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Analysis of interfacial misfit dislocation by X-ray multiple diffraction
Solid State Communications, Vol. 88, No. 6, pp. 465-469, 1993 Printed in Great Britain.
0038-1098/93$6.00+.00 Pergamon Press Ltd
ANALYSIS OF INTERFACIAL MISFIT DISLOCATION BY X-RAY MULTIPLE DIFFRACTION
S. L. Morelhfio
and L.P. Cardoso
Institute de Fisica - UNICAMP, CP 6165, 13083-970, Campinas, SP, Brazil (Received 1 June 1993 by C.E.T. GonGalves da Silva) (in revised form August 3, 1993)
We have developed a new method to analyze the stress state of heteroepitaxial systems using X-ray multiple diffraction (MD). A fitting program extends the MD theory for mosaic crystals to provide the position and profile of the normal and hybrid MD peaks. We use surface secondary beams in order to achieve high resolution in intensity and peak position. These conditions together with the absorption involved in the LS hybrid reflections enable us to test the stress state of the layer by determining the misfit dislocation and the degree of cohesion between the buffer and epitaxial layers. Here, the method was applied in the analysis of thin (SOOA)and thick (1.2l.un) GaAs layers grown by Vacuum Chemical Epitaxy (VCE) on Si (001).
Introduction
In systems such as GaAs/Si in which the nominal lattice mismatch presents a high value (4%) the layer thickness plays an important role in the misfit relaxation process which occurs through the dislocation formation. X-ray diffraction techniques are used to monitor this process by measuring either asymmetrical reflections’ or symmetrical reflections together with the curvature radius’ in order to obtain the misfit dislocation density. In comparison with these rocking curve techniques, the X-ray multiple diffraction (MD) technique presents particular three beam cases (incident, primary and secondary) in which the secondary beams are diffracted almost parallel to the sample surface. These surface secondary beams are suitable for measuring lattice mismatch parallel to the interface layer/substrate since they are diffracted under conditions of extreme asymmetry. X-Ray MD applied to the analysis of epilayered semiconductor materials, shows hybrid MD’s features observed together with the normal MD one$-‘. Hybrid MD involving substrate and layer (SL) or layer and substrate [LS) paths have been observed in the Renninger Scans :RS)? Recently”‘, a new method of characterizing leteroepitaxial structures using the SL hybrid MD peak &ich appears in the layer RS was proposed. GaAs/Si ramples with different layer thicknesses, in the range of 0.6 Am to 2.8 pm, were analyzed as an application of the nethod. However, the characterization of thin layers ( - 500 due to the low intensity of the RS 4) was impossible leaks. On the other hand, it has also been observed that the ,S hybrid peak is measurable in the substrate RS even for hin layers, although its position and profile cannot be :xplained by the above mentioned method. In this work, we have modified the MD theory for 465
mosaic crystals to account for the directions of the secondary beam scattered by each mosaic block within an epitaxial layer. The modified simulation program was used to determine the misfit dislocation density from a1 values measured by LS peak position in the substrate RS. The misiit dislocation density was analyzed in two GaAslSi samples; one with just a thin (500A) buffer layer and other with a 1.2pm epilayer grown by VCE on top of the buffer. The degree of cohesion between epilayer and buffer was investigated by applying an external bending moment in order to compensate the stress caused by the epilayer growth. The absorption involved in the surface secondary beam propagation is also analyzed as a function of the grazing angle at which the surface beam crosses the interface since this angle should select contributions stemming from different depths inside the layer.
