- Email: [email protected]
X-ray studies of interfacial roughness in ZnSeGaAs heterostructures
435
Superlattices and Microstructures, Vol. 4, No. 415, 1988
X-RAY STUDIES OF IBTERFACIAL ROUGHlESS IA ZnSe/GaAs HETEROSTRUCTURES A. Krol, C. J. Sher, S. C. Voronick, Y. II.Kao Department of Physics, State University of Bew York at Stony Brook Stony Brook, RY 11794 R. J. Dalby, D. A. Cammack, R. Ii.Bhargava Philips Laboratories, Rorth Anerican Philips Corporation Briarcliff Hanor, UY 10510 (Received 17 August 1987)
The angular dependence of x-ray reflectivity and fluorescence yield of ZnSe/GaAs heterostructures was measured. By an analysis based on scalar scattering, the root-mean-square values of two roughness parameters pertaining to the top surface and the buried interface have been determined.
The angular dependence of x-ray reflection and fluorescence yield in the grazing incident,angle regime can be utilized to obtain important information on interfacial roughness of layered structures in a nondestructive manner. Specular reflection of x-rays by a planar smoth boundary between two different media is usually described by the well known Fresnel formula.' However, when roughness is present at the boundary, the reflectivity derived from the simple Fresnel formula must be modified in order to account for the effect of scattering due to interfacial roughness.2-7 For a layered material system, e.g., a semiconductor heterostructure or superlittice, the interference due to x-rays reflected by the top surface and the interface can give rise to oscillations in the reflectivity as a function of the grazing angle.8*g The period of these oscillations is mainly determined by the thickness of the layer, and the variation of the amplitudes is affected by the roughness at the interfacial boundaries. In addition to the roughness effect on reflectivity, we have postulated that the interference oscillations and roughness effect can also be observed by measuring the x-ray fluorescence yield.lOThe total fluorescence is proportional to the intensity of the x-ray wave in the material convoluted with the concentration profile of the x-ray absorbing atoms, hence it Is related to the roughness at the interfaces. This technique offers an additional advantage for investigating the layered structures because it is element specific. The nonoscillatory fluorescence yield has been used to study the concentration profile of a dissolved polymer Wore near the liquid-gas interface.i' recently, oscillations in the fluorescence yield were observed in a semiconductor
heterortructure grown by molecular beam epitaxy (NBE).12 In the present work, we have investigated ZnSe/CaAs heterostructures with different epilayer thicknesses grown by MBE. Three samples with nominal epilayer thickness 200, 500, and 50001. were studied by using x-ray energies between 9.5 and 9.7 keV (around the The experiment was K absorption edge of Zn). performed at the Cornell High Energy Synchrotron Source (CHESS). Typical experimental curves are shown in Figures 1 and 2. For simplicity, we have assumed that the effect of the roughness at the boundaries between two media can be described by a scalar scattering theory'r'and two parameters s and (I are defined to represent the rootmean-square roughness at the ZnSe top surface and the ZnSe/GaAs interface, respectively. To determine these roughness parameters, we have performed theoretical calculations of the reflectivity R(B,s,r) and fluorescence yield F(~,s,w) as a function of the grazing angle 9 corresponding to the present experimental conditions; the parameters s and k are determined by a comparison between the experimental data and calculations using a least-squares curve-fitting technique. For the calculations, the wavelength dependence of the complex index of refraction of both ZnSe and GaAs is needed. For this reason, we have also perfomed measurements of the reflectivity and fluorescence yield of bulk ZnSe and GaAs samples in order to determine the refractive index of these constituent semiconductors in the same wavelength region. This step is necessary in order to minimize the number of adjustable parameters in the curve-fitting procedure. To analyze the fluorescence yield and the reflectivity, it is useful to decompose the electric field at any depth z in the iraterial
0 1988 Academic
Press Limited
436
Superlattices
and Microstructures,
Vol. 4. No. 415, 7988
20OA
2OOA
"
,.’ /
.
