- Email: [email protected]
InP
Applied Surface Science 161 Ž2000. 286–290 www.elsevier.nlrlocaterapsusc
Energy barrier for the growth transition step-flowrstep-bunching during epitaxy of InPrInP H. Dumont ) , Y. Monteil, J. Bouix LMI-UCB Lyon I, UMR-5615, 43 BouleÕard du 11 NoÕembre 1918, 69622 Villeurbanne Cedex, France Received 13 September 1999; received in revised form 24 November 1999; accepted 30 March 2000
Abstract We report the growth mode evolution of homoepitaxially grown InP by metal organic vapour phase epitaxy examined by ex-situ atomic force microscope ŽAFM.. We varied the growth temperature between 5008C and 6308C and used substrates with different miscut angle from 0.158 to 28 off towards Ž111.A. After annealing under phosphine above 5008C, the wafer surface recovers its terrace structure with nominal width terraces. At growth temperatures of 580–6008C, the step flow is dominantly observed. At higher temperatures of 6308C, the step flow growth evolves towards step bunching when increasing the miscut angle from 0.28 to 28 off and the terrace width saturates at f 40 nm. The effect of the growth temperature is analysed taking account for the different surface energy barrier for the transition step flowrstep bunching. A clear evidence of the dependence of the activation energy with miscut angle will be shown. The Schwoebel’s barrier evolution is shown from the growth onto differently misoriented substrates. q 2000 Elsevier Science B.V. All rights reserved. PACS: 68.55.Jk; 81.15.Gh Keywords: MOVPE; AFM; InP; Vicinal surfaces
1. Introduction It has long been known that a semiconductor surface present various morphology depending on the growth conditions. The difference in these surface morphologies is small from the point of view of III–V compounds devices, nevertheless, it is significant from a fundamental point of view in the frame of the study of growth mechanisms during metalorganic vapor phase epitaxy ŽMOVPE.. Especially, various surface modifications on vicinal surface have ) Corresponding author. Tel.: q33-4-72-43-18-98; fax: q33-472-44-06-18. E-mail address: [email protected] ŽH. Dumont..
been studied extensively for GaAs and much less for the InP and InGaAs-based system. With the use of misoriented substrates Žvicinal surfaces., resulting from intentional miscut angle u , it appears that an attracting tool can be exploited. An illustration of the type of results observed after epitaxy is a consequence of the dominant growth processes occurring on such surfaces, which are the step flow growth and the step bunching mechanism. Early in 1950 and 1969, both mechanisms have been described theoretically by the well-known paper of Burton Cabrera Franck ŽBCF. and by R.L. Schwoebel, respectively w1,2x. In case of step bunching, an assumption of first importance is the so-called Schwoebel’s effect; i.e. different rate of incorporation of adatoms between
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 3 0 9 - 3
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
the up-side and the down-side steps sites due to an energy barrier at the step edge. It has been tacitly accepted that such a barrier exists, and direct estimation are often based on thermal activation processes on vicinal surfaces. We report the evolution of the growth mechanisms on vicinal Ž001. InP as a function of temperature for different miscut angle and will present a simplified model which allows an estimation of the energy barrier for that transition step flowrstep bunching. The study is based on ex-situ atomic force microscope ŽAFM. observation of the surface morphology after growth. The mono-atomic height resolution can be routinely observed as previously reported w3x. Like many other works in the literature, it will be assumed that the oxidized surface does replicate the original surface morphology with the presence of mono-atomic steps. As far as surface morphology is concerned, it is not clear what kind of disturbance would be caused by this oxide layer, however, the oxide layer thickness seems homogeneous since mono-atomic steps are visible at large surface scale Ž10 = 10 mm..