Theory In this work, a mosaic crystal is described by an isotropic and gaussian mosaic block distribution (11 being the mosaic spread) in which the fraction of the total number (NJ of illuminated blocks with reciprocal lattice vector H’, oriented inside the solid angle di2 is given by
As shown in Fig. 1, H’, is misoriented of A from the reciprocal lattice vector B, which represents the average distribution direction. We assume that a well-collimated, nearly monochromatic beam of X-rays is incident on the mosaic
466
INTERFACIAL MISFIT DISLOCATION Ewold
Sphere
Vol. 88, No. 6
angle describes the possible H’, positions on the ring for a fixed incident beam. The two coordinate systems shown in Fig. 2 are very useful in the above mentioned calculation. The unit vectors I;,. c, and 6, describe the orthogonal coordinate system fixed at the substrate reciprocal lattice being i, and i, the directions of the reference vector6 and the H, vector, respectively. In this system, the incident beam wave vector is given by &,=-~-‘(cosw’cosg’~,+cosa,‘sinblC,+sinw’~,) while the H’, coordinates are (H,sinAcos& H,sinAsin& H,cosA). The other orthogonal system described by the unit vectors &, & and f3 has &=-hk, and the H’, coordinates are expressed as (H,cos~,~cos(P, H,co&+,sincp, H,sinS,,). According to Fig. 2, these coordinate systems are related through the rotation matrix A, where A’=R,(x)R,(xlZ-o’)R,(&). Therefore, the transformation between the H’, coordinates is given by
Fig. 1: Intersection ring in the reciprocal space showing the relative orientation of II’, as a function of A((cp)for all diffracting mosaic blocks.
distribution, making a n/2-w’ angle with II,, such that Bragg reflections occur from all mosaic blocks, with II’, oriented on the ring formed by the intersection of the Ewald sphere with the sphere of radius H,. This ring is represented in Fig. 1. The ring portion which contributes to the scattering is given by the mosaic distribution (Eq. 1). The angular width associated with the incident beam collimation and wavelength spread is assumed to be much larger than the width of a perfect crystal reflection curve, but is much smaller than the width (q) of the mosaic distribution. We wish to calculate the change in the reflected beam direction due to H’, misorientation. In conventional MD theory for mosaic crystals, the reflected beam direction is given by R,=H,+& and, to consider the change in this direction, H, will be replaced by H’,. The cp
Thus, the A misorientation ring as a function of cpis
of those H’, positions on the
WWKUXS ( cad c.0~6,~cuq
+ aid
air@,) . (2)
Under MD condition, the k, beam reflected by the secondary planes (H,) reaches the coupling planes (HJ in Bragg condition. The position and the protile of the RS peak corresponding to the contribution of this H,+H, MD path have already been simulated using the expression*
--
A@,’
--
At+’
(3)
where K is a constant related with the integrated reflectivity per unit volume of a small crystallite. q, and Q are the mosaic spread of the secondary and the coupling planes and they can be different since we are analyzing simultaneously the layer and substrate lattices. Using (2), the angular deviations from Bragg’s angles A0, for the secondary reflection and A0, for the coupling reflection can now be expressed as a function of cp. In order to consider the contribution of all blocks to the position and profile of the RS peaks, the expression (3) turns out to be
Fig. 2: Coordinate
systems Fe<
5
describe H’, with
respect to the substrate lattice (II,, II,, h,) and to the incident
beam (Q,, Q2,&,). The reference vectorAdirection is given by I;, and 0, lies on the plane defined by b, and 0,.
At&)
= 0,
_ *(
-%g4)
(5)
Vol. 88, No. 6
INTERFACIAL
In the LS hybrid and substrate (Q,) mosaic The influence of presence of K,, and previously’.
MISFIT DISLOCATION
467
case q, and rb are the layer (rk,) spreads, respectively. incident beam divergence and the Ko2 doublet are considered as
a> Experimental
Details
using an X-ray Renninger Scans were performed beam provided by a divergent beam generator with a effective focal size of 50 p x 50 p, using a Cu target. The beam passes through a 115 cm long collimator and reaches. the sample mounted on a full circle Eulerian cradle with 5.8 min of arc divergence. Two samples were analyzed: sample 1 has a 0.05pm GaAs buffer layer grown by VCE (Vacuum Chemical Epitaxy)’ on a Si[OOl] substrate cut 4’ off towards [llO], at a temperature of 450°C with a low growth rate (-0.0025 &min). The sample was then annealed at 700°C for 10 min. Sample 2 has a 1.2~ GaAs second layer grown on top of the first one with a growth rate of 1.2 pm/h and temperature of 680°C.