....5OOA
5001
5OOOA
e.0 1.‘
‘4
7.6
,@A
9%‘
ri.0
(1.‘
10.0
Figure 1 -- Fluorescence yield from ZnSe/GaAs heterostructures measured at the Zn Ku1 energy. Data are plotted as points and the curves are theoretical calculations using Eq. (1) and parameters given in Table 1.
Figure 2 -- X-ray reflectivity of ZnSefGaAs heterostructures measured with incident photon energy at 9.66 keV. Data are plotted as points and the curves are theoretical calculations using Eq. (2) and parameters given in Table 1.
into two parts: the in-going component E(z) and the out-going component E'(z). By assuming that the concentration of the x-ray absorbing atom (Zn) is constant in the epilayer, the fluorescence yield CAII be obtained from
analysis will be described in a separate publication. The roughness parameters determined by our analysis are presented in the following table: Table 1.
Roughness parameters of ZnSe/CaAs heterostructures ~___.._ __..-__ _
d
F(B,s,a) = C
0
E(z) t E'tz)j2 dz
(1) d (A)
0
where C is a constant, and d is the thickness of the epilayer (ZnSe). The reflectivity 1s given by the ratio of the two electric field components at the sample surface z = 0 :
200
s (A)
0 (A)
?i2
20 f 2
500
10 f 5
>20
5000
10 f 2
---
2 R(B,s,cr) = IE'(O)/E(O)j
(2)
The electric field components were calculated by using the wave equations and applying the appropriate boundary conditions similar to the calculations by Vidal and Vincent.' The other parameters involved in the curvefitting procedure are the background and a normalization factor. Details of this
The accuracy in this determination is not as high as in our previous studies of other semiconductor beterostructures where many pronounced oscillations were observed.' This could be partly due to structural imperfections in the ZnSe epilayers used in the present experiment. For the 5001, epilayer, the interference signal is so weak that only a lower bound of the value of o can
Superlattices
and Microstructures,
Vol. 4, No. 415, 1988
be set by our measurements. For the thick (5000A) layer, no oscillation was observed in the experimental curve, (I could not be determined. In summary, we have demonstrated that grazing incident angle x-ray fluorescence yield and reflectivity can be used as microprobes for nondestructive evaiuation of the roughness at the top surface a~ Well as the interface in II-VI/III-V semiconductor heterostructures. This technique can be useful for Investigating the effect of interfacial roughness due to specific elemnt,s in d layered structuz-e consisting of several different at.omic species. Acknowledgeroent -This research ,supported by the U.S. Department under arant No. DE-FG02-e7ER4528.3.
is of Energy
References 1. L. (1954). 2. P.
G.
Parratt,
Beckmann
Physical and
A.
Review
Spizzichino,
95,
359
The
Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon Press, Bew York,1963).
437 3. C. K. Carniglia, Optical Engineering 1_8, 104 (1979); and references cited therein. 4. T. V. Barbee, Jr., Optical Engineering 25, 895 (1986). 5. E. Spiller and A. E. Rosenbluth, Optical Engineering 25, 954 (1986). 6. D. II. Bilderback, SPIE 315, 90 (1981). 7. A. Braslau, II. Deutsch, P. S. Pershan, A. H. Weiss, J. Als-Hielsen, and J. Bohr, Physical Review Letters 54, 114 (1985); and references cited therein. a. B. Vidal and P. Vincent, Applied Optics 23, 1794 (1984). 9. S. C. Voronick, B. X. Yang, A. Krol, Y. Ii. Kao, H. Nunekata, L. L. Chang, and J. C. Phillips, Proceedings of Third International Conference on Hodulated Structures of Semiconductors, 1987, in press. 10. A. Krol, C. J. Sher, and Y. H. Kao, to be published. 11. J. 11. Bloch, K. Sansone, F. Rondelez, D. G. Peiffer, P. Pincus, M. Kim, and P. II. Eisenberger, Physical Review Letters 54, 1039 (1985). 12. S. C. Voronick, A. Krol, C. 3. Sher, Y. H. Kao, K. L. Vang, and Y. C. Kao, to be published.
