Future X-ray missions such as Lynx require large-format imaging detectors with performance at least as good as the best current-generation devices but with much higher readout rates. We are investigating a Digital CCD detector architecture, under development at MIT Lincoln Laboratory, for use in such missions. This architecture features a CMOS-compatible detector integrated with parallel CMOS signal processing chains. Fast, low-noise amplifiers and highly parallel signal processing provide the high frame-rates required. CMOS-compatibility of the CCD provides low-power charge transfer and signal processing. We report on the performance of CMOS-compatible test CCDs read at rates up to 5 Mpix s−1 (50 times faster than Chandra ACIS CCDs), with transfer clock swings as low as ±1.5 V (power/area < 10% of that of ACIS CCDs). We measure read noise below 6 electrons RMS at 2.5 MHz and X-ray spectral resolution better than 150 eV FWHM at 5.9 keV for single-pixel events. We discuss expected detector radiation tolerance at these relatively high transfer rates. We point out that the high pixel ’aspect ratio’ (depletion-depth : pixel size ≈ 9 : 1) of our test devices is similar to that expected for Lynx detectors, and illustrate some of the implications of this geometry for X-ray performance and noise requirements.
Silicon charge-coupled devices (CCDs) are commonly utilized for scientific imaging in wavebands spanning the near infrared to soft X-ray. These devices offer numerous advantages including large format, excellent uniformity, low read noise, noiseless on-chip charge summation, and high energy resolution in the soft X-ray band. By building CCDs on bulk germanium, we can realize all of these advantages while covering an even broader spectral range, notably including the short-wave infrared (SWIR) and hard X-ray bands. Since germanium is available in wafer diameters up to 200 mm and can be processed in the same tools used to build silicon CCDs, large-format (>10 MPixel, >10 cm2 ) germanium imaging devices with narrow pixel pitch can be fabricated. Furthermore, devices fabricated on germanium have recently demonstrated the combination of low surface state density and high carrier lifetime required to achieve low dark current in a CCD. At MIT Lincoln Laboratory, we have been developing germanium imaging devices with the goal of fabricating large-format CCDs with SWIR or broadband X-ray sensitivity, and we recently realized our first front-illuminated CCDs built on bulk germanium. In this article, we describe design and fabrication of these arrays, analysis of read noise and dark current on these devices, and efforts to scale to larger device formats.
We describe recent advances in backside passivation of large-format charge-coupled devices (CCDs) fabricated on 200- mm diameter wafers. These CCDs utilize direct oxide bonding and molecular-beam epitaxial (MBE) growth to enable high quantum efficiency in the ultraviolet (UV) and soft X-ray bands. In particular, the development of low-temperature MBE growth techniques and oxide bonding processes, which can withstand MBE processing, are described. Several highperformance large-format CCD designs were successfully back-illuminated using the presented process and excellent quantum efficiency (QE) and dark current are measured on these devices. Reflection-limited QE is measured from 200 nm to 800 nm, and dark current of less than 1e- /pixel/sec is measured at 40°C for a 9.5 μm pixel.
The Transiting Exoplanet Survey Satellite, a NASA Explorer-class mission in development, will discover planets around
nearby stars, most notably Earth-like planets with potential for follow up characterization. The all-sky survey requires a
suite of four wide field-of-view cameras with sensitivity across a broad spectrum. Deep depletion CCDs with a silicon
layer of 100 μm thickness serve as the camera detectors, providing enhanced performance in the red wavelengths for
sensitivity to cooler stars. The performance of the camera is critical for the mission objectives, with both the optical
system and the CCD detectors contributing to the realized image quality. Expectations for image quality are studied
using a combination of optical ray tracing in Zemax and simulations in Matlab to account for the interaction of the
incoming photons with the 100 μm silicon layer. The simulations include a probabilistic model to determine the depth of
travel in the silicon before the photons are converted to photo-electrons, and a Monte Carlo approach to charge diffusion.
The charge diffusion model varies with the remaining depth for the photo-electron to traverse and the strength of the
intermediate electric field. The simulations are compared with laboratory measurements acquired by an engineering unit
camera with the TESS optical design and deep depletion CCDs. In this paper we describe the performance simulations
and the corresponding measurements taken with the engineering unit camera, and discuss where the models agree well in
predicted trends and where there are differences compared to observations.