Results and Discussion The RS measurements were carried out using the forbidden 002 substrate Si reflection as the primary and [l lo] as the reference vector (1$=0). The LS hybrid MD case studied involves the IfI,> secondary reflection in the layer and the ill, coupling reflection in the substrate, and is represented by the MD path 1 i 1,+i 11s. Fig. 3 shows the same small portions of several RS for the Si substrate of sample 2. The normal MD contributions from the substrate lattice are the strongest peak corresponding to the 111,+111, MD path. The position of this peak is used as a reference_ -and, - the peak in its right side is the contribution of the 351 353 four-beam case which is not important in this work. The other peak at the left side, is the LS hybrid MD contribution. In Fig. 3.~ the experimental RS for sample 2 is shown. The MD theory (Eq.3) already used to explain the normal and the SL hybrid peak does not provide a good fit with the LS peak, neither to the position nor to the profile, as one can see in Fig. 3.a when compared with Fig. 3.~. It should be noted that sample 2 had been characterized beforehand’ so, we used perpendicular and parallel lattice parameters, layer and substrate mosaic spreads and relative tilt in the fitting program. Thus, it vas necessary to modify the theory to reproduce the observed peak. This was done by taking into account the changes in the secondary beam direction due to the misorientation of the mosaic blocks, as expressed in Eq. 4. Using this equation in the fitting program, the simulated LS peak in Fig. 3.b shows a better fit with the LS experimental peak (Fig. 3.~). The LS simulated profiles n Fig. 3 are defined by the convolution between the beam divergence and the hybrid path given by Eq. 3 or Eq. 4. The secondary beam involved in the LS hybrid case :rosses the interface at a small angle (5) on the order of 1.6” in on-cut substrate samples. Fig. 4 shows the
b)
lo%-5 Phi
(dec$
I
Fig. 3: 002 Si (substrate) RS for sample 2. Simulated RS using a) Eq. 3 and b) Eq. 4 are shown as well as c) the experimental RS.
secondary beam path length inside the layer as a function of the depth (x) in which it is generated. The transmission of the beam scattered by this hybrid MD path can be written as
A(x/l)
(6)
=
where T and CL,are the thickness and the linear absorption coefficient of the layer, respectively. The 5 angle for a particular LS path is calculated by (7)
sin<=
A&,-r
where n is the normal to the sample surface. The asymmetry between the secondary beam and the sample surface makes the contributions generated closer to the surface be strongly absorbed in comparison with that generated closer to the interface. This effect can be seen in
Incident Beam
Primary
I
I I
Secondor)
Beam
I
Beam
Fig. 4: Scheme of the surface secondary inside the layer.
beam path length
468
INTERFACIAL
Vol. 88, No. 6
MISFIT DISLOCATION
400 1
(2)
Fig. 5: Behavior of A(x/T) for different 5 angles: a) 4.4”, b) 1.8” and c) 0.6”. In the calculations pI=402cm-’ and T=l,Zpm.
Fig. 6: 002 Si (substrate) RS. a) Simulated LS peaks with all(I) = 5 583A and a,,(‘) = 5.663A. Experimental scans for sample 2: b) without and c) with an external bending moment. d) Experimental scan for sample 1.
