*Corresponding author. Tel. #81 3 3812 2111 6773; fax:#81 3 5803 3975; e-mail: yan@cryst.t.u-tokyo.ac.jp.

Journal of Crystal Growth 198/199 (1999) 1077—1081

Interface supersaturation dependence of step velocityin liquid-phase epitaxy of InP

Zheng Yan*, Shigeya Naritsuka, Tatau NishinagaDepartment of Electronic Engineering, The Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo,

Tokyo 113, Japan

Abstract

By employing microchannel epitaxy (MCE), it became possible to reduce the dislocation density in liquid-phaseepitaxy (LPE) of InP, so that steps supplied from only one screw dislocation can cover whole surface of MCE island. Thisenabled us to measure interstep distance by AFM and to calculate interface supersaturation even in metallic solutionwith the help of the formula given by Cabrera and Levine. From the interstep distance, the step velocity was calculated byemploying the macroscopic vertical growth velocity. It was found that the step velocity increases linearly with theincrease of the interface supersaturation, and the slope of the curve, which gives a step kinetic coefficient of the growth,increases with the increase of the growth temperature. From the Arrhenius plot of the kinetic coefficient, the activationenergy of step advance was found as E"32.8 kJ/mol. A critical value of the interface supersaturation p

#, below which

steps do not move, has also been found to exist. It was also found that p#

decreases with the increase of the growthtemperature. The presence of p

#probably means that step advance is stopped by the impurity pinning effect. ( 1999

Elsevier Science B.V. All rights reserved.

PACS: 78.66.Fd; 81.15.Lm

Keywords: Interface supersaturation; Step velocity; Microchannel epitaxy; Spiral step

1. Introduction

Interface supersaturation is an important para-meter in crystal growth. However, as it differs frombulk supersaturation, few study has reported its

dependence on the growth conditions in liquid-phase epitaxy (LPE) of semiconductors. We havesucceeded in drastically decreasing the number ofdislocations by using LPE microchannel epitaxy[1—3]. In this technique, LPE growth starts tooccur on substrate in a line window (microchannel)cut in SiO

2film deposited on the substrate and then

the growth continues in the lateral direction to givea layer on the SiO

2film. From one microchannel,

0022-0248/99/$ — see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 1 2 5 - 7

Fig. 1. (a) Optical microphotograph of microchannel epitaxy(MCE) island. (b) Schematic illustration of the MCE islandindicating the crystallographic orientations and the orientationof the microchannel.

one gets a flat top island with large dislocation freearea except a narrow straight region above the lineseed. Since the number of screw dislocations isa few in the island, it is possible to observe spiralsteps spreading all over the grown layer by atomicforce microscope (AFM). Very often only one ac-tive spiral per island was observed. The spiral wasfound frequently located at a corner of the island[4]. By employing the equilibrium relation betweenthe interface supersaturation and the interstep dis-tance of the spiral steps given by Cabrera andLevine [5], we can determine the interface super-saturation even in metallic solution like LPE ofsemiconductors by assuming interface free energybetween the metallic solution and the growingsemiconductor. The step velocity is also possible tobe calculated from the interstep distance and themacroscopic velocity of the vertical growth. Thevalue of the step velocity has the order of a fewlm/s to a few 10 lm/s, which is much larger thanthose in vapor growth, but similar to those re-ported in solution growth of ADP [6] and KDP[7]. The step velocity was found depending on theinterface supersaturation as well as the growth tem-perature. Both the interface supersaturation andthe temperature dependencies of step velocity werestudied.

2. Experimental procedure

InP wafers with the orientation of (1 0 0) just wasused as the substrates. Prior to LPE growth, a SiO

2layer with a thickness of about 100 nm was depos-ited on the substrate by spinning of organic solu-tion (OCD, Tokyo Ouka) and baking at 450°C. Thelinear microchannels were opened in the SiO

2mask

with an angle of 22° off from S0 1 1T using a con-ventional photolithographic technique. The lengthand width of the microchannels were 700 and 5 lm,respectively. The LPE was carried out with In (7 N)solution using a conventional horizontal slidingboat system. The growth temperature, the coolingrate and the growth time were varied from 450 to600°C, from 0.05 to 0.3°C/min and from 0.5 to 15 h,respectively. The interstep distance of the spiralsteps on the surfaces of the MCE layers was mea-sured by AFM.

3. Results and discussion

3.1. Determinations of interface supersaturationand step velocity

Fig. 1a shows a MCE island grown at 550°Cwith the cooling rate and the growth time of0.1°C/min and 1 h, respectively. A schematic illus-tration of the grown island indicating its crystallo-graphic orientations and the orientation of themicrochannel is shown in Fig. 1b. The MCEgrowth occurs in the lateral and vertical directionssimultaneously. As shown schematically in Fig. 1b,(1 1 1)B and (0 0 1) facets appear near the edges ofthe microchannel. Since the direction of the micro-channel is chosen as 22° off from S0 1 1T orienta-tion, the side surface becomes atomically rough.Due to this, the lateral growth is conducted bysimple incorporation of the solute onto the roughsurface. On the other hand, the vertical growthis conducted by the spiral steps from a screw

1078 Z. Yan et al. / Journal of Crystal Growth 198/199 (1999) 1077–1081

Fig. 2. AFM image showing the center of the spiral steps. TheAFM was taken in the area at the right and lower corner of theMCE island shown in Fig. 1a.

