D2) were found to be 0.71 pF  ±  0.07 pF and 0.66 pF  ±  0.07 pF, respectively; and the capacitances of the 409 μm diameter photodiodes (D3 and D4) were found to be 2.48 pF  ±  0.09 pF and 2.49 pF  ±  0.09 pF, respectively.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

At the highest investigated reverse bias (100 V), the calculated depletion widths and associated uncertainties (including the error in the diameter of these photodiodes, the uncertainties in the capacitance measurements, and the Debye length) of the photodiodes were found to be 5.13 μm  ±  0.87 μm and 5.57 μm  ±  0.98 μm for the 217 μm diameter photodiodes (D1 and D2), and 5.26 μm  ±  0.75 μm and 5.26 μm  ±  0.75 μm for the 409 μm diameter photodiodes (D3 and D4). Reduction of capacitance with increasing reverse bias became insignificant at reverse biases  >80 V. These devices have a thicker depletion region than the previously reported Al_0.52In_0.48P x-ray detectors (i layer thickness of 0.5 μm with an avalanche layer thickness of 1 μm [2]; i layer thickness of 2 μm [3]).

3.1.2. Current–voltage measurements.

Leakage currents as functions of applied reverse bias for the four Al_0.52In_0.48P photodiodes were measured in dark condition in a dry N₂ environment (relative humidity  <5%) at room temperature (24 °C). Using a Keithley 6487 Picoammeter/Voltage Source, each photodiode was reverse biased from 0 V to 100 V, in increments of 1 V. National Instruments Labview software was used to automate the measurements. Low leakage currents (<3.0 pA  ±  0.4 pA) (including the package's leakage current) were found for all the photodiodes even at high reverse bias (100 V), as shown in figure 5. The leakage current associated with the package itself was estimated by measuring the leakage current of an empty pin on the same package and common pin of the package. The package's leakage current was found to be less than the picoammeter's uncertainty (0.4 pA). Hence, the package's leakage current was considered to be negligible.

Zoom In Zoom Out Reset image size

At 40 V reverse bias (electric field strength  ≈  105 kV cm⁻¹), the leakage current densities of the Al_0.52In_0.48P photodiodes (217 μm diameter devices, D1  =  0.34 nA cm⁻², D2  =  0.24 nA cm⁻²; 409 μm diameter devices, D3  =  0.03 nA cm⁻², D4  =  0.08 nA cm⁻²) were greater than has been reported with custom-made SiC x-ray detectors (e.g. 1 pA cm⁻² at an electric field strength of 103 kV cm⁻¹ at room temperature [21]) but comparable to the leakage current densities reported with commercially available SiC UV detectors (1.2 nA cm⁻² at electric field strength of 227 kV cm⁻¹ at room temperature [6]). In contrast, the leakage current densities of the Al_0.52In_0.48P photodiodes were lower than has been reported for semi-insulating SiC x-ray photodiodes (65 nA cm⁻² with internal electric field of 28 kV cm⁻¹ at room temperature [22]) and Al_0.8Ga_0.2As photodiodes (4.72 nA cm⁻² with an electric field of 29 kV cm⁻¹ at room temperature [10]).

The four packaged photodiodes were each in turn soldered to a wire-ended packaged silicon input JFET (2N4416A, capacitance  =  2 pF) which was the first transistor of a custom-made low-noise charge-sensitive preamplifier of feedback resistorless design [23]. An ORTEC 572A shaping amplifier and an ORTEC EASY-MCA 8k multi-channel analyser (MCA) were connected to the preamplifier. The photodiodes were each in turn illuminated with an ⁵⁵Fe radioisotope x-ray source (Mn Kα  =  5.9 keV; Mn Kβ  =  6.5 keV; activity  =  175 MBq). The ⁵⁵Fe radioisotope x-ray source was placed 4 mm above the 217 μm diameter photodiodes and 10 mm above the 409 μm diameter photodiodes. In each case, the system was investigated at six different shaping times (0.5 μs, 1 μs, 2 μs, 3 μs, 6 μs, and 10 μs) with each photodiode reverse biased at 0 V, 10 V, 20 V, 30 V, 40 V, 60 V, 80 V, and 100 V. Each spectrum was accumulated for 240 s. The photodiodes and the preamplifier were operated at room temperature (24 °C) in a dry N₂ environment (relative humidity  <5%).

