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Epitaxial growth of PbTe on (111)BaF2 and (100)GaAs
Superlattices
and Microstructures,
EPITAXIAL
591
Vol. 4, No. 415, 1988
GROWTH OF PbTe ON (1111BaF2 AND
(100)GaAs
H.Clemens, H.Krenn, B.Tranta, P.Ofner and G.Bauer Institut ftir Physik,Montanuniversitat Leoben, Austria 16 August 1987) (Received The growth of PbTe on cleaved (111)BaF and polished (100)GaAs substrates has been studied & reflection high the nuclea-energy electron diffraction. For (111)BaF tion orientation is always (111) whereas $or (100)GaAs both (111) and (100) orientations occur. Due to the difference in thermal expansion coefficients between PbTe and GaAs, for growth temperatures of about 300 OC, microcracks appear at room temperature. The epitaxial layers were examined by X-ray diffraction and from an analysis of the observed line-shapes a layer roughness is deduced.
1 . INTRODUCTION
The cubic IV-VI compound PbTe which crystallizes in the NaCl structure has been deposited epitaxially so far mainly on alkali halides, (NaCl and KBr), on BaF2 and on PbTe.i Whereas excellent carrier mobilities of epitaxial grown PbTe films on BaF have been achieved, the drawback of t & is substrate are cleavage steps which are formed for the usual(ll1) substrate orientation. The advantage of BaF is the fact that electrical and opt 1 cal properties of epitaxial films can be investigated easily. For a PbTe substrate which is always used for PbTe based laser structures, the high carrier concentration within the substrate makes the analysis of the properties of the epitaxial films difficult. Therefore an insulating semiconductor material which is transparent in the midinfrared region seems to be an ideal candidate for PbTe epitaxy. CdTe has a lattice constant mismatch with PbTe of about0.3%.However,bulk CdTe crystals with small dislocation densities are not readily available. GaAs,which has been used extensively as a substrate material for the growth of CdTe,seems also to be a reasonable substrate material for PbTe and offers the advantage of nearly dislocation free wafers. Recently Yoshino et al.' have grown PbTe on GaAs using molecular beam epitaxial growth. It is the purpose of this paper to compare the growth modes of PbTe on BaF2 and GaAs using in-situ RHEED analysis (reflection high energy electron diffraction).
0749-6036/88/040591+
06 $02.00/O
2. RHEED PATTERNS (i) PbTe/BaF2: The lattice constant misfit between PbTe and BaF2 at room temperature is about 4%, whereas the thermal expansion coefficients do not differ substantially between room tempergture and the growth temperature (Ts=300 Cl. It is well known that the initial growth of PbTe on BaF starts three-dimensional, i.e. in for J of islands. These islands merge together for film thicknessesin @.xCeSS of 1000 8. Fig.1 shows a sequence of RHEED patterns taken in the [O'Tl] azimuth, indicating a rather Smgoth BaF surface after heating at 500 C for 16 min (Il*h*s). In the initial stages the PbTe overqrowth is shown in the central part of this figure. (111) diffraction spots appear for this [Oil! azimuth and the WEED pattern is w&l described by the corresponding cross section through the reciprocal lattice. For lay r thicknesses in excess of about 3000 fi, a streaked pattern appears. The growth rate is about 2pm/b. This pattern does not change if the PbTe flux is interrupted by closing the shutter of this furnace for several seconds. (ii) PbTe/GaAs: GaAs is an attractive substrate material for PbTe films, since semiinsulating crystals are readily available. All substrates were (100) oriented with 2 Off. After a degrease procedure (rinsing in trichlorethylene, acetone and methanol) the substrate ia then etched in a solution of H2S04:
0 1988 Academic Press Limited
592
.%JPerhttlces
and Microstructures,
Vol. 4, No. 415, 1988
b)
growth Fig.1: (a) RHEED patterns durin of PbTe on (lll)BaF, (35keV,pll-7 azimuth). Left: BaF, substrate prior to deposition. Middle: initial stage of PbTe overgrowth. Right: final stage of growth (lum layer thickness). (b) Corresponding cross sections through the reciprocal lattice. (c) Orientation of the PbTe film in respect to the substrate.
