- Email: [email protected]
Bolometer array development at the Max-Planck-Institut für Radioastronomie
Infrared Physics & Technology 40 Ž1999. 191–197 www.elsevier.comrlocaterinfrared
Bolometer array development at the Max-Planck-Institut fur ¨ Radioastronomie E. Kreysa a,) , H.-P. Gemund ¨ a, J. Gromke a, C.G.T. Haslam a, L. Reichertz a, E.E. Haller b, J.W. Beeman b, V. Hansen c , A. Sievers d , R. Zylka e a
Max-Planck-Institut fur ¨ Radioastronomie, Bonn, Germany b UCB and LBNL, Berkeley, USA c Bergische UniÕersitat, ¨ Wuppertal, Germany d IRAM, Granada, Spain e ITA, UniÕersitat ¨ Heidelberg, Heidelberg, Germany
Abstract Continuum radiometers based on bolometers have a long tradition at the Max-Planck-Institut fur ¨ Radioastronomie ŽMPIfR. in Bonn, Germany. Arrays of bolometers have been under development since the early 1990s. A small seven-element system, operating at 300 mK, saw first light in 1992 at the IRAM 30-m telescope and has been used successfully by numerous observers at that facility since then. While this array had a conventional ‘composite’ design, it was obvious that larger arrays, especially for higher frequencies, could take advantage of microfabrication technology. The recent MPIfR bolometer arrays employ a hybrid approach. They combine a single-mode horn array with a planar bolometer array on a single crystal Silicon wafer with Silicon–Nitride membranes. With efficient absorbing structures, the bolometers couple to the single mode of the radiation field collected by the horns, without needing integrating cavities. Readout is provided by NTD-Germanium thermistors that are attached to the absorbers. This paper covers the history of this development, the design aspects of the bolometer arrays, including the coupling to the telescope, and the status of work in progress. q 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Bolometers; Absorbers; Micromachining
1. Introduction The bolometer development effort at the MPIfR in Bonn concentrates on the mmrsubmm spectral range and groundbased facilities like the SEST 15-m, the IRAM 30-m and SOrMPIfR 10-m telescopes. A particular strength of the group at MPIfR is that it covers the bolometer array hard- and software, in)
Corresponding author. E-mail: [email protected].
cluding the observations and the final data reduction. Essential and close cooperations exist with the group of E.E. Haller ŽLBNLrUCB. for the NTD-thermistors and that of V. Hansen ŽWuppertal University. for numerical calculations of the electromagnetic field, with respect to filters and absorbing structures of bolometers. We favor a gradual approach to bolometer array development, progressing from small to large arrays with increasing complexity, in manageable steps.
1350-4495r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 1 3 5 0 - 4 4 9 5 Ž 9 9 . 0 0 0 1 0 - 9
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E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
2. General design Nearly all our bolometers are designed to detect a single mode of the radiation field in the focal plane. The full spatial resolution of the telescope will therefore be preserved and the sensitivity to point sources maximized. In this case, the same considerations with respect to aperture and beam efficiency apply as for coherent, single mode receivers. For example, for general purpose observations one is led to the same goal of a 13-dB edge taper of the illumination of the telescope primary. Each bolometer or array is designed for one frequency and can therefore be optimized for that frequency without any compromise. The feedhorns can be corrugated, or smooth-walled conical horns. For arrays, we combine them in closepacked hexagonal pattern. Each horn feeds into a circular waveguide, about two diameters long. The guide acts as a mode filter and we make use of the highpass cutoff of the fundamental mode ŽH11. of the circular waveguide for filtering. A lowpass filter in front of the horn array restricts the bandwidth to that of the fundamental mode of the circular waveguide of about 27%. For narrow atmospheric windows this filter is replaced by a bandpass filter corresponding to that window. We have the facilities
to design and fabricate filters, made of stacks of capacitive andror inductive metal mesh. Most mmrsubmm telescopes are equipped with chopping secondaries which, for minimal moment of inertia, have to be small, and therefore lead to high frd ratios at the secondary focus. This would require uncomfortably large feedhorns. We use small horns with a wide beams for the arrays and make an optical transformation to the required telescope fratio. For ease of fabrication, the horns in the arrays have their axes parallel. This also has the advantage that all horns are electromagnetically identical and can be matched to the same absorber structure. The optical system effecting the transformation can be designed and optimized for parallel incident beams. If a small planar bolometer structure can be made to match to the highly concentrated radiation emerging from the exit of the waveguide, then the rest of the cross-sectional area of each horn is available for interconnections. In this concept, which one may call hybrid, all bolometers and their interconnections are micromachined on a silicon wafer and matched to a horn array, which determines the beam pattern. In this way, one can take advantage both of the excellent beam shapes of conical corrugated horns and the
