- Email: [email protected]
Bragg zone plates for hard X-ray focusing
72
Nuclear Instruments and Methods in Physics Research A261 (1987) 72-74 North-Holland, Amsterdam
BRAGG ZONE PLATES FOR HARD X-RAY FOCUSING V.V. A R I S T O V , Y u . A . B A S O V , S.V. R E D K I N ,
A.A. SNIGIREV
a n d V.A. Y U N K I N
Institute of Problems of Microelectronics Technology and Superpure Materials, USSR Academy of Sciences, 142432, Chernogolovka, USSR
The experimental results of observing hard X-ray focusing during Bragg diffraction on a perfect crystal with Fresnel zone surface structure are reported. Possibilities of developing X-ray Bragg optics are considered.
The absence of X-ray optics (X ~- 1 A), analogous to light optics, is due to the fact that X-ray radiation is not in practice refracted by materials (1 - n -~ 10 5-10-6). A crystal lattice at the exact Bragg position can be used as an effective deviative element for X-ray beams. This principle serves as a base for the focusing by Cauchois [1] and Johann [2] consisting in geometrical intersection at one point of incoherent beams from different parts of the crystal. Recently, in a number of studies coherent dynamic focusing of X-ray beams by a perfect crystal in the Laue case (" transmission") have been realized [3-8] using the abnormal dispersion of the index of refraction within a narrow angular range (of order 1 0 " ) close to the exact Bragg condition. The present work puts forward and realizes the idea of using Bragg diffraction on a crystal integrally with that on a structure artificially formed in it. Recent studies have shown that at the exact Bragg condition, a diffraction spectrum within a wide angular range (of order 100") appears on a perfect crystal with a thin relief formed on its surface [9,10]. Within the framework of the kinematic approximation, the theory taking into account X-ray wave scattering by a perfect crystal at small source-to-crystal distance (L1) and crystal-to-observation plane distance (L2) was worked out [11] (fig. 1). This theory is based on evaluating (as well as the Fresnel diffraction theory) wave phases q0 reaching the observation point P after scattering of an incident wave from S by different crystal points r c. At rc << L 1 and rc << L 2
!
ILl L2 [kl × rc]z2t 9~(r) = 2~r ~ - + ~ - + (k, - k2)r,. + 2L 1
+ [k2 where
x
~,.]2
I k l I = I k2 I = 1 / X
integer, i.e. when at point r = 0, the Bragg condition is rigidly fulfilled, the change in phase q0(r) is determined however by the last terms in eq. (1). At k 1 = k 2 expression (1) is a well-known condition in optics for changing the wave phase, which is utilized to obtain Fresnel zones. Thus, if according to this condition a relief is formed on a perfect single crystal surface, diffraction on such a zone structure, as in optics, results in wave focusing in direction kz. In our work a Fresnel linear zone structure (figi 2) was fabricated in a perfect Si single crystal and used as a means of X-ray focusing. The essential lens dimensions are (1) the central zone halfwidth r 1 = 10/~m, (2) the last zone width = 0 . 5 /~m, (3) the total lens width = 200 /~m, (4) the length = 1 m m and (5) the focal distance f = 39 mm. The relief height is 2.5 /~m exceeding the extinction depth A e (in our case A e = 1.53 /~m) at which radiation penetrates the crystal. Fig. 3 demonstrates the main stages of zone plate fabrication. These are as follows: a) exposure of P M M A (an electron resist) 0.75 /lm thick by an electron beam of energy 30 keV; b) A1 thermal sputtering 0.1 /~m thick; c) lift-off; d) 2.5 /~m deep etching of Si in an electric discharge under a pressure of 8 × 1 0 3 Torr in SF6 + O 2 through an aluminium mask formed on the Si surface.
(1)
--2
are the w a v e vectors o f the
diffracted and incident waves in the direction of the optic axis SOP. For ( k l k2)r,. = n, where n is an 0168-9002/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. Schematic illustration of the experiment.
73
V. V. A ristov et al. / Bragg zone plates for hard X-ray focusing
50
~O~.m
~m El
0,4
~m
0,3 J
0.2 0,1 Fig. 2. Fresnel zone structure. The experimental scheme in fig. 1 demonstrates X-ray wave focusing by a Fresnel lens for radiation diffraction CuK~ (X = 1.54 A) on plates Si(III). Distances L a and L 2 were equal to 1 m and 0.04 m, respectively. The size of the X-ray source d s was 10 /~m, the magnification factor k = 1 : 25. The image was registered on the photoplate with a resolution of 200 lines/ram. Fig. 4 (upper topogram) shows the image experimentally obtained in the scheme in fig. 1. In the absence of prior radiation monochromatization the width of the topographic image is dictated by that of the slit D positioned before the crystal-lens, and nearly equals 50 ~m. In the centre of the topogram there is a focused image of the X-ray source. The focus width experimentally observed equals 7.5 #m and is likely to be determined by the photoemulsion resolution since the image of the tube focus reduced by a factor of 25 equals 0.4 t~m. Next to the topogram one can see its photometric curve. With deviation of the zone plate centre from the exact Bragg position (fig. 4, lower topograph) the lens diffraction efficiency decreases while the focusing
a .