Fig. 5 which shows the plot of A(x/T) versus x/T. Due to the substrate miscut angle in our sample (4’ off towards [l lo] ), the secondary beam scattered by the hybrid h4D paths lil,+ill, and iil,+lll, cross the interface at 5=4.4” and t= 1.8”, respectively, Fig. 5 also shows that the intensity scattered by these paths should carry contributions from different depths in the layer. Consequently, if the dislocation density changes in depth inside the layer, the LS peaks due to these paths should have their positions sligthly shifted (144flSarcsec in our measurements) in the RS. The absorption characteristics associated with the of the LS peak position to cl,, high sensitivity measurements’ make this peak extremely useful to analyze thin layers and interfaces. Experimental RS for sample 1 depicted in Fig. 6.d shows that the LS peak could be detected in the same intensity scale as sample 2. However, its position is significantly shifted with respect to that of the thick layer shown in Fig. 6.b. Our fitting program was able to simulate the LS positions in samples as shown in Fig. 6.a, by using al (‘I=5 583A and a11(2)=5.663Afor thin and thick GaAs layers, respectively. Then, the interfacial dislocation densities determined from these values will be different in each case p%p(2). Considering all dislocations as essentially 60“ type, the modulus of the Burgers vector along the interface is a,,,/J2 = 4.0A giving rise to p(‘)=1.40x106/cm and p’*)=2.14x106/cm. Since the critical value for inversion of lattice curvature is pc=2.05x106/cm, the measurements indicate’ that the samples are bent in opposite directions (p”’ < pc < p”’ ). Sample 1 is convex to the layer surface (layer under compressive stress) while sample 2 is concave (layer under tensile stress). In the GaAs/Si system, it is well known2 that the stress generated to accommodate lattice mismatch has an opposite direction to that generated by the difference in the thermal expansion
coefficients of the two materials. Since thick layers allow misfit relaxation, thick and thin layers show inverse curvature radii as it was concluded from our results. This application of the LS hybrid MD method, clearly shows the potential of the method in the characterization of heteroepitaxial structures including the reasonable thin layers (500 A). An additional experiment was performed using sample 2 to check the LS peak position as a function of the applied stress. An external bending moment in an opposite direction to that provided by the difference in thermal expansion coefficients was applied to the sample 2. We observed that the expected shift in the peak position towards that of the thin layer peak did not occur instead, the split of both the layer and the buffer LS peaks as shown in Fig. 6.c, was found. This effect is obtained even for the minimum value of the applied moment that is needed to fix the sample on the stress cell. If the stress is increased, the split shows no significant changes and all peaks are broadened. When the external moment is completely removed, the original RS is obtained. Otherwise, if the sample suffers several curvature inversion cycles or ultrasonic cleaning process, the split turns out to be permanent. Conclusions We have presented a method to analyze the misfit dislocation density and cohesion at heteroepitaxial interfaces based on the LS hybrid MD observed in the substrate RS. The MD theory was extended to account for the changes in the secondary beam direction due to the mosaic blocks scattering. This extension is done through Eq. 4. This was very important to allow the simulation of the LS hybrid peak position and profile and always will be
Vol. 88, No. 6
INTERFACIAL MISFIT DISLOCATION
important when one simulates heteroepitaxial structures in which the layer has a mosaic spread bigger than the substrate one. In this case, rk = 270 set of arc x t-l, = 16 set of arc and, even with this difference, the al measured by using the LS position has enough precision to analyze the stress states of the epitaxial and buffer layers. The absorption involved in the hybrid MD path provides information about the misfit dislocation density inside the layer. The different LS peak positions measured for MD paths with different 5 crossing angles (4.4” and 1.8”) show that the misfit dislocation density is increasing from the interface towards the layer surface. The investigation of the dislocation density gradient with this method will be carried out in detail in a forthcoming paper. The buffer layer characterized in this work is 500 A thick however, thinner layers can be analyzed once the illuminated area is increased. Our results indicate that the degree of cohesion is bigger in the substrate-buffer layer interface than in the buffer-epilayer one since, when the
469
stress due to the difference in the thermal expansion coefficients is compensated by the external bending moment, one can observe the LS buffer layer peak. It has been demonstrated, for the first time that, when the heteroepitaxial structure repeatedly suffers a mechanical stress, as in a fatigue process, the cohesion between the epilayer and the buffer layer diminishes until the stress induced by the epilayer growth has ceased.
Acknowledgements
The authors would like to thank M.M.G. de Can&ho for supplying the samples used in this work; S.L. Games for technical assistance. We also acknowledge the financial support from the Brazilian Agencies FAPESP, CNPq and FAEPRTNICAMP.
References
[1] S.N.G. Chu, A.T. Macrander, K.E. Strege and W.D. Johnston Jr., J. Appl. Phys., 57 (2), 249 (1985).
[6] S.L. MorelhHo, L.P. Cardoso, J.M. Sasaki and M.M.G. de Carvalho, J. Appl. Phys., 70 (5), 2589 (1991).
[2] W.Stolz, Y. Horikoshi and M. Naganuma, Jpn. J. Appl. Phys. 27 (6), Lll40 (1988). [3] B.J. Isherwood, B.R. Brown, and M.A.G.Halliwell, J. Crystal Growth 54, 449 (1981).