Fig. 1. General design of hybrid arrays.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
well-developed planar micromachining technology. ŽFig. 1. Neutron-Transmutation-Doped ŽNTD .-Germanium is an excellent and reliable material for thermistors at temperatures below 1 K. The main disadvantage, especially for arrays, is that it requires at least one manual step in the integration. Presently, we integrate the thermistor with the absorbers and the wires, and glue this assembly on the membranes. With some care, there is not much danger for the membranes. More highly integrated arrays are being planned. 3. Micromachining Silicon–nitride membranes, deposited on Silicon wafers by LPCVD-techniques, are very strong, and
193
by virtue of their quasi amorphous structure have a very low thermal conductivity at low temperatures Žabout 10y5 WrŽK cm. at 300 mK w1x.. Free standing membranes of submicron thicknesses can be fabricated in diameters of several millimeters. They make excellent low thermal conductivity supports for the absorbers of composite bolometers. For the relatively high backgrounds at groundbased telescopes, the thermal conductivity of a 4 = 4 mm membrane, 1 mm thick, is lower than necessary and can therefore conveniently be controlled by the electrical connection. Still lower thermal conductivities are available by structuring the membranes. All membranes for the array are fabricated in one step by anisotropic etching with KOH. Starting with a standard 1–0–0 wafer, the result are square membranes arranged in the same hexagonal pattern as the horns. By design,
Fig. 2. Bolometer array inside copper mounting ring. The 10 MV bias resistors are visible on the thermal shunts.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
194
the differential thermal contraction between the silicon frame and the horn array Žcopper. is taken care of. Obviously, the yield of unbroken membranes is a matter of concern. It seems that the most important parameter for high yield is low film stress. This is done by depositing a film that is rich in silicon compared to the stoichiometric composition corresponding to Si 3 N4 . With good process control, near 100% yields for 4 mm = 4 mm membranes, 1 mm thick are easy to get. The gaps between the membranes are used for evaporated AurCr wires. We make interconnections by ultrasonic bonding between the gold wires although more sophisticated lithographic wiring is feasible. The array is mounted inside a copper ring to electrically insulating thermal shunts by gold wire bonding. In addition, the thermal shunts carry the bias resistor chips, which are also connected by bonded gold wires. Copper screws connect the ring carrying the bolometers on one side to the horn array, and on the other side to the cold plate at 300 mK or 100 mK. ŽFig. 2.
4. Waveguide–bolometer coupling The absorption of electromagnetic waves by metal films on dielectric substrates, which are commonly used as absorbers in composite bolometers, can be calculated analytically for the case of plane layers and plane incident waves of infinite extent. Results with respect to bolometer applications can be found in Ref. w2x, together with some of the original references. In general, a bolometer absorber consists of a dielectric substrate of thickness t, refractive index n, and metal films on both surfaces. The metal films are characterized by their surface conductance f, normalized to that of free space Ž1r377 V .. f refers to the film on the side of the incident beam, f X to that on the opposite side. The following three cases are of special interest for the design of bolometers: f s 0,
f X s n y 1.
f X s n2 q 1.
t s lr4n.
Ž 3.
High purity, single crystal silicon is a substrate with low heat capacity, and can easily be machined or etched to the required dimensions. For a center wavelength of 1.2 mm, the substrate should be 88 mm thick. For that choice, the surface resistance has to be 30 V per square, which is conveniently achieved with sputtered titanium films. f s 1,
f X s `.
Ž 4.
With a reflective film on the back side, the absorption reaches a maximum of 100%. The thickness condition is the same as for case Ž2.. It is interesting that f and f X do not depend on n for this configuration. A surface impedance equal to that of free space on the front of the substrate may be difficult to achieve for a cryogenic, stable film, but refractive metals like tungsten have been suggested for that purpose, and might work. Inside the cylindrical waveguide, wavelength and impedance are different from those in free space and they might be significantly different again in the
Ž 1.