: H 0 (4:l:l at 60°C) for 5 minuHO I&? Thareafter, it is rinsed in deionized water and blow dried with pure nitrogen gas. For the epitaxial growth a modified RIBER 1000 system with a samole load lock was used. The pressure in the growth chamber during the lead salt growth was 5x10-'mbar. The surface oxide desorption on GaAs was monitored by observing the changing RHEED pattern during the substrate preheating procedure. RHEED pattern taken in a [liO] azimuth with respect to the GaAs substrate are shown in Fig.2 (Ilhs). The dentral and r.h.s. part of this figure show the pattern for PbTe overgrowth for substrate temperatures around 300°C and growth rates of 2pm/b. As already pointed out by Yoshino et al.' the growth of PbTe on (100) GaAs exhibits complicated features. In the initial stages of the growth, a (111) layer is deposited on (100)GaAs resembling the CdTe epitaxy on the same substrate. However, as the growth proceeds, a change of the orientation of the PbTe film to a (100) surface normal occurs. This may be related to a solid phase recrystallization which was observed by Yoshino et al. The RHEED pattern shown in Fig.2, for PbTe thickness of about 1000 8 indeed exhibits several orientations. (i.) (111)PbTe layers parallel to (100) GaAs for the orientation [111]PbTeI 1 [l TojGaAs.
Fig.2: (a) RHEED patterns during deeosition of PbTe on (100)GaAs (35keV, [110] azimuth). Left: GaAs substrate Middle: initial stage of PbTe overgrowth. Right: lum layer thickness. (b) Corresponding cross sections through the reciprocal lattice. (c) Recovered film orientations during the growth.
(iii) as (ii) but with the orientation [lOO]PbTeI 1 [liO]GaAs. With increasing film thickness the (111) spots disappear and just the (100) spots remain, but in both orientations. Also the streaked pattern, shown in Fig.2 exhibit both orientations. Figure 3a shcws a phase contrast micrograph of a PbTe film on GaAs which is approximately 2000 8 thick. If the layer thickness increases further microcracks appear as shown (Fig.3b). In contrast to the situation CdTe/GaAs for the growth of PbTe on GaAs the difference in thermal expansion coefficients is much larger which makes this type of epitaxy rather difficult. Whether (111) spots occur or not depends apparently on the substrate preparation. For PbTg/GaAs the thermal misfit (between 300 C and room temperature) amounts to 4x10m3 whereas for CdTe/GaAs this value is about 4.4~10~~. The expansion coefficients were taken from Refs. 4,5. Also for PbTe on CdTe the thermal misfit is rather large (4.5x10-3).
Superlattices
and
Microstructures,
Vol.
4, No.
4/5,
593
1988
n 515’
(ZOO)-CuK.,
105 t lobIn
-Theory 2750~
2755.
- --. Expenment
2760’
Fig.3 : Phase contrast micrograph of a 2000 1 thick PbTe film on (lOO)GaAs.
2600’
28.00’
2700’ 20
29 00’
-
Fig.Qa: (200) Bragg reflection of a (100)PbTe bulk sample in a logarithmic intensity scale. The shape is Lorentsian, the angular broadening comes about mainly due to the exponential absorption of X-rays in bulk PbTe. Fig.3b: Appea ante of microcracks for thick ( 4000 li1 PbTe layers on GaAs.
3.