Fig. 4. Interface supersaturation dependence of the step velo-city.

Fig. 3. Interface supersaturation dependence of the verticalgrowth rate.

dislocation. In this case, we can determine thevalues of the interface supersaturation and the stepvelocity by measuring the interstep distance of thespiral steps and the growth thickness.

In Fig. 2, an AFM image of the center of thespiral steps is shown. All the spiral steps havemonolayer height and have almost equal interstepdistances. From the interstep distance of the spiralsteps, the interface supersaturation can be derivedfrom the following equation which was given byCabrera and Levine [5],

p"19ack¹j

, (1)

when the spiral is single folded and the spiralsteps have monolayer height. In Eq. (1), a, c, k, ¹and j denote lattice constant, step free energy,Boltzmann constant, growth temperature andinterstep distance, respectively. We tentativelycalculated the step free energy from the latent heatof InP based on a bond-breaking model, asc"0.122 J/m2.

The step velocity is calculated from the verticalgrowth rate (R) and the interstep distance as

follows:

v45"(2j/a)R. (2)

3.2. The linear interface supersaturation dependenceof step velocity

Figs. 3 and 4 show, respectively, the verticalgrowth rate and the step velocity as functions ofinterface supersaturation for different temperaturesof 450, 500 and 550°C. Both the vertical growthrate and the step velocity are found to increase withthe increase of the interface supersaturation. Thevalue of step velocity is on the order of 10 lm/s.This magnitude of the step velocity means that ina unit length of 1 lm of a step with monolayer

Z. Yan et al. / Journal of Crystal Growth 198/199 (1999) 1077–1081 1079

Fig. 5. Natural logarithm of the step kinetic coefficient, b, asa function of the reciprocal temperature.

Table 1Values of b and p

#at different growth temperatures

Temperature (°C) b (m/s) p#

450 7.87]10~4 0.0205500 1.21]10~3 0.0163550 1.52]10~3 0.00903

height, about 5.75]107 InP units enter the step persecond. Similar magnitude of step velocity has beenreported in solution growth of ADP [6] and KDP[7], where in situ interference technique was ap-plied to measure the step velocity.

Employing linear approximation in Fig. 4, wecan determine the kinetic coefficient of the stepvelocity, b, as,

b"v45(p!p

#)~1 (p'p

#), (3)

where p#

is the critical interface supersaturationunder which the step cannot move. The existence ofp#can be attributed to the effect of step pinning by

the impurity at the step front.

3.3. The temperature dependence of b and p#

In Table 1, the values of b and p#

at differenttemperatures obtained from Fig. 4 and Eq. (3) arelisted. It is found that b increases while p

#decreases

with the increase of temperature. Fig. 5 shows ln bas a function of reciprocal temperature. The activa-tion energy of step advance is derived from the

slope to be E"32.8 kJ/mol. This value of activa-tion energy has the same order as that in ADPsolution growth [6] reported as 65 kJ/mol for¹(40°C and 47 kJ/mol for ¹'40°C. However,in the case of InP, the value is smaller. This may beattributed to the difference in the kind of bondingbetween the atoms. The value of p

#shows the

relative strength of the step pinning. The largerp#

at the lower temperature shows stronger steppinning resulted possibly from either higher stiff-ness of the step or larger population of impuritiesabsorbed at the step front when the temperature islower.

4. Conclusions

The step velocity was calculated from the inter-step distance of the spiral steps and the verticalgrowth velocity. The interface supersaturation wasderived from the interstep distance by using theformula given by Cabrera and Levine. The stepvelocity was found to increase linearly with theincrease of the interface supersaturation. The slopeof the curve, which gives the step kinetic coefficientb, increases with the increase of the temperature.From the Arrhenius plot of the kinetic coefficient,the activation energy of step advance is found asE"32.8 kJ/mol. A critical value p

#under which

step cannot move was found to exist. The presenceof the critical interface supersaturation probablymeans that step advance is stopped by the effect ofstep pinning resulted from impurity at the stepfront. The critical interface supersaturation wasfound to decrease with the increase of the growthtemperature.

Acknowledgements

The authors would like to thank Dr. M. Tanakafor his discussion. This work was supported bya Grant-in-Aid (B) “Studies of InP layers grownon Si substrates by epitaxial lateral overgrowthand fabrication of long-wavelength lasers” No.07555107 from the Ministry of Education, Science,Sports and Culture of Japan. One of the authors(Z. Yan) was also supported by the Research

1080 Z. Yan et al. / Journal of Crystal Growth 198/199 (1999) 1077–1081

Fellowship of the Japan Society for the Promotionof Science for Young Scientists.

References

[1] T. Nishinaga, T. Nakano, S. Zhang, Jpn. J. Appl. Phys. 27(1988) L964.

[2] Y. Ujiie, T. Nishinaga, Jpn. J. Appl. Phys. 28 (1989) L337.

[3] S. Naritsuka, T. Nishinaga, J. Crystal Growth 146 (1995)314.

[4] Z. Yan, S. Naritsuka, T. Nishinaga, J. Crystal Growth 192(1998) 11.

[5] N. Cabrera, M.M. Levine, Phil. Mag. 1 (1956) 450.[6] P.G. Vekilov, Yu.G. Kuznetsov, A.A. Chernov, J. Crystal

Growth 121 (1992) 44.[7] L.N. Rashkovich, N.V. Kronsky, J. Crystal Growth 182

(1997) 434.

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