[7] S.L. Morelha and L.P. Cardoso, Mat. Res. Sot. Symp. Proc., 262, 175 (1992).
[4] S.L. Morelh& L.P. Cardoso, J.M. Sasaki, and A.C. Sach, Defect Control in Semiconductors, edited by K. Sumino (Elsevier, North Holland, 1990) p. 1117.
[8] S.L. Morelh8o and L.P. Cardoso, J. Appl. Phys. 73 (9), (1993).
[5] S.L. MorelhHo and L.P. Cardoso, J. Crystal Growth, 110,543 (1991).
[9] M.A. Cotta and M.M.G. de Carvalho, J. Appl.Phys. 69 (2) 732 (1991).
0038-1098/93$6.00+.00 Pergamon Press Ltd
ANALYSIS OF INTERFACIAL MISFIT DISLOCATION BY X-RAY MULTIPLE DIFFRACTION
S. L. Morelhfio
and L.P. Cardoso
Institute de Fisica - UNICAMP, CP 6165, 13083-970, Campinas, SP, Brazil (Received 1 June 1993 by C.E.T. GonGalves da Silva) (in revised form August 3, 1993)
We have developed a new method to analyze the stress state of heteroepitaxial systems using X-ray multiple diffraction (MD). A fitting program extends the MD theory for mosaic crystals to provide the position and profile of the normal and hybrid MD peaks. We use surface secondary beams in order to achieve high resolution in intensity and peak position. These conditions together with the absorption involved in the LS hybrid reflections enable us to test the stress state of the layer by determining the misfit dislocation and the degree of cohesion between the buffer and epitaxial layers. Here, the method was applied in the analysis of thin (SOOA)and thick (1.2l.un) GaAs layers grown by Vacuum Chemical Epitaxy (VCE) on Si (001).
Introduction
In systems such as GaAs/Si in which the nominal lattice mismatch presents a high value (4%) the layer thickness plays an important role in the misfit relaxation process which occurs through the dislocation formation. X-ray diffraction techniques are used to monitor this process by measuring either asymmetrical reflections’ or symmetrical reflections together with the curvature radius’ in order to obtain the misfit dislocation density. In comparison with these rocking curve techniques, the X-ray multiple diffraction (MD) technique presents particular three beam cases (incident, primary and secondary) in which the secondary beams are diffracted almost parallel to the sample surface. These surface secondary beams are suitable for measuring lattice mismatch parallel to the interface layer/substrate since they are diffracted under conditions of extreme asymmetry. X-Ray MD applied to the analysis of epilayered semiconductor materials, shows hybrid MD’s features observed together with the normal MD one$-‘. Hybrid MD involving substrate and layer (SL) or layer and substrate [LS) paths have been observed in the Renninger Scans :RS)? Recently”‘, a new method of characterizing leteroepitaxial structures using the SL hybrid MD peak &ich appears in the layer RS was proposed. GaAs/Si ramples with different layer thicknesses, in the range of 0.6 Am to 2.8 pm, were analyzed as an application of the nethod. However, the characterization of thin layers ( - 500 due to the low intensity of the RS 4) was impossible leaks. On the other hand, it has also been observed that the ,S hybrid peak is measurable in the substrate RS even for hin layers, although its position and profile cannot be :xplained by the above mentioned method. In this work, we have modified the MD theory for 465
mosaic crystals to account for the directions of the secondary beam scattered by each mosaic block within an epitaxial layer. The modified simulation program was used to determine the misfit dislocation density from a1 values measured by LS peak position in the substrate RS. The misiit dislocation density was analyzed in two GaAslSi samples; one with just a thin (500A) buffer layer and other with a 1.2pm epilayer grown by VCE on top of the buffer. The degree of cohesion between epilayer and buffer was investigated by applying an external bending moment in order to compensate the stress caused by the epilayer growth. The absorption involved in the surface secondary beam propagation is also analyzed as a function of the grazing angle at which the surface beam crosses the interface since this angle should select contributions stemming from different depths inside the layer.
