A Technique to Measure Trap Characteristics in CCDs Using X-rays K. C. Gendreau, G. Y. Prigozhin, R. K. Huang, M. W. Bautz Center For Space Research, Massachusetts Institute of Technology, Cambridge, MA, 02139 USA Abstract An important type of radiation damage in CCDs used for X-ray spectroscopy is the degradation of charge transfer eciency (CTE). Traps associated with radiation induced defects are the basic cause of the damage. Here, we describe a method to extract trap characteristics using small charge packets produced by individual X-ray photon interactions in rectangular imaging CCDs. The method applies the principles of trap occupancy to the framestore CCD conguration. We have measured trap characteristics in radiation damaged CCDs in a range of operating temperatures from 170 to 200 K, and have found that these data compare well to the expected phosphorus-vacancy (P-V) trap characteristics. 1 Introduction At MIT, we are developing photon counting imaging X-ray spectrometers using Charge Coupled Device (CCD) detectors for several astronomical research satellites. The rst of these, the Japan/US mission ASCA, has been developed jointly by the Japanese Institute for Space and Aeronautical Science (ISAS) and the National Aeronautics and Space Administration (NASA) [1]. We are also developing the CCD imaging spectrometer for NASA's Advanced X-ray Astrophysics Facility [2]. In both of these instruments, we employ CCDs developed at the MIT Lincoln Laboratories [3] and optimized for soft X-ray (0.1-10 kev) photon counting and spectroscopy. It has been known for some time that the space radiation environment (especially the proton ux) can aect CCD performance on time scales of years or less [4] (and references therein). The performance of photon-counting X-ray CCDs is particularly sensitive to radiation damage because very small charge packets (50-3000 electrons) must be transferred with high eciency. Charge transfer performance is quantied by the \charge transfer eciency" (CTE), or its complement, the \charge transfer ineciency" (CTI). CTI is the fractional charge loss per pixel transfer. The 1
CCDs discussed here have imaging and framestore arrays each containing 420420 pixels. Thus a typical charge packet must undergo several hundred transfers. To achieve high spectral resolution (charge loss less than 1%), our CCDs must have CTI < 10?5 per pixel. In a previous paper [5] we reported on a series of experiments to determine the sensitivity of our X-ray CCD detectors to the trapped proton eld we expect to encounter in low earth orbit. We showed that the performance of an irradiated CCD depends strongly upon CCD temperature, transfer speed, and the ux of X-rays used to characterize the detector damage. In particular, the spectral resolution was shown to be better at lower temperatures, higher transfer rates, and higher X-ray uences. In the following sections, we review the equations governing the trap occupancy. We apply this formalism to the particular case of a radiation damaged CCD operated in a frame transfer mode and illuminated by monoenergetic X-rays. Finally, we show how to extract detrapping times and trap densities from the X-ray CCD data. The method is analogous to the \double pulse" experiments of Mohsen and Tompsett [6]. 2 Radiation Damage Model in X-Ray CCDs Proton radiation reduces CCD spectral resolution through increases of both CTI and dark current. It is widely believed that both of these phenomena result from traps due to proton induced displacements in the silicon lattice [7], [4], [8], (and references therein). We describe here how trapping aects CTI. Shockley-Read-Hall theory [9] describes the dependence of minority carrier capture and release time scales on temperature and carrier density. Traps capture electrons from passing charge packets in a capture time scale c : c = 1 v t n The traps then release the captured electrons on an escape time scale e : (1) e = 1 v t N c e?(ec?e t) kt (2) The resulting trap occupancy rate is given by: dn t dt =? n t e + N t? n t c (3) 2
Where: v t n N c E c E t k T n t N t is the electron capture cross section is the thermal velocity of an electron is the number density of free electrons is the density of states in the conduction band is the bottom of the conduction band is the trap energy is Boltzmann's constant is the temperature is the number density of trapped electrons is the number density of traps. The phosphorus-vacancy (P-V) complex is a displacement induced trap which is regarded by many workers to be the most signicant in the phosphorous-doped n-buried channels of CCDs such as the devices we are using for ASCA [7], [4], [8]. It is characterized with a cross section of 3:5 10?15 cm 2 and a trap energy of 0.4 ev. With such a trap and a typical charge packet of 1000 electrons, the capture time is virtually instantaneous (less than 10?7 s) compared