This combination results in uniform absorption of 50% when n is close to 3. It is often applied for bolometers, when operation over large frequency range is essential. By enclosing the absorbers in a cavity, one tries to increase the absorption. f s 0,
In this case, the absorption displays broad peaks, which can reach nearly 100% for high values of n. The thickness of the substrate has to be chosen such that the first maximum coincides with the design wavelength of the bolometer.
Ž 2.
Fig. 3. Absorption of single metal film on the back of a dielectric substrate. The curve at the top is the free space absorption. The absorbed power is normalised to 1 W. For the lower curves, the distance between waveguide and absorber is varied in the sequence 0, 50, 81.5, 100 and 163 mm.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
transition region just outside the waveguide. In cooperation with the group of V. Hansen at Wuppertal University we try to optimize the absorption by numerical 3-dimensional calculations. Results for case Ž2. are shown in Fig. 3 for a few values of substrate-to-waveguide distances. The results showed only minor changes compared to the free space solutions. So far, all our bolometer arrays have used absorbers with optimized single frequency absorbers, designed according to case Ž2.. Numerical investigations of more interesting structures are in progress.
5. Spatial sampling There are two options for bolometer arrays: antenna-coupled-arrays and absorber-coupled-arrays. In the first case, the focal plane is covered with a closepacked array of horn antennas, each of them feeding into a bolometer absorber; in the second, the focal surface is covered with absorbers, acting as their own antennas. For full spatial resolution, the pixels in both types will be smaller than the diameter of the Airy disk, and therefore each element will be single moded. In this case, a comparison of the efficiencies of two types of bolometer arrays can be based on the treatment of general multibeam antenna systems by Johansson w3x. His report is an elaboration of the original work by Stein w4x. Both types of arrays could be fabricated with fully-efficient or Nyquist sized pixels, but the difficulty of machining the antennas would favor fully-efficient, undersampled antenna arrays. However, independent of technology, Stein’s theorem demands the efficiency and sampling interval are connected. For most types of tilings of the focal plane, fully-efficient pixels require an undersampling factor of about 4, i.e., a sampling interval four times larger than the critical sampling interval ŽNyquist sampling.. Consider as example a square tiling of 16 elements Ž4 = 4 array.. The Nyquist-sampled array will be four times smaller than the fully-efficient array. For both arrays, we assume the same integration time per pointing. The fully-sampled array will need 16 pointings in order to make a fully-sampled map of the area of the large Žundersampled. array. The same number of pointings will be needed by the large array for fully-sampling its area. The total
195
integration time for full sampling is therefore the same in both cases. In Johansson’s report, the Stein efficiency is calculated for the case of n s 16 and square tiling. We can assume that the undersampled array will have tapered illumination, therefore, U ; 4 and 95% efficiency ŽFig. 6.4 of Ref. w3x.. The small pixels of the fully-sampled array will lead to a uniform illumination, and from Fig. 6.2 and U ; 1, we conclude that the Stein efficiency will be about 19%. Because the Stein efficiency relates to the coupling between the collecting aperture and the pixel, both the background and the signal will be reduced by a factor of about 5 for the fully-sampled, relative to the fully-efficient array. Assuming background-photon-fluctuation-limited performance, the noise will decrease proportional to the square root of the background. The signal to noise ratio therefore degrades by 51r2 s 2.24 for the fully-sampled array. Here we made the assumptions that the fully-sampled array can be made photon-noise-limited even under a five times lower background Žwhich might require a lower operating temperature. and that its oversized illumination pattern does not pick up extra background Žbaffles and cold Lyot stop essential.. Johansson’s calculations also cover the more relevant cases of hexagonal tilings with n s 7 and n s 19. Here the signal to noise ratio degrades by a factor of 2.1 and 2.5, respectively, relative to the fully-sampled array. Such comparisons are biased by the assumptions. There is no doubt that a fully-sampled array, large enough to cover all source sizes of interest, without the need of scanning, will have an advantage. It seems, therefore, that the main disadvantage of the antenna-coupled arrays is the difficulty of machining horns for the highest frequencies. In a background limited situation, this type of array can operate at a higher temperature. We have a 37-element array of corrugated horns for 350 mm wavelength available and ones for much higher frequencies have been described in the literature. Smooth-walled conical horns are always a fallback solution.