2. Experimental apparatus Epitaxial growth was performed in a T-shape reactor at atmospheric with H 2 as a carrier gas with 12 slm on Ž001. Fe-doped InP epiready substrates for additional electrical measurements. The substrates were intentionally misoriented from 0.28 Ž"0.058. to 28 off towards Ž111.A Žindium rich surface. for the purpose of the study. No special cleaning and etching steps were applied to the InP substrates prior to growth. Annealing and growth temperatures ranged from 5008C to 6308C. Before the epitaxy was done, thermal annealing under phosphine was performed with a flow rate of 80 sccm. The growth rate of InP was 2.5 mmrh and layer thickness were in the range 0.1–0.2 mm. Precursors were trimethylindium ŽTMI. and phosphine ŽPH 3 . for group. The VrIII ratio Žmolar flux of group Vrmolar flux of group III. was fixed at 70. The surface morphology was firstly examined with optical microscope under Nomarski contrast. Thus, mirror like samples at high magnification Ž=1000. were observed by ex-situ AFM with a Digital Instrument Nanoscope II in a constant
287
mode force Žforce of about 0.58 Nrm.. The AFM images presented here were performed with a height scale of 5 nm.
3. Results and discussion 3.1. Thermal annealing and diffusion As stated earlier, it would be desirable to determine the growth mechanisms which governs the steprterrace structure evolution with temperature and growth conditions. The most direct procedure to evaluate that evolution is a measure of the average terrace width L and the step height. In considering numerous experimental studies, it is recognised practically that the diffusion coefficient Ds and the miscut angle, govern the validity of the step flow growth regime; i.e. step flow becomes unstable either at low temperatures where surface diffusion is low, at high growth rate, or at high temperatures, where diffusion and evaporation of adatoms is rapid w4,5x. On the basis of our experimental results during thermal annealing and those of literature, we firstly will focus on surface diffusion mechanisms during annealing and forget the surface reconstruction effects. It should be noted that after thermal annealing at temperatures higher than 5808C, the oxide desorption is effective and the regular terrace network could be recovered with nominal terrace width as shown in Fig. 1. During that stage, In adatoms are considered to come from the substrate because there is no growth. From the examination of surface morphology of Fig. 1 for a 0.58 off miscut wafer, we can roughly estimate the diffusion length during thermal annealing. During the formation of terraces regularly spaced, adatoms Žespecially In. should migrate along a terrace to form a new step edge whose mechanism gives a rough estimation of l in the w110x direction Ž L F l with L s 115 nm.. Based on that simplified assumption, where the migration distance is largely underestimated, adatoms may be regarded as having an average life estimated by its residence time t and its surface diffusion coefficient Ds , which is thermally activated Ds s D 0 expŽyEdrRT .. As noted by Shitara et al. w6x, the cristallographic anisotropy and miscut angle may be pronounced in the activation energy Ed . Thus, the average life of adatoms; i.e. the
288
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
and Kobayashi w11x calculated that after a time interval of 1 s, at a temperature of 6008C, an InP surface should be completely In-terminated. On the other hand, a value in the range 0.4–0.5 eV for the activation energy for the diffusion of Ga on GaAs was also given by Nishinaga et al. w12x close to the value we consider here. Concerning the surface diffusion energy, another higher estimate of 2.3 eV, in case of GaAs step flow growth, has been given by Kisker et al. w13x using in-situ X-ray techniques during MOVPE in the temperature range 475–5758C. That value probably overestimates the activation energy and seems linked to the Ga–As bonding energy. 3.2. Growth Fig. 1. AFM image Ž1000=1000 nm. scan of the InP surface after annealing at 6008C under phosphine.
average length of time it can stay at the surface before it is incorporated into the crystal lattice or it is re-emitted to the vapour may vary considerably. For instance, an ex-situ AFM study of InP surface grown by MOVPE has been conducted by Merlin et al. w7x. In the case of annealing at 6308C, it results that the surface diffusion length was estimated to 350 nm, close to the half-terrace width. We propose here, a smaller estimation; l ) 120 nm, is underestimated but of the same order of magnitude and in agreement with results of Merlin et al. If we consider surface diffusion into one direction only, the residence time may be evaluated from the well-known Einstein relation: t s l2rD. Using the value of Ed f 0.5–0.7 eV for InP Ž100. given by Vershuren et al. w8x, L s 100 nm for the terrace width and D 0 f 1 = 10y9 m2 sy1 ŽIn diffusion onto GaAs surfaces. w9x, we obtained t f 0.02 s at 5008C and value of 0.01 s at 6008C. Even though the residence time cannot be directly measured during the annealing process by MOVPE, it is a significant property of the surface diffusion process, for it means that the time scale for the surface to be changed correspond to that of the actual experimental based on in-situ optical surface characterisation, such as reflectance differential spectroscopy or surface photo absorption which typically needs time resolution better than 100 ms w10x. For instance, according to the InP stability, Kobayashi
We present in Fig. 2 the evolution of L for epitaxially deposited InPrInP as a function of the substrate miscut angle at different temperatures. The nominal terrace width is also shown for mono-atomic and double-height steps for the sake of comparison. The results can be expressed as following: at low temperatures and for angles 0.068 F u F 0.28, the terrace width is kept close to the nominal value. Thus, steps propagate according to the step flow growth mode and a slight misorientation of the substrate allows a regular spacing of the step edge reducing surface defects. When u G 0.358, terraces are always larger than the nominal value characteristic of the step bunching. At 6308C, L is approxi-
Fig. 2. Terrace width as a function of miscut angle at different growth temperatures.
