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Langmuir 2006, 22, 5504-5508
CdTe Electrodeposition on InP(100) via Electrochemical Atomic Layer Epitaxy (EC-ALE): Studies Using UHV-EC Madhivanan Muthuvel and John L. Stickney* Department of Chemistry, UniVersity of Georgia, Athens, Georgia 30602 ReceiVed December 11, 2005. In Final Form: March 29, 2006 The II-VI compound semiconductor CdTe was electrodeposited on InP(100) surfaces using electrochemical atomic layer epitaxy (EC-ALE). CdTe was deposited on a Te-modified InP(100) surface using this atomic layer by atomic layer methodology. The deposit started with formation of an atomic layer of Te on the InP(100) surface, as Cd was observed not to form an underpotential deposition (UPD) layer on InP(100), although it was found to UPD on Te atomic layers. On the In-terminated ‘clean’ InP(100) surface, Te was deposited at -0.80 V from a 0.1 mM solution of TeO2, resulting in formation of a Te atomic layer and some small amount of bulk Te. The excess bulk Te was then removed by reduction in blank solution at -0.90 V, leaving a Te atomic layer. Given the presences of the Te atomic layer, it was then possible to form an atomic layer of Cd by UPD at -0.58 V to complete the formation of a CdTe monolayer by EC-ALE. That cycle was then repeated to demonstrate the applicability of the cycle to the formation of CdTe nanofilms. Auger spectra recorded after the first three cycles of CdTe deposition on InP(100) were consistent with the layer-by-layer CdTe growth. It is interesting to note that Cd did not form a UPD deposit on the In-terminated InP(100) surface and only formed Cd clusters at an overpotential. This issue is probably related to the inability of the Cd and In to form a stable surface compound.
Introduction Electrochemical atomic layer epitaxy (EC-ALE) is a method for the deposition of nanofilms of materials an atomic layer at a time, layer-by-layer, using surface-limited electrochemical reactions.1 EC-ALE is the electrochemical analogue of atomic layer epitaxy (ALE) or deposition (ALD). The driving force for EC-ALE is the thermodynamic stability afforded by forming a surface compound or alloy in a surface-limited reaction. Many surface-limited reactions are referred to as underpotential deposition (UPD), a phenomenon where an atomic layer of one element is deposited on a second at a potential prior to (under) that needed to deposit the element on itself.2 The majority of materials formed using EC-ALE have been compound semiconductors, including CdTe, CdSe, CdS, InAs, InSb, In2Se3, Bi2Te3, PbTe, PbSe, HgSe, and HgTe. Substrates studied have been, for the most part, metallic, including Au, Ag, and Pt, although deposits have been formed on ITO.3-9 Compound semiconductors are finding a plethora of possible applications in the electronics and optoelectronics industries. Those industries are most interested in forming deposits on Si substrates, the standard for the industries. In general, however, electrodeposition on silicon results in a nucleation and growth mechanism, leading to roughened deposits.10,11 However, there (1) Stickney, J. L. In AdVances in Electrochemical Science and Engineering; Kolb, D. M., Alkire, R., Eds.; Wiley-VCH: Weinheim, 2002; Vol. 7, pp 1-107. (2) Kolb, D. M.; Przasnyski, M.; Gerischer, H J. Electroanal. Chem. 1974, 54, 25-38. (3) Varazo, K.; Lay, M. D.; Sorenson, T. A.; Stickney, J. L. J. Electroanal. Chem. 2002, 522, 104-114. (4) Mathe, M. K.; Cox, S. M.; Flowers, B. H.; Vaidyanathan, R.; Pham, L.; Srisook, N.; Happek, U.; Stickney, J. L. J. Cryst. Growth 2004, 271, 55-64. (5) Wade, T. L.; Vaidyanathan, R.; Happek, U.; Stickney, J. L. J. Electroanal. Chem. 2001, 500, 322-332. (6) Vaidyanathan, R.; Stickney, J. L.; Cox, S. M.; Compton, S. P.; Happek, U. J. Electroanal. Chem. 2003, 559, 55-61. (7) Vaidyanathan, R.; Stickney, J. L.; Happek, U. Electrochim. Acta 2004, 49, 1321-1326. (8) Innocenti, M.; Cattarin, S.; Cavallini, M.; Loglio, F.; Foresti, M. L. J. Electroanal. Chem. 2002, 532, 219-225. (9) Zhu, W.; Yang, J. Y.; Gao, X. H.; Bao, S. Q.; Fan, X. A.; Zhang, T. J.; Cui, K. Electrochim. Acta 2005, 50, 4041-4047. (10) Sugimoto, Y.; Peter, L. M. J. Electroanal. Chem. 1995, 381, 251-255.
