Introduction
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Measuring CCD Resistivity (Dan Weatherill)
The resistivity of a material is likely a familiar property to the readers already, and one of the current experimental activities in WP3.9 is using indirect optical measurements to constrain the resistivity of LSST sensors, so in this brief note I wanted to explain why this is an important property for CCDs and how we approach measuring it in a working device non-destructively. The explanations will be brief and lacking in detail, but as always if there are any questions or further interest in this topic please don’t hesistate to get in touch with me at daniel.weatherill@physics.ox.ac.uk or the WP3.9 lead, prof Ian Shipsey ian.shipsey@physics.ox.ac.uk.
Resistivity in Silicon
Silicon is most useful to us due to its semiconducting properties, and some patterned semiconductor devices (for example MOSFETS) might be described simplistically as operating as devices whose resistance can be altered dynamically by applications of potential difference. It’s quite clear then why we might care about the resistivity of the material these devices are built on, because in a transistor it will determine several important performance characteristics. In a CCD, though, we don’t have any patterned transistor structures within the pixels of the device, only at the output amplifiers. It turns out that resistivity also has important consequences for imaging in the pixels. Firstly, and most importantly, the resistivity of a semiconductor depends strongly on the doping introduced. The devices we use in the LSST camera are so-called “n-channel” devices where the signal charges are the minority carrier electrons, which means the silicon substrate we start from in constructing them is p-type silicon. A rough but reasonably accurate expression for the resistivity ρ of the silicon is given by:
ρ ≈ 1 / (q p μ)
where q is the charge on an electron, p is the concentration of holes, and μ is the mobility of holes. The concentration of holes at increases exponentially with the number of acceptor sites introduced by doping, and the mobility of holes itself also depends (though much more weakly) on the doping. It is clear, then, that a less doped device has higher resistivity. For high precision astronomy sensors, for reasons I will describe below, we desire very high resistivities, typically p >= 5000 Ohm cm. This implies very low doping densities, the exact numbers depending on what dopant is used and operating temperature, but in the region of Na ~ (1E12-1E13 ) cm^-3. It turns out that these low doping densities are almost impossible to achieve in silicon typically used for commercial device construction (constructed epitaxially e.g. via some vapour deposition process), and so for thick CCDs we need to use so-called “bulk” silicon, usually produced using the high-purity float zone technique (https://en.wikipedia.org/wiki/Float-zone_silicon ), though some varieties of Czochralski process silicon might be suitable (https://en.wikipedia.org/wiki/Czochralski_method ).
Resistivity for Astronomical Sensors
The primary reason we need high resistivity for thick CCD sensors is to allow us to produce high electric fields across the device with minimal leakage current (via a simple application of Ohm’s law). We need these high electric fields in a thick, back illuminated device, because most of the photo-electrons are produced near the back surface of the device and have to traverse the full depth of the sensor before being collected and read out. During this traversal they are subject to thermal diffusion, and this is the dominant mechanism for increasing the width of the detector PSF in such a sensor. By applying a high electric field across the device, we give these electrons a “push” towards the collection points, reducing the traversal time and hence decreasing the width of the detector PSF.
It is also worth noting that the phenomenon of “tree rings” – fixed pattern circular anomalies that appear in images at shorter wavelengths (https://iopscience.iop.org/article/10.1088/1748-0221/12/05/C05015 ) - is believed to be a consequence of spatially varying resistivity across the silicon crystal from which the device is constructed.
Device Resistivity Measurement
It is, of course, quite easy in a standard semiconductor device lab to measure the resistivity of a prepared device or test structure. We just put it on a semiconductor probe station, drop a few needles onto it and use a standard Kelvin resistance measurement technique. As you can imagine, this is not possible to do on a finished LSST sensor including its incredibly fragile anti-reflection coating without destroying the device irreparably. In addition, the resistivity of a single crystal of silicon depends on the direction you measure it in, and we are primarily interested in the resistivity in the depth direction of the device, which is somewhat harder to measure using a standard technique. We have a probe station in the OPMD lab, but we are not (hopefully!) in the business of destroying working production sensors. In addition, for our purposes we don’t need a highly accurate resistivity measurement, just a reasonable “ball park” number to be useful. A technique developed originally by S. Holland (https://ieeexplore.ieee.org/document/1185186 ) is used to indirectly determine an approximate resistivity optically. It was mentioned above that detector PSF will decrease with increasing applied voltage, because the electron transit time will reduce. However, this was assuming a device already fully depleted, meaning without the presence of the majority carriers. If we apply very low voltages instead of the high ones we typically use in operation, eventually the device will not be fully depleted, and regions of majority carriers will develop which screen out the electric field. We will then observe a drastic change in the device PSF, which we find by projecting a single small spot onto the device and measuring its width. By finding the applied voltage at which this occurs we can tell where the onset of full depletion is, and knowing the device thickness, we can use a simplified model of the pn-junction of the device to determine from this measurement what the resistivity (and, importantly for simulation work, doping) of the substrate is.
The Figure shows previous work by myself on measuring this property on a CCD261 device from e2v, which is in many ways similar in construction to the e2v CCD250 used in the LSST focal plane. The qualitative change in gradient indicates the different operating regimens of field free (at low applied bias) and full depletion (at high applied bias). The resistivity of the CCD261 measured was estimated at 6600+700-600 Ohm cm, and we expect the LSST device to be higher still. Tracing down the line for the field free regimen we can find the full depletion voltage. We have had some slight hardware issues in the lab with our vacuum system over the last few weeks, but we anticipate that we can produce a similar (and indeed much more thorough) survey of the LSST devices in the next few weeks.
Placeholder title for Andy
Forthcoming meetings of interest