--------------[ Using PIN photodiodes for X-ray photon counting: ]--------------
Publication date: 2024-02-14
 

PIN photodiodes are diodes with a thick undopped/intrinsic layer between
the P and N-type regions. When light shines into the depletion layer it
liberates electron-hole pairs, which, if reverse biased drift into the dopped
regions, allowing a small current to flow. 

An X-ray photon can also knock an electron free, but all the excess energy
causes it fly through the semiconductor creating more electron-hole pairs:


[IMG diode.png ]

(not to scale) 

Because a photodiode is designed for light, higher energy X-rays can pass
through the depletion layer without interacting. This causes the sensitivity
to fall off above a photon energy of 22 keV. Because of this, the count
rate in a metal enclosure will be very low: any photons that can pass into
the enclosure are not likly not be detected. 

Despite the photocurrent from a single photon being much higher then with
visible light, the signal from a single photon is still tiny: Around 3.6
eV of energy is required for each electron-hole pair, which allows one electron
of current. A 10 keV X-ray photon will allow 2780 electrons to flow, moving
.44 femto-Coulombs of charge. 

To prevent it from being overpowered by stray capacitance or noise, the
signal has to be amplfied. I used this configuration with a BPW34S photodiode,
which has a .1 mm thick intrinsic region, a 7.5 mm active area and 70 pF
of capacitance at zero volts: 

[IMG preamp.png ]

The supply voltage is shown as 12 Volts, but is not critical; 9 Volts from
a battery works just fine. This circuit slighly modified from this paper:
"A novel charge sensitive preamplifier without the feedback resistor" 

The amplifier uses an unconventional input stage, with a forward biased
JFET.. JFETs can still amplify in this configuration, but also bleed off
any accumulated charge without using a hard to find gigaohm resistor. R2
is not super critical, it should be chosen so that Q1's drain should be
at least .8 volts above ground. 

C1 provides negative feedback, setting and stabilizing the gain, a smaller
capacitor would provide more gain, and a larger less. 

Results:
########
 

When a X-ray hits the photodiode, the amplifier produces a dip in output
with a short fall time (90 ns), but a long tail lasting around a millisecond:


[IMG trace.jpg ]

A single ~10 keV photon event. 1 mV and 1 ms per division. 

The amplifier and detector are very sensitive to stray electric fields,
and must be placed in a grounded metal box. Additionally, the detector needs
to shielded from light, even a small amount of light will reduce gain and
increase noise, as well as creating ringing and even oscillation. A piece
of aluminum foil (16 μm thickness) can be used as an window to let x-rays
in, while blocking light and RF. 

The supply also needs to be clean, the filtering can improved with a 100
Ohm resistor in series with the supply, or alternatively just by using batteries.


From C1's value, the theoretical output can be calculated: 

    10 keV / 3.6 (eV/e) / .5 pF = .89 mV
    

This is nearly identical to the measured .9 mV per 10 keV. 

The signal is still quite weak, and the long tails often overlap, cleaning
this up will be detailed in the next post. 

Noise:
######
 

The noise, once shielded from RF and light, is dominated by the detector's
noise and JFET's noise. Both of these can be reduced by cooling down the
circuit, but this does effect the optimal value of R2. 

If you can, use a fancier FET instead of the J310. 

A sneaky source of noise is detector capacitance: a large capacitance will
reduce the voltage the JFET sees. The feedback loop will compensate with
more gain, resulting in increased noise. 

An easy way to reduce the capacitance is to increase the bias voltage, but
this also increases leakage current, so the optimal voltage mustto be experimentally
determined. 

Another fix is to use a smaller area photodiode, but that results in lower
sensitivity. Specialized X-ray detectors with very small capacitances and
a built in FET exist, but they are very expensive. 

Osciloscopes are also not the best for small signals: mine has ~200 μV of
noise peak to peak, even on the lowest bandwith setting. Most of the noise
in the trace still appears even with the probe unpluged. 

A simple trick is to use a 1x probe or directly connect the scope to the
circuit with coax: A 10x probe will attenuate the signal to 1/10 of the
orignal amplitude, making scope noise 10 times worse. With a 10x probe the
signal shown in the image section would be burried under ~2 mV of noise.