was a report of the formation of a high-quality CdTe nanofilm on p-type Si(111), deposited using light-assisted electrodeposition methodology.12 In addition, there has been a report of CdTe deposited on n-type Si using co-deposition; however, those deposits required annealing to evidence any compound using XRD.13 Indium phosphide (InP), a III-V compound semiconductor, has found increasing use as a substrate for the formation of electronic and optoelectronic devices. InP has applications in the optoelectronic industry because of its high charge carrier mobility. InP has been the understudy in this group for a couple years to understand the fundamental surface electrochemistry of the InP.14 This paper is a continuation of that work, with the intent of understanding InP surface chemistry during UPD and to see if the technique of EC-ALE can be used to form epitaxial deposits of CdTe on InP(100) electrochemically. This is the first report of a compound semiconductor electrodeposited with atomic layer control on a semiconductor wafer, InP(100). The EC-ALE deposition of CdTe has been studied repeatedly but generally on Au substrates. InP has been used as a substrate for the electrodeposition of various compound semiconductors such as CdSe, PbSe, ZnSe, PbTe, and Cu2O using other electrodeposition methods,15-19 but not with the atomic-level control inherent in EC-ALE. Lincot et al. have studied the epitaxial electrodeposition of CdTe on InP surfaces with the help of a chemically deposited (11) Gomez, H.; Henriquez, R.; Schrebler, R.; Cordova, R.; Ramirez, D.; Riveros, G.; Dalchiele, E. A. Electrochim. Acta 2005, 50, 1299-1305. (12) Takahashi, M.; Todorobaru, M.; Wakita, K.; Uosaki, K. Appl. Phys. Lett. 2002, 80, 2117-2119. (13) Jackson, F.; Berlouis, L. E. A.; Rocabois, P. J. Cryst. Growth 1996, 159, 200-204. (14) Muthuvel, M.; Stickney, J. J. Electrochem. Soc. 2006, 153, C67-C73. (15) Beaunier, L.; Cachet, H.; Cortes, R.; Froment, M.; Etcheberry, A. Thin Solid Films 2001, 387, 108-110. (16) Beaunier, L.; Cachet, H.; Froment, M. Mater. Sci. Semicond. Process 2001, 4, 433-436. (17) Henriquez, R.; Gomez, H.; Riveros, G.; Guillemoles, J. F.; Froment, M.; Lincot, D. Electrochem. Solid-State Lett. 2004, 7, C75-C77. (18) Beaunier, L.; Cachet, H.; Cortes, R.; Froment, M. J. Electroanal. Chem. 2002, 532, 215-218. (19) Liu, R.; Bohannan, E. W.; Switzer, J. A.; Oba, F.; Ernst, F. Appl. Phys. Lett. 2003, 83, 1944-1946.
10.1021/la053353q CCC: $33.50 © 2006 American Chemical Society Published on Web 05/10/2006
CdTe Electrodeposition on InP(100)
CdS buffer layer.20 Similar results were observed in MBE studies, using Si and GaAs substrates, where modification with a layer of Ba2F-Ca2F (on Si) or a Te precursor (on GaAs) promoted epitaxial growth of CdTe.21,22 The objective of this work was to electrodeposit CdTe on InP(100) using EC-ALE and to investigate the formation of the first few monolayers of CdTe on InP(100). Studies were performed in an ultrahigh vacuum surface analysis instrument, which included an antechamber for electrochemical experiments. This methodology has been referred to as UHV-EC.23 In this way, techniques such as Auger electron spectroscopy (AES) and low-energy electron diffraction (LEED) could be used before and after an electrochemical treatment to follow the resulting surface composition and structure, respectively, without exposure of the deposit to air.
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Figure 1. Cyclic voltammogram of Te on InP(100) in 0.1 mM TeO2, 1 mM Na2B4O7 (pH 9).