We report on two recently developed charge-coupled devices (CCDs) for adaptive optics wavefront sensing, both designed to provide exceptional sensitivity (low noise and high quantum efficiency) in high-frame-rate low-latency readout applications. The first imager, the CCID75, is a back-illuminated 16-port 160×160-pixel CCD that has been demonstrated to operate at frame rates above 1,300 fps with noise of < 3 e-. We will describe the architecture of this CCD that enables this level of performance, present and discuss characterization data, and review additional design features that enable unique operating modes for adaptive optics wavefront sensing. We will also present an architectural overview and initial characterization data of a recently designed variation on the CCID75 architecture, the CCID82, which incorporates an electronic shutter to support adaptive optics using Rayleigh beacons.
The Regolith x-ray Imaging Spectrometer (REXIS) is a coded-aperture soft x-ray imaging instrument on the OSIRIS-REx spacecraft to be launched in 2016. The spacecraft will fly to and orbit the near-Earth asteroid Bennu, while REXIS maps the elemental distribution on the asteroid using x-ray fluorescence. The detector consists of a 2×2 array of backilluminated 1k×1k frame transfer CCDs with a flight heritage to Suzaku and Chandra. The back surface has a thin p+-doped layer deposited by molecular-beam epitaxy (MBE) for maximum quantum efficiency and energy resolution at low x-ray energies. The CCDs also feature an integrated optical-blocking filter (OBF) to suppress visible and near-infrared light. The OBF is an aluminum film deposited directly on the CCD back surface and is mechanically more robust and less absorptive of x-rays than the conventional free-standing aluminum-coated polymer films. The CCDs have charge transfer inefficiencies of less than 10-6, and dark current of 1e-/pixel/second at the REXIS operating temperature of –60 °C. The resulting spectral resolution is 115 eV at 2 KeV. The extinction ratio of the filter is ~1012 at 625 nm.
Orthogonal transfer array CCDs were originally developed by the University of Hawaii and MIT Lincoln Laboratory
for use in the focal planes of the ground-based Panoramic Survey Telescope and Rapid Response System
(Pan-STARRS). These devices have relatively large area (5x5 cm) and a novel, multiple-output readout architecture
that makes them attractive for certain applications in spaced-base X-ray astronomy. We have therefore
conducted a series of tests to determine their sensitivity to proton radiation encountered on-orbit. We report
effects of typical on-orbit proton exposure on charge transfer efficiency, dark current, noise and spectral resolution
as a function of device operating temperature and readout parameters.
Dark current for back-illuminated (BI) charge-coupled-device (CCD) imagers at Lincoln Laboratory has historically been higher than for front-illuminated (FI) detectors. This is presumably due to high concentrations of unpassivated dangling bonds at or near the thinned back surface caused by wafer thinning, inadequate passivation and low quality native oxide growth. The high dark current has meant that the CCDs must be substantially cooled to be comparable to FI devices. The dark current comprises three components: frontside surface-state, bulk, and back surface. We have developed a backside passivation process that significantly reduces the dark current of BI CCDs. The BI imagers are passivated using molecular beam epitaxy (MBE) to grow a thin heavily boron-doped layer, followed by an annealing step in hydrogen. The frontside surface state component can be suppressed using surface inversion, where clock dithering reduces the frontside dark current below the bulk. This work uses surface inversion, clock dithering and comparison between FI and BI imagers as tools to determine the dark current from each of the components. MBE passivated devices, when used with clock dithering, have dark current reduced by a factor of one hundred relative to ion-implant/laser annealed devices, with measured values as low as 10-14 pA/cm2 at 20°C.
The Pan-STARRS project has completed its first 1.4 gigapixel mosaic focalplane CCD camera using 60 Orthogonal Transfer
Arrays (OTAs). The devices are the second of a series of planned development lots. Several novel properties were
implemented into their design including 4 phase pixels for on-detector tip-tilt image compensation, selectable region logic
for standby or active operation, relatively high output amplifier count, close four side buttable packaging and deep depletion
construction. The testing and operational challenges of deploying these OTAs required enhancements and new approaches
to hardware and software. We compare performance achieved with that which was predicted, and discuss on-sky results,
tools developed, shortcomings, and plans for future OTA features and improvements.
The CCD detectors in the X-ray Imaging Spectrometers (XIS) aboard Suzaku have been equipped with a precision
charge injection capability. The purposes of this capability are to measure and reduce the detector degradation
caused by charged particle radiation encountered on-orbit. Here we report the first results from routine operation
of the XIS charge injection function. After 12 months' exposure of the XIS to the on-orbit charged particle
environment, charge injection already provided measurable improvements in detector performance: the observed
width of the 5.9 keV line from the onboard calibration source was reduced from 205 eV to less than 145 eV.
