Research into the Spatial Resolution of CCDs

The CCD group is currently working on a PPARC funded project to investigate the Spatial Resolution of CCDs.

Introduction
When operated at UV, EUV and X-ray wavelengths the spatial resolution of a CCD is defined not only by the pixel size but also by electron diffusion in the field free-region beneath the back surface. This diffusion will lead to "charge spreading" in which the actual resolution of the CCD will be lower than that expected from consideration of the pixel size alone. The optimum CCD configuration is a trade-off between CCD thickness, silicon resistivity, and the presence or absence of antiblooming drains. In addition, the backside thinning process used also has an effect on the amount of charge spreading that occurs since it determines the nature of the electric field below the rear surface.
Charge Spreading is particularly important in the UV and EUV range since single photon event reconstruction is not possible. CCD requirements tend to focus on the pixel size without an appreciation of the electron diffusion consequences (which is generally the dominating factor).

By studying a wide range of CCD types supplied by Marconi Applied Technologies (ex. EEV) it is proposed to produce a clear understanding of these trade-offs and so be able to predict the overall CCD imaging performance (and also related issues such as typical QE as a function of wavelength, typical dark and bright defect levels, spatial resolution as a function of accumulated charge and radiation hardness).

Objectives of this research
This work has the following main objectives:
* to develop an empirically based performance model which can be used to predict the imaging performance in terms of device parameters such as resistivity, back-thinning process, etc.;
* to characterise a wide range of Marconi devices in terms of their imaging performance;
* to use the measured device performances to validate and refine the performance model.
The proposed research is discussed in more detail below.

Background to this research
At EUV/UV wavelengths the photon absorption depth is very small (significantly less than 1*m). In front-illuminated devices this absorption depth is so small that a high proportion of the incident photon flux is absorbed in the electrode gate structures above the CCD surface. To maximise the QE at these wavelengths, the CCD is usually illuminated from the back surface (i.e., back-illuminated) and a number of back thinning techniques have been developed.

Unfortunately, it is not possible to completely thin the backside region right up to the depletion region (where an electric field is present) as is it not possible to calculate exactly the dimensions of the depletion depth. In addition, even if it were possible to thin the depletion region completely, the depletion region would now come into contact with the backside surface of the CCD, and would generate a vastly increased dark signal from electrons from the backside surface states. Manufacturing tolerances are also an important consideration.

Consequently, any photon-induced electrons will have to diffuse through a field free region before being collected in a potential well. During this diffusion there will be an expansion of the charge cloud. Consequently, some of the charge which would otherwise be collected in the illuminated "pixel" will in fact be collected in adjacent pixels. Such charge spreading is highly dependent on photon wavelength, due to the variation in absorption depth.

At a given moment the accumulated charge within a pixel affects the electric field near the back surface. Thus, the diffusion induced degradation of imaging performance is also related to source brightness and integration time. For a particular application, early analysis of the potential problem can provide important information at the design stage - e.g optics design, and may even drive the device type purchased.

Certainly, if the charge spreading can be predicted (even through an empirical type model) then it is possible to "tailor" the device fabrication to optimise performance for a given application. For example, thinner devices would result in less charge spreading; but such a device would be more susceptible to damage by Solar X-rays; yet a particular back-thinning process may also provide additional protection against Solar X-ray damage. Hence, selection of a suitable CCD type for a particular imaging requirement can involve complex trade-offs against quite a large matrix of potential device design features.

The work in this project will enable the trade offs for device types to be determined. In particular, it will identify the range of device types optimised for different imaging regimes (for example, image structure, source intensity) enabling device fabrication to be more efficiently optimised for the requirements.

In addition, the work will significantly add to our knowledge of the physical processes occuring during charge spreading and will be particularly relevant to CCDs imaging in integrating mode, as the majority of work on this subject so far has concentrated on CCDs operating in photon counting modes for X-ray spectroscopic work.

A number of methods will be adopted to measure the charge spreading within a device. These methods are outlined immediately below since no single approach will provide all the necessary information.

Vernier measurement of the Modulation Transfer Function (MTF)
As a pixelated structure a CCD will not possess a "unique" MTF since the input image is sampled at fixed spatial frequencies (which could lead to beat frequency modulation patterns). However, it is possible to measure a "pseudo" MTF which will have excellent repeatability and can be used to estimate the degradation in image performance.  Routine "MTF" measurements are made using a Vernier technique in which a line image is tilted slightly with respect to a CCD column such that successive pixel rows sample the response function with each set of samples displaced by a fraction of a pixel per row. These samples can be used to calculate a "pseudo" MTF. As an alternative the use of a closely spaced grid will also be explored.

Spot measurements
Scanning a small spot across the CCD will allow the CCD line spread funtion to be measured in the spatial domain, and it is also possible to measure the MTF directly in the Fourier domain by generating fringe patterns on the CCD and converting this to the line spread function.

Charge collection using an Fe55 source
An Fe55 source generates a known number of electrons (~1600) per detected photon. Using a suitably weak source, a small number of pixels in each integration or frame will have charge generated within them. The ratio of individual pixel events to "split" events (whereby the charge has been shared between several pixels) can be calculated by comparing the ratio of pixels which contain the maximum amount of charge with those that do not. MSSL has significant experience in the software reconstruction of split events, developed for the XMM-RGS project.

A comparison will be made of the above methods.

Improvement and Validation of Existing Models
A number of models exist for calculating the expected charge spreading of a given device. For example, extensive work at Penn. State University has modeled the shape and the subsequent diffusion of a charge cloud through a number of "slabs" with the propagation through each slab dependent on the properties of that layer. However, this model is both highly mathematically detailed and dependent on a number of intrinsic parameters which can only be estimated with some uncertainty and cannot be directly determined. Thus, whilst detailed models such as this are essential for modelling the device physics to achieve a full understanding of the charge spreading, a more empirical model which is easier to understand is required to assist choice of CCD in the procurement stage.

A simpler model can be made by using geometrical relationships of the undepleted and depleted depths to the pixel pitch such that, for any electron cloud generated very close to the back surface of the CCD, the amount by which the charge cloud will spread is solely a function of these ratios. The simplicity of such a model means that only a few parameters need to be estimated. For example, the undepleted depth will depend on the actual thickness of the device after the back-thinning process, the resistivity of the silicon and the amount of charge generated in each potential well (as charge compensation will reduce the depleted depth as the potential well fills up). In addition, the behaviour of electrons which travel back to the rear surface (i.e, 50% of the electron) is presumed with little justification.
 


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