Beam bending using graded composition strained layers

NOMB

Beam Interactions with Materials & Atoms Nuclear Instruments

ELSEVIER

and Methods

in Physics Research

B 132 (1997) 540-547

Beam bending using graded composition strained layers M.B.H. CFNUL.

Breese ’

Univrrsidade de Lishocr. Ar. Prqf. Gums Pinto 2. 169Y Lisbou. Portugal

Received

13 May 1997; revised form received

16 July 1997

Abstract Curved crystals are commonly used to bend and extract GeV charged particle beams from high-energy accelerators. There is growing interest in multiturn extraction schemes, whereby the circulating beam makes several passages through the curved crystal, to increase the bending efficiency and also for extending their use to TeV energies. The optimum crystal length in such schemes is typically 5 mm, which imposes difficulties both in accurately aligning and bending such short lengths. This paper examines the use of Si,_,Ge,/Si graded composition strained layers to satisfy the optimum crystal dimensions and small bend angles required in such schemes. The use of Si,_,Ge,/Si graded layers to bend low-energy charged particles is experimentally demonstrated using 3 MeV protons. 0 1997 Elsevier Science B.V. PACS: 61.85.+p; 2927.-a: Kq~ords: Beam bending; microprobe

41.7.5.Ak Multiturn

extraction:

Graded

composition

strained

layers; Channeling

patterns:

Nuclear

1. Introduction Positively charged particles which are incident on a crystal at small angles with respect to a plane or axis are steered away from regions of high electron density close to the lattice walls, i.e. they are channeled [l-3]. The maximum angle of incidence of particles to the lattice direction for which channeling will occur is called the critical angle. For very high energy (> 1 GeV) protons with a momentum p incident on the silicon 10 1 1 i planes this is equal to

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When a crystal is slightly curved, most high-energy planar channeled protons follow the bent lattice planes and are steered away from the initial beam direction, as shown in Fig. l(a). Following the original proposal by Tsyganov [4], there has been considerable interest in the use of curved crystals in channeling alignment to bend and extract GeV charged particle beams from circular accelerators [5-lo]. Refs. [8,9] cover many aspects associated with their use, and many recent papers are given in Ref. [lo]. Their use is attractive because the bending occurs over the short crystal length and can be equivalent to a magnetic dipole field strength of hundreds of Teslas.

dcllrct~l bfL%m (4

drHected bram (11)

Fig. 1. Geometry used to bend beams using (a) curved crystals and (b) graded composition strained layers. The two schematics are not to the same scale and are both exaggerated in angle. (b) shows the lattice planes bent with a uniform radius of curvature along off-normal directions. such as at the [Ol I] axis, whereas planes along the surface-normal [OOI] direction are straight.

Natural dechanneling arises in straight crystals due to the increase in transverse energy of the channeled beam in collisions with the lattice electrons and nuclei. and causes channeled protons to revert to a random trajectory (e.g.. see ch. 7 of Ref. [2]). The additional effect of bending dechanneling occurs in curved crystals due to the shifting of the minimum potential towards the lattice walls, and consequently the channeled beam moves towards the outer planes [4,11]. The critical minimum bending radius of the lattice planes for protons to remain channeled in the silicon (011) planes is R, E 1.6 m.p [TeV/c].

(2)

A long path length through a curved crystal reduces the bending dechanneling since it enables a larger radius of curvature of the bent lattice planes. However, a shorter path length through the curved crystal reduces the natural dechanneling. The optimum path length for a particular beam energy and bend angle is dictated by these opposing constraints. Ref. [8] gives calculated curves for the bending efficiency which incorporate these two effects in single pass mode, i.e., where the beam makes a single passage through a curved crystal. Typical bend and extraction angles which have been used to date are l-60 mrad for l-900 GeV protons in single pass mode. High bending efficiencies have been achieved for this range of angles using curved crystal lengths of 2-10 cm and thicknesses of 0.5-3 mm.