X-RAY
DIFFRACTION
For a PbTe layer of about340 8 thickness deposited on (100)GaAs the (200) Bragg diffraction intensity wan monitored for CuUa radiation with a resolution of 0.016. Since the number of lattice planes which contributes to the total diffracted intensity is finite (approximately 55 lattice planes) the intensity exhibits as a function of diffraction angle resolvable intensity oscillations and broadening. In Fig.4 a comparison between the diffracted intensities for a PbTe film on Gags and a bulk PbTe sample is shown. The count rate in both plots extende to 2 and 4 orders of magnitude, respectively. The PbTe bulk diffraction peak is described by a functional dependence of Lorentzian shape: Imax
I(0) =
10'
2Q-
Fig.4b: (200) Bragg reflection of a single layer of PbT on (100) GaAs with thickness of D=340 8 (0)- The calculated data are either for a surface rough ess of r*=45 2 (full lines) or w (broken'lines) . r*=O 0
(1) l+ c
Q-0, (AQ
1' I
1.04
where 0 corresponds to the Bragg angle A0 is the of maxi&m intensity I half width of this cur?%x'Instead of an
exponent one in the denominator the best fit was obtained for 1.04. The rather perfect fit with a Lorentzian indicates that the exponential data are not influenced by instrumental effects causing deteriorations of the line shape.
594
Superlattices
and Microstructures,
Vol. 4. No. 415, 1988
By an inverse Fourier transformation of this Lorentzian Bragg diffract-on, the following dependence can be derived: A(i)=Ao.exp(
-i/i,)
(2)
where A, is related to the amplitude corresponding to maximum count rate = 2.7x105s-') i corresponds (for I to pen%?ation depth and denotes the number of lattice planes i where the amplitude is reduced to l/e. For the thin film sample the calculated intensity is obtained from N
I(O)= 1 Aiexp(4ri i=l
d.sin(B) i Z 2-y-21) j=l 1% +k-+1
where N is the total number of lattice planes (in Fig.5 N=55) and (h,k,Z) are the Miller indices and dj=do is the lattice constant. However, such a fit corresponds to the boxcar function (sin z/z) if d. is constant and A independent of i. $herefore it is necessary to include A(i) according to Eq.2 and also a roughness describing the fact that the factor r PbTe filg is not flat on the scale of lattice planes. This fact is included in the fit by replacing for A(i) in Eq.2 A, by Ao(a) =(+)2
C&=0,...,
r.
)
0
and Ao(il)= 1
(R=ro+l.....N
)
The full curve corresponds to such a fit used for r =7 (which corresponds to a roughness"of 45 8), see Fig.4b. In addition it is necessary to use for the PbTe film a slightly different lattice constant in growth direction as evideneced by.the shift of the maxito a ma by about 0.05 correspondin tetragonal distortion ~=2X10- 9 . This distortion is not equivalent to this resulting from the lattice constant misfit of PbTe and GaAs which would cause much higher E. The fit uses the fact that the penetration depth of CuKcr radiation in PbTe is finite and for i about 370 was obtained for bulk PbTe. 8 owever, the best fit for the film sample requires ai which is approximately equal to the'actual number of lattice planes contributing to the diffraction,i = 47. In Fig.5, for the same PbTe'film on GaAs the (222) Bragg reflection is shown in a logarithmic intensity plot vs Bragg angle. From the difference of the count rates of Fig.4b and Fig.5 we estimate that the ratio between the
2
490
50"
2Q(222) Bragg reflection Of the Fig.5: PbTe film on (2OO)GaAs. The experimental data are fit with the same parameters as those used for Fig.lb with r;=45 8. The intensity scale is however,by a factor of 50 smaller.
(100) oriented PbTe to that exhibiting orientation is about 5O:l. These data were taken since the RHEED pattern showed the presence of (111) oriented PbTe. For the fits in Fig.4a and b indicated by the full and broken lines either a roughness corresponding to r,=7 and one corresponding to r =0 was used. The fit with r =7 yields ?he correct intensities Oup to a sattelite index of 5 or 6. We would like to point out that the calculated data fit the experimental within the accuracy of percents over the whole range of intensities. In order to check the spatial variation of the diffraction pattern the sample was rotated by 90' and shifted by about 2rnm (focal diameter of X-rays on sample surface (lmm)). The resulting diffraction data are shown in Fig.6 and are nearly identical which proves the lateral homogeneity of the growth. Whether the amount of surface roughness as determined from this procedure is correlated to the degree to which mixed (100) and (111)PbTe oriented grains or domains occur, needs further investigations. Using a X-ray diffracted intensity scale which encompasses 3 orders of magnitude, the accuracy of the determination of the surface roughness depends on the number of sattelite peaks which can be resolved. E.g. for (111)
Superlattices and Microstructures, Vol. 4, No. 415, 1988
10'
21"
280 20
20 Fig.6: As Fig.4b for the
340
8
PbTe
film deposited on GaAs. The full and broken line correspond to experimental data taken from two different spots on the film surface as indicated in the insert.