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
mately three to four times greater than the nominal value, and the formation of double-height steps is more energetically favorable than forming monoatomic steps for the same horizontal distance. That evolution is in accordance with the previous results obtained for the growth of GaAsrGaAs by MOVPE reported by Shinohara and Inoue w14x. The influence of growth temperature upon the transition step flowrstep bunching can be experimentally resumed. At 6308C, the step bunching appears for u G 0.158, at 5808C, it appears for u G 0.358, and so on. Generally speaking, step-bunched surfaces are not completely bunched and single steps also co-exist. From the experimental results of Fig. 2, we tried to extract an activation energy for the step-bunching mechanism. It has been done by evaluating, for a given miscut angle, the slope of the change in the terrace width as a function of temperature as shown in Fig. 3. The relationship between the terrace width Žat the stage of saturation. and temperature is thermally activated and can be expressed as L s L 0 expŽyEarRT . where L0 and Ea are the nominal terrace width and apparent activation energy, respectively. It can be noticed from Fig. 3 that Ea is depends on miscut angle ranging from 0.35 Žfor 0.28 off. to 0.2 eV Žfor 0.58 off. misoriented samples. Presented in Fig. 4 is the evolution of Ea as a function of u . Ea corresponds theoretically to the Schwoebel’s barrier for the change from the dashed line to the bold line in Fig. 2. Because of the
Fig. 3. Evolution of the terrace width as a function of growth temperature and miscut angle.
289
Fig. 4. Evolution of the apparent activation energy for step bunching as a function of miscut angle.
coexistence of mono-steps and bunched steps for a similar surface, the accuracy of Ea is estimated at "0.05 eV, but it is rather interesting to take note of the decrease in Ea as the miscut angle increases. Some results obtained on 28 off samples are rather difficult to interpret because of the roughening of the step front but an extrapolation from Fig. 4 would lead to a low value of 0.1 eV, which is smaller than for GaAs. On the opposite, a value of f 0.4 eV would also be graphically deduced for the growth onto exactly oriented Ž001. InP. Let us now turn to the physical meaning of the measured activation energy Ea . It can be recalled that the Schwoebel’s barrier is an energetic barrier near the step which assumption allows the observation of the step bunching and formation of multisteps. As illustrated by Ishizaki et al. w15x, Ea can be represented for an adatom by the difference between the activation energy for migration to an up-side site Eup and evaporation from the terraces’ surface Eterrace Ž Ea s Eup y Eterrace .. In other words, Eterrace is also the average potential energy of adatoms far from the step edge. In considering the growth of InP by chemical beam epitaxy, recent results of Vershuren et al. have shown that typical values of Ea are in the range of 0.47 eV for exactly oriented Ž001. InP. Those values can be compared with our experimental measurements of 0.4–0.5 eV for InP and consistent with previous results ŽFig. 3.. In case of growth onto
290
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
exactly oriented substrates, the step density is very low and their contribution to the step flow growth is reduced. It results that the apparent activation energy becomes the difference between desorption and hopping, and the physical meaning of the Schwoebel’s barrier disappears because Eup s 0. The decrease of Ea as a function of the miscut angle is an indication that the initial step density increases, the probability for adatoms to reach an up-side step increases at constant diffusion length, and that individual steps may interact with an attractive force. It can be recalled that Ishizaki et al. obtained an apparent activation energy of f 0.47 eV for the growth onto Ž001.GaAs 28 off by MOVPE taking account for the best simulation for the saturation of the terrace width at 60 nm. It is of interest to mention that the saturation length of terraces Ž40–60 nm. is of the same order of magnitude for 28 off miscut if we compare homoepitaxy of InPrInP and thermal annealing of GaAs under arsine w16x. We cannot consider that this saturation length is a rough estimation of the diffusion length for a given growth temperature and a given growth rate. In fact, it is rather a value given by the order of magnitude of Ea which are quite different for the two systems under consideration.