The resulting spectra were calibrated in energy terms by using the positions of the zero energy noise peak and the fitted Mn Kα peak at 5.9 keV for each spectrum as points of known energies on MCA's charge scale, and assuming a linear variation of detected charge with energy. The energy resolutions (FWHM at 5.9 keV) of the systems as functions of shaping times are shown for a detector reverse bias of 100 V in figure 6. The best energy resolutions of the 217 μm diameter photodiode (D2) and 409 μm diameter photodiodes (D4) at each reverse bias are presented in figure 7. FWHM at 5.9 keV as good as 0.89 keV  ±  0.04 keV and 1.05 keV  ±  0.08 keV were found for the 217 μm diameter photodiode (D2) and the 409 μm diameter photodiode (D4), respectively, at 100 V reverse bias. Figure 8 shows the spectra obtained with each photodiode at the best shaping time when reverse biased 10 V, 20 V, 40 V, and 100 V.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The energy resolutions obtained (0.89 keV and 1.05 keV at 5.9 keV, for the 217 μm and 409 μm diameter detectors, respectively) are not as good as some of those obtained using other wide bandgap x-ray photodiodes at room temperature. For example, a 200 μm diameter GaAs mesa photodiode spectrometer had a FWHM at 5.9 keV of 745 eV [24], and a 200 μm  ×  200 μm SiC x-ray pixel detector had a FHWM at 5.9 keV of 196 eV at 30 °C when coupled to lower noise readout electronics [21]. However, the energy resolutions achieved with these AlInP devices are better than those previously reported for 2 μm i layer AlInP mesa devices (0.93 keV for a 200 μm diameter photodiode; 1.2 keV for a 400 μm diameter photodiode [3]). They are also better than has been reported with some other custom wide bandgap photodiodes, e.g. AlGaAs (1.07 keV at 20 °C for a 200 μm diameter diode [25], 1.06 keV at 20 °C for a 200 μm diameter photodiode [26]). A shaping time noise analysis is presented in section 3.3.

The valley-to-peak (V/P) ratio (as defined as the ratio between the number of counts at 4.1 keV and 5.9 keV) at the optimum shaping time and the greatest investigated reverse bias (100 V) were 0.048 and 0.058 for the 217 μm diameter photodiode (D2) and the 409 μm diameter photodiode (D4), respectively. These are not as good as those reported for cooled silicon DEPFET detectors (V/P  =  ~0.0001) [27] and GaAs detectors (V/P  =  0.03) [28], but better than those of some AlGaAs photodiodes (V/P  =  0.08 [10, 26]). The low energy tail of the photopeak which gives rise to the valley is a consequence of the partial collection of charge created by x-ray photons absorbed in the semiconductor layers often assumed to be inactive (e.g. substrate) [10]. The V/P ratio is therefore expected to improve as AlInP detectors with thicker i layers are grown.

Figure 9 shows how the number of counts in the 5.9 keV photopeak changed as the reverse bias was increased. The number of counts was found to increase from 5.79  ×  10⁶ at 0 V reverse bias to 5.94  ×  10⁷ at 100 V reverse bias for the 217 μm diameter photodiode (D2), and from 3.40  ×  10⁶ at 0 V reverse bias to 4.39  ×  10⁷ at 100 V reverse bias for the 409 μm diameter photodiode (D4).