A L
b
Fig. 3. Stages of zone plate fabrication.
I
0.3~! 0.2[ O.!
Fig. 4. Experimental topograms and their densitograms.
is retained. An ordinary topographic image of the crystal part at the exact Bragg position is observed as well as a focused image of the X-ray source on its boundary. The experiment reveals the possibility of fabricating Fresnel diffraction optics of a new type, which uses Bragg scattering on a perfect crystal or Bragg Fresnel optics (BFO). The vertically shaped zone structure utilized is optimal only for distances L 1 and L2 being equal. For L 1 >> L 2 (for which the topograms in fig. 4 were obtained) the zones should be oriented in the direction of the observation point [11]. Proper zone orientation is likely to give good efficiency and contrast of the diffraction image. Let us evaluate the limiting spatial resolution that can be obtained in Bragg Fresnel optics (BFO). In the "reflection case" the radiation penetration depth during Bragg diffraction is defined by the extinction depth X sin OB/CIxh[T?, which is, for instance for Si(III) with Cu K~, equal to 1.53 /~m. Then, it is hoped that structures with a minimum size for the last zone and, consequently, with spatial resolution up to 0.1-0.2 /tm can be fabricated (we believe that a structure with the width-to-height ratio of an order 10 can be formed). Extinction length for Ge, GaAs crystals is three times II. INSTRUMENTATION
74
v. 1/\ A ristov et al. / Bragg zone plaws for hard X-ray ]housing
less which permits increasing resolution to 300-500 ,~. In the case of scattering in the Laue diffraction geometry (" the transmission case"), the relief depth is to be much greater (for Cu K~ Si(III) the extinction depth equals 18.5/~m). Laue diffraction, however, gives rise to complex interference phenomena [12] which can be employed to design specific X-ray optics and leads to a more complex expression for the zone structure than in ref. [11]. Thus, for example, in the specific case of an incident plane wave a focusing structure of Fresnel zones is described by a Bessel function [13]. Thus, experimental results and estimations obtained demonstrate the potentialities of X-ray optics of a new type, that is of Bragg Fresnel optics. A BFO structure fabricated on a single crystal substrate is, in fact, the structure of a single block X-ray interferometer [14]. The phenomenon described opens the possibility of controling BFO elements and forming structures with phase modulation.
References [l] I. Cauchois, J. Phys. et Radium 7 (1932) 320. [2] H.H. Johann, Z. Phys. 82 (1933) 507.
[3] V.L. Indenbom, I.Sh. Slobogetskiy and K.G. Truny, Zh. Exsp. Teor. Fiz. 62 (1974) 1110. [4] E.V. Suvorov and V.I. Polovinkina, Pis'ma Zh. Exsp. Teor. Fiz. 20 (1974) 326. [5] A.M. Afanas'ev and V.G. Kohn, Fiz. Tver. Tela 19 (1977) 1775. [6] V.V. Aristov, V.I. Polovinkina, I.M. Shmytko and E.V. Shulakov, Pis'ma Zh. Eksp. Teor. Fiz. 28 (1978) 69. [7] P.V. Petrashen, F.N. Chukhovskii, Pis'ma Zh. Exsp. Teor. Fiz. 23 (1976) 385. [8] V.I. Kushnir and E.V. Suvorov, Pis'ma Zh. Exsp. Teor. Fiz. 32 (1980) 551. [91 V.V. Aristov, A.Yu. Nikulin and A.A. Snigirev, 12th Hungarian Diffraction Conf., Sopron (1985). [10] V.V. Aristov, A.I. Erko, A.Yu. Nikulin and A.A. Snigirev, Opt. Commun. 58 (1986) 300. [ll] E.V. Shulakov and V.V. Aristov, Kristallographiya (1986) in press. [12] V.V. Aristov, V.I. Polovinkina, A.M. Afanas'ev, V.G. Kohn, Acta Cryst. A36 (1980) 1002. [13] V.A. Indenbom, Pis'ma Zh. Exsp. Teor. Fiz. 29 (1979) 7. [14] M. Hart, Rep. Prog. Phys. 34 (1971) 435.