4. Conclusion In this paper, it is shown that during the thermal annealing of InP, no step bunching occurs which allows an estimation of the diffusion constant of In adatoms on Ž001. InP at temperatures close to 6008C . For the growth of InP epilayers, the effect of miscut angle on the terrace width is shown. The transition step flowrstep bunching with temperature is analyzed and we deduced an experimental activa-
tion energy corresponding to the Schwoebel’s barrier for the step bunching mechanism.
Acknowledgements Authors would like to thank sincerely the help of V. Thevenot and V. Souliere ´ ` for the AFM measurements done in the study.
References w1x W.K. Burton, N. Cabrera, F.C. Franck, Philos. Trans. R. Soc. Lodon, Ser. A 243 Ž1951. 299. w2x R.L. Schwoebel, J. Appl. Phys. 40 Ž1969. 614. w3x H. Dumont, L. Auvray, J. Dazord, Y. Monteil, J. Bouix, A. Ougazzaden, Appl. Surf. Sci. 150 Ž1999. 161. w4x M. Kasu, N. Kobayashi, J. Appl. Phys. 78 Ž1995. 3026. w5x J. Villain, in: Physique de la Croissance Cristalline, Editions Eyrolles, Paris, 1995, p. 72. w6x T. Shitara, J. Zhang, J.H. Neave, B.A. Joyce, J. Cryst. Growth 111 Ž1991. 83. w7x V. Merlin, T.M. Duc, G. Younes, Y. Monteil, V. Souliere, ` P. Regreny, J. Appl. Phys. 78 Ž1995. 5048. w8x C.A. Vershuren, M.R. Leys, H. Vonk, J.H. Wolter, Appl. Phys. Lett. 74 Ž1999. 2197. w9x A. Palma, E. Semprini, A. Talamo, N. Tomassini, Mater. Sci. Eng., B 37 Ž1996. 135. w10x D.E. Aspnes, I. Kamiya, H. Tanaka, R. Bhat, J. Vac. Sci. Technol., B, 10 Ž1992. 1725. w11x N. Kobayashi, Y. Kobayashi, Jpn. J. Appl. Phys. 30 Ž1991. 1699. w12x T. Nishinaga, T. Shitara, K. Mochizuki, K.I. Cho, J. Cryst. Growth 99 Ž1990. 482. w13x D.W. Kisker, G.B. Stephenson, P.H. Fuoss, F.J. Lamelas, S. Brennan, P. Imperatori, J. Cryst. Growth 124 Ž1992. 1. w14x M. Shinohara, N. Inoue, Appl. Phys. Lett. 66 Ž1995. 1936. w15x J. Ishizaki, K. Ohkuri, T. Fukui, Jpn. J. Appl. Phys. 35 Ž1996. 1280. w16x K. Hata, H. Shigekawa, T. Ueda, M. Akiyama, T. Okano, Phys. Rev. B 57 Ž1998. 4500.
