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Low Angle X-Ray Re ection Studies of InGaAs/InP Multiple Quantum Wells Jose Brant-de-Campos and Roberto R. de Avillez
Departamento de Ci^encia dos Materiais e Metalurgia, Pontifcia Universidade Catolica do Rio de Janeiro, Rua Marqu^es de S~ao Vicente 225, 22453-900 Rio de Janeiro, Brazil
Patricia Lustoza Souza and Boris Yavichy
Centro de Estudos em Telecomunicaco~es, Pontifcia Universidade Catolica do Rio de Janeiro, Rua Marqu^es de S~ao Vicente 225, 22453-900 Rio de Janeiro, Brazil
Received February 2, 1997
Low angle x-ray re ectometry was applied to an InGaAs/InP multiple quantum well structure containing 20 periods and a cap layer. A dynamical simulation was employed to determine the thickness of the di erent layers. The thickness of the InGaAs quantum wells and of the InP barriers were determined to be 3.0 nm and 9.2 nm, respectively, with a 0.1 nm precision. Also, the cap layer thickness was evaluated to be (20.0 0.5) nm.
Introduction In the recent years, x-ray re ectometry has been frequently applied to the characterization of thin lm multilayer systems. This non-destructive technique is well suited for analyzing layers with thickness below 100nm[1]. In particular, the grazing incidence geometry has been used in several material systems like III-V semiconductor bilayers[2] and metal/semiconductor[3-4] with excellent results in the investigation of thickness[2-4], roughness[4-9] and diffusion[10]. In the work reported in this communication, an InGaAs/InP MQW (Multiple Quantum Well) structure was investigated using low angle x-ray re ectometry together with a dynamical simulation method. The thickness of the well, the barrier and the cap layer were determined with less than a monolayer accuracy. One monolayer is de ned as one atomic layer of the element III plus one atomic layer of the element V. In addition, the monolayer interface roughness was evaluated. Two approaches can be taken in studying grazing incidence x-ray re ection, namely, kinematic and dy e-mail:
[email protected] y On leave from A. F. Io e Physico-Technical Institute, Saint
namic. Fullerton et al 9 have already undertaken a thorough study of the kinematics involved in such experiments. They have shown, however, that this approach fails to accurately describe the results for angles of incidence of the x-ray beam smaller than 2 = 3o . Therefore, a dynamical approach would be required for studying a more general III-V semiconductor system in the very low incidence angle regime. The dynamics of light re ectometry has been rst described by Abeles[11] in 1948. In determining the re ectance of a speci c multilayer structure, the multiple re ections on all interfaces are considered. The electric eld re ected from the sample surface, E0; , is a function of the total incident electric eld, E0+ , and of all the re ected and incident electric elds at each individual interface (En;+1, En++1 , respectively. n is the number of layers), as described by the recursive expression given below:
; E0 = (C1 )(C2):::(Cn+1) E0+ t1t2 :::tn+1 - Petersburg, Russia.
En++1 En;+1
(1)
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where
(Cm ) =
eim;1 rm eim;1 rm e;im;1 e;im;1
(2)
In the Cm matrix, rm is the Fresnel coecient for the re ection at each interface m (an interface m is de ned as the interface between layer m ; 1 and m) and m;1 is given by 2 , nm;1 dm;1, where nm;1 is the refractive index of the corresponding medium and dm;1 its thickness. tm is the Fresnel coecient for the transmission at each interface m. The signal to be measured in the experiment is E0; , which will depend on all multire ections. Thus, En;+1 will be equal to zero, rendering equation (1) simpler to solve. The sample used was an InGaAs/InP MQW structure which was grown by Low-Pressure Metalorganic Vapor Phase Epitaxy (LP-MOVPE) at 640 o C. First a 0.2 m wide InP bu er layer was deposited, followed by a 20 period structure of In:53Ga:47As wells where the nominal composition is matched to InP (the composition is such that the lattice parameter of In:53Ga:47As coincides with that InP) and a nominal thickness of 3.6 nm separated by InP barriers of 9.0 nm. Finally, a cap layer of 0.18 nm was grown. The structure is depicted as an insert in Fig.1. The x- ray experimental measurements have been performed in a D-5000 Siemens, using a Cu K 1 wavelength, 40 KV and tube current of 30 mA current. The 2q x-rays scans were performed with a 0.003 angle steps, angle range between 0.05 and 10.00o and 1.0 s counting time. A coupled ; 2 scan was used. The standard grazing incidence re ection geometry was employed [12]. The results obtained are shown in gure 1, where the solid line is the experimental scan and the dotted one is the simulated curve. No thickness uctuation or interface roughness were included in the calculation. The input parameters were the x-ray wavelength, the alloy composition for determining the appropriate index of re ection and the layer thickness. The layer thickness is the parameter to be determined by the simulation. The best simulation provides the correct thickness of the di erent layers. As a starting point the nominal thickness was used.