Experimental Section An n-type, S-doped InP(100) single-crystal wafer (CrystaComm, Inc.) with a carrier density of 4.9 × 1018 cm-3 was used as the substrate for these studies. Surface analysis and electrochemical experiments with the InP wafer were performed in an ultrahigh vacuum electrochemistry (UHV-EC) system. This system was equipped with an antechamber where electrochemical experiments were performed, directly interfaced to the UHV surface analysis system. In this way, samples could be transferred back and forth between the chambers without exposure to air in ultra-high-purity (UHP) gases. The UHV-EC chamber was equipped with optics for AES (Physical Electronics) and LEED (Princeton Research Instruments). To perform electrochemical experiments, the antechamber was isolated from the main chamber and backfilled to atmospheric pressure with UHP Ar. The Pyrex electrochemical cell consisted of a Au wire counter electrode, a Ag/AgCl (3M NaCl) (Bioanalytical Systems) reference electrode, and an InP(100) sample (1.8 cm2) as the working electrode. Electrochemical studies on the InP(100) wafer were carried out under room light conditions using an µAutoLab Type III potentiostat (Eco Chemie). Cyclic voltammetry was performed at a sweep rate of 5 mV/s. Solutions used were 0.1 mM TeO2 in 1 mM Na2B4O7 (pH 9), the Te solution; 1 mM K2SO4 in 1 mM Na2B4O7 (pH 9), the blank solution; and 0.2 mM CdSO4, 10 mM K2SO4, 0.4 mM CH3COONa and 0.4 mM CH3COOH (pH 4.7), the Cd solution. All solutions were prepared with deionized water (18 MΩ), and dearated with UHP Ar gas for an hour.
Results and Discussion Cleaning InP(100) wafers has been discussed in a previous article.14 In the present study, the InP(100) wafer, as received from the company, was pretreated in 10% HF for 40 s to remove any possible SiOx particles left after wafer polishing. The wafer was then rinsed and sonicated in deionized water for 5 min. Following wet etching, the InP(100) wafer was transferred to the UHV-EC chamber and cleaned by Ar ion bombardment and annealing to produce the ‘clean’ InP(100) surface, displaying the (2 × 4) reconstruction LEED pattern. ‘Clean’ InP(100) surfaces were free from carbon and oxygen but had small nanoclusters of metallic In randomly distributed across the surface.14 The In clusters, formed during ion bombardment and annealing, were oxidized in 10 mM HCl at -0.60 V to form the ‘stable’ InP(100) surface, which displayed a (1 × 1) LEED pattern. The surface compositions of both the ‘clean’ and ‘stable’ InP(20) Lincot, D.; Kampmann, A.; Mokili, B.; Vedel, J.; Cortes, R.; Froment, M. Appl. Phys. Lett. 1995, 67, 2355. (21) Tiwari, A. N.; Floeder, W.; Blunier, S.; Zogg, H.; Weibel, H. Appl. Phys. Lett. 1990, 57, 1108-1110. (22) Bourret, A.; Fuoss, P.; Feuillet, G.; Tatarenko, S. Phys. ReV. Lett. 1993, 70, 311-314. (23) Soriaga, M. P.; Harrington, D. A.; Stickney, J. L.; Wieckowski, A. In Modern aspects of electrochemistry; Conway, B.; Bockris, J. O. M., White, R., Eds.; Plenum Press: New York, 1996; Vol. 28, p 1.