Energy barrier for the growth transition step-flowrstep-bunching during epitaxy of InPrInP H. Dumont ) , Y. Monteil, J. Bouix LMI-UCB Lyon I, UMR-5615, 43 BouleÕard du 11 NoÕembre 1918, 69622 Villeurbanne Cedex, France Received 13 September 1999; received in revised form 24 November 1999; accepted 30 March 2000
Abstract We report the growth mode evolution of homoepitaxially grown InP by metal organic vapour phase epitaxy examined by ex-situ atomic force microscope ŽAFM.. We varied the growth temperature between 5008C and 6308C and used substrates with different miscut angle from 0.158 to 28 off towards Ž111.A. After annealing under phosphine above 5008C, the wafer surface recovers its terrace structure with nominal width terraces. At growth temperatures of 580–6008C, the step flow is dominantly observed. At higher temperatures of 6308C, the step flow growth evolves towards step bunching when increasing the miscut angle from 0.28 to 28 off and the terrace width saturates at f 40 nm. The effect of the growth temperature is analysed taking account for the different surface energy barrier for the transition step flowrstep bunching. A clear evidence of the dependence of the activation energy with miscut angle will be shown. The Schwoebel’s barrier evolution is shown from the growth onto differently misoriented substrates. q 2000 Elsevier Science B.V. All rights reserved. PACS: 68.55.Jk; 81.15.Gh Keywords: MOVPE; AFM; InP; Vicinal surfaces
1. Introduction It has long been known that a semiconductor surface present various morphology depending on the growth conditions. The difference in these surface morphologies is small from the point of view of III–V compounds devices, nevertheless, it is significant from a fundamental point of view in the frame of the study of growth mechanisms during metalorganic vapor phase epitaxy ŽMOVPE.. Especially, various surface modifications on vicinal surface have ) Corresponding author. Tel.: q33-4-72-43-18-98; fax: q33-472-44-06-18. E-mail address: [email protected] ŽH. Dumont..
been studied extensively for GaAs and much less for the InP and InGaAs-based system. With the use of misoriented substrates Žvicinal surfaces., resulting from intentional miscut angle u , it appears that an attracting tool can be exploited. An illustration of the type of results observed after epitaxy is a consequence of the dominant growth processes occurring on such surfaces, which are the step flow growth and the step bunching mechanism. Early in 1950 and 1969, both mechanisms have been described theoretically by the well-known paper of Burton Cabrera Franck ŽBCF. and by R.L. Schwoebel, respectively w1,2x. In case of step bunching, an assumption of first importance is the so-called Schwoebel’s effect; i.e. different rate of incorporation of adatoms between
0169-4332r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 3 0 9 - 3
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
the up-side and the down-side steps sites due to an energy barrier at the step edge. It has been tacitly accepted that such a barrier exists, and direct estimation are often based on thermal activation processes on vicinal surfaces. We report the evolution of the growth mechanisms on vicinal Ž001. InP as a function of temperature for different miscut angle and will present a simplified model which allows an estimation of the energy barrier for that transition step flowrstep bunching. The study is based on ex-situ atomic force microscope ŽAFM. observation of the surface morphology after growth. The mono-atomic height resolution can be routinely observed as previously reported w3x. Like many other works in the literature, it will be assumed that the oxidized surface does replicate the original surface morphology with the presence of mono-atomic steps. As far as surface morphology is concerned, it is not clear what kind of disturbance would be caused by this oxide layer, however, the oxide layer thickness seems homogeneous since mono-atomic steps are visible at large surface scale Ž10 = 10 mm..
2. Experimental apparatus Epitaxial growth was performed in a T-shape reactor at atmospheric with H 2 as a carrier gas with 12 slm on Ž001. Fe-doped InP epiready substrates for additional electrical measurements. The substrates were intentionally misoriented from 0.28 Ž"0.058. to 28 off towards Ž111.A Žindium rich surface. for the purpose of the study. No special cleaning and etching steps were applied to the InP substrates prior to growth. Annealing and growth temperatures ranged from 5008C to 6308C. Before the epitaxy was done, thermal annealing under phosphine was performed with a flow rate of 80 sccm. The growth rate of InP was 2.5 mmrh and layer thickness were in the range 0.1–0.2 mm. Precursors were trimethylindium ŽTMI. and phosphine ŽPH 3 . for group. The VrIII ratio Žmolar flux of group Vrmolar flux of group III. was fixed at 70. The surface morphology was firstly examined with optical microscope under Nomarski contrast. Thus, mirror like samples at high magnification Ž=1000. were observed by ex-situ AFM with a Digital Instrument Nanoscope II in a constant
287
mode force Žforce of about 0.58 Nrm.. The AFM images presented here were performed with a height scale of 5 nm.
