In image processing, a pixel is used to describe the smallest discernable element in given process or device. A pixel detector is therefore a device capable of detecting an image, with the size of the pixel corresponding to the granularity of the image. For the case of pixel sensor photons of different energies are integrated in the sensing element and generate an intensity distribution which is the image. The pixel sensor used in this project are so-called hybrid pixel 3D detectors. Hybrid detectors is called hybrid because the electronics and sensor are made separately and then combined. (Rossie, et al, 2006) To simulate years of operation inside the ATLAS detector, these 3D pixel sensors were highly radiated. We can then measure the leakage current to determine the problems the sensor may have. (Rossie, et al, 2006)
Semiconductor detectors are doped semiconducting materials such as silicon. When putting together a n-doped and
a p-doped semiconductor, a depletion zone will occur between the n-doped and the p-doped material. In this depletion
zone the electron and the holes will start to diffuse. Electrons from the n-doped material will recombine with the holes
in the p-doped material. This will leave a "hole" n the n-doped region, which will lead to a region depleted of free charge
carriers. If we now apply a reverse bias voltage, the depletion zone will now expand. We can now apply a large enough reverse
bias voltage the depletion zone will cover the whole thickness of the device. The device is now fully depleted. (Rossie, et al, 2006)
In absence of any radiation there will always be a leakage current or a dark current. This is due to diffusion of free carries into the depletion zone. The biggest contribution to the leakage current is the thermal generation in the depleted volume. The thermal volume current will roughly double every 8K. If we increase the bias voltage beyond the depletion voltage the device will eventually reach a voltage breakdown. At the breakdown voltage the leakage current will begin to increase exponentially. The sensor has to operate under the breakdown voltage, but it also needs to be fully depleted. A good sensor therefore needs to have a breakdown voltage in the higher voltage range, while being fully depleted on the operational voltage. Measuring the leakage current and using the IV-curves we can see what problem the sensor may have. (Rossie, et al, 2006)
A macro has been used to plot these IV-curve. The slopes after the breakdown voltage have been calculated using a linear fit. Since the curve are plotted current against voltage, the slope is the resistance. The temperature depends looks to be an exponential growth functions, therefore an exponential fit has been tested to see if this was the case. Using the fact that:
can be written as:
we can use a linear fit to find B, then the doubling time is:
The code used to plot and linear fit these IV-scan can be found here: IVscan.zip The IVscan.zip file includes IVscan.h IVscan.cpp Run.c
Figure 1: IV-Curve of the RD53A-D59-2 sensor. Irratiated with 1.5E16 Neq/cm^2.
Table 1: Table of the slope calculation from 2V to 6V for the RD53A-D59-2 sensor at different temperatures. The IV-Curve was linearfitted from 2V to 6V
Figure 2: IV-Curve of the RD53A-D67-1 sensor. Irratiated with 1.5E16 Neq/cm^2.
Table 2: Table of the slope calculation from 8 to 18V for the RD53A-D67-1 sensor at different temperatures. The IV-Curve was linearfitted from 8V to 18V
Figure 3: IV-Curve of the RD53A-D67-2 sensor. Irratiated with 1.5E16 Neq/cm^2
Figure 4: Temperature depends of the RD53A-D67-2 sensor with the linearfit at constant 50V. The y-axis is the natural logarithm of the leaked current. The linearfit gave a constant B = 0.115677 seen in equation (1). Irratiated with 1.5E16 Neq/cm^2
From figure 1 we can see that the RD53A-D59-2 sensor is completely broken. The sensor immediately reach the breakdown voltage and we
get a close linear increase of the leakage current. We can ignore the last point at 7 volts at -50 °C as the current compliance
of the voltage source was set to around 0.110 mA. This means that the voltage source will limit the voltage so that the current never reaches over 0.110 mA.
Therefore the data shown at 7 volt is not the correct voltage. Figure 2 shows that RD53A-D67-1 sensor have a slightly better IV-curve where at least
the sensor does not reach voltage breakdown immediately. It seems to have a breakdown at around 5V - 6V where is also exhibit the same feature
as figure 1. The leakage current continues to increase linearly. From table 1 and 2 we can see that both sensor seems to have an electrical
resistance of 4-5 μΩ after the voltage breakdown. The slope of this linear increase does not appear to change much with the temperature.
This mean the resistance of the sensor after the breakdown does not depend on the temperature. It seems that after the breakdown the sensor will
start to act like a diode with a resistance of around 4-5 μΩ.
Figure 3 shows the IV-curve for the RD53A-D67-2. Here we can see that at 170V, the leakage current at emperature -50 °C and -40 °C shows a leakage current at around 0.110 mA. This was the compliance current.This could mean that the breakdown voltage is around 170V since it seems to have a very large increase in leakage current at that point. At temperature -10 °C the curve looks a bit strange. Here instead of increasing steadily, it increases linearly until it reaches a plateau. This could mean that we are measuring something else other than the leakage current.
Figure 4 shows the natural logarithm of leakage current against the temperature and the linear fit for the RD53A-D67-2. The bias voltage is at a constant -50V. Figure 4 seems to indicate that the temperature dependens is a exponential growth function, as the plot is very linear. The linear fit gave us B = 0.115677 from equation (1). Using equation (1) will give us that the leakage current doubles around 6K. This is not exactly 8K, which is roughly the temperature increace for the thermal volume current generation to double. There are also other contributions to the leakage current, which may affect the results. We also only have 6 temperature measurements, which means that the are also too few data to actually tell that the fit is good or not. Other effect that may have affected the results could be that the sensor may have reacted to other sources like light. This would mean that what we measured may not be the leakage current.
Two of those sensors are what we call bad sensors. The RD53A-D59-2 breaks down immediately and the RD53A-D67-1 has an early breakdown. The RD53A-D67-2 does seem to be rather good with a high breakdown voltage, but the measurement could indicate that we were not only measuring the leakage current. These sensors have been highly irradiated, so it is not so strange that these sensors are not perfect. Calculating the slopes after the breakdown also seems to indicate that the sensor will begin to act like a diode after the voltage breakdown.
Rossie. L., Fisher. P., Rohe, T., Wermes. N. (2006). Pixel Detectors From Fundamentals to Applications. New York: Springer Publishing, pp.1-57.