Nuclear Instruments and Methods in Physics Research A261 (1987) 72-74 North-Holland, Amsterdam
BRAGG ZONE PLATES FOR HARD X-RAY FOCUSING V.V. A R I S T O V , Y u . A . B A S O V , S.V. R E D K I N ,
A.A. SNIGIREV
a n d V.A. Y U N K I N
Institute of Problems of Microelectronics Technology and Superpure Materials, USSR Academy of Sciences, 142432, Chernogolovka, USSR
The experimental results of observing hard X-ray focusing during Bragg diffraction on a perfect crystal with Fresnel zone surface structure are reported. Possibilities of developing X-ray Bragg optics are considered.
The absence of X-ray optics (X ~- 1 A), analogous to light optics, is due to the fact that X-ray radiation is not in practice refracted by materials (1 - n -~ 10 5-10-6). A crystal lattice at the exact Bragg position can be used as an effective deviative element for X-ray beams. This principle serves as a base for the focusing by Cauchois [1] and Johann [2] consisting in geometrical intersection at one point of incoherent beams from different parts of the crystal. Recently, in a number of studies coherent dynamic focusing of X-ray beams by a perfect crystal in the Laue case (" transmission") have been realized [3-8] using the abnormal dispersion of the index of refraction within a narrow angular range (of order 1 0 " ) close to the exact Bragg condition. The present work puts forward and realizes the idea of using Bragg diffraction on a crystal integrally with that on a structure artificially formed in it. Recent studies have shown that at the exact Bragg condition, a diffraction spectrum within a wide angular range (of order 100") appears on a perfect crystal with a thin relief formed on its surface [9,10]. Within the framework of the kinematic approximation, the theory taking into account X-ray wave scattering by a perfect crystal at small source-to-crystal distance (L1) and crystal-to-observation plane distance (L2) was worked out [11] (fig. 1). This theory is based on evaluating (as well as the Fresnel diffraction theory) wave phases q0 reaching the observation point P after scattering of an incident wave from S by different crystal points r c. At rc << L 1 and rc << L 2
!
ILl L2 [kl × rc]z2t 9~(r) = 2~r ~ - + ~ - + (k, - k2)r,. + 2L 1
+ [k2 where
x
~,.]2
I k l I = I k2 I = 1 / X
integer, i.e. when at point r = 0, the Bragg condition is rigidly fulfilled, the change in phase q0(r) is determined however by the last terms in eq. (1). At k 1 = k 2 expression (1) is a well-known condition in optics for changing the wave phase, which is utilized to obtain Fresnel zones. Thus, if according to this condition a relief is formed on a perfect single crystal surface, diffraction on such a zone structure, as in optics, results in wave focusing in direction kz. In our work a Fresnel linear zone structure (figi 2) was fabricated in a perfect Si single crystal and used as a means of X-ray focusing. The essential lens dimensions are (1) the central zone halfwidth r 1 = 10/~m, (2) the last zone width = 0 . 5 /~m, (3) the total lens width = 200 /~m, (4) the length = 1 m m and (5) the focal distance f = 39 mm. The relief height is 2.5 /~m exceeding the extinction depth A e (in our case A e = 1.53 /~m) at which radiation penetrates the crystal. Fig. 3 demonstrates the main stages of zone plate fabrication. These are as follows: a) exposure of P M M A (an electron resist) 0.75 /lm thick by an electron beam of energy 30 keV; b) A1 thermal sputtering 0.1 /~m thick; c) lift-off; d) 2.5 /~m deep etching of Si in an electric discharge under a pressure of 8 × 1 0 3 Torr in SF6 + O 2 through an aluminium mask formed on the Si surface.
(1)
--2
are the w a v e vectors o f the
diffracted and incident waves in the direction of the optic axis SOP. For ( k l k2)r,. = n, where n is an 0168-9002/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. Schematic illustration of the experiment.
73
V. V. A ristov et al. / Bragg zone plates for hard X-ray focusing
50
~O~.m
~m El
0,4
~m
0,3 J
0.2 0,1 Fig. 2. Fresnel zone structure. The experimental scheme in fig. 1 demonstrates X-ray wave focusing by a Fresnel lens for radiation diffraction CuK~ (X = 1.54 A) on plates Si(III). Distances L a and L 2 were equal to 1 m and 0.04 m, respectively. The size of the X-ray source d s was 10 /~m, the magnification factor k = 1 : 25. The image was registered on the photoplate with a resolution of 200 lines/ram. Fig. 4 (upper topogram) shows the image experimentally obtained in the scheme in fig. 1. In the absence of prior radiation monochromatization the width of the topographic image is dictated by that of the slit D positioned before the crystal-lens, and nearly equals 50 ~m. In the centre of the topogram there is a focused image of the X-ray source. The focus width experimentally observed equals 7.5 #m and is likely to be determined by the photoemulsion resolution since the image of the tube focus reduced by a factor of 25 equals 0.4 t~m. Next to the topogram one can see its photometric curve. With deviation of the zone plate centre from the exact Bragg position (fig. 4, lower topograph) the lens diffraction efficiency decreases while the focusing
a .