Superlattices and Microstructures, Vol. 4, No. 415, 1988
X-RAY STUDIES OF IBTERFACIAL ROUGHlESS IA ZnSe/GaAs HETEROSTRUCTURES A. Krol, C. J. Sher, S. C. Voronick, Y. II.Kao Department of Physics, State University of Bew York at Stony Brook Stony Brook, RY 11794 R. J. Dalby, D. A. Cammack, R. Ii.Bhargava Philips Laboratories, Rorth Anerican Philips Corporation Briarcliff Hanor, UY 10510 (Received 17 August 1987)
The angular dependence of x-ray reflectivity and fluorescence yield of ZnSe/GaAs heterostructures was measured. By an analysis based on scalar scattering, the root-mean-square values of two roughness parameters pertaining to the top surface and the buried interface have been determined.
The angular dependence of x-ray reflection and fluorescence yield in the grazing incident,angle regime can be utilized to obtain important information on interfacial roughness of layered structures in a nondestructive manner. Specular reflection of x-rays by a planar smoth boundary between two different media is usually described by the well known Fresnel formula.' However, when roughness is present at the boundary, the reflectivity derived from the simple Fresnel formula must be modified in order to account for the effect of scattering due to interfacial roughness.2-7 For a layered material system, e.g., a semiconductor heterostructure or superlittice, the interference due to x-rays reflected by the top surface and the interface can give rise to oscillations in the reflectivity as a function of the grazing angle.8*g The period of these oscillations is mainly determined by the thickness of the layer, and the variation of the amplitudes is affected by the roughness at the interfacial boundaries. In addition to the roughness effect on reflectivity, we have postulated that the interference oscillations and roughness effect can also be observed by measuring the x-ray fluorescence yield.lOThe total fluorescence is proportional to the intensity of the x-ray wave in the material convoluted with the concentration profile of the x-ray absorbing atoms, hence it Is related to the roughness at the interfaces. This technique offers an additional advantage for investigating the layered structures because it is element specific. The nonoscillatory fluorescence yield has been used to study the concentration profile of a dissolved polymer Wore near the liquid-gas interface.i' recently, oscillations in the fluorescence yield were observed in a semiconductor
heterortructure grown by molecular beam epitaxy (NBE).12 In the present work, we have investigated ZnSe/CaAs heterostructures with different epilayer thicknesses grown by MBE. Three samples with nominal epilayer thickness 200, 500, and 50001. were studied by using x-ray energies between 9.5 and 9.7 keV (around the The experiment was K absorption edge of Zn). performed at the Cornell High Energy Synchrotron Source (CHESS). Typical experimental curves are shown in Figures 1 and 2. For simplicity, we have assumed that the effect of the roughness at the boundaries between two media can be described by a scalar scattering theory'r'and two parameters s and (I are defined to represent the rootmean-square roughness at the ZnSe top surface and the ZnSe/GaAs interface, respectively. To determine these roughness parameters, we have performed theoretical calculations of the reflectivity R(B,s,r) and fluorescence yield F(~,s,w) as a function of the grazing angle 9 corresponding to the present experimental conditions; the parameters s and k are determined by a comparison between the experimental data and calculations using a least-squares curve-fitting technique. For the calculations, the wavelength dependence of the complex index of refraction of both ZnSe and GaAs is needed. For this reason, we have also perfomed measurements of the reflectivity and fluorescence yield of bulk ZnSe and GaAs samples in order to determine the refractive index of these constituent semiconductors in the same wavelength region. This step is necessary in order to minimize the number of adjustable parameters in the curve-fitting procedure. To analyze the fluorescence yield and the reflectivity, it is useful to decompose the electric field at any depth z in the iraterial
0 1988 Academic
Press Limited
436
Superlattices
and Microstructures,
Vol. 4. No. 415, 7988
20OA
2OOA
"
,.’ /
.