There is interest in further increasing the bending efficiency and in extending the use of curved crystals to even higher beam energies. Several papers have discussed and simulated the use of curved crystals for multiturn extraction of proton beams with TeV energies [12-191. In multiturn exthe circulating proton beam passes traction, through the crystal many times which greatly increases the extraction efficiency. This is because protons with incident angles less than the channeling critical angle are extracted more efficiently and the angular acceptance of the curved crystal also increases. The optimum crystal length and bend angle for multiturn extraction are significantly smaller than those for single pass mode. The optimum path length is less because a short crystal disturbs the circulating beam less, so enabling more passes through the crystal with less scattering of each proton [12-141. Biryukov [12] calculated for multiturn extraction of 20 TeV protons from the proposed SSC accelerator. optimum path lengths of 3 and 9 mm for bend angles of 30 and 90 prad, respectively. Tsyganov [ 141 simulated the extraction of a 1 TeV proton beam from the Tevatron accelerator, and demonstrated the increased efficiency for multiturn extraction compared with single pass mode. An optimum crystal length of 5 mm was calculated for a bend angle of 100 prad for multiturn extraction. Biryukov [I 51 has simulated the extraction of 900 GeV protons from the Tevatron. using an optimal crystal length of 4-10 mm for a bend angle of 640 prad. Ref. [20] gives a theoretical example of how the use of more than one crystal could be used for a combination of beam bending and focusing. This paper examines an alternative method of bending high-energy proton beams using curved lattice planes in Si,_,Ge,/Si graded composition strained layers. Their suitability for giving bend angles and layer thicknesses required for proposed multiturn extraction schemes is discussed. Their geometry differs in that the proton beam is channeled in bent lattice planes when the large-area surface is presented to the beam. as shoTyin in Fig. l(b). not the narrow transverse face as for curved crystals. The mechanism which gives rise to bending of the lattice planes and to limitations on the epilayer thickness is described in Section 2.

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Brecw I Nucl. Instr. und Met/r

Section 3 gives a brief discussion of the methods of growing suitable Si, _,Ge,/Si graded composition layers. Section 4 gives an example of their use to bend 3 MeV protons through 5 mrad. also demonstrating how graded composition layers can bend much lower energy beams than curved crystals.

2. Graded composition strained layers When a lattice-mismatched epitaxial layer, such as Si,~,Ge, with a germanium content of x, is grown on a substrate such as silicon, the resultant lattice strain produces tetragonal distortion of the equilibrium cubic unit cell within the growing epitaxial layer. The average lattice parameter, a,, of the unstrained Si,_,Ge, layer is larger than that of the silicon substrate, asi. This results in compressive strain where uL2 > uIl, causing an abrupt change in angle at the bilayer interface at planes and axes away from the surface-normal direction, as shown in Fig. 2. At the (011) axes this bend angle is given by

in which the epilayer lattice planes are inclined towards the surface-normal [OOl] axis compared with those of the substrate. For a pure germanium layer (X = 1.0) the interface bend angle is 2.1” (36.7 mrad); at lower germanium contents the bend an-

in Phys. Rrs. B 132 (1997)

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gle is proportional to X. Many aspects of strained layer technology are discussed in detail in [21]. Channeled ions are sensitive to lattice strain in uniform composition epitaxial layers because the abrupt bend in angle at the interface along off-normal crystal directions alters the ions’ trajectories. MeV ion channeling [22] is regularly used to measure this interface bend angle, and hence to determine the amount of strain within uniform content epilayers with thicknesses up to -1 pm, as described in ch. 3 of Ref. [21] and Ref. [23]. Thin strained layers are generally grown by molecular beam epitaxy (MBE), by deposition of controlled amounts of silicon and germanium on to a [OOl] silicon substrate. If there is too much strain present within the growing epilayer, it is relaxed by the generation of misfit dislocations at the bilayer interface. Several models for calculating the critical epilayer thickness, h,, at which this starts to occur have been used. The model which agrees with many experimentally determined critical thicknesses was derived by People and Bean [24] by equating the area1 strain energy density associated with a film thickness h. hf”. with the area1 energy density associated with an isolated screw dislocation at a distance h from a free surface, (5)

[WI f’ Si,_,Ge,

a111 ,,,,,/‘I I

1/

layer

1 Si substrate I

/

-allFig. 2. Tetragonal lattice distortion of the Si, ,Ge, unit cell grown on the silicon substrate. giving rise to a bend angle ri along off-normal directions. The substrate has an in-plane lattice parameter of D,,, which also occurs in the growing epilayer. In the silicon substrate alI = a ,_

where L‘is the Poisson ratio (-0.3), G is the shear modulus and b is the magnitude of the dislocation burgers vector. The lattice mismatch between the silicon substrate and the Silp.YGe.X epilayer is f’ = (a, - asi)/asi, or more simply expressed as If’ = 0.0416x. The increase in area1 strain energy with epilayer growth imposes an upper limit on the Si,_,Ge., layer thickness which can be grown before misfit dislocations are formed to relieve the strain. Fig. 3(a) shows the SiIm.Ge, critical layer thickness as a function of uniform germanium content X, obtained by setting h equal to h, in Eqs. (4) and (5). The variation of the interface bend angle 6 at the (011) axes as a function of germanium content is also shown. Thus for a uniform