Zoom In Zoom Out Reset image size

In order to explore the cause of the observed change in the number of the detected counts in the 5.9 keV photopeak as a function of applied reverse bias (see figure 9), the relative number of counts expected to be detected in the 5.9 keV photopeak was calculated at each reverse bias. The expected number of counts was computed by multiplying the experimentally detected number of counts at 100 V reverse bias by the ratio of the depletion width of the detector at the desired reverse bias to its depletion width at 100 V. The predictions of numbers of detected counts were made assuming that there was complete charge collection across the bias range, and that the measured variation in the thickness of each photodiode's depletion region as function of reverse bias was the sole contributing factor to variation in numbers of detected counts for that photodiode. The results of this work can be seen in figure 9 where the predictions are presented for comparison with the experimental data. The uncertainties (error bars) in the predictions shown in the figure reflect the uncertainties in the photodiodes' calculated depletion widths at each reverse bias. Agreement was found between the experimental and predicted numbers of counts at high reverse biases (⩾10 V for D2;  ⩾60 V for D4). Therefore, it is interpreted from this that at these reverse biases, the change in number of experimentally detected counts as a function of applied bias for each photodiode was a result of the changes in the depletion width as a function of reverse bias. At low reverse biases (<10 V for D2 and  <60 V for D4), the disagreement between the experimental and predicted numbers of counts may be due to incomplete charge collection as a consequence of the low internal electric fields present in these bias conditions.

The energy resolution of a photodiode x-ray spectrometer is the result of contributions from three noise components: Fano noise; electronic noise from the detector and the preamplifier; and incomplete charge collection noise [14]. The Fano noise is determined by the statistical fluctuations in the number of the electron–hole pairs created in the process of photon absorption [14]. The expected Fano-limited resolution (FWHM_Fano) of the Al_0.52In_0.48P photodiode can be estimated to be 145 eV at 5.9 keV, assuming an electron–hole pair creation energy of 5.34 eV [29], and a Fano factor of 0.12 (it should be noted that there has been no reported measurement of the Fano factor in Al_0.52In_0.48P to date). The electronic noise includes the series white noise, induced gate drain current noise, parallel white noise, 1/f  series noise, and dielectric noise [14]; explanations of the origin of each electronic noise component can be found in [17, 30]. The noise components were calculated as per [30]. Incomplete charge collection is related to the trap density distribution and the charge diffusion and collection properties of the detector [14].

The series white noise including induced gate current noise, 1/f  series noise, and dielectric noise are related to the total capacitance at the input of the preamplifier. The parallel white noise is related to the leakage current of the detector and the leakage current of the input JFET. A longer shaping time can reduce the series white noise including induced gate current noise and increase the parallel white noise. The 1/f  series noise and dielectric noise are independent of shaping time [30]. The quadratic sum of the dielectric noise and incomplete charge collection noise can be estimated by subtracting (in quadrature) the calculated series white noise (including induced gate current noise), parallel white noise, 1/f  series noise, and the predicted Fano noise in quadrature from the measured FWHM at 5.9 keV. The calculated noise contributions for one of the 217 μm diameter devices (D2) and one of the 409 μm diameter devices (D4) as functions of shaping time at 100 V reverse bias are shown in figure 10. Figure 10 also shows the quadratic sum of the dielectric noise and incomplete charge collection noise; this combination is the dominant contributor to the total noise of the systems, and it is relatively constant at all the investigated shaping times, as would be expected. At 100 V reverse bias, the best FWHM for the 217 μm diameter photodiode (D2) and the 409 μm diameter photodiode (D4) were found at with shaping times of 2 μs and 3 μs, respectively. For the 217 μm diameter photodiodes, the series white noise dominates all other noise components except the combination of the dielectric and incomplete charge collection noise; at shaping time  >2 μs, the same can be said for the parallel white noise. For the 409 μm diameter photodiodes, 3 μs is the shaping time at which dominance shifts between the white series and white parallel noise components.

Zoom In Zoom Out Reset image size

It is interesting to further consider the dielectric noise and the incomplete charge collection noise such that their respective contributions can be established. As such, the quadratic sum of dielectric noise and incomplete charge collection noise of the 217 μm diameter device (D2) and the 409 μm diameter device (D4) were analysed as a function of applied reverse bias at a fixed shaping time of 3 μs, as shown in figure 11. A reduction in this equivalent noise charge with increased detector bias can be due to the either a reduction of the system capacitance or a reduction in the incomplete charge collection noise as a consequence of improved charge transport at higher electric field, or both.