Theory In this work, a mosaic crystal is described by an isotropic and gaussian mosaic block distribution (11 being the mosaic spread) in which the fraction of the total number (NJ of illuminated blocks with reciprocal lattice vector H’, oriented inside the solid angle di2 is given by
As shown in Fig. 1, H’, is misoriented of A from the reciprocal lattice vector B, which represents the average distribution direction. We assume that a well-collimated, nearly monochromatic beam of X-rays is incident on the mosaic
466
INTERFACIAL MISFIT DISLOCATION Ewold
Sphere
Vol. 88, No. 6
angle describes the possible H’, positions on the ring for a fixed incident beam. The two coordinate systems shown in Fig. 2 are very useful in the above mentioned calculation. The unit vectors I;,. c, and 6, describe the orthogonal coordinate system fixed at the substrate reciprocal lattice being i, and i, the directions of the reference vector6 and the H, vector, respectively. In this system, the incident beam wave vector is given by &,=-~-‘(cosw’cosg’~,+cosa,‘sinblC,+sinw’~,) while the H’, coordinates are (H,sinAcos& H,sinAsin& H,cosA). The other orthogonal system described by the unit vectors &, & and f3 has &=-hk, and the H’, coordinates are expressed as (H,cos~,~cos(P, H,co&+,sincp, H,sinS,,). According to Fig. 2, these coordinate systems are related through the rotation matrix A, where A’=R,(x)R,(xlZ-o’)R,(&). Therefore, the transformation between the H’, coordinates is given by
Fig. 1: Intersection ring in the reciprocal space showing the relative orientation of II’, as a function of A((cp)for all diffracting mosaic blocks.
distribution, making a n/2-w’ angle with II,, such that Bragg reflections occur from all mosaic blocks, with II’, oriented on the ring formed by the intersection of the Ewald sphere with the sphere of radius H,. This ring is represented in Fig. 1. The ring portion which contributes to the scattering is given by the mosaic distribution (Eq. 1). The angular width associated with the incident beam collimation and wavelength spread is assumed to be much larger than the width of a perfect crystal reflection curve, but is much smaller than the width (q) of the mosaic distribution. We wish to calculate the change in the reflected beam direction due to H’, misorientation. In conventional MD theory for mosaic crystals, the reflected beam direction is given by R,=H,+& and, to consider the change in this direction, H, will be replaced by H’,. The cp
Thus, the A misorientation ring as a function of cpis
of those H’, positions on the
WWKUXS ( cad c.0~6,~cuq
+ aid
air@,) . (2)
Under MD condition, the k, beam reflected by the secondary planes (H,) reaches the coupling planes (HJ in Bragg condition. The position and the protile of the RS peak corresponding to the contribution of this H,+H, MD path have already been simulated using the expression*
--
A@,’
--
At+’
(3)
where K is a constant related with the integrated reflectivity per unit volume of a small crystallite. q, and Q are the mosaic spread of the secondary and the coupling planes and they can be different since we are analyzing simultaneously the layer and substrate lattices. Using (2), the angular deviations from Bragg’s angles A0, for the secondary reflection and A0, for the coupling reflection can now be expressed as a function of cp. In order to consider the contribution of all blocks to the position and profile of the RS peaks, the expression (3) turns out to be
Fig. 2: Coordinate
systems Fe<
5
describe H’, with
respect to the substrate lattice (II,, II,, h,) and to the incident
beam (Q,, Q2,&,). The reference vectorAdirection is given by I;, and 0, lies on the plane defined by b, and 0,.
At&)
= 0,
_ *(
-%g4)
(5)
Vol. 88, No. 6
INTERFACIAL
In the LS hybrid and substrate (Q,) mosaic The influence of presence of K,, and previously’.
MISFIT DISLOCATION
467
case q, and rb are the layer (rk,) spreads, respectively. incident beam divergence and the Ko2 doublet are considered as
a> Experimental
Details
using an X-ray Renninger Scans were performed beam provided by a divergent beam generator with a effective focal size of 50 p x 50 p, using a Cu target. The beam passes through a 115 cm long collimator and reaches. the sample mounted on a full circle Eulerian cradle with 5.8 min of arc divergence. Two samples were analyzed: sample 1 has a 0.05pm GaAs buffer layer grown by VCE (Vacuum Chemical Epitaxy)’ on a Si[OOl] substrate cut 4’ off towards [llO], at a temperature of 450°C with a low growth rate (-0.0025 &min). The sample was then annealed at 700°C for 10 min. Sample 2 has a 1.2~ GaAs second layer grown on top of the first one with a growth rate of 1.2 pm/h and temperature of 680°C.