M.B. H. Breesr I Nucl. Instr. und Meth. in Phys. Rrs. B 132 [ 1997) 540-547

IO

-uJ.*oo

10-3

10

10-Z

-2

10-I

germanium content 2

bend angle (mrad) Fig. 3. (a) Calculated curves for the critical layer thickness h, for a uniform content Sil ,Ge, layer, and a graded composition Si,_,Ge, layer for the same maximum germanium content Y. The calculated epilayer bend angle 6 is also shown (dashed line. scale on right) as a function of germanium content. (b) Calculated maximum path length, h,,,, along the (011) planes of a graded layer when tilted to the (011) axes, as a function of epilayer bend angle.

germanium content of x = 0.5, S =18.3 mrad and il, - 0.01 pm, whereas for a much lower germanium content of x = 0.003. S =I00 prad and 11, - 2.3 mm. The critical layer thickness thus increases rapidly with decreasing germanium content owing to the large reduction in strain energy, whereas the bend angle decreases slowly. In a Si,_,Ge, graded composition layer the germanium content varies linearly between zero at the

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silicon substrate interface (1 = 0) and a maximum of x at the Si,_,Ge, surface (1 = h), though other profiles may be chosen. The total bend angle is the same as that at the interface in a uniform content strained layer, but in a graded layer the offnormal lattice planes become gradually more bent with a uniform radius of curvature over the full epilayer thickness, as shown in Fig. l(b). The lattice mismatch through the graded composition SiI_,Ge, layer is f = O.O416x(l/hj. Substituting this into Eq. (4) and equating it again with Eq. (5) gives a calculated critical layer thickness which is more than three times that of a uniform layer for the same germanium content x, as shown in Fig. 3(a). The additional thickness for the same x arises due to the reduced strain through the graded layer compared with a uniform composition layer. When the graded layer is tilted 45” away from the surface-normal to a (011) axis, the maximum path length, h,,,, of the beam through the epilayer is fi larger than the layer thickness, and Fig. 3(b) plots II,,, as a function of bend angle along the (011) planes. Other off-normal planar directions could be chosen but just the (01 1} planes are considered since the epilayer bend angle is largest here. Thus for bend angles of 30, 90 and 100 PLrad, the maximum path length through the { 011) planes is, respectively, h,,, = 108, 12 and 10 mm. These path lengths satisfy the requirements for proposed multiturn extraction schemes for bend angles of d 100 prad [12,14]. For larger bend angles, such as 640 yrad, A,,, = 180 pm which is too thin to meet the required optimum thickness of 4-10 mm in the extraction scheme by Biryukov [15]. In this case a thick enough layer cannot be grown because of the rapid reduction in critical layer thickness with increasing bend angle. Curved crystals are typically produced using a 3 or 4 point bending device. There can be difficulties in producing a uniform radius of curvature with such devices, which are exacerbated on very short crystals. Bending devices may also produce anticlastic bending at the ends of the crystal [8,2.5,26]. With graded layers the plane bending is determined by the germanium content through the epilayer and a uniform curvature radius is attainable. Furthermore there is no change in the orientation of the channeling planes across the layer surface.

The large surface area presented to the beam by a graded layer has other advantages for bending and extraction schemes. The amount of beam accepted into a curved crystal is limited by the transverse thickness of 0.5-3 mm, compared with beam diameters which may be many millimetres, depending on the crystal location relative to a beam waist. Curved crystals can also be difficult to align with the beam axis owing to their small transverse thickness [6]. Because graded layers present a large transverse surface area to the beam, the amount accepted into the bending planes is independent of the beam size and spatial alignment problems are also negated. There has been little work on the dechanneling effects of beam induced damage at GeV energies [27-291. This has indicated that proton doses as large as 10’” cm- 2 do not produce an unacceptable amount of damage for beam bending purposes. Damage is. however. unavoidable in a curved crystal since there is little room to translate to a new surface area whereas a graded layer can easily be translated.