to transfer rates used in our devices (tens of microseconds per shift). However, as shown in equation 2, the trapping time is a function of the free electron density. For small charge packets (0-10 electrons for dark current and 50-3000 for X-ray signals), the dependence of the capture time on electron density must be explicity accounted for. The potential and electron density in the buried channel were calculated numerically, using the 2 dimensional Poisson equation solver \PISCES II" [10]. Figure 1 shows the electron concentrations for packets of several electron numbers in comparison to the concentration of phosphorus implanted to make the channel. The large electron concentrations result in extremely short capture times. The detrapping times, however, are on the order of tens of milliseconds. Figure 2 shows the detrapping times for traps of various energies as a function of temperature. The trapping model explains the X-ray pulseheight, uence, clocking, and temperature dependence of our X-ray CCD performance [5]. When a charge packet from an incident X-ray encounters an empty trap during a CCD readout, the trapping time is suciently short that by the time the 3
Figure 1: The concentrations of charge packets ranging in size from 43 (lowest curve) to 3100 (second highest curve) electrons. The highest curve in the gure is the concentration of phosphorus. 4
Figure 2: Detrapping times for traps of various energies as a function of temperature.the P-V center trap has an energy level of 0.4 ev. 5
Time Trap Charge Packets 0 1 2 3 4 5 τ e 6 T p 7 8 9 10 11 Figure 3: The case where both charge packets loose electrons to a given trap. The detrapping time is less than the time between passing charge packets. charge packet is shifted away, it is nearly certain that the trap is left full and the charge packet has lost charge and will provide a poor estimate of the incident photon energy. Consider two charge packets and a trap in a single column of a CCD. We call the rst charge packet the \sacricial charge packet" (SCP). The empty trap is lled with some charge from the SCP. The second charge packet is called the \beneciary charge packet" (BCP). A time, T p, passes between the moment that the SCP crosses a given point and the moment that the BCP crosses the same point. T p is the product of the transfer rate and the spacing between the SCP and the BCP. There are two possible fates for the BCP, depending on the magnitude of T p relative to the detrapping time e. If T p > e, then the BCP loses charge to the trap (see gure 3). In this case, both the SCP and BCP contribute poorly to the pulseheight spectrum. If T p < e, then the BCP does not lose charge to the trap (see gure 4). In this case, the degradation of resolution is minimized. At lower temperatures, the detrapping time increases, increasing the interval during which a BCP will benit from an SCP. The X-ray uence and clockrate results are also explained by this 6
Time Trap Charge Packets 0 1 2 3 4 T p 5 6 τ e 7 8 9 10 11 Figure 4: The case where only one of the charge packets looses electrons to a given trap. The detrapping time is greater than the time between passing charge packets. 7
model since they control the mean time, T p, between charge packets for a trap in the register. To test this model further, we have analyzed the X-ray data in such a way as to extract the trap densities and detrapping times. In the next section, we describe this analysis. 3 Deriving Trap Characteristics From X-Ray Data The devices we use are frame transfer CCDs. A frame transfer CCD has two sections, an image section and a frame-store section. X-ray photons strike the silicon in the image section, interacting photoelectrically to generate electron charge packets. We illuminate the imaging array with X- rays for a given exposure time, collecting tens to thousands of X-ray events per frame. After each exposure, the charge in the imaging array is transferred relatively quickly (40 microseconds per pixel transfer) into the X-ray shielded framestore region. Once the transfer is complete, the imaging array begins accumulating its next exposure while the frame store array is slowly readout (approximately, 11 msec per row transfer). The readout is accomplished by transferring the framestore array row by row into the serial register, where each row is clocked out serially into an output node. Typically tens to hundreds of frames of X-rays are collected. In the laboratory, characteristic Mn-K (5.9 kev) and Mn-K (6.4 kev) produced by an Fe 55 source are used to provide the X-rays. These X-ray energies result in charge packets of mean sizes 1620 electron and 1753 electrons. We extract pulseheight, position, and detection time data for each X-ray interaction event in these frames. Figure 5 compares the Fe 55 pulseheight spectra obtained from the irradiated and control halves of a radiation test