sattelite peaks of the order 10 the ultimate resolution of the roughness determination is estimated to be 1% for a total film thickness of about 1000 8. Of course this limit is determined by the available dynamic range of the count rates corresponding to scattered X-ray intensity. In order to show the influence of a sufficiently thick buffer layer with a lattice constant which is much closer to that of PbTe d-6.462 % than that of GaAs t&5.65325 g1 we have grown a sandwich structure PbTe/CdTe/GaAs (CdTe:cl=6.2409). For two PbTe films of comparable thickness, the intensity oscillations as a function of Bragg angle 28 are shown in Figs.7a and b. Experimentally,it is obvious that with increasing film thickness the total roughness of PbTe cmGaAs does not decrease but rather increases. For the case of the lum thick (100)CdTe buffer layer on (lOO)GaAs, the roughness of the PbTe film is much smaller which can be deduced by inspection of Figs.7a and b. Despite the fact that the intensity oscillationuin Fig.7b are not completely represented by the fit, such an analysis lends itself to a determination of the elastic strain in the two layers. With the intermediate CdTe layer apparently not only the surface roughness is reduced but the count rates on both sides of the main peaks
-
Fig.7a: (200) Brag reflection of a PbTe film (D=1450 ii) deposited on (100)GaAs. Experimental data: ?? , fit: full line with a surface roughness of 130 s.
270
280 20
-
Fig.7b: As Fig.7a but for a PbTe film (D=1250 w) deposited on a lwrn thick (100) oriented CdTe buffer on (100) GaAs. The data are fit with a roughness r*=80 R, a strain profile for E* as i%icated in the insert is used for the calculation.
of equally indexed sattelite peaks are different. For the strain profile-fit a step like gradient in E* was introduced with the following values: cL (PbTe)=8xlO-* and Ed (CdTe)=4x10-4.
596
Superlattices
Thus the lum thick CdTe layer reduces the total strain exerted by the GaAs substrate on the top layer. It is Important to note, that an attempt to detect (111) oriented grains in the film shown in Fig.7b turned out to be‘unsuccesful. Within the noise limit (~8 counts/set) no (222) Bragg reflection was detected. Thus from the comparison of Figs. 7a and 7b and the absence of (111) oriented PbTe grains it can be concluded that Is seems to be easier to grow single crystalline (1OO)PbTe on (lOO)CdTe than on (100) oriented GaAs substrates. 4. CONCLUSION The I%pitaxial growth of PbTe on BaF yields perfect layers in which two dimsnsional growth is possible and rather thick films (several microns) can be grown. For the deposition of PbTe on GaAs, on the contrary, film thicknesses in excess of 4000 2 exhibit micro cracks if a substrate temperature of about 300 OC is chosen. In addition, it seems to be difficult to achieve an overlayer growth with a single orientation.
and Microstructures,
Vol. 4, No. 415, 1988
ACKNOWLEDGEMENTS We thank K.Ploog and A.Fischer for a vast amount of information on MBE growth procedures, J. Oswald for the electronic system used in conjunction with the X-ray apparatus, D.Schikora for helpful discussions and H.Ulrich for expert technical assistance. This work was supported by "Fonds zur Forderung der wissenschaftlichen Forschung" (P5321) and Jubilaumsfonds der Nationalbank (2697) Austria.