(100) surfaces displayed the same AES spectra, as the low coverage of In clusters did not appreciably change the AES spectrum. Both the ‘clean’ and ‘stable’ InP(100) surfaces were used as starting points in the present studies. Electrodeposition of Te. A clean InP(100) sample was immersed in the Te solution, resulting in an open circuit potential (OCP) of -0.48 V, at which potential, all metallic In clusters would have been oxidatively stripped from the surface, as previously observed.14 The cyclic voltammogram (CV) of the InP(100) in the Te solution (Figure 1) was begun negative from the OCP. During the negative-going scan, the reduction current continuously increased but displaying no other reduction features. This suggests that Te does not undergo a UPD, partially the result of the wellknown irreversibility of the Te electrodeposition process. In the subsequent positive-going scan, oxidation current started about -0.40 V, indicating that Te was stable at lower potentials. The oxidation process was continued to 0.2 V, where both the deposited Te and the InP surface oxidized. On the second scan, the InP(100) substrate was emersed (withdrawn) at -0.70 V, leaving some bulk Te on the surface. EC-ALE is based on the use of surface-limited reactions. Each atomic layer should be formed using UPD or an equivalent surface-limited electrochemical reaction. That is how atomic layer control of the deposition is maintained. However, Te deposition showed no UPD feature on the InP(100) stable surface. Te deposition on Au does show apparently surface-limited features, although due to the irreversibility of the reaction, they occur at overpotentials with slow deposition kinetics.24 The net result is that, during Te deposition, an atomic layer is formed, along with some bulk, second layer Te. Experience with Te deposition on Au has shown that excess Te can be removed selectively from the first Te atomic layer by selection of the correct reduction potential in a blank solution, where the excess is reduced at a fairly negative potential to a soluble telluride species, leaving a surface-limited Te atomic layer. In the present study, first 2-3 ML of Te (where a monolayer (ML) is defined as the deposition of one Te atom for each In surface atom (5.81 × 1014 atoms/cm2) on the InP surface) was deposited at -0.8 V on the InP(100) surface for 2 min from the Te solution. This was followed by exchange of solution for the blank (pH 9) solution, where a CV was performed (Figure 2). The scan in Figure 2 started negative from -0.55 V, resulting in the reduction peak evident at -0.98 V. This reduction peak corresponds to bulk Te reduction to a soluble telluride species, which dissolves into the electrolyte, leaving only the last atomic (24) Lay, M. D.; Stickney, J. L. J. Electrochem. Soc. 2004, 151, C431-C435.
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Figure 2. Cyclic voltammogram of Te-covered InP(100) in 10 mM K2SO4, 10 mM Na2B4O7 (pH 9).
layer of Te on the InP(100) surface. Scanning further in the negative direction results in hydrogen evolution. After reversal of the scan direction at -1.4 V, a small oxidation peak was observed at -0.80 V, related to oxidative deposition of Te from traces of telluride ion in the vicinity of the electrode. At -0.4 V, Te oxidation from the surface begins. Reduction of Te to telluride, while leaving an atomic layer, was confirmed by Auger of the resulting InP(100) surfaces (Figure 3). Figure 3a shows a Te/In ratio as 0.436 after bulk deposition of Te on InP(100) by scanning to -0.70 V in the Te solution, whereas Figure 3b displays the spectrum after reduction of excess Te to telluride in borate blank solution, at -1.15 V. In that case, the ratio was only 0.365 (Figure 3b), clearly showing the Te loss and attesting to the stability of the remaining Te atomic layer. As with Au,25 only Te atoms bound to Te were lost, leaving the surface-limited Te atomic layer, those Te atoms bound to In. The result is most likely a precursor for a layer of In2Te3, another compound semiconductor with interesting applications. Previous results have shown that the ‘clean’ or ‘stable’ InP(100) surfaces are terminated with In atoms, as P atoms with less than the tetrahedral coordination found within the zinc blende structure
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of InP are insufficiently stable to remain on the surface in solution.14 These results thus suggest steps for the formation of an atomic layer of Te on the InP(100) surface: Initial bulk Te deposition at -0.80 V, 2-3 ML of Te, followed by excess Te reduction to telluride at -1.15 V in the borate blank solution. Electrodeposition of Cd. Deposition of Cd on the ‘stable’ InP(100) surface was studied using the Cd solution (Figure 4). The substrate was immersed at -0.5 V and scanned in negative, producing only a large peak for bulk Cd deposition beginning at -0.80 V, resulting in a coverage of 29 ML. Reversal of the scan direction at -1.1 V produced the corresponding bulk Cd oxidation peak at -0.60 V, again amounting to 29 ML of Cd stripped from the surface. No Cd UPD feature was observed, either for deposition or stripping, suggesting that atomic layer control for Cd deposition was not possible. The Cd CV also suggests a nucleation and growth mechanism, based on the hysteresis in the voltammetry. From Auger, it is evident that Cd is not covering the surface, but depositing in clusters, by the lack of a significant Cd signal and the strong presences of the In and P peaks. With 29 ML of Cd, there should be no In or P showing. Evidently, In and Cd show little tendency to bond under these conditions. Although Cd deposition on the InP(100) surface was not surface-limited, forming only Cd clusters, earlier studies of CdTe deposition on Au substrates, by this group, had shown Cd to deposit homogeneously on Te surfaces.3 This suggested studies of Cd deposition on the Te-terminated InP(100) surfaces. Figure 5 displays a Cd CV on the InP(100) surface terminated with 1.5 ML of Te. The Cd CV was started negative from -0.25 V. A reduction peak, corresponding to the deposition of nearly 1 ML of Cd is clearly evident at -0.43 V on the Te terminated InP(100) surface. Scanning further negative, bulk Cd deposition was again observed beginning at -0.80 V, consistent with the formation of bulk Cd. The scan direction was immediately reversed, again displaying the hysteresis loop characteristic of nucleation and growth of the bulk Cd. A sharp peak for bulk Cd oxidation was observed at -0.75 V in the positive-going scan, and oxidation of Cd UPD was evident at -0.10 V. This CV, compared with
Figure 3. Auger spectra of InP(100) surface after (a) Bulk Te deposition and (b) reduction of Te to telluride.