3. Results and discussion 3.1. Thermal annealing and diffusion As stated earlier, it would be desirable to determine the growth mechanisms which governs the steprterrace structure evolution with temperature and growth conditions. The most direct procedure to evaluate that evolution is a measure of the average terrace width L and the step height. In considering numerous experimental studies, it is recognised practically that the diffusion coefficient Ds and the miscut angle, govern the validity of the step flow growth regime; i.e. step flow becomes unstable either at low temperatures where surface diffusion is low, at high growth rate, or at high temperatures, where diffusion and evaporation of adatoms is rapid w4,5x. On the basis of our experimental results during thermal annealing and those of literature, we firstly will focus on surface diffusion mechanisms during annealing and forget the surface reconstruction effects. It should be noted that after thermal annealing at temperatures higher than 5808C, the oxide desorption is effective and the regular terrace network could be recovered with nominal terrace width as shown in Fig. 1. During that stage, In adatoms are considered to come from the substrate because there is no growth. From the examination of surface morphology of Fig. 1 for a 0.58 off miscut wafer, we can roughly estimate the diffusion length during thermal annealing. During the formation of terraces regularly spaced, adatoms Žespecially In. should migrate along a terrace to form a new step edge whose mechanism gives a rough estimation of l in the w110x direction Ž L F l with L s 115 nm.. Based on that simplified assumption, where the migration distance is largely underestimated, adatoms may be regarded as having an average life estimated by its residence time t and its surface diffusion coefficient Ds , which is thermally activated Ds s D 0 expŽyEdrRT .. As noted by Shitara et al. w6x, the cristallographic anisotropy and miscut angle may be pronounced in the activation energy Ed . Thus, the average life of adatoms; i.e. the
288
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
and Kobayashi w11x calculated that after a time interval of 1 s, at a temperature of 6008C, an InP surface should be completely In-terminated. On the other hand, a value in the range 0.4–0.5 eV for the activation energy for the diffusion of Ga on GaAs was also given by Nishinaga et al. w12x close to the value we consider here. Concerning the surface diffusion energy, another higher estimate of 2.3 eV, in case of GaAs step flow growth, has been given by Kisker et al. w13x using in-situ X-ray techniques during MOVPE in the temperature range 475–5758C. That value probably overestimates the activation energy and seems linked to the Ga–As bonding energy. 3.2. Growth Fig. 1. AFM image Ž1000=1000 nm. scan of the InP surface after annealing at 6008C under phosphine.
average length of time it can stay at the surface before it is incorporated into the crystal lattice or it is re-emitted to the vapour may vary considerably. For instance, an ex-situ AFM study of InP surface grown by MOVPE has been conducted by Merlin et al. w7x. In the case of annealing at 6308C, it results that the surface diffusion length was estimated to 350 nm, close to the half-terrace width. We propose here, a smaller estimation; l ) 120 nm, is underestimated but of the same order of magnitude and in agreement with results of Merlin et al. If we consider surface diffusion into one direction only, the residence time may be evaluated from the well-known Einstein relation: t s l2rD. Using the value of Ed f 0.5–0.7 eV for InP Ž100. given by Vershuren et al. w8x, L s 100 nm for the terrace width and D 0 f 1 = 10y9 m2 sy1 ŽIn diffusion onto GaAs surfaces. w9x, we obtained t f 0.02 s at 5008C and value of 0.01 s at 6008C. Even though the residence time cannot be directly measured during the annealing process by MOVPE, it is a significant property of the surface diffusion process, for it means that the time scale for the surface to be changed correspond to that of the actual experimental based on in-situ optical surface characterisation, such as reflectance differential spectroscopy or surface photo absorption which typically needs time resolution better than 100 ms w10x. For instance, according to the InP stability, Kobayashi
We present in Fig. 2 the evolution of L for epitaxially deposited InPrInP as a function of the substrate miscut angle at different temperatures. The nominal terrace width is also shown for mono-atomic and double-height steps for the sake of comparison. The results can be expressed as following: at low temperatures and for angles 0.068 F u F 0.28, the terrace width is kept close to the nominal value. Thus, steps propagate according to the step flow growth mode and a slight misorientation of the substrate allows a regular spacing of the step edge reducing surface defects. When u G 0.358, terraces are always larger than the nominal value characteristic of the step bunching. At 6308C, L is approxi-
Fig. 2. Terrace width as a function of miscut angle at different growth temperatures.