Results and Discussion The RS measurements were carried out using the forbidden 002 substrate Si reflection as the primary and [l lo] as the reference vector (1$=0). The LS hybrid MD case studied involves the IfI,> secondary reflection in the layer and the ill, coupling reflection in the substrate, and is represented by the MD path 1 i 1,+i 11s. Fig. 3 shows the same small portions of several RS for the Si substrate of sample 2. The normal MD contributions from the substrate lattice are the strongest peak corresponding to the 111,+111, MD path. The position of this peak is used as a reference_ -and, - the peak in its right side is the contribution of the 351 353 four-beam case which is not important in this work. The other peak at the left side, is the LS hybrid MD contribution. In Fig. 3.~ the experimental RS for sample 2 is shown. The MD theory (Eq.3) already used to explain the normal and the SL hybrid peak does not provide a good fit with the LS peak, neither to the position nor to the profile, as one can see in Fig. 3.a when compared with Fig. 3.~. It should be noted that sample 2 had been characterized beforehand’ so, we used perpendicular and parallel lattice parameters, layer and substrate mosaic spreads and relative tilt in the fitting program. Thus, it vas necessary to modify the theory to reproduce the observed peak. This was done by taking into account the changes in the secondary beam direction due to the misorientation of the mosaic blocks, as expressed in Eq. 4. Using this equation in the fitting program, the simulated LS peak in Fig. 3.b shows a better fit with the LS experimental peak (Fig. 3.~). The LS simulated profiles n Fig. 3 are defined by the convolution between the beam divergence and the hybrid path given by Eq. 3 or Eq. 4. The secondary beam involved in the LS hybrid case :rosses the interface at a small angle (5) on the order of 1.6” in on-cut substrate samples. Fig. 4 shows the
b)
lo%-5 Phi
(dec$
I
Fig. 3: 002 Si (substrate) RS for sample 2. Simulated RS using a) Eq. 3 and b) Eq. 4 are shown as well as c) the experimental RS.
secondary beam path length inside the layer as a function of the depth (x) in which it is generated. The transmission of the beam scattered by this hybrid MD path can be written as
A(x/l)
(6)
=
where T and CL,are the thickness and the linear absorption coefficient of the layer, respectively. The 5 angle for a particular LS path is calculated by (7)
sin<=
A&,-r
where n is the normal to the sample surface. The asymmetry between the secondary beam and the sample surface makes the contributions generated closer to the surface be strongly absorbed in comparison with that generated closer to the interface. This effect can be seen in
Incident Beam
Primary
I
I I
Secondor)
Beam
I
Beam
Fig. 4: Scheme of the surface secondary inside the layer.
beam path length
468
INTERFACIAL
Vol. 88, No. 6
MISFIT DISLOCATION
400 1
(2)
Fig. 5: Behavior of A(x/T) for different 5 angles: a) 4.4”, b) 1.8” and c) 0.6”. In the calculations pI=402cm-’ and T=l,Zpm.
Fig. 6: 002 Si (substrate) RS. a) Simulated LS peaks with all(I) = 5 583A and a,,(‘) = 5.663A. Experimental scans for sample 2: b) without and c) with an external bending moment. d) Experimental scan for sample 1.