6. Transforming optics It is well-known that in the Gaussian beam approximation, a set of parallel beams can be trans-
196
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
operate at 300 mK, with a system limited flux density of about 50 mJyrHz 1r2 . At the site of the 30-m telescope, sky noise limits the sensitivity to higher values for most of the time. The success of even small arrays stems from two factors. Firstly, in the presence of sky-noise, the noise is partially correlated across the array, and algorithms for sky noise reduction can be developed. Secondly, there is a fixed spatial relationship between the beams, which makes the registration of the individual beam maps more precise than if they had been recorded sequentially with a single beam instrument. A 37-element array, also operating at 300 mK, had its first telescope test in spring 1997 and has been operating at the 30-m telescope since January 1998. A beam pattern is shown in Fig. 4. Fig. 4. Beam pattern of the 37-beam array at 30-m telescope at 250 GHz. Contour levels are at 22, 60 and 95% of peak intensity.
formed to an similar one with different parameters by a Gaussian beam telescope ŽGBT.. The GBT is a combination of two lenses Žor mirrors. with a common focus between them. A beamwaist at the front focus of the first lens is transformed into another one at the back focus of the second lens. It can be shown that this transformation is broadband and that the waist radii will be in the ratio of the focal lengths. These results are easily derived in the thin lens approximation. For a large field, this condition is no longer valid, and therefore, our design starts with one that satisfies the GBT design on axis. Then, by ray tracing, we make sure that the image quality across the image plane within the boundary conditions of vertical incidence of off-axis bundles and low distortion. Empirically, this approach gives good beam patterns as shown in Fig. 4.
7. Examples of complete systems One of our seven-element bolometer arrays saw first light on the 30-m telescope in the year 1992, followed by a 19-element system in 1995. The 19element array already employed silicon–nitride membrane technology in the hybrid design. From 1993 onwards, the arrays were also available for guest observers, and have resulted in many publications. Both arrays were designed for 250 GHz, and
8. Work in progress Construction of a 37-element array for the 350 mm atmospheric window is quite advanced. It will also be operated at 300 mK. The membrane arrays and the individual horns have been fabricated and are at present being integrated. The waveguides are only 0.2 mm in diameter, which is about the smallest manageable size for a NTD-thermistor. This suggests that some sort of direct coupling between the radiation and the thermistor could be devised. We are pursuing this idea together with our colleagues at LBNL. We are also investigating the advantages of lower operating temperatures for groundbased observations. Among the mmrsubmm atmospheric windows, the one at 2 mm wavelength has the best transmission, and is interesting for cosmological studies. It seems particularly suitable for taking advantage of the lower NEP available at 100 mK. A 19-element array for that wavelength, similar to the 37-element array, has been built around a dilution insert, purchased from Leiden Cryogenics. The insert is capable of reaching 35 mK and can be tilted by "458, in order to permit operation in a Cassegrain focus. Another interesting feature of the insert is that the He-3 is circulated by a turbomolecular pump attached to the top of it in combination with a membrane forepump. This makes clogging of capillaries in the insert much less of a problem and requires only small diameter flexible tubing between
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
the insert and the gas handling system. Compared to other dilution systems, it is quite compact. This array had first light on the 10 m Heinrich-Hertz-Telescope on Mt. Graham, AZ, in February 1998, during the times when weather conditions did not permit submillimeter observations. The dilution insert stayed cold continuously for the whole run of 18 days. Technically, the run was successful, but was rather spoiled by poor weather conditions.
Acknowledgements E.K. enjoyed the help and hospitality of the staff and many student members of the Microfabrication
197
Facility of UC Berkeley, where most of the micromachining for the arrays was done.
References w1x W. Holmes et al., Measurement of thermal transport in low stress silicon nitride films, Appl. Phys. Lett., submitted. w2x B. Carli, D. Iorio-Fili, Absorption of composite bolometers, J. Opt. Soc. Am. 71 Ž1981. 1020–1025. w3x J.F. Johansson, Theoretical Limits for Aperture Efficiency in Multi-Beam Antenna Systems, Vol. 161, Research Report, Department of Radio and Space Science, Chalmers University of Technology, Gothenburg, 1988. w4x S. Stein, On cross coupling in multiple-beam antennas, IRE Trans. Antennas Propagat. AP 10 Ž1962. 430–436.