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
mately three to four times greater than the nominal value, and the formation of double-height steps is more energetically favorable than forming monoatomic steps for the same horizontal distance. That evolution is in accordance with the previous results obtained for the growth of GaAsrGaAs by MOVPE reported by Shinohara and Inoue w14x. The influence of growth temperature upon the transition step flowrstep bunching can be experimentally resumed. At 6308C, the step bunching appears for u G 0.158, at 5808C, it appears for u G 0.358, and so on. Generally speaking, step-bunched surfaces are not completely bunched and single steps also co-exist. From the experimental results of Fig. 2, we tried to extract an activation energy for the step-bunching mechanism. It has been done by evaluating, for a given miscut angle, the slope of the change in the terrace width as a function of temperature as shown in Fig. 3. The relationship between the terrace width Žat the stage of saturation. and temperature is thermally activated and can be expressed as L s L 0 expŽyEarRT . where L0 and Ea are the nominal terrace width and apparent activation energy, respectively. It can be noticed from Fig. 3 that Ea is depends on miscut angle ranging from 0.35 Žfor 0.28 off. to 0.2 eV Žfor 0.58 off. misoriented samples. Presented in Fig. 4 is the evolution of Ea as a function of u . Ea corresponds theoretically to the Schwoebel’s barrier for the change from the dashed line to the bold line in Fig. 2. Because of the
Fig. 3. Evolution of the terrace width as a function of growth temperature and miscut angle.
289
Fig. 4. Evolution of the apparent activation energy for step bunching as a function of miscut angle.
coexistence of mono-steps and bunched steps for a similar surface, the accuracy of Ea is estimated at "0.05 eV, but it is rather interesting to take note of the decrease in Ea as the miscut angle increases. Some results obtained on 28 off samples are rather difficult to interpret because of the roughening of the step front but an extrapolation from Fig. 4 would lead to a low value of 0.1 eV, which is smaller than for GaAs. On the opposite, a value of f 0.4 eV would also be graphically deduced for the growth onto exactly oriented Ž001. InP. Let us now turn to the physical meaning of the measured activation energy Ea . It can be recalled that the Schwoebel’s barrier is an energetic barrier near the step which assumption allows the observation of the step bunching and formation of multisteps. As illustrated by Ishizaki et al. w15x, Ea can be represented for an adatom by the difference between the activation energy for migration to an up-side site Eup and evaporation from the terraces’ surface Eterrace Ž Ea s Eup y Eterrace .. In other words, Eterrace is also the average potential energy of adatoms far from the step edge. In considering the growth of InP by chemical beam epitaxy, recent results of Vershuren et al. have shown that typical values of Ea are in the range of 0.47 eV for exactly oriented Ž001. InP. Those values can be compared with our experimental measurements of 0.4–0.5 eV for InP and consistent with previous results ŽFig. 3.. In case of growth onto
290
H. Dumont et al.r Applied Surface Science 161 (2000) 286–290
exactly oriented substrates, the step density is very low and their contribution to the step flow growth is reduced. It results that the apparent activation energy becomes the difference between desorption and hopping, and the physical meaning of the Schwoebel’s barrier disappears because Eup s 0. The decrease of Ea as a function of the miscut angle is an indication that the initial step density increases, the probability for adatoms to reach an up-side step increases at constant diffusion length, and that individual steps may interact with an attractive force. It can be recalled that Ishizaki et al. obtained an apparent activation energy of f 0.47 eV for the growth onto Ž001.GaAs 28 off by MOVPE taking account for the best simulation for the saturation of the terrace width at 60 nm. It is of interest to mention that the saturation length of terraces Ž40–60 nm. is of the same order of magnitude for 28 off miscut if we compare homoepitaxy of InPrInP and thermal annealing of GaAs under arsine w16x. We cannot consider that this saturation length is a rough estimation of the diffusion length for a given growth temperature and a given growth rate. In fact, it is rather a value given by the order of magnitude of Ea which are quite different for the two systems under consideration.
4. Conclusion In this paper, it is shown that during the thermal annealing of InP, no step bunching occurs which allows an estimation of the diffusion constant of In adatoms on Ž001. InP at temperatures close to 6008C . For the growth of InP epilayers, the effect of miscut angle on the terrace width is shown. The transition step flowrstep bunching with temperature is analyzed and we deduced an experimental activa-
tion energy corresponding to the Schwoebel’s barrier for the step bunching mechanism.
Acknowledgements Authors would like to thank sincerely the help of V. Thevenot and V. Souliere ´ ` for the AFM measurements done in the study.
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