REFERENCES 1) H.Holloway, in "Physics of Thin Films", Eds. G.Hass and M.H.Francombe (Academic, New York 1980), Vol.ll,p.l05. 2) J.Yoshino, M.Munekata and L.L.Chang, J.Vac.Sci.Technol.B5 (3), 683 (1987). 3) P.Pongratz, H.CGmens, E.J.Fantner and G.Bauer, Inst.Conf.Series z,Sect.7, 313 (1985). 4) Landolt-Bernstein, Vo1.17, Eds.K.H. Hellwege and O.Madelung (Springer, Berlin 1982). 5) J.S.Blakemore, J.Appl.Phys. 53, R123 (1982). 6) D.L.Partin,J.Electronic Materials 2, 493 (1984).
and Microstructures,
EPITAXIAL
591
Vol. 4, No. 415, 1988
GROWTH OF PbTe ON (1111BaF2 AND
(100)GaAs
H.Clemens, H.Krenn, B.Tranta, P.Ofner and G.Bauer Institut ftir Physik,Montanuniversitat Leoben, Austria 16 August 1987) (Received The growth of PbTe on cleaved (111)BaF and polished (100)GaAs substrates has been studied & reflection high the nuclea-energy electron diffraction. For (111)BaF tion orientation is always (111) whereas $or (100)GaAs both (111) and (100) orientations occur. Due to the difference in thermal expansion coefficients between PbTe and GaAs, for growth temperatures of about 300 OC, microcracks appear at room temperature. The epitaxial layers were examined by X-ray diffraction and from an analysis of the observed line-shapes a layer roughness is deduced.
1 . INTRODUCTION
The cubic IV-VI compound PbTe which crystallizes in the NaCl structure has been deposited epitaxially so far mainly on alkali halides, (NaCl and KBr), on BaF2 and on PbTe.i Whereas excellent carrier mobilities of epitaxial grown PbTe films on BaF have been achieved, the drawback of t & is substrate are cleavage steps which are formed for the usual(ll1) substrate orientation. The advantage of BaF is the fact that electrical and opt 1 cal properties of epitaxial films can be investigated easily. For a PbTe substrate which is always used for PbTe based laser structures, the high carrier concentration within the substrate makes the analysis of the properties of the epitaxial films difficult. Therefore an insulating semiconductor material which is transparent in the midinfrared region seems to be an ideal candidate for PbTe epitaxy. CdTe has a lattice constant mismatch with PbTe of about0.3%.However,bulk CdTe crystals with small dislocation densities are not readily available. GaAs,which has been used extensively as a substrate material for the growth of CdTe,seems also to be a reasonable substrate material for PbTe and offers the advantage of nearly dislocation free wafers. Recently Yoshino et al.' have grown PbTe on GaAs using molecular beam epitaxial growth. It is the purpose of this paper to compare the growth modes of PbTe on BaF2 and GaAs using in-situ RHEED analysis (reflection high energy electron diffraction).
0749-6036/88/040591+
06 $02.00/O
2. RHEED PATTERNS (i) PbTe/BaF2: The lattice constant misfit between PbTe and BaF2 at room temperature is about 4%, whereas the thermal expansion coefficients do not differ substantially between room tempergture and the growth temperature (Ts=300 Cl. It is well known that the initial growth of PbTe on BaF starts three-dimensional, i.e. in for J of islands. These islands merge together for film thicknessesin @.xCeSS of 1000 8. Fig.1 shows a sequence of RHEED patterns taken in the [O'Tl] azimuth, indicating a rather Smgoth BaF surface after heating at 500 C for 16 min (Il*h*s). In the initial stages the PbTe overqrowth is shown in the central part of this figure. (111) diffraction spots appear for this [Oil! azimuth and the WEED pattern is w&l described by the corresponding cross section through the reciprocal lattice. For lay r thicknesses in excess of about 3000 fi, a streaked pattern appears. The growth rate is about 2pm/b. This pattern does not change if the PbTe flux is interrupted by closing the shutter of this furnace for several seconds. (ii) PbTe/GaAs: GaAs is an attractive substrate material for PbTe films, since semiinsulating crystals are readily available. All substrates were (100) oriented with 2 Off. After a degrease procedure (rinsing in trichlorethylene, acetone and methanol) the substrate ia then etched in a solution of H2S04:
0 1988 Academic Press Limited
592
.%JPerhttlces
and Microstructures,
Vol. 4, No. 415, 1988
b)
growth Fig.1: (a) RHEED patterns durin of PbTe on (lll)BaF, (35keV,pll-7 azimuth). Left: BaF, substrate prior to deposition. Middle: initial stage of PbTe overgrowth. Right: final stage of growth (lum layer thickness). (b) Corresponding cross sections through the reciprocal lattice. (c) Orientation of the PbTe film in respect to the substrate.