A L
b
Fig. 3. Stages of zone plate fabrication.
I
0.3~! 0.2[ O.!
Fig. 4. Experimental topograms and their densitograms.
is retained. An ordinary topographic image of the crystal part at the exact Bragg position is observed as well as a focused image of the X-ray source on its boundary. The experiment reveals the possibility of fabricating Fresnel diffraction optics of a new type, which uses Bragg scattering on a perfect crystal or Bragg Fresnel optics (BFO). The vertically shaped zone structure utilized is optimal only for distances L 1 and L2 being equal. For L 1 >> L 2 (for which the topograms in fig. 4 were obtained) the zones should be oriented in the direction of the observation point [11]. Proper zone orientation is likely to give good efficiency and contrast of the diffraction image. Let us evaluate the limiting spatial resolution that can be obtained in Bragg Fresnel optics (BFO). In the "reflection case" the radiation penetration depth during Bragg diffraction is defined by the extinction depth X sin OB/CIxh[T?, which is, for instance for Si(III) with Cu K~, equal to 1.53 /~m. Then, it is hoped that structures with a minimum size for the last zone and, consequently, with spatial resolution up to 0.1-0.2 /tm can be fabricated (we believe that a structure with the width-to-height ratio of an order 10 can be formed). Extinction length for Ge, GaAs crystals is three times II. INSTRUMENTATION
74
v. 1/\ A ristov et al. / Bragg zone plaws for hard X-ray ]housing
less which permits increasing resolution to 300-500 ,~. In the case of scattering in the Laue diffraction geometry (" the transmission case"), the relief depth is to be much greater (for Cu K~ Si(III) the extinction depth equals 18.5/~m). Laue diffraction, however, gives rise to complex interference phenomena [12] which can be employed to design specific X-ray optics and leads to a more complex expression for the zone structure than in ref. [11]. Thus, for example, in the specific case of an incident plane wave a focusing structure of Fresnel zones is described by a Bessel function [13]. Thus, experimental results and estimations obtained demonstrate the potentialities of X-ray optics of a new type, that is of Bragg Fresnel optics. A BFO structure fabricated on a single crystal substrate is, in fact, the structure of a single block X-ray interferometer [14]. The phenomenon described opens the possibility of controling BFO elements and forming structures with phase modulation.
References [l] I. Cauchois, J. Phys. et Radium 7 (1932) 320. [2] H.H. Johann, Z. Phys. 82 (1933) 507.
[3] V.L. Indenbom, I.Sh. Slobogetskiy and K.G. Truny, Zh. Exsp. Teor. Fiz. 62 (1974) 1110. [4] E.V. Suvorov and V.I. Polovinkina, Pis'ma Zh. Exsp. Teor. Fiz. 20 (1974) 326. [5] A.M. Afanas'ev and V.G. Kohn, Fiz. Tver. Tela 19 (1977) 1775. [6] V.V. Aristov, V.I. Polovinkina, I.M. Shmytko and E.V. Shulakov, Pis'ma Zh. Eksp. Teor. Fiz. 28 (1978) 69. [7] P.V. Petrashen, F.N. Chukhovskii, Pis'ma Zh. Exsp. Teor. Fiz. 23 (1976) 385. [8] V.I. Kushnir and E.V. Suvorov, Pis'ma Zh. Exsp. Teor. Fiz. 32 (1980) 551. [91 V.V. Aristov, A.Yu. Nikulin and A.A. Snigirev, 12th Hungarian Diffraction Conf., Sopron (1985). [10] V.V. Aristov, A.I. Erko, A.Yu. Nikulin and A.A. Snigirev, Opt. Commun. 58 (1986) 300. [ll] E.V. Shulakov and V.V. Aristov, Kristallographiya (1986) in press. [12] V.V. Aristov, V.I. Polovinkina, A.M. Afanas'ev, V.G. Kohn, Acta Cryst. A36 (1980) 1002. [13] V.A. Indenbom, Pis'ma Zh. Exsp. Teor. Fiz. 29 (1979) 7. [14] M. Hart, Rep. Prog. Phys. 34 (1971) 435.