3. Growth of thick graded composition layers

strained

There are several methods of growing epitaxial layers [30,31], most of which are not appropriate for growing very thick layers. Since only the crystallographic properties of the epilayer are important for beam bending purposes, growth considerations are simplified since factors which affect the electronic properties, such as oxygen impurities and point defects, are not crucial. Thick Si, ,Ge, epilayers with a very low germanium content of .Y< 0.01 have not been previously grown since they have no obvious use for microelectronics applications, so preliminary work to determine the optimum growth conditions is needed. MBE is the most commonly used method of growing thin epitaxial strained layers 132.331. It can produce complex structures with good control of content and thickness. with a typical growth temperature of 55O”C-750°C. However a growth rate of 0.1 um/min is considered very fast for MBE, and to grow a 1 mm thick layer would take one week at this rate.

There are several forms of vapor phase epitaxy which have been used to grow strained layers, with variations mainly of the wafer temperature and the pressure within the reactor vessel. Low temperature chemical vapor deposition (CVD) has been used with wafer temperatures of 5OO”C~7OO”C to give typical growth rates of 0.1 um/min [34,35], i.e. a rate comparable to MBE. High temperature CVD is used for growing epitaxial layers hundreds of microns thick and seems a better choice. A rate of I um/min can be achieved for silicon growth at a wafer temperature of approximately 9Oo”C, so to grow a 1 mm thick layer would only take 17 h. Ref. [35] also showed how the germanium content of a Sit ,Ge, epilayer was reduced at growth temperatures of 900°C compared with low temperature growth under similar conditions. The discussion in Section 2 used the relationship of People and Bean [24] for determining the Sir ,Ge, critical epilayer thickness. which was based on the generation of non-interacting screw dislocations within the epilayer. Other authors have refined this analysis by considering the generation of 60” mixed dislocations in epilayers with a low germanium content [36,37], resulting in a smaller calculated critical thickness. Refs. [36,37] also reported the reduction of the critical epilayer thickness at elevated growth temperatures and explained it on the basis of thermal expansion effects during layer growth. Ref. [38] gives an example of the growth of a graded composition Sir _rGe,r epilayer using high temperature CVD, where the germanium content was varied from x = 0.09 to 0.17. Ref. [39] describes the production of a graded composition Sit rGer layer by implantation of Ge ions. Gradually curved epilayer lattice planes were observed along off-normal directions as a result of the varying germanium content. The dislocation density present in an epitaxial layer strongly depends on the growth conditions used. The effect of dislocations in curved crystals on beam bending efficiency has been studied [40.41] and it has been shown that line dislocations are the most deleterious since their dechanneling effect increases with beam energy. Particular attention must therefore be paid to minimizing the dislocation density within the epilayers.

M. B. H. Breese I Nucl. Instr. und Meth. in Phys. Rex B 132 (1997) 540-547

A more detailed study of the growth conditions for growing suitable layers is required. Although long growth periods using any method are inevitable, the production of a single large-area wafer means that many suitable bending crystals can be produced from it.

4. Results A 3 MeV proton beam from a Van de Graaff accelerator was used to demonstrate the ability of Sii._,Ge, graded composition layers to bend protons in a single pass through the crystal. This beam energy was used because of its ready availability and ease of MBE growth of a suitable Sio xsGeO.,s graded layer. Bending of 3 MeV protons does not require unduly large magnetic fields and this section is only intended to give qualitative visual confirmation of the bending ability of graded composition layers. It also demonstrates that bending using such structures is applicable to beam energies of considerably less than 1 GeV, where curved crystals cannot be used owing to their limited minimum thickness. A SiUxjGeo.is/Si graded bilayer with a germanium content which varied linearly from x = 0.0 at the interface to x = 0.15 at the surface of the 200 nm thick epilayer was chosen. The critical layer thickness for a uniform content layer of Sio.ssGeo.,s is -400 nm, and - 1.5 urn for a graded layer, according to Fig. 3(a). Nomarski optical microscopy was used to verify the absence of misfit dislocations. The tetragonal lattice distortion produced a bend angle of 0.29” with a radius of curvature of 50 pm at the (111) planes close to the [112] axis (compared with R, - 8 pm), with the crystal tilted 37” away from the surface-normal [OOl] direction. 3 MeV protons have a { 111) channeling critical angle of 0.12”, a dechanneling length of approximately 4 pm, and a range of 90 urn in silicon. Therefore it was necessary to thin the sample to considerably less than the proton range. It was first mechanically thinned and polished from the rear surface to a thickness of approximately 20 pm. It was then further thinned using a 5 keV argon ion beam. as described in [42]. This procedure sputtered away the silicon substrate, leaving a thin bi-