The rate of degradation is also significantly smaller with charge injection, so its benefit will increase as the
mission progresses. Measured at 5.9 keV, the radiation-induced rate of gain degradation is reduced by a factor
of 4.3 ± 0.1 in the front-illuminated sensors when injecting charge greater than 6 keV equivalent per pixel. The
corresponding rate of degradation in spectral resolution is reduced by a factor 6.5 ± 0.3. Injection of a smaller
quantity of injected charge in the back-illuminated XIS sensor produces commensurately smaller improvement
factors. Excellent uniformity of the injected charge pattern is essential to the effectiveness of charge injection in
Recent development efforts on the orthogonal transfer array (OTA) for the Pan-STARRS gigapixel camera 1 (GPC1) are described. A redesign of the prototype OTAs has been completed, and fabrication and packaging of the devices for the GPC1 are nearly complete. We briefly review the final design features and the resolution of the performance issues that arose in the first prototype devices. We then describe the packaging of the device and the challenges arising in achieving the necessary flatness at the device operating temperature. Plans and schedule for deploying focal-plane arrays of these devices are described.
A project to upgrade PUEO, the CFHT AO system, was first proposed in 2002. As part of the upgrade effort, a
technology project was conceived to evaluate and characterize the backside-illuminated CCID-35 detector as suitable a
replacement for the array of avalanche photo diode modules (APDs) in the curvature wavefront sensor. The CCID-35
was envisioned to replace an array of expensive APDs thus providing a cost-effective means of upgrading PUEO to a
higher-order system. Work on the project, dubbed FlyEyes, occurred sporadically until Oct 2005 but substantial
progress has been made since. This paper was intended to report on the performance of FlyEyes in PUEO but
unfortunately the instrument was not ready for tests at the time of this writing. This paper summarizes the progress
made on the project thus far and touches upon some of the difficulties encountered.
The orthogonal-transfer array (OTA) is a new charge-coupled device (CCD) concept for wide-field imaging in groundbased astronomy based on the orthogonal-transfer CCD (OTCCD). This device combines an 8×8 array of small OTCCDs, each about 600×600 pixels with on-chip logic to provide independent control and readout of each CCD. The device provides spatially varying electronic tip-tilt correction for wavefront aberrations, as well as compensation for telescope shake. Tests of prototype devices have verified correct functioning of the control logic and demonstrated good CCD charge-transfer efficiency and high quantum efficiency. Independent biasing of the substrate down to -40 V has enabled fully depleted operation of 75-μm-thick devices with good charge PSF. Spurious charge or "glow" due to impact ionization from high fields at the drains of some of the NMOS logic FETs has been observed, and reprocessing of some devices from the first lot has resolved this issue. Read noise levels have been 10 - 20 e-, higher than our goal of 5 e-, but we have identified the likely sources of the problem. A second design is currently in fabrication and uses a 10-μm pixel design resulting in a 22.6-Mpixel device measuring 50×50 mm. These devices will be deployed in the U. of Hawaii Pan-STARRS focal plane, which will comprise 60 OTAs with a total of nearly 1.4 Gpixels.
We have developed X-ray CCD sensors for the Astro-E2 X-ray Imaging
Spectrometer. Here we describe the performance benefits obtained from two innovations implemented in the CCD detectors developed for this instrument. First, we discuss the improved radiation tolerance afforded by a novel charge-injection structure. Second, we demonstrate for the first time the potential of a previously-developed chemisorption charging backside treatment process to produce back-illuminated X-ray sensors with excellent soft X-ray spectral resolution as well as improved quantum efficiency. We
describe the changes in X-ray event detection algorithms required to obtain this improved performance, and briefly compare the performance of XIS sensors to that of back-illuminated detectors currently operating on-orbit.
The orthogonal-transfer array (OTA) is a new CCD architecture designed to provide wide-field tip-tilt correction of astronomical images. The device consists of an 8x8 array of small (~500x500 pixels) orthogonal-transfer CCDs (OTCCD) with independent addressing and readout of each OTCCD. This approach enables an optimum tip-tilt correction to be applied independently to each OTCCD across the focal plane. The first design of this device has been carried out at MIT Lincoln Laboratory in support of the Pan-STARRS program with a collaborative parallel effort at Semiconductor Technology Associates (STA) for the WIYN Observatory. The two versions of this device are functionally compatible and share a common pinout and package. The first wafer lots are complete at Lincoln and at Dalsa and are undergoing wafer probing.