Figure 1. X-ray grazing incidence re ection spectrum of an InGaAs/InP multiple quantum well structure. The dotted line depicts the simulated spectrum. The insert shows the sample structure.
The best t of the experimental data (dotted line on gure 1), both in terms of peak positions as well as peak intensities, was obtained for a well and barrier thicknesses of 3.0 nm and 9.2 nm, respectively, corresponding to a bilayer thickness of 12.2 nm. When varying the thickness of the bilayer (barrier + well) by 0.1 nm, one already observes signi cant changes in the peak positions. Therefore, the precision of the method for the bilayer thickness is better than 0.1 nm. Note that these changes are not a simple translation shift. Also, keeping the thickness of the barrier constant, a drastic change in the relative intensity of the peaks in the 2 > 3o region was observed for smallchanges (0.1 nm) in the well thickness. This e ect is not noted when the thickness of the barrier is changed b the same amount and the thickness of the well is kept constant. This behavior is not yet well understood. High angle x-ray di raction measurements using a home made double crystal di ractometer were performed, at CPqD-Telebras, to check the validity of these results. The value obtained for the thickness of the bilayer was 12.0 nm, which is in close agreement with our simulation. It should be noted that this type of x-ray di raction experiment takes between 8 and 12 hours of data acquisition, due to the large angle range scanning (2000 arc s) and the high measuring time (30s), while the x-ray re ection reported here takes 1 hour, at the most. The value of the well thickness was compared with the data obtained from the 12 K photoluminescence
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spectrum of the sample. The rst electron to heavyhole optical transition is at (0.902 0.001) eV which corresponds to an In0:53Ga0:47As well of (3.0 0.2) nm[13] , in excellent agreement with the results obtained from the low angle x-ray re ection measurements. The broad bands between the sharp peaks (indicated by the arrows in gure 1) are directly related to the presence of a cap layer. They are completely absent if the cap layer is not introduced in the calculations. The thickness of the cap layer was determined to be (20.0 0.5) nm according to the best visual agreement between experimental results and calculations for those band position. Another method which applies a simple expression (3) for the low angle x-ray re ection has been used by Miceli et al[12]. (3) Sin( ) = m 2d + 2 In the above equation is the x-ray beam angle, m is the peak order, is the x-ray wavelength, d is the thickness of the bilayer and is the refractive index deviation. Fitting our experimental peak positions to the above equation, one has determined the thickness of the bilayer to be (12.70 + 0.15) nm. Therefore, one can conclude that the simulation reported here, even though it requires more computational work, it gives a more precise value for the thickness of the bilayer. In summary, low angle x-ray re ectometry together with a dynamical simulation of the spectrum was used to determine the thickness of the di erent layers of a non-periodic semiconductor heterostructure. Results for an InGaAs/InP multiple quantum well structure with a 0.1 nm precision using low angle re ectometry technique were obtained. In order to achieve a similar precision with high angle x-ray di raction either one needs a more sophisticated and expensive equipment or, using the double crystal di ractometer, the experi-
ment should take ten times longer to be performed.
Acknowledgements This work has been partially supported by FINEP, CNPq and TELEBRA S. One of the authors (J. Brantde-Campos) wishes to thank CAPES for the nancial support.
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