Bolometer array development at the Max-Planck-Institut fur ¨ Radioastronomie E. Kreysa a,) , H.-P. Gemund ¨ a, J. Gromke a, C.G.T. Haslam a, L. Reichertz a, E.E. Haller b, J.W. Beeman b, V. Hansen c , A. Sievers d , R. Zylka e a
Max-Planck-Institut fur ¨ Radioastronomie, Bonn, Germany b UCB and LBNL, Berkeley, USA c Bergische UniÕersitat, ¨ Wuppertal, Germany d IRAM, Granada, Spain e ITA, UniÕersitat ¨ Heidelberg, Heidelberg, Germany
Abstract Continuum radiometers based on bolometers have a long tradition at the Max-Planck-Institut fur ¨ Radioastronomie ŽMPIfR. in Bonn, Germany. Arrays of bolometers have been under development since the early 1990s. A small seven-element system, operating at 300 mK, saw first light in 1992 at the IRAM 30-m telescope and has been used successfully by numerous observers at that facility since then. While this array had a conventional ‘composite’ design, it was obvious that larger arrays, especially for higher frequencies, could take advantage of microfabrication technology. The recent MPIfR bolometer arrays employ a hybrid approach. They combine a single-mode horn array with a planar bolometer array on a single crystal Silicon wafer with Silicon–Nitride membranes. With efficient absorbing structures, the bolometers couple to the single mode of the radiation field collected by the horns, without needing integrating cavities. Readout is provided by NTD-Germanium thermistors that are attached to the absorbers. This paper covers the history of this development, the design aspects of the bolometer arrays, including the coupling to the telescope, and the status of work in progress. q 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Bolometers; Absorbers; Micromachining
1. Introduction The bolometer development effort at the MPIfR in Bonn concentrates on the mmrsubmm spectral range and groundbased facilities like the SEST 15-m, the IRAM 30-m and SOrMPIfR 10-m telescopes. A particular strength of the group at MPIfR is that it covers the bolometer array hard- and software, in)
Corresponding author. E-mail: [email protected].
cluding the observations and the final data reduction. Essential and close cooperations exist with the group of E.E. Haller ŽLBNLrUCB. for the NTD-thermistors and that of V. Hansen ŽWuppertal University. for numerical calculations of the electromagnetic field, with respect to filters and absorbing structures of bolometers. We favor a gradual approach to bolometer array development, progressing from small to large arrays with increasing complexity, in manageable steps.
1350-4495r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 1 3 5 0 - 4 4 9 5 Ž 9 9 . 0 0 0 1 0 - 9
192
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
2. General design Nearly all our bolometers are designed to detect a single mode of the radiation field in the focal plane. The full spatial resolution of the telescope will therefore be preserved and the sensitivity to point sources maximized. In this case, the same considerations with respect to aperture and beam efficiency apply as for coherent, single mode receivers. For example, for general purpose observations one is led to the same goal of a 13-dB edge taper of the illumination of the telescope primary. Each bolometer or array is designed for one frequency and can therefore be optimized for that frequency without any compromise. The feedhorns can be corrugated, or smooth-walled conical horns. For arrays, we combine them in closepacked hexagonal pattern. Each horn feeds into a circular waveguide, about two diameters long. The guide acts as a mode filter and we make use of the highpass cutoff of the fundamental mode ŽH11. of the circular waveguide for filtering. A lowpass filter in front of the horn array restricts the bandwidth to that of the fundamental mode of the circular waveguide of about 27%. For narrow atmospheric windows this filter is replaced by a bandpass filter corresponding to that window. We have the facilities
to design and fabricate filters, made of stacks of capacitive andror inductive metal mesh. Most mmrsubmm telescopes are equipped with chopping secondaries which, for minimal moment of inertia, have to be small, and therefore lead to high frd ratios at the secondary focus. This would require uncomfortably large feedhorns. We use small horns with a wide beams for the arrays and make an optical transformation to the required telescope fratio. For ease of fabrication, the horns in the arrays have their axes parallel. This also has the advantage that all horns are electromagnetically identical and can be matched to the same absorber structure. The optical system effecting the transformation can be designed and optimized for parallel incident beams. If a small planar bolometer structure can be made to match to the highly concentrated radiation emerging from the exit of the waveguide, then the rest of the cross-sectional area of each horn is available for interconnections. In this concept, which one may call hybrid, all bolometers and their interconnections are micromachined on a silicon wafer and matched to a horn array, which determines the beam pattern. In this way, one can take advantage both of the excellent beam shapes of conical corrugated horns and the