....5OOA
5001
5OOOA
e.0 1.‘
‘4
7.6
,@A
9%‘
ri.0
(1.‘
10.0
Figure 1 -- Fluorescence yield from ZnSe/GaAs heterostructures measured at the Zn Ku1 energy. Data are plotted as points and the curves are theoretical calculations using Eq. (1) and parameters given in Table 1.
Figure 2 -- X-ray reflectivity of ZnSefGaAs heterostructures measured with incident photon energy at 9.66 keV. Data are plotted as points and the curves are theoretical calculations using Eq. (2) and parameters given in Table 1.
into two parts: the in-going component E(z) and the out-going component E'(z). By assuming that the concentration of the x-ray absorbing atom (Zn) is constant in the epilayer, the fluorescence yield CAII be obtained from
analysis will be described in a separate publication. The roughness parameters determined by our analysis are presented in the following table: Table 1.
Roughness parameters of ZnSe/CaAs heterostructures ~___.._ __..-__ _
d
F(B,s,a) = C
0
E(z) t E'tz)j2 dz
(1) d (A)
0
where C is a constant, and d is the thickness of the epilayer (ZnSe). The reflectivity 1s given by the ratio of the two electric field components at the sample surface z = 0 :
200
s (A)
0 (A)
?i2
20 f 2
500
10 f 5
>20
5000
10 f 2
---
2 R(B,s,cr) = IE'(O)/E(O)j
(2)
The electric field components were calculated by using the wave equations and applying the appropriate boundary conditions similar to the calculations by Vidal and Vincent.' The other parameters involved in the curvefitting procedure are the background and a normalization factor. Details of this
The accuracy in this determination is not as high as in our previous studies of other semiconductor beterostructures where many pronounced oscillations were observed.' This could be partly due to structural imperfections in the ZnSe epilayers used in the present experiment. For the 5001, epilayer, the interference signal is so weak that only a lower bound of the value of o can
Superlattices
and Microstructures,
Vol. 4, No. 415, 1988
be set by our measurements. For the thick (5000A) layer, no oscillation was observed in the experimental curve, (I could not be determined. In summary, we have demonstrated that grazing incident angle x-ray fluorescence yield and reflectivity can be used as microprobes for nondestructive evaiuation of the roughness at the top surface a~ Well as the interface in II-VI/III-V semiconductor heterostructures. This technique can be useful for Investigating the effect of interfacial roughness due to specific elemnt,s in d layered structuz-e consisting of several different at.omic species. Acknowledgeroent -This research ,supported by the U.S. Department under arant No. DE-FG02-e7ER4528.3.
is of Energy
References 1. L. (1954). 2. P.
G.
Parratt,
Beckmann
Physical and
A.
Review
Spizzichino,
95,
359
The
Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon Press, Bew York,1963).
437 3. C. K. Carniglia, Optical Engineering 1_8, 104 (1979); and references cited therein. 4. T. V. Barbee, Jr., Optical Engineering 25, 895 (1986). 5. E. Spiller and A. E. Rosenbluth, Optical Engineering 25, 954 (1986). 6. D. II. Bilderback, SPIE 315, 90 (1981). 7. A. Braslau, II. Deutsch, P. S. Pershan, A. H. Weiss, J. Als-Hielsen, and J. Bohr, Physical Review Letters 54, 114 (1985); and references cited therein. a. B. Vidal and P. Vincent, Applied Optics 23, 1794 (1984). 9. S. C. Voronick, B. X. Yang, A. Krol, Y. Ii. Kao, H. Nunekata, L. L. Chang, and J. C. Phillips, Proceedings of Third International Conference on Hodulated Structures of Semiconductors, 1987, in press. 10. A. Krol, C. J. Sher, and Y. H. Kao, to be published. 11. J. 11. Bloch, K. Sansone, F. Rondelez, D. G. Peiffer, P. Pincus, M. Kim, and P. II. Eisenberger, Physical Review Letters 54, 1039 (1985). 12. S. C. Voronick, A. Krol, C. 3. Sher, Y. H. Kao, K. L. Vang, and Y. C. Kao, to be published.