: H 0 (4:l:l at 60°C) for 5 minuHO I&? Thareafter, it is rinsed in deionized water and blow dried with pure nitrogen gas. For the epitaxial growth a modified RIBER 1000 system with a samole load lock was used. The pressure in the growth chamber during the lead salt growth was 5x10-'mbar. The surface oxide desorption on GaAs was monitored by observing the changing RHEED pattern during the substrate preheating procedure. RHEED pattern taken in a [liO] azimuth with respect to the GaAs substrate are shown in Fig.2 (Ilhs). The dentral and r.h.s. part of this figure show the pattern for PbTe overgrowth for substrate temperatures around 300°C and growth rates of 2pm/b. As already pointed out by Yoshino et al.' the growth of PbTe on (100) GaAs exhibits complicated features. In the initial stages of the growth, a (111) layer is deposited on (100)GaAs resembling the CdTe epitaxy on the same substrate. However, as the growth proceeds, a change of the orientation of the PbTe film to a (100) surface normal occurs. This may be related to a solid phase recrystallization which was observed by Yoshino et al. The RHEED pattern shown in Fig.2, for PbTe thickness of about 1000 8 indeed exhibits several orientations. (i.) (111)PbTe layers parallel to (100) GaAs for the orientation [111]PbTeI 1 [l TojGaAs.
Fig.2: (a) RHEED patterns during deeosition of PbTe on (100)GaAs (35keV, [110] azimuth). Left: GaAs substrate Middle: initial stage of PbTe overgrowth. Right: lum layer thickness. (b) Corresponding cross sections through the reciprocal lattice. (c) Recovered film orientations during the growth.
(iii) as (ii) but with the orientation [lOO]PbTeI 1 [liO]GaAs. With increasing film thickness the (111) spots disappear and just the (100) spots remain, but in both orientations. Also the streaked pattern, shown in Fig.2 exhibit both orientations. Figure 3a shcws a phase contrast micrograph of a PbTe film on GaAs which is approximately 2000 8 thick. If the layer thickness increases further microcracks appear as shown (Fig.3b). In contrast to the situation CdTe/GaAs for the growth of PbTe on GaAs the difference in thermal expansion coefficients is much larger which makes this type of epitaxy rather difficult. Whether (111) spots occur or not depends apparently on the substrate preparation. For PbTg/GaAs the thermal misfit (between 300 C and room temperature) amounts to 4x10m3 whereas for CdTe/GaAs this value is about 4.4~10~~. The expansion coefficients were taken from Refs. 4,5. Also for PbTe on CdTe the thermal misfit is rather large (4.5x10-3).
Superlattices
and
Microstructures,
Vol.
4, No.
4/5,
593
1988
n 515’
(ZOO)-CuK.,
105 t lobIn
-Theory 2750~
2755.
- --. Expenment
2760’
Fig.3 : Phase contrast micrograph of a 2000 1 thick PbTe film on (lOO)GaAs.
2600’
28.00’
2700’ 20
29 00’
-
Fig.Qa: (200) Bragg reflection of a (100)PbTe bulk sample in a logarithmic intensity scale. The shape is Lorentsian, the angular broadening comes about mainly due to the exponential absorption of X-rays in bulk PbTe. Fig.3b: Appea ante of microcracks for thick ( 4000 li1 PbTe layers on GaAs.
3.