Fig. 1. General design of hybrid arrays.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
well-developed planar micromachining technology. ŽFig. 1. Neutron-Transmutation-Doped ŽNTD .-Germanium is an excellent and reliable material for thermistors at temperatures below 1 K. The main disadvantage, especially for arrays, is that it requires at least one manual step in the integration. Presently, we integrate the thermistor with the absorbers and the wires, and glue this assembly on the membranes. With some care, there is not much danger for the membranes. More highly integrated arrays are being planned. 3. Micromachining Silicon–nitride membranes, deposited on Silicon wafers by LPCVD-techniques, are very strong, and
193
by virtue of their quasi amorphous structure have a very low thermal conductivity at low temperatures Žabout 10y5 WrŽK cm. at 300 mK w1x.. Free standing membranes of submicron thicknesses can be fabricated in diameters of several millimeters. They make excellent low thermal conductivity supports for the absorbers of composite bolometers. For the relatively high backgrounds at groundbased telescopes, the thermal conductivity of a 4 = 4 mm membrane, 1 mm thick, is lower than necessary and can therefore conveniently be controlled by the electrical connection. Still lower thermal conductivities are available by structuring the membranes. All membranes for the array are fabricated in one step by anisotropic etching with KOH. Starting with a standard 1–0–0 wafer, the result are square membranes arranged in the same hexagonal pattern as the horns. By design,
Fig. 2. Bolometer array inside copper mounting ring. The 10 MV bias resistors are visible on the thermal shunts.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
194
the differential thermal contraction between the silicon frame and the horn array Žcopper. is taken care of. Obviously, the yield of unbroken membranes is a matter of concern. It seems that the most important parameter for high yield is low film stress. This is done by depositing a film that is rich in silicon compared to the stoichiometric composition corresponding to Si 3 N4 . With good process control, near 100% yields for 4 mm = 4 mm membranes, 1 mm thick are easy to get. The gaps between the membranes are used for evaporated AurCr wires. We make interconnections by ultrasonic bonding between the gold wires although more sophisticated lithographic wiring is feasible. The array is mounted inside a copper ring to electrically insulating thermal shunts by gold wire bonding. In addition, the thermal shunts carry the bias resistor chips, which are also connected by bonded gold wires. Copper screws connect the ring carrying the bolometers on one side to the horn array, and on the other side to the cold plate at 300 mK or 100 mK. ŽFig. 2.
4. Waveguide–bolometer coupling The absorption of electromagnetic waves by metal films on dielectric substrates, which are commonly used as absorbers in composite bolometers, can be calculated analytically for the case of plane layers and plane incident waves of infinite extent. Results with respect to bolometer applications can be found in Ref. w2x, together with some of the original references. In general, a bolometer absorber consists of a dielectric substrate of thickness t, refractive index n, and metal films on both surfaces. The metal films are characterized by their surface conductance f, normalized to that of free space Ž1r377 V .. f refers to the film on the side of the incident beam, f X to that on the opposite side. The following three cases are of special interest for the design of bolometers: f s 0,
f X s n y 1.
f X s n2 q 1.
t s lr4n.
Ž 3.
High purity, single crystal silicon is a substrate with low heat capacity, and can easily be machined or etched to the required dimensions. For a center wavelength of 1.2 mm, the substrate should be 88 mm thick. For that choice, the surface resistance has to be 30 V per square, which is conveniently achieved with sputtered titanium films. f s 1,
f X s `.
Ž 4.
With a reflective film on the back side, the absorption reaches a maximum of 100%. The thickness condition is the same as for case Ž2.. It is interesting that f and f X do not depend on n for this configuration. A surface impedance equal to that of free space on the front of the substrate may be difficult to achieve for a cryogenic, stable film, but refractive metals like tungsten have been suggested for that purpose, and might work. Inside the cylindrical waveguide, wavelength and impedance are different from those in free space and they might be significantly different again in the
Ž 1.