CdTe Electrodeposition on InP(100)
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Figure 4. Cyclic voltammogram of InP(100) in 0.2 mM CdSO4, 10 mM K2SO4, 0.4 mM CH3COONa, and 0.4 mM CH3COOH.
Figure 5. Cyclic voltammogram of Cd on Te-covered InP(100) surface in 0.2 mM CdSO4, 10 mM K2SO4, 0.4 mM CH3COONa, and 0.4 mM CH3COOH. Table 1. Te and Cd Coverage on InP(100) as a Function of the Telluride Reduction Potential Te-to-telluride reduction potential (V)
bulk Te coverage (ML)
telluride reduction (ML)
Te left on InP(100) (ML)
UPD Cd (ML)
-0.7 -0.8 -0.9 -1.0 -1.1
2.22 2.21 1.88 2.13 2.00
0.30 0.63 1.08 1.83 2.40
1.92 1.58 0.80 0.30 -0.40
1.86 1.33 0.54 0.45 0.32
that in Figure 4, clearly illustrates the importance of initially depositing Te on InP(100) surface to obtain Cd UPD. CdTe Electrodeposition on InP(100). As noted, Cd deposition was homogeneous on Te-covered InP(100), and inhomogeneous, nucleation and growth, on InP(100) surfaces without Te. This lead to Te atomic layer formation as the first step in the formation of CdTe on InP(100) surfaces using EC-ALE. To optimize the first step, a series of deposits were formed, each initiated by Te deposition at -0.8 V, followed by reduction of the excess Te to telluride in blank solution at a series of reduction potentials, from -0.70 to -1.10 V. The initial bulk Te coverages and the coverages of Te left on the InP(100) surface after the reductive stripping step are listed in Table 1. Te left on InP(100) was the difference between the initial Te deposited and the Te reduced (25) Colletti, L. P.; Stickney, J. L. J. Electrochem. Soc. 1998, 145, 3594.
to telluride. At the most negative potential, -1.10 V, the Te left on InP(100) was negative, which is impossible. The 2.4 ML of Te reduced from the surface to telluride was 0.4 ML more than initially deposited, suggesting a second reaction, probably hydrogen evolution, given previous results for InP(100) reduction at -1.10 V in 1 mM K2SO4, with 1 mM Na2B4O7, where hydrogen evolution was observed.14 Moreover, the resulting Cd UPD coverage (0.32 ML), dependent on the Te coverage, suggests a Te coverage of 0.26 ML by extrapolation in Figure 6. Figure 6 lists the Auger ratios for Cd/In and Te/In as a function of the Te reductive stripping potential. These ratios were 0.254 and 0.356, respectively, at -1.10 V, again consistent with the presences of Te on InP(100) surface, and indicating that hydrogen evolution was a significant contribution to the observed charge at this potential (Table 1). The second step in this proposed CdTe EC-ALE cycle was Cd atomic layer formation on the Te-coated InP by UPD. Using a potential of -0.58 V for Cd UPD, the resulting Cd coverages are also listed in Table 1. All deposition and stripping steps were performed for 1 min, and all coverages were determined via coulometry. As noted, the resulting Cd UPD coverages were dependent on the amount of Te left on the surface. The plots in Figure 6 display a plateau region for Cd deposition, from -0.90 to -1.10 V, where the coverage for Cd was relatively constant, suggesting the Te coverage should be constant as well. In this potential region, the coverage was controlled by the surface area, rather than potential. The plot indicates a Te reduction potential near -0.90 V would be good, as it results in 0.80 ML of Te left on the InP(100) surface, after reduction of 1.08 ML of excess Te from the initially deposited 1.88 ML of Te (Table 1). Table 1 indicates that not all bulk Te was removed when potentials positive of -0.9 V were used for reductive Te stripping, while for potentials between -0.9 and -1.1 V, resulting in Te coverages in the range of an atomic layer. From the above results for Cd and Te, an initial EC-ALE cycle was designed to form a CdTe monolayer. Prior to deposition, the initial ‘clean’ InP(100) was scanned from -0.7 to -0.57 V in 10 mM HCl to form the ‘stable’ InP(100) surface. The EC-ALE cycle