A frame transfer CCD intended for X-ray detection on-board ASTRO-E2 spacecraft was modified to include an input serial register and a charge injection structure which allows a very uniform injection of
charge into the imaging section of the device. A variation of the fill-and-spill method was implemented to inject charge into the CCD.
The operation of the structure is described, and results of the measurements are presented. Very small charge packets (a few tens of electrons) can be reproducibly injected with noise as low as 5 electrons rms. The amount of injected charge can be controlled by
the external voltage with very high accuracy. We have applied this technique to study various characteristics of the proton irradiated CCD, such as the column-to-column nonuniformity of charge losses and the amplitude dependence of the charge loss. The latter is related to the charge-volume relation in the charge storage site and for the first time we accurately measure this relationship at very low signal levels.
CFHT is planning to upgrade its adaptive optics system, PUEO, to a high order system with 104 elements, PUEO NUI. Currently PUEO uses a 19 element deformable mirror with the equivalent 19 avalanche photodiode (APD) detectors as its curvature wavefront sensor. PUEO NUI plans to implement the curvature wavefront sensor using back illuminated CCID-35 detectors developed by J. Beletic et al. instead of 104 APDs, which are prohibitively expensive under the present budget conditions. The CCID-35 detectors, developed at ESO and MIT/LL, were specifically designed to serve as direct replacements for APDs in curvature sensing. The first step in the upgrade is to build and test a system using two CCID-35 detectors, dubbed FlyEyes. These new detectors were successfully tested and integrated in the lab by R. Dorn at ESO but have yet to see sky time. FlyEyes will be their first opportunity. They will directly replace the 19 APDs in PUEO temporarily for a few engineering nights in January of 2005.
At the European Southern Observatory (ESO) in Garching, Germany, several adaptive optics systems using curvature wavefront sensors are being developed for the Very Large Telescope (VLT) and the VLT interferometer (VLTI). Curvature AO-systems have traditionally used avalanche photodiodes (APDs) as detectors due to strict requirements of very short integration times (200 microsec) and very low readout noise. Advances in CCD technology motivated an investigation of the use of a specially designed CCD as the wavefront sensor detector in a 60-element curvature AO system. A CCD has never been used before as the wavefront sensor in a low light level curvature adaptive optics system. This CCD can achieve nearly the same performance as APDs at a fraction of the cost and with reduced complexity for high order wavefront correction. Moreover the CCD has higher quantum efficiency and a greater dynamic range than APDs. A readout noise of less than 1.5 electrons at 4000 frames per second was achieved. Back-illuminated thinned versions of this CCD can replace APDs as a new detector for high order curvature wavefront sensing.
We report on design updates for the XIS (X-ray Imaging Spectrometer)
on-board the Astro-E2 satellite. Astro-E2 is a recovery mission of Astro-E, which was lost during launch in 2000. Astro-E2 carries a total of 5 X-ray telescopes, 4 of which have XIS sensors as their focal plane detectors. Each XIS CCD camera covers a field of view of 19×19 arcmin in the energy range of 0.4-12 keV. The design of the Astro-E2 XIS is basically the same as that for Astro-E, but some improvements will be implemented. These are (1) CCD charge injection capability, (2) a revised heat-sink assembly, and (3) addition of a 55Fe radio-isotope on the door. Charge injection may be used to compensate for and calibrate radiation-induced degradation of the CCD charge transfer efficiency. This degradation is expected to become significant after a few year's operation in space. The new heat-sink assembly is expected to increase the mechanical reliability and cooling capability of the XIS sensor. The new radio-isotope on the door will provide better calibration data. We present details of these improvements and summarize the overall design of the XIS.