X-RAY
DIFFRACTION
For a PbTe layer of about340 8 thickness deposited on (100)GaAs the (200) Bragg diffraction intensity wan monitored for CuUa radiation with a resolution of 0.016. Since the number of lattice planes which contributes to the total diffracted intensity is finite (approximately 55 lattice planes) the intensity exhibits as a function of diffraction angle resolvable intensity oscillations and broadening. In Fig.4 a comparison between the diffracted intensities for a PbTe film on Gags and a bulk PbTe sample is shown. The count rate in both plots extende to 2 and 4 orders of magnitude, respectively. The PbTe bulk diffraction peak is described by a functional dependence of Lorentzian shape: Imax
I(0) =
10'
2Q-
Fig.4b: (200) Bragg reflection of a single layer of PbT on (100) GaAs with thickness of D=340 8 (0)- The calculated data are either for a surface rough ess of r*=45 2 (full lines) or w (broken'lines) . r*=O 0
(1) l+ c
Q-0, (AQ
1' I
1.04
where 0 corresponds to the Bragg angle A0 is the of maxi&m intensity I half width of this cur?%x'Instead of an
exponent one in the denominator the best fit was obtained for 1.04. The rather perfect fit with a Lorentzian indicates that the exponential data are not influenced by instrumental effects causing deteriorations of the line shape.
594
Superlattices
and Microstructures,
Vol. 4. No. 415, 1988
By an inverse Fourier transformation of this Lorentzian Bragg diffract-on, the following dependence can be derived: A(i)=Ao.exp(
-i/i,)
(2)
where A, is related to the amplitude corresponding to maximum count rate = 2.7x105s-') i corresponds (for I to pen%?ation depth and denotes the number of lattice planes i where the amplitude is reduced to l/e. For the thin film sample the calculated intensity is obtained from N
I(O)= 1 Aiexp(4ri i=l
d.sin(B) i Z 2-y-21) j=l 1% +k-+1
where N is the total number of lattice planes (in Fig.5 N=55) and (h,k,Z) are the Miller indices and dj=do is the lattice constant. However, such a fit corresponds to the boxcar function (sin z/z) if d. is constant and A independent of i. $herefore it is necessary to include A(i) according to Eq.2 and also a roughness describing the fact that the factor r PbTe filg is not flat on the scale of lattice planes. This fact is included in the fit by replacing for A(i) in Eq.2 A, by Ao(a) =(+)2
C&=0,...,
r.
)
0
and Ao(il)= 1
(R=ro+l.....N
)
The full curve corresponds to such a fit used for r =7 (which corresponds to a roughness"of 45 8), see Fig.4b. In addition it is necessary to use for the PbTe film a slightly different lattice constant in growth direction as evideneced by.the shift of the maxito a ma by about 0.05 correspondin tetragonal distortion ~=2X10- 9 . This distortion is not equivalent to this resulting from the lattice constant misfit of PbTe and GaAs which would cause much higher E. The fit uses the fact that the penetration depth of CuKcr radiation in PbTe is finite and for i about 370 was obtained for bulk PbTe. 8 owever, the best fit for the film sample requires ai which is approximately equal to the'actual number of lattice planes contributing to the diffraction,i = 47. In Fig.5, for the same PbTe'film on GaAs the (222) Bragg reflection is shown in a logarithmic intensity plot vs Bragg angle. From the difference of the count rates of Fig.4b and Fig.5 we estimate that the ratio between the
2
490
50"
2Q(222) Bragg reflection Of the Fig.5: PbTe film on (2OO)GaAs. The experimental data are fit with the same parameters as those used for Fig.lb with r;=45 8. The intensity scale is however,by a factor of 50 smaller.