then consisted of Te deposition at -0.80 V in the Te solution followed by reductive dissolution of the excess Te to telluride at -0.90 V in the blank solution to leave a Te atomic layer and finally Cd UPD at -0.58 V, in the Cd solution to complete the deposition cycle. This cycle could then be repeated to grow nanofilms of CdTe on InP(100). In the present study, this cycle was repeated one, two, and three times. Auger spectra for the three CdTe deposits are displayed in Figure 7. Note the gradual decrease in peak heights for In and P as they become covered by the depositing CdTe layers. In addition, the peak heights for Cd and Te increased with each cycle (Figure 7), demonstrating the layer-by-layer growth of CdTe on InP(100). The Cd/Te AES peak ratio was strikingly constant after the second and third cycles, at 1.13. Interestingly, in the first cycle, the observed Cd coverages from AES and coulometry were significantly lower than those for Te. This is probably results from extra Te incorporating into the In layer, the transition between the In-terminated InP(100) surface, and the growing CdTe nanofilm. In2Te3 is a stable metal chalcogenide, and given the Te/In ratio of 1.5, it is understandable that the first monolayer of CdTe deposited displays more Te than subsequent layers. The nature and structure of this transition layer is in question and will be the subject of future in-situ STM studies. The transition was quickly achieved, however, as the subsequent CdTe monolayers established a steady-state Cd/Te value. No structural information from LEED was obtained for the
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Figure 6. Coverage and Auger ratio for Cd and Te deposition as a function of Te-to-telluride reduction potential.
Figure 7. Auger spectra for CdTe cycles on InP(100) surface (a) first cycle, (b) second cycle, and (c) third cycle.
CdTe deposit on InP(100), as no patterns were observed after the first deposition of Te. The lattice constants for InP and CdTe are 5.869 and 6.477 Å, respectively, an almost 10% lattice mismatch, making epitaxy difficult to achieve. Again, information concerning the atomic-level structure of CdTe electrodeposits on InP(100) will need to be performed using in-situ STM.
Conclusion The objective of this investigation was development of a procedure for the atomic layer by atomic-layer electrodeposition of the compound semiconductor, CdTe, on a semiconductor substrate, InP(100). Previous studies have suggested how to prepare InP(100) surfaces for electrodeposition, using ion bombardment and annealing to produce the ‘clean’ surface followed by electrochemical oxidation of In metal islands in dilute HCl solution for the ‘stable’ surface. The EC-ALE deposition cycle consisted of the following. Te deposition on InP(100) and leaving an atomic layer and some bulk Te with no indication of a UPD feature observable. This
was followed by reduction of bulk Te to telluride in blank solution, leaving a Te atomic layer. Finally, Cd UPD was formed at -0.58 V from the Cd solution. Of note was the absence of a UPD features for Cd electrodeposition on the InP(100) surface, and bulk Cd deposition was based on nucleation and growth, which did not even cover the surface after deposition of 29 Cd ML. Multiple applications of the above cycle resulted in the layerby-layer growth of CdTe, as demonstrated with both AES and coulometry. A constant ratio of AES peak heights for Te and Cd was observed after the first transition layer. These results demonstrated that the EC-ALE methodology is applicable to the deposition of compound semiconductor nanofilms in an atomiclayer fashion using EC-ALE, resulting in formation of nanofilms of semiconductors on semiconductors with atomic-layer control. Acknowledgment. The authors are grateful to the National Science Foundation, divisions of Materials and Chemistry, for their financial support of this research. LA053353Q