Until now, only avalanche photodiodes (APD) have been used as the detectors in curvature wavefront sensors in astronomy. This is due to the strict requirements of very short integration time and very low readout noise. In 1999, Beletic et al. invented a new CCD design which should achieve the same performance as APDs but with higher reliability and lower cost. In addition, this CCD has higher quantum efficiency than APD modules and larger dynamic range, eliminating the need for neutral density filters on bright objects. The CCD was designed and fabricated by MIT Lincoln Laboratory in collaboration with ESO and IfA. R. Dorn extensively tested the CCD in laboratory at ESO and proved that it achieves the predicted performance. CFHT is currently implementing this CCD on PUEO, CFHT’s Adaptive Optics system, to assess its performance for the first time in real conditions on the sky for a direct comparison with the current 19 APD detector system. In this article we present the current implementation scheme and discuss the upgrade we foresee for PUEO NUI, a 104-element high-order curvature AO system envisaged to replace the current AO system at Canada-France-Hawaii Telescope.
The WIYN One Degree Imager (ODI) will be a well-sampled (0.11” per pixel) imager that provides a full one degree square field of view (32K×32K pixels). ODI will utilize high resistivity, red sensitive, orthogonal transfer (OT) CCDs to provide rapid correction for image motion arising from telescope shake, guider errors, and atmospheric effects. ODI will correct the full field of view by deploying 64 array packages having a total of 4096 independently controllable OTCCDs that can correct individually for local (2 arcmin) image motion. Each array package is an orthogonal transfer array (OTA) of 64 CCDs arranged in an 8×8 grid. Each CCD has 512×512 pixels. We expect the median image quality at the WIYN 3.5m telescope in RIZ to be 0.52”, 0.43”, and 0.35” FWHM. ODI makes optimal use of the WIYN telescope, which has superb optics, excellent seeing characteristics, a natural 1.4 degree field of view (with a new corrector), and can serve as a pathfinder for LSST in terms of detectors, data pipelines, operations strategies, and scientific motivation.
The IFA and collaborators are embarking on a project to develop a 4-telescope synoptic survey instrument. While somewhat smaller than the 6.5m class telescope envisaged by the decadal review in their proposal for a LSST, this facility will nonetheless be able to accomplish many of the LSST science goals. In this paper we will describe the motivation for a 'distributed aperture' approach for the LSST, the current concept for Pan-STARRS -- a pilot project for the LSST proper -- and its performance goals and science reach. We will also discuss how the facility may be expanded.
We describe progress in removing image motion over large fields of view. A camera using a new type of CCD has been commissioned and we report first results which are very promising for wide field imaging. We are embarking on a project to build a new type of astronomical CCD which should provide image motion compensation over arbitrarily large fields of view, very fast readout, autoguiding capability, good red sensitivity, and should be significantly less expensive than the present generation of CCDs.
In this paper we describe a new technology which fabricates CCDs and fully depleted silicon on insulator CMOS circuits on the same 150-mm silicon wafer. We present results from 7.5 X 7.5-micrometers 2 and 15 X 15-micrometers 2-pixel imagers that are 512 X 512 frame transfer devices. The 7.5-micrometers -pixel device exhibits a charge handling capacity in excess of 100,000 electrons at 3.3 V and the 15-micrometers - pixel device exhibits a charge-transfer efficiency over 99.998%. In addition, we demonstrate functional SOI CMOS ring oscillators with delay of 47 ps/stage at 3.3 V and 68 ps/stage at 2 V.
We describe recent results from a new type of CCD imager which is capable of transferring charge in all four directions and is called an orthogonal-transfer CCD or OTCCD. This device has applications in adaptive imaging where the image motion is fast in relation to the frame time. We have built a 512 X 512 pixel frame-transfer device in which the imaging section has OT pixels and the frame store has conventional three-phase pixels. We have demonstrated at the Michigan-Dartmouth-MIT (MDM) observatory on Kitt Peak that significant improvements in seeing can be obtained by partially correcting for atmosphere-induced phase distortions using this device. By imaging a bright guide star on the frame store and operating it as a fast- framing tracker we are able to measure the lowest-order distortion. We then use this information to clock the OT section to maintain registration between the charge packets and the shifting star images. The preliminary results show that the OTCCD can remove approximately 0.5 inches in quadrature with the remaining sources of broadening at MDM. Pockets are more numerous in this device than expected, and their effects are exacerbated by the multiple transfers during image tracking. Some evidence has been found that links the pockets to the use of aluminum as the fourth gate level.
NOAA has commissioned a solar x-ray imager to be built for use on the GOES spacecraft. The mission of the SXI is to provide soft x-ray imagery of the Sun. The current instrument design employs a microchannel plate detector stack to convert the incident x-rays to an electrically detectable signal. In this paper, we discuss the SXI performance improvements possible by replacing the detector with a back-illuminated, x-ray sensitive CCD fabricated using technology developed at MIT/LL. In addition to a description of the x-ray sensitive CCD, we discuss possible improvements in data quality, reduction in instrument mass and power requirements, and simplified instrument handling.