(100) oriented PbTe to that exhibiting orientation is about 5O:l. These data were taken since the RHEED pattern showed the presence of (111) oriented PbTe. For the fits in Fig.4a and b indicated by the full and broken lines either a roughness corresponding to r,=7 and one corresponding to r =0 was used. The fit with r =7 yields ?he correct intensities Oup to a sattelite index of 5 or 6. We would like to point out that the calculated data fit the experimental within the accuracy of percents over the whole range of intensities. In order to check the spatial variation of the diffraction pattern the sample was rotated by 90' and shifted by about 2rnm (focal diameter of X-rays on sample surface (lmm)). The resulting diffraction data are shown in Fig.6 and are nearly identical which proves the lateral homogeneity of the growth. Whether the amount of surface roughness as determined from this procedure is correlated to the degree to which mixed (100) and (111)PbTe oriented grains or domains occur, needs further investigations. Using a X-ray diffracted intensity scale which encompasses 3 orders of magnitude, the accuracy of the determination of the surface roughness depends on the number of sattelite peaks which can be resolved. E.g. for (111)
Superlattices and Microstructures, Vol. 4, No. 415, 1988
10'
21"
280 20
20 Fig.6: As Fig.4b for the
340
8
PbTe
film deposited on GaAs. The full and broken line correspond to experimental data taken from two different spots on the film surface as indicated in the insert.
sattelite peaks of the order 10 the ultimate resolution of the roughness determination is estimated to be 1% for a total film thickness of about 1000 8. Of course this limit is determined by the available dynamic range of the count rates corresponding to scattered X-ray intensity. In order to show the influence of a sufficiently thick buffer layer with a lattice constant which is much closer to that of PbTe d-6.462 % than that of GaAs t&5.65325 g1 we have grown a sandwich structure PbTe/CdTe/GaAs (CdTe:cl=6.2409). For two PbTe films of comparable thickness, the intensity oscillations as a function of Bragg angle 28 are shown in Figs.7a and b. Experimentally,it is obvious that with increasing film thickness the total roughness of PbTe cmGaAs does not decrease but rather increases. For the case of the lum thick (100)CdTe buffer layer on (lOO)GaAs, the roughness of the PbTe film is much smaller which can be deduced by inspection of Figs.7a and b. Despite the fact that the intensity oscillationuin Fig.7b are not completely represented by the fit, such an analysis lends itself to a determination of the elastic strain in the two layers. With the intermediate CdTe layer apparently not only the surface roughness is reduced but the count rates on both sides of the main peaks
-
Fig.7a: (200) Brag reflection of a PbTe film (D=1450 ii) deposited on (100)GaAs. Experimental data: ?? , fit: full line with a surface roughness of 130 s.
270
280 20
-
Fig.7b: As Fig.7a but for a PbTe film (D=1250 w) deposited on a lwrn thick (100) oriented CdTe buffer on (100) GaAs. The data are fit with a roughness r*=80 R, a strain profile for E* as i%icated in the insert is used for the calculation.
of equally indexed sattelite peaks are different. For the strain profile-fit a step like gradient in E* was introduced with the following values: cL (PbTe)=8xlO-* and Ed (CdTe)=4x10-4.
596
Superlattices
Thus the lum thick CdTe layer reduces the total strain exerted by the GaAs substrate on the top layer. It is Important to note, that an attempt to detect (111) oriented grains in the film shown in Fig.7b turned out to be‘unsuccesful. Within the noise limit (~8 counts/set) no (222) Bragg reflection was detected. Thus from the comparison of Figs. 7a and 7b and the absence of (111) oriented PbTe grains it can be concluded that Is seems to be easier to grow single crystalline (1OO)PbTe on (lOO)CdTe than on (100) oriented GaAs substrates. 4. CONCLUSION The I%pitaxial growth of PbTe on BaF yields perfect layers in which two dimsnsional growth is possible and rather thick films (several microns) can be grown. For the deposition of PbTe on GaAs, on the contrary, film thicknesses in excess of 4000 2 exhibit micro cracks if a substrate temperature of about 300 OC is chosen. In addition, it seems to be difficult to achieve an overlayer growth with a single orientation.
and Microstructures,
Vol. 4, No. 415, 1988
ACKNOWLEDGEMENTS We thank K.Ploog and A.Fischer for a vast amount of information on MBE growth procedures, J. Oswald for the electronic system used in conjunction with the X-ray apparatus, D.Schikora for helpful discussions and H.Ulrich for expert technical assistance. This work was supported by "Fonds zur Forderung der wissenschaftlichen Forschung" (P5321) and Jubilaumsfonds der Nationalbank (2697) Austria.
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