CCD. The control half was protected by a shield during irradiation, so that it is not damaged by the proton ux. For details on the irradiations, see [5]. By analyzing suitably chosen subsets of these events for a given CCD operating temperature, we can derive trap densities and energies for radiation induced traps in the CCD. If there is more than one type of trap population in the CCD channel, then multiple temperature data are required to derive these quantities. We have made selected event subsets containing events (BCPs) each of which has a neighboring event (the SCP) lower in the same column of the same readout frame within a certain range of distances, and no other events closer. The SCP is not included in the event subset. Dierent subsets are made for dierent ranges of row distance between the SCPs and BCPs. Pulseheight spectra made for each event subset indicate how much charge is lost to traps as a 8
Figure 5: Fe 55 spectra obtained from the irradiated and control (protected) sides of an irradiated CCD. The prominent feature is the Mn-K peak centered at about 1620 electrons (2450 ADU) on the protected side. The CTI degradation on the damaged side shifts the spectral peak of the Mn-K feature downward. The loss of spectral resolution on the damaged side is apparrent. 9
Figure 6: Measured pulseheight centroid as a function of distance to sacricial charge packet. The CCD used is an ASCA-like CCD [3] operated at 202 Kelvin. The device was previously irradiated protons with 1:2 10 8 2.1 MeV protons=cm 2 using a Cockroft-Walton accelerator at the MIT Plasma Fusion Center [3]. Note that the measured gain varies by 5%. We describe the function used to t the trap density and detrapping time in the text. The best t has a linear trap density of 0.0053 traps per micron and a detrapping time of about 60 msec. function of the event spacing. In the case of uniform illumination by a monoenergetic source like Fe 55, the charge loss for a particular range is simply the original (undamaged) charge packet size minus the center position (mean) of a gaussian tted to the pulseheight spectrum measured in the subset. Figure 6 shows the measured pulseheight as a function of the range to the sacricial charge packet in a set of Fe 55 data collected with a radiation damaged CCD operated at 206 K. Figure 6 conrms that more charge is lost from the BCP with increasing distance to the SCP. The increasing separation corresponds to an increasing time and an increasing probability that the traps lled by the SCP have detrapped. In frame transfer mode, the time interval between packets depends on two time scales because of the dierent transfer rates during the image array to framestore transfer and the framestore to serial register transfer. In our devices, we have a further 10
Charge Transfer Direction X D N Frame Store Array SCP BCP N Imaging Array Figure 7: Two charge packets in the same column of the imaging array. Both the imaging array and framestore array have N pixels. The sacricial charge packet, SCP, is located at pixel \x" and the beneciary charge packet BCP is located a distance \d" behind the SCP. complication in that the physical lengths of the framestore pixels are slightly dierent than the lengths of the imaging array pixels. We model the relationship between these measurements and the trap parameters as follows. Consider two charge packets in one column of the image array as shown in gure 7. Both the imaging array and framestore array have N pixels. The sacricial charge packet, SCP, is located at pixel \x" and the beneciary charge packet, BCP, is located a distance \d" behind S. The following constraint holds on x, d, and N: (x + d); x N (4) Thus for a given distance to the sacricial charge packet, the maximum row number that the sacricial charge packet could come from is: x max = N? d (5) 11
Let: N L p f p i c if c f s be the number of traps per micron along the transfer direction, be the pixel length along the transfer direction in the framestore array, be the pixel length along the transfer direction in the image array, be the time it takes to transfer from one pixel to the next during the image array to framestore array transfer, be the time it takes to transfer from one pixel to the next during the framestore array to serial array transfer, The number of traps per pixel in the imaging and framestore arrays are respectively given by: N i = N L p i ; N f = N L p f (6) The number seen by the SCP in gure 7 is: N s = NN f + xn i (7) and the number of traps seen by the BCP is: N o = NN f + xn i + dn i (8) For reasons discussed in section 2,, we assume that the capture times are negligible compared to the pixel to pixel transfer times. Therefore, empty traps have unity probability of capturing electrons from the passing packets. We calculate the number of empty traps (N e ) seen by the BCP:?dc if?dc if N e (x; d) = N i d + N i x(1? e e ) + N f (N? x? d)(1? e e )?dc fs +N f x(1? e e ) +N f dx?dc if +j(c if?c fs ) (1? e e ) (9) j=1 The rst three terms in equation 9 describe traps encountered by both packets exclusively during the image to framestore transfer. The rst term corresponds to the traps not encountered 12