We report progress on our development of a color night vision capability, using biological models of opponent-color processing to fuse low-light visible and thermal IR imagery, and render it in realtime in natural colors. Preliminary results of human perceptual testing are described for a visual search task, the detection of embedded small low-contrast targets in natural night scenes. The advantages of color fusion over two alterative grayscale fusion products is demonstrated in the form of consistent, rapid detection across a variety of low- contrast (+/- 15% or less) visible and IR conditions. We also describe advances in our development of a low-light CCD camera, capable of imaging in the visible through near- infrared in starlight at 30 frames/sec with wide intrascene dynamic range, and the locally adaptive dynamic range compression of this imagery. Example CCD imagery is shown under controlled illumination conditions, from full moon down to overcast starlight. By combining the low-light CCD visible imager with a microbolometer array LWIR imager, a portable image processor, and a color LCD on a chip, we can realize a compact design for a color fusion night vision scope.
We describe the development at Lincoln Laboratory of large-area CCD imager arrays for soft x-ray astronomy. One such array consists of four, closely abutted, 420 X 420-pixel CCDs for the ASCA (formerly Astro-D) satellite that was launched on February 20, 1993. The CCDs were fabricated on p-type 6500-(Omega) -cm material in order to attain the deep depletion depths needed for the higher-energy (> 4 keV) photons. The use of high- resistivity material and the effects of space-radiation are among the principal technical issues which will be discussed. We are also developing the next-generation CCD sensors for the Advanced X-ray Astrophysics Facility which is currently scheduled for launch in 1998. This mission will use two multichip focal planes comprising ten chips, each of a larger format (approximately 1000 X 1000 pixels). In addition to a new CCD, this program will require other technology developments such as an innovative packaging method for the nonplanar focal planes.
A new technology is introduced for developing potentially low cost, high throughput DNA sequence analysis. This approach utilizes novel bioelectronic genosensor devices to rapidly detect hybridization events across a DNA probe array. Detection of DNA probe/target hybridization has been achieved by two electronic methods. The first method utilizes a permittivity chip which interrogates the miniature test fixtures with a low voltage alternating electric field. The second method, which is the emphasis of this paper, utilizes a charge- coupled device (CCD) to detect the hybridization of appropriately tagged (radioisotope, fluorescent, or chemiluminescent labels) target DNA to an array of DNA probes immobilized above the pixels. Such direct electronic-biologic coupling is shown to provide a tenfold sensitivity improvement over conventional lens-based detection systems.
focusing on work on large device formats, improvements in quantum efficiency, and reduction of CCD degradation in the natural space-radiation environment. Research was based on a 420 x 420-pixel frame-transfer device and a new 1024 x 1024-pixel device. To obtain high quantum efficiency from the visible into the UV, a technology for making back-illuminated versions of these devices is being developed. Quantum efficiencies greater than 80 percent in the 500-800 nm band have been obtained with a SiO antireflection coating. Particular attention is given to the problem of charge-transfer inefficiency degradation caused by energetic protons in space-based systems. It is shown that CCDs can be significantly hardened to radiation effects by a combination of special buried channel potential profiles and operation at temperatures around 150 K, where the trap sites created by the protons have emission times much longer than the clock periods.
An analytical model has been developed for predicting the spectral response of thinned, p+-doped back-illuminated charge-coupled device (CCD) imagers. The device is divided into two regions: a thin, uniformly doped p+ layer used to passivate the illuminated back surface from external electrical effects, and a p- region that extends from the p+ region across the approximately 10-micrometers thickness of the device to the potential well in the buried channel. The one-dimensional steady-state continuity equation for low-injection conditions has been solved analytically for the surface p+ region, which is characterized by electron diffusion length and coefficients appropriate for the doping level and a surface recombination velocity Sn that represents the loss of photoelectrons at the surface. All photoelectrons generated in the p- region are assumed to be collected in the buried channel because of the long diffusion length and the presence of a field sweeping the carriers into the CCD channel. The effect of multiple internal reflections on photoabsorption at long wavelengths is included. The quantum efficiency of this device is calculated as a function of the depth and recombination velocity of the p+ surface layer, using Sn as the only independent fitting parameter, and matches experimental results well over the wavelength range from 360 to 1100 nm.