Zoom In Zoom Out Reset image size

At high reverse biases (⩾80 V), the change in the capacitances and the associated depletion widths of these devices were insignificant (see figures 3 and 4), hence, the dielectric noises of each device is expected to be constant since the dielectric noise, ENC_D, is related to the capacitance, such that

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm EN}{{{\rm C}}_{D}}=\frac{1}{q}\sqrt{{{A}_{2}}2kTDC}\nonumber \end{align} \tag{ 2 }$$

where q is the electric charge, A₂ is a constant depending on the type of signal shaping (assumed here to be 1.18 [31]), k is the Boltzmann constant, D is the dielectric dissipation factor, and C is the capacitance [17].

From figure 11, the constant equivalent noise at  ⩾80 V demonstrates that was no significant contribution from incomplete charge collection noise in this bias condition because there was no reduction in the combination as the bias was increased beyond 80 V. As such, the quadratic sum in these conditions can be said to be solely composed of dielectric noise, which is independent of bias and shaping time.

Given these statements, for each spectrometer separately, it is possible to consider any small apparent variations in dielectric noise which may occur with varied shaping time, as arising from repetition in measurement of the same physical quantity rather than real physical differences in dielectric noise—so long as each detector is reverse biased at  ⩾80 V. This then provides six measurements at each reverse bias  ⩾80 V of the same dielectric noise for each spectrometer. There are six measurements because six shaping times were used. These six measurements, the computed dielectric noises, for a 217 μm diameter photodiode (D2) and a 409 μm diameter photodiode (D4) at reverse bias of 80 V and 100 V, respectively, are shown in figure 12.

Zoom In Zoom Out Reset image size

Since the dielectric noises of D2 spectrometer, ENC_DT217, and D4 spectrometer, ENC_DT409, each consist of the dielectric noises of their respective detectors (ENC_D217 for 217 μm photodiode and ENC_D409 for 409 μm photodiode), and some other system dielectric noise which is common between both spectrometers, the dielectric dissipation factor (see equation (2)) of Al_0.52In_0.48P can be estimated. First, the common system dielectric noise, ENC_Dx, must be considered; it is given by,

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm ENC}_{Dx}^{2}={\rm ENC}_{DT217}^{2}-{\rm ENC}_{D217}^{2}={\rm ENC}_{DT409}^{2}-{\rm ENC}_{D409}^{2}\nonumber \end{align} \tag{ 3 }$$

where all terms have been previously defined.

Following this, since the variation in the dielectric noise between the detectors themselves is solely due to the difference in their capacitances (equation (2)), the relationship between ENC_D217 and ENC_D409 can be expressed as,

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \frac{{\rm EN}{{{\rm C}}_{D217}}}{{\rm EN}{{{\rm C}}_{D409}}}=\sqrt{\frac{{{C}_{217}}}{{{C}_{409}}}}\nonumber \end{align} \tag{ 4 }$$

where C₂₁₇ and C₄₀₉ are the capacitances of the 217 μm diameter photodiode (0.72 pF and 0.67 pF at reverse bias of 80 V and 100 V, respectively) and 409 μm diameter photodiode (2.68 pF and 2.50 pF at reverse bias of 80 V and 100 V, respectively), respectively.

Thus, by combining equations (2)–(4), and considering all the data at 80 V and 100 V, the dielectric dissipation factor of Al_0.52In_0.48P was estimated to be (2.2  ±  1.1)  ×  10⁻³. This value is smaller than that reported for In_0.5Ga_0.5P (6.5  ×  10⁻³) [12] but larger than Si (0.8  ×  10⁻³) [15], GaAs (0.1  ×  10⁻³) [32], and 4H-SiC (3.4  ×  10⁻⁵) [33].

In a feedback resistorless charge-sensitive preamplifier the current of the detector in part sets the bias of the forward biased input JFET [23], which in turn influences the JFET's capacitance. The above determination is predicated on the assumption that the variations in detector leakage current between the 217 μm and 409 μm diameter photodiodes and in operating the detectors at biases of 80 V and 100 V, is sufficiently small that the capacitance of the JFET is not substantially changed. Given the low leakage currents of the detectors (<3 pA), it is believed that the assumption is valid.