Fig. 5 which shows the plot of A(x/T) versus x/T. Due to the substrate miscut angle in our sample (4’ off towards [l lo] ), the secondary beam scattered by the hybrid h4D paths lil,+ill, and iil,+lll, cross the interface at 5=4.4” and t= 1.8”, respectively, Fig. 5 also shows that the intensity scattered by these paths should carry contributions from different depths in the layer. Consequently, if the dislocation density changes in depth inside the layer, the LS peaks due to these paths should have their positions sligthly shifted (144flSarcsec in our measurements) in the RS. The absorption characteristics associated with the of the LS peak position to cl,, high sensitivity measurements’ make this peak extremely useful to analyze thin layers and interfaces. Experimental RS for sample 1 depicted in Fig. 6.d shows that the LS peak could be detected in the same intensity scale as sample 2. However, its position is significantly shifted with respect to that of the thick layer shown in Fig. 6.b. Our fitting program was able to simulate the LS positions in samples as shown in Fig. 6.a, by using al (‘I=5 583A and a11(2)=5.663Afor thin and thick GaAs layers, respectively. Then, the interfacial dislocation densities determined from these values will be different in each case p%p(2). Considering all dislocations as essentially 60“ type, the modulus of the Burgers vector along the interface is a,,,/J2 = 4.0A giving rise to p(‘)=1.40x106/cm and p’*)=2.14x106/cm. Since the critical value for inversion of lattice curvature is pc=2.05x106/cm, the measurements indicate’ that the samples are bent in opposite directions (p”’ < pc < p”’ ). Sample 1 is convex to the layer surface (layer under compressive stress) while sample 2 is concave (layer under tensile stress). In the GaAs/Si system, it is well known2 that the stress generated to accommodate lattice mismatch has an opposite direction to that generated by the difference in the thermal expansion
coefficients of the two materials. Since thick layers allow misfit relaxation, thick and thin layers show inverse curvature radii as it was concluded from our results. This application of the LS hybrid MD method, clearly shows the potential of the method in the characterization of heteroepitaxial structures including the reasonable thin layers (500 A). An additional experiment was performed using sample 2 to check the LS peak position as a function of the applied stress. An external bending moment in an opposite direction to that provided by the difference in thermal expansion coefficients was applied to the sample 2. We observed that the expected shift in the peak position towards that of the thin layer peak did not occur instead, the split of both the layer and the buffer LS peaks as shown in Fig. 6.c, was found. This effect is obtained even for the minimum value of the applied moment that is needed to fix the sample on the stress cell. If the stress is increased, the split shows no significant changes and all peaks are broadened. When the external moment is completely removed, the original RS is obtained. Otherwise, if the sample suffers several curvature inversion cycles or ultrasonic cleaning process, the split turns out to be permanent. Conclusions We have presented a method to analyze the misfit dislocation density and cohesion at heteroepitaxial interfaces based on the LS hybrid MD observed in the substrate RS. The MD theory was extended to account for the changes in the secondary beam direction due to the mosaic blocks scattering. This extension is done through Eq. 4. This was very important to allow the simulation of the LS hybrid peak position and profile and always will be
Vol. 88, No. 6
INTERFACIAL MISFIT DISLOCATION
important when one simulates heteroepitaxial structures in which the layer has a mosaic spread bigger than the substrate one. In this case, rk = 270 set of arc x t-l, = 16 set of arc and, even with this difference, the al measured by using the LS position has enough precision to analyze the stress states of the epitaxial and buffer layers. The absorption involved in the hybrid MD path provides information about the misfit dislocation density inside the layer. The different LS peak positions measured for MD paths with different 5 crossing angles (4.4” and 1.8”) show that the misfit dislocation density is increasing from the interface towards the layer surface. The investigation of the dislocation density gradient with this method will be carried out in detail in a forthcoming paper. The buffer layer characterized in this work is 500 A thick however, thinner layers can be analyzed once the illuminated area is increased. Our results indicate that the degree of cohesion is bigger in the substrate-buffer layer interface than in the buffer-epilayer one since, when the
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stress due to the difference in the thermal expansion coefficients is compensated by the external bending moment, one can observe the LS buffer layer peak. It has been demonstrated, for the first time that, when the heteroepitaxial structure repeatedly suffers a mechanical stress, as in a fatigue process, the cohesion between the epilayer and the buffer layer diminishes until the stress induced by the epilayer growth has ceased.
Acknowledgements
The authors would like to thank M.M.G. de Can&ho for supplying the samples used in this work; S.L. Games for technical assistance. We also acknowledge the financial support from the Brazilian Agencies FAPESP, CNPq and FAEPRTNICAMP.
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