This combination results in uniform absorption of 50% when n is close to 3. It is often applied for bolometers, when operation over large frequency range is essential. By enclosing the absorbers in a cavity, one tries to increase the absorption. f s 0,
In this case, the absorption displays broad peaks, which can reach nearly 100% for high values of n. The thickness of the substrate has to be chosen such that the first maximum coincides with the design wavelength of the bolometer.
Ž 2.
Fig. 3. Absorption of single metal film on the back of a dielectric substrate. The curve at the top is the free space absorption. The absorbed power is normalised to 1 W. For the lower curves, the distance between waveguide and absorber is varied in the sequence 0, 50, 81.5, 100 and 163 mm.
E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
transition region just outside the waveguide. In cooperation with the group of V. Hansen at Wuppertal University we try to optimize the absorption by numerical 3-dimensional calculations. Results for case Ž2. are shown in Fig. 3 for a few values of substrate-to-waveguide distances. The results showed only minor changes compared to the free space solutions. So far, all our bolometer arrays have used absorbers with optimized single frequency absorbers, designed according to case Ž2.. Numerical investigations of more interesting structures are in progress.
5. Spatial sampling There are two options for bolometer arrays: antenna-coupled-arrays and absorber-coupled-arrays. In the first case, the focal plane is covered with a closepacked array of horn antennas, each of them feeding into a bolometer absorber; in the second, the focal surface is covered with absorbers, acting as their own antennas. For full spatial resolution, the pixels in both types will be smaller than the diameter of the Airy disk, and therefore each element will be single moded. In this case, a comparison of the efficiencies of two types of bolometer arrays can be based on the treatment of general multibeam antenna systems by Johansson w3x. His report is an elaboration of the original work by Stein w4x. Both types of arrays could be fabricated with fully-efficient or Nyquist sized pixels, but the difficulty of machining the antennas would favor fully-efficient, undersampled antenna arrays. However, independent of technology, Stein’s theorem demands the efficiency and sampling interval are connected. For most types of tilings of the focal plane, fully-efficient pixels require an undersampling factor of about 4, i.e., a sampling interval four times larger than the critical sampling interval ŽNyquist sampling.. Consider as example a square tiling of 16 elements Ž4 = 4 array.. The Nyquist-sampled array will be four times smaller than the fully-efficient array. For both arrays, we assume the same integration time per pointing. The fully-sampled array will need 16 pointings in order to make a fully-sampled map of the area of the large Žundersampled. array. The same number of pointings will be needed by the large array for fully-sampling its area. The total
195
integration time for full sampling is therefore the same in both cases. In Johansson’s report, the Stein efficiency is calculated for the case of n s 16 and square tiling. We can assume that the undersampled array will have tapered illumination, therefore, U ; 4 and 95% efficiency ŽFig. 6.4 of Ref. w3x.. The small pixels of the fully-sampled array will lead to a uniform illumination, and from Fig. 6.2 and U ; 1, we conclude that the Stein efficiency will be about 19%. Because the Stein efficiency relates to the coupling between the collecting aperture and the pixel, both the background and the signal will be reduced by a factor of about 5 for the fully-sampled, relative to the fully-efficient array. Assuming background-photon-fluctuation-limited performance, the noise will decrease proportional to the square root of the background. The signal to noise ratio therefore degrades by 51r2 s 2.24 for the fully-sampled array. Here we made the assumptions that the fully-sampled array can be made photon-noise-limited even under a five times lower background Žwhich might require a lower operating temperature. and that its oversized illumination pattern does not pick up extra background Žbaffles and cold Lyot stop essential.. Johansson’s calculations also cover the more relevant cases of hexagonal tilings with n s 7 and n s 19. Here the signal to noise ratio degrades by a factor of 2.1 and 2.5, respectively, relative to the fully-sampled array. Such comparisons are biased by the assumptions. There is no doubt that a fully-sampled array, large enough to cover all source sizes of interest, without the need of scanning, will have an advantage. It seems, therefore, that the main disadvantage of the antenna-coupled arrays is the difficulty of machining horns for the highest frequencies. In a background limited situation, this type of array can operate at a higher temperature. We have a 37-element array of corrugated horns for 350 mm wavelength available and ones for much higher frequencies have been described in the literature. Smooth-walled conical horns are always a fallback solution.