?dc if by the SCP. The expression (1? e e ) is the probability that a trap encountered by the BCP is empty. This increases with a time constant e or equivalently with a position constant e c if. The fourth term corresponds to traps encountered by both packets exclusively during the framestore to serial transfer. The availability of these traps have a position constant e c fs. For the ASCA CCDs, c f s =c if = 280. Figure 8 shows how a 40 msec time constant would then get mapped to position for the image to framestore operation and for the framestore to serial register operation. The fth term is due to traps lled by the SCP during the image to framestore transfer, but seen by the BCP during the framestore to serial transfer. For these traps, the passing time between the SCP and BCP is a function of position- each term in the summation corresponds to a dierent pixel. The summation term can be evaluated: N f dx So for N e, we nd:?dc if +j(c if?c fs ) (1? e e ) = N f fd? e(c if?dc if?dc fs )= e fe dc fs= e? e dc if = e g j=1 e c fs= e? e c g (10) if = e?dc if N e (x; d) = N i d + N f N(1? e e )?dc if?n f fd(1? e e )?d + e(c if?dc if?dc fs )= e fe dc fs= e? e dc if = e g e c fs= e? e c g if = e?dc if?dc fs +xf(n i? N f )(1? e e ) + N f (1? e e )g (11) If the ux of X-rays per row is given by the function g(x), then we can calculate the average number of empty traps, N avg (d) seen by charge packets a distance d away from SCPs. This equals the average loss of charge due to trapping and is given by: where, N avg (d) = xx max f(x; d)n e (x; d); (12) x=0 g(x) f(x; d) = P xmax (13) x=0 g(x): In order to determine the trap density for the ASCA CCDs using ight data, the ux per row, g(x), must be determined for a given observation by looking at the image. In general, the resulting f(x; d) may be very complicated. 13
Figure 8: A 40 msec decay constant mapped to pixel space using the transfer rates for the two types of parallel transfer in the ASCA SIS. 14
In the case of uniform illumination, f(x; d) = = 1 x max 1 N? d : (14) and equation 12 becomes: N avg (d) = 1 x max xx max N e (x; d) x=0 = N L f(p f + p i )d + p f N(1? e?dc if?p f fd(1? e e )?dc if e ) + e(c if?dc if?dc fs )= e fe dc fs= e? e dc if = e g e c fs= e? e c g if = e + (x max + 1) f(p i? p f )(1? e 2?dc if e?dc fs ) + p f (1? e e )gg (15) The only unknowns in the expression are the linear density of traps, N L, and the detrapping time constant, e. For ASCA CCDs, the following values hold: p f p i c if c f s 18 microns 27 microns 40 microseconds 8.8 msec. Figure 6 shows the best t for a data set taken with a device irradiated with low energy protons. The detrapping time found is consistent with that for a P-V trap at 202 kelvin [8]. Figure 9 shows how the tted detrapping times change as a function of temperature for the irradiated device discussed above. The temperature dependence of the detrapping time between 190 and 210 Kelvin is consistent with a trap of energy near 0.4 ev{the P-V trap energy. At temperatures above 210 Kelvin, dark current in the CCD is signicant and invalidates the assumptions made here. At temperatures below 190 K, the data deviates from the 0.4 ev P-V trap model. There may be two reasons for this discrepancy. At these low temperatures, the time constant for the 0.4 ev trap is on the order of seconds, comparable to the readout time of the CCD. With these readout times, we cannot accurately measure time constants on the order of seconds, as the traps 15
Figure 9: Fitted detrapping times as a function of CCD temperature for an irradiated CCD. The t for the detrapping time was done for the 4 highest temperature points. Deviations between the model and the data below 184 K may reect the existence of a second population of traps with lower energy. are eectively \frozen out" for the duration of a frame. The second reason is that a shallower trap of lower energy may be coming into prominence as the P-V trap freezes out, thereby reducing the eective time constant. This is suggested in gure 2, which indicates that, at a given temperature, a shorter time constant is associated with a lower energy traps. 4 Future Work Currently, we are studying irradiated CCDs at colder temperatures to probe the existence of shallower traps. We are motivated to do this by the deviations between the data and the single P-V trap model in the 170 to 190 Kelvin range. We are also concerned about device performance at the low temperatures (173 K) planned for the CCDs to be used in the future missions like AXAF and XMM. 16
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