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layer membrane, approximately 1 urn thick, which was supported on all sides by the thicker surrounding material. Channeling patterns were produced using a nuclear microprobe [43] which focuses a low-divergence MeV ion beam to a spot of N 1 pm on the crystal surface. The beam divergence was set to w2qP for similarity with bending experiments at GeV energies where the beam divergence in the bending direction is usually larger than 2$,. This also ensures that the observed behavior in the channeling patterns is not due to planar oscillation effects, which might dominate for divergence angles of much less than $,. The channeling patterns were observed on a fluorescent viewing screen consisting of willemite (ZnSi04:Mn), located 220 mm downstream of the crystal. Fig. 4 shows six channeling patterns as a function of tilt angle of the substrate (111) planes close to the [ 1121 axis with respect to the beam direction. The beam enters through the epilayer surface and exits through the thinned substrate. The vertically running (111) planes of the substrate can be seen and the (111) planes of the front Sio.xsGeo.is graded layer are to the left of this, as in Fig. l(b). In Fig. 4(c), the substrate (111) planes are aligned with the beam direction but the beam does not emerge channeled because it is misaligned with the (111) planes of the Sio.ssGeo.ij layer. In Fig. 4(d) and (e) the (111) planes of the Sio.ssGeo.i5 surface are aligned near the beam direction, which results in the beam being bent through 0.3” (-5 mrad) to the right and emerging within the substrate (111) planes. This is best demonstrated in Fig. 4(e) where the ( 111) planes of the epilayer surface are best aligned with the beam direction. Here, the left-hand edge of the marker bar indicates the beam direction into the crystal and the right-hand edge shows the location of the substrate (111) planes, i.e. the beam direction out of the crystal. Measurement of the beam current in a Faraday cup, which was centred on the substrate (111) planes with an acceptance half-angle of O.l”, indicated that 55% flO% of the incident beam was bent by an average angle 0.3”. This behavior is markedly different from that observed in channeling patterns produced using 3 MeV protons transmitted through a uniform con-

Fig. 4. Channeling patterns recorded from a Si,,x5Ge,, &i graded composition bilayer. The tilt angle of the substrate (I 11) planes close to the [I 121 axis are shown in the bottom right as a function of tilt angle with respect to the beam direction. The epilayer planes are bent towards the left of the substrate planes, in these patterns as in Fig. I(b). The patterns are more blurred than is normal for such thin crystals with 3 MeV protons due to residual damage on the exit surface from the ion beam thinning process [42.44].

tent Sit_,Ge, layer of a similar thickness and with a similar bend angle at the interface [44]. In this case there was no large beam fraction deflected away from the initial beam direction at any tilt angle, since there was always a large amount of dechanneling at the abrupt bilayer interface.

5. Conclusions The deflection of high-energy protons through small angles of -100 urad using millimetre-thick layers of graded composition Sit_,Ge, has been discussed, suitable for multiturn extraction schemes. Beam bending has been demonstrated in graded composition strained epilayers at much lower energies than for curved crystals because the bending can occur over very short path lengths. The use of graded composition strained layers differs from curved crystals in the range of attainable bending radii. The minimum elastic bending radius for silicon curved crystals is typically 0.5 m whereas there is no limitation on the maximum radius. In graded composition strained layers, the maximum bending radius is limited by the critical

epilayer thickness, but there is no limitation on the minimum curvature radius. Detailed Monte Carlo simulations are required to properly assess the bending efficiency of graded composition layers. Only the epilayer thickness along the {Ol 1) planes at the (011) axes have been considered here since the bend angle is largest at this orientation. Other planar directions may be chosen, as demonstrated in Section 4. This would allow the wafer to be tilted to steeper angles to increase the path length through the layer, enabling a thinner Si,_,Ge, layer to be grown. If slightly narrower, higher-index channeling planes could be used for beam bending, this option would be particularly suitable for multiturn extraction schemes.

Acknowledgements Prof. E. Parker and Dr. P. Phillips from the Dept. of Physics, University of Warwick are gratefully acknowledged for growing the Si, _.,Ge,/Si graded bilayer. Dr. P.J.M. Smulders, University of Groningen, is also thanked for useful discussions.

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