NATURE MATERIALS DOL:10.1038/NMAT2400 INSIGHT I REVIEW ARTICLES b 46.6 -02 SOI (x10- 46.5 -0.4 BOX 46.4 -0.6 15015050510 463 Si 46.2 -1.0 .1352 46.0 0.6 -12 0.3 -0.4 0.4 -1.4 46.6 -1.0 -05 0.5 1.0 2.7 x (um) 41 0.04 0 1.5 -0.04 -0.2 0.2 0.4 x (um) 46.0 0.6 0.3 0.40.8121.62.02.42.83.23.64.0 (x10) 0.4 0 -0.2 0.2 04 9x (nm) Figure 2 Strain due to patterning of silicon.a,xz cross-section of the measured structure showing the FEA calculation of the g,,strain component shown on the indicated colour scale.A magnified view of the silicon on insulator(SOl)portion is shown below on a finer colour scale.The supporting oxide layer is denoted BOX.b,Measured diffraction pattern surrounding the 004 reflection of the SOl structure as a function of its g.and g,components. c,Corresponding diffraction pattern calculated for the structure shown in a.Figure reprinted with permission from ref.33.2007 AlP. visible at the otherwise forbidden(200)reflection2.An important Again,averaging is used to increase the signal in the experiment, limitation of this X-ray work so far is the need to average the data which was carried out at BM32,a bending magnet beamline at ESRE over a large number of quantum dots,which have to be made with Slight disorder in the relative positions of the wires making up the the same shape and similar size,with identical orientations on the array removes any effect of interference between them;the limited substrate.The situation is helped by the tendency of the islands to coherence of the BM32 beam,in the range of several micrometres, self-assemble at a particular size determined by the strain of the would not be enough to achieve this.However,as the wires are effec- misfit with the substrate.In the most recent work,a microfocused tively floating on amorphous oxide,it is reasonable that any spatial beam was used to isolate the contributions of individual quantum correlations present in the parent SOI layer would be lost. dots".The size distribution can also be controlled by suitable pat- The silicon nitride stress of 1.5 GPa that was found to explain the terning of the starting substrate,which leads to various applications observations is a relatively large value.Without stress,the SOI wires in nanotechnology32 would give diffraction patterns extending less than one-twentieth of the width seen in Fig.2.In effect,many 'phase wraps'are present Strain due to lithographic patterning in the structure(see below).The X-ray methods discussed here are Another perspective of strain measurement using X-rays comes sensitive to stresses orders of magnitude smaller than this,yet use of from the group of Thomas at the Centre National de la Recherche the fabrication method of ref.33 is not uncommon in the construc- Scientifique IM2NP laboratory in Marseille6.They have used tion of semiconductor devices and'strain engineering'is a powerful high-resolution X-ray diffraction to examine the strain distributions method of producing high-performance semiconductor devices". in lithographically prepared micrometre-size structures composed Today's semiconductor industry is producing devices with feature as arrays to enhance the signal3.Finite element analysis (FEA) sizes('design rules')of 45 nm;at this level the resulting strain asso- methods were used to model the strain,followed by a kinematical ciated with the chemically processed interfaces will be much greater diffraction calculation.Like the quantum dot work mentioned than those identified by ref.33.At some point,the FEA bulk model- above,the structures correspond to an array and are averaged over ling will start to break down as the specific structural details of the its periodicity.No attempt was made to model the properties of this crystal interfaces become relevant3,as may already be the case at artificial lattice,but only the shape and strain of the Si bars within 45 nm.Other work by the same group has applied the method to it,which results in the intensity distribution of the diffraction.It Si trench-array structures*and succeeded in using iterative direct- was arguedss that very small deviations from ideal periodicity cause phasing methods (described below)to obtain spatial images of the smearing out of any ultrafine fringes that would arise from the the strain". entire array. In future,strain patterns could be created in model devices The example shown in Fig.2 is from a patterned structure with sizes more relevant to current technology (45 nm)that only engraved in a silicon-on-insulator (SOI)layer lying on its bur- partly penetrate the thickness of the SOI layer,or else in GeSi,as is ied oxide substrate and underlying bulk Si handle.An array of relevant.For example,strain on the scale addressable with X-rays are 1-um-wide wires,spaced 2 um apart,was cut in the SOI(100 nm of expected to result from local heating in the channels ofactive model Si on 200 nm of SiO,)using a silicon nitride lithography mask.After transistors.The embedding environment of a real device will also reactive ion etching,the wire structures are left standing on the bare create strain.As the IM2NP group has found,it is important to use oxide substrate as illustrated in Fig.2.A residual stress of 1.5 GPa SOI methods because the active layer of Si has a different orienta- remains in the silicon nitride layer,causing significant distortions tion from the much thicker handle;the diffraction of interest would in the Si wire,calculated using FEA,as shown.The kinematical dif- be in the shape of the 111 or 220 Bragg peak of the layer,which fraction pattern of the strained wire,shown in Fig.2c,is in good would be completely swamped by the bulk substrate diffraction if agreement with the experimental data in Fig.2b. SOI technologies were not used. NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 293 2009 Macmillan Publishers Limited.All rights reservednature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 293 NaTure maTerials doi: 10.1038/nmat2400 insight | review articles visible at the otherwise forbidden (200) reflection25. An important limitation of this X-ray work so far is the need to average the data over a large number of quantum dots, which have to be made with the same shape and similar size, with identical orientations on the substrate. The situation is helped by the tendency of the islands to self-assemble at a particular size determined by the strain of the misfit with the substrate. In the most recent work, a microfocused beam was used to isolate the contributions of individual quantum dots27. The size distribution can also be controlled by suitable pat￾terning of the starting substrate, which leads to various applications in nanotechnology32. strain due to lithographic patterning Another perspective of strain measurement using X-rays comes from the group of Thomas at the Centre National de la Recherche Scientifique IM2NP laboratory in Marseille33,36,37. They have used high-resolution X-ray diffraction to examine the strain distributions in lithographically prepared micrometre-size structures composed as arrays to enhance the signal33. Finite element analysis (FEA) methods were used to model the strain, followed by a kinematical diffraction calculation. Like the quantum dot work mentioned above, the structures correspond to an array and are averaged over its periodicity. No attempt was made to model the properties of this artificial lattice, but only the shape and strain of the Si bars within it, which results in the intensity distribution of the diffraction. It was argued33 that very small deviations from ideal periodicity cause the smearing out of any ultrafine fringes that would arise from the entire array. The example shown in Fig. 2 is from a patterned structure engraved in a silicon-on-insulator (SOI) layer lying on its bur￾ied oxide substrate and underlying bulk Si handle. An array of 1-μm-wide wires, spaced 2 μm apart, was cut in the SOI (100 nm of Si on 200 nm of SiO2) using a silicon nitride lithography mask. After reactive ion etching, the wire structures are left standing on the bare oxide substrate as illustrated in Fig. 2. A residual stress of 1.5 GPa remains in the silicon nitride layer, causing significant distortions in the Si wire, calculated using FEA, as shown. The kinematical dif￾fraction pattern of the strained wire, shown in Fig. 2c, is in good agreement with the experimental data in Fig. 2b. Again, averaging is used to increase the signal in the experiment, which was carried out at BM32, a bending magnet beamline at ESRF. Slight disorder in the relative positions of the wires making up the array removes any effect of interference between them; the limited coherence of the BM32 beam, in the range of several micrometres, would not be enough to achieve this. However, as the wires are effec￾tively floating on amorphous oxide, it is reasonable that any spatial correlations present in the parent SOI layer would be lost. The silicon nitride stress of 1.5 GPa that was found to explain the observations is a relatively large value. Without stress, the SOI wires would give diffraction patterns extending less than one-twentieth of the width seen in Fig. 2. In effect, many ‘phase wraps’ are present in the structure (see below). The X-ray methods discussed here are sensitive to stresses orders of magnitude smaller than this, yet use of the fabrication method of ref. 33 is not uncommon in the construc￾tion of semiconductor devices and ‘strain engineering’ is a powerful method of producing high-performance semiconductor devices34. Today’s semiconductor industry is producing devices with feature sizes (‘design rules’) of 45 nm; at this level the resulting strain asso￾ciated with the chemically processed interfaces will be much greater than those identified by ref. 33. At some point, the FEA bulk model￾ling will start to break down as the specific structural details of the crystal interfaces become relevant35, as may already be the case at 45 nm. Other work by the same group has applied the method to Si trench-array structures36 and succeeded in using iterative direct￾phasing methods (described below) to obtain spatial images of the strain37. In future, strain patterns could be created in model devices with sizes more relevant to current technology (45 nm) that only partly penetrate the thickness of the SOI layer, or else in GeSi, as is relevant. For example, strain on the scale addressable with X-rays are expected to result from local heating in the channels of active model transistors. The embedding environment of a real device will also create strain. As the IM2NP group has found, it is important to use SOI methods because the active layer of Si has a different orienta￾tion from the much thicker handle; the diffraction of interest would be in the shape of the 111 or 220 Bragg peak of the layer, which would be completely swamped by the bulk substrate diffraction if SOI technologies were not used33. 0 –0.2 –0.4 –0.5 0 0.5 x (μm) z (μm) x (μm) εzz z (μm) –0.6 –0.8 –1.0 –1.2 –1.4 –1.0 –0.04 0 0.04 –0.2 0.2 0.4 0.4 2 0.8 1.2 1.6 .0 2.4 2.8 3.2 3.6 4.0 –0.4 0 1.0 –6.0 –0.4 46.0 46.1 46.2 46.3 46.4 46.5 46.6 46.0 46.1 46.2 46.3 46.4 46.5 46.6 –0.2 0.2 0.3 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 0 0.4 –0.4 –0.2 0 0.2 0.4 0 –4.5 –3.0 –1.5 1.5 3.0 4.5 0 (×10–3) (×10–3) Si BOX SOI Si3N4 qx (nm–1) qz (nm–1) qz (nm–1) a c b Figure 2 | strain due to patterning of silicon. a, xz cross-section of the measured structure showing the FEA calculation of the εzz strain component shown on the indicated colour scale. A magnified view of the silicon on insulator (SOI) portion is shown below on a finer colour scale. The supporting oxide layer is denoted BOX. b, Measured diffraction pattern surrounding the 004 reflection of the SOI structure as a function of its qx and qz components. c, Corresponding diffraction pattern calculated for the structure shown in a. Figure reprinted with permission from ref. 33. © 2007 AIP. nmat_2400_APR09.indd 293 13/3/09 12:04:29 © 2009 Macmillan Publishers Limited. All rights reserved