6. Transforming optics It is well-known that in the Gaussian beam approximation, a set of parallel beams can be trans-
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E. Kreysa et al.r Infrared Physics & Technology 40 (1999) 191–197
operate at 300 mK, with a system limited flux density of about 50 mJyrHz 1r2 . At the site of the 30-m telescope, sky noise limits the sensitivity to higher values for most of the time. The success of even small arrays stems from two factors. Firstly, in the presence of sky-noise, the noise is partially correlated across the array, and algorithms for sky noise reduction can be developed. Secondly, there is a fixed spatial relationship between the beams, which makes the registration of the individual beam maps more precise than if they had been recorded sequentially with a single beam instrument. A 37-element array, also operating at 300 mK, had its first telescope test in spring 1997 and has been operating at the 30-m telescope since January 1998. A beam pattern is shown in Fig. 4. Fig. 4. Beam pattern of the 37-beam array at 30-m telescope at 250 GHz. Contour levels are at 22, 60 and 95% of peak intensity.
formed to an similar one with different parameters by a Gaussian beam telescope ŽGBT.. The GBT is a combination of two lenses Žor mirrors. with a common focus between them. A beamwaist at the front focus of the first lens is transformed into another one at the back focus of the second lens. It can be shown that this transformation is broadband and that the waist radii will be in the ratio of the focal lengths. These results are easily derived in the thin lens approximation. For a large field, this condition is no longer valid, and therefore, our design starts with one that satisfies the GBT design on axis. Then, by ray tracing, we make sure that the image quality across the image plane within the boundary conditions of vertical incidence of off-axis bundles and low distortion. Empirically, this approach gives good beam patterns as shown in Fig. 4.
7. Examples of complete systems One of our seven-element bolometer arrays saw first light on the 30-m telescope in the year 1992, followed by a 19-element system in 1995. The 19element array already employed silicon–nitride membrane technology in the hybrid design. From 1993 onwards, the arrays were also available for guest observers, and have resulted in many publications. Both arrays were designed for 250 GHz, and
8. Work in progress Construction of a 37-element array for the 350 mm atmospheric window is quite advanced. It will also be operated at 300 mK. The membrane arrays and the individual horns have been fabricated and are at present being integrated. The waveguides are only 0.2 mm in diameter, which is about the smallest manageable size for a NTD-thermistor. This suggests that some sort of direct coupling between the radiation and the thermistor could be devised. We are pursuing this idea together with our colleagues at LBNL. We are also investigating the advantages of lower operating temperatures for groundbased observations. Among the mmrsubmm atmospheric windows, the one at 2 mm wavelength has the best transmission, and is interesting for cosmological studies. It seems particularly suitable for taking advantage of the lower NEP available at 100 mK. A 19-element array for that wavelength, similar to the 37-element array, has been built around a dilution insert, purchased from Leiden Cryogenics. The insert is capable of reaching 35 mK and can be tilted by "458, in order to permit operation in a Cassegrain focus. Another interesting feature of the insert is that the He-3 is circulated by a turbomolecular pump attached to the top of it in combination with a membrane forepump. This makes clogging of capillaries in the insert much less of a problem and requires only small diameter flexible tubing between
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the insert and the gas handling system. Compared to other dilution systems, it is quite compact. This array had first light on the 10 m Heinrich-Hertz-Telescope on Mt. Graham, AZ, in February 1998, during the times when weather conditions did not permit submillimeter observations. The dilution insert stayed cold continuously for the whole run of 18 days. Technically, the run was successful, but was rather spoiled by poor weather conditions.
Acknowledgements E.K. enjoyed the help and hospitality of the staff and many student members of the Microfabrication
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Facility of UC Berkeley, where most of the micromachining for the arrays was done.
References w1x W. Holmes et al., Measurement of thermal transport in low stress silicon nitride films, Appl. Phys. Lett., submitted. w2x B. Carli, D. Iorio-Fili, Absorption of composite bolometers, J. Opt. Soc. Am. 71 Ž1981. 1020–1025. w3x J.F. Johansson, Theoretical Limits for Aperture Efficiency in Multi-Beam Antenna Systems, Vol. 161, Research Report, Department of Radio and Space Science, Chalmers University of Technology, Gothenburg, 1988. w4x S. Stein, On cross coupling in multiple-beam antennas, IRE Trans. Antennas Propagat. AP 10 Ž1962. 430–436.