Influence of clustering on the mobility of IIIV semiconductor alloysP. Blood and A. D. C. Grassie Citation: Journal of Applied Physics 56, 1866 (1984); doi: 10.1063/1.334200 View online: http://dx.doi.org/10.1063/1.334200 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/56/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enhancing hole mobility in III-V semiconductors J. Appl. Phys. 111, 103706 (2012); 10.1063/1.4718381 Computational band-structure engineering of III–V semiconductor alloys Appl. Phys. Lett. 79, 368 (2001); 10.1063/1.1383282 Effects of atomic clustering on the optical properties of IIIV alloys Appl. Phys. Lett. 64, 2882 (1994); 10.1063/1.111403 Atomic ordering in III/V semiconductor alloys J. Vac. Sci. Technol. B 9, 2182 (1991); 10.1116/1.585761 Velocityfield characteristics of IIIV semiconductor alloys: Band structure influences J. Appl. Phys. 61, 1475 (1987); 10.1063/1.338079

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Influence of clustering on the mobility of U,-V semiconductor arroys P. Blood Philips Research Laboratories, Redhill, Surrey RHI 5HA, England

A. D. C. Grassie University of Sussex, Brighton, Sussex BNl 9QH, England

(Received 9 January 1984; accepted for publication 14 March 1984)

Using published structural data we estimate that the conduction band in GaInAsP alloys matched to InP has a spatial variation with an amplitude of about 0.08 e V as a result of partial segregation into clusters. We argue that the electrons may be located in isolated "lakes" and that since the conduction band fluctuation is larger than kTat room temperature and below, current conduction may be inhomogeneous and may be restricted to percolation paths. This could account for reported differences in mobility of alloys grown within and outside the miscibility gap.

From thermodynamic considerations a miscibility gap has been predicted in the Gax In I _ x Asy P I _ y alloy system for growth temperatures as high as 660 ·C, I nevertheless growth of single crystal layers within this gap is possible with stabilization by the strain energy inherent in any clustering. 2

In their transmission electron microscope (TEM) study of GalnAsP grown lattice matched to InP by liquid-phase epi­taxy (LPE) Henoc et al.3 found a quasiperiodic variation of strain contrast on a scale of about 1000 A only in those layers grown within the region of the solid phase instability. Mea­surements on one sample showed that this contrast was re­lated to a modulation in the alloy composition such that the In:As ratio remained constant, with variations in x and y as large as 10%. Renoc et aC also observed a structure on a smaller scale, and similar TEM images have been reported by Gowers4 who found strain contrast with periodicities of 60, 80, and 100 A for alloys of GaInAs and GaInP grown by molecular beam epitaxy (MBEJ and GalnAsP grown by LPE, respectively. The contrast amplitudes are consistent with composition deviations of about ± 10%. Strain con­trast was not observed for AIGaAs.4

To achieve a satisfactory description of the composition and temperature dependence of the electron mobility in qua­ternary alloys lattice matched to lnP (y = 2.2x), it has been necessary to include an aHoy scattering process character­ized by an aHoy scattering potentia! .& Ue , S supposed to be due to short range compositional disorder in the distribution of group HI and V atoms on their respective sublattices. However there are differences in the reported behavior of A Ue as a function of compositionS which would not be ex­pected if the disorder is truly random, and the value of .& Ue ~ O. 7 e V necessary to fit the data is large compared with values of 0.289, 0.263, and 0.54 eV calculated from dectro­negativity, electron affinity and band gap differences, re­spectively6 (the last value is considered the least reliable6).

Haynes et al. S comment that these discrepancies show that the physical interpretation of A Ue is not clear. Recently Quillec et aI.7 have shown that the Hall mobility of GIlo.29 IIlo 71 ASo.65 P O.3~ grown by LPE on lnP is 20%-25% higher for growth at 740·C than for growth at 630-660 ·C

within the miscibility gap. This mobility difference cannot be ascribed to higher compensation or greater random alloy scattering in the sample grown at low temperature so the authors proposed that an additional scattering mechanism exists in these samples which, by comparison with the TEM studies,3 they associate with composition fluctuations. In this paper we will show that conduction band fluctuations may explain this mobility difference and we suggest that consideration of such effects may help in understanding the mechanism of "alloy scattering".

Our model is based on the results of the structural inves­tigations summarized above3

,4 appUed to the sample grown by Quillec et al. 7 at 650 ·C in the miscibility gap with a low mobiJjty. This sample had a mean composition of y(As) = 0.60, and since it is matched to InP x(Ga) = 0.27. We assume a composition fluctuation in x of ± 10% and a corresponding value of y such that the As:ln ratio is kept constane at the value of 0.82 determined by the mean com­position. This leads us to consider two extreme composi­tions: (l)x = 0.24,y = 0.62 and (2)x = 0.30 andy = 0.57.

The band diagram for a macroscopic n-isotype hetero­barrier between these two materials is shown in Fig. 1. We assume that the doping levels are the same and that the dif-

FIG. 1. Conduction band structure of an n-isotype heterobarrier between two Ga. In, _ .As,P, _y crystals with (I)x = 0.24,y = 0.62 and (2)x = 0.30 and y = 0.57. From the calculations outlined in the text we obtain t.Ec =0.083 eV and d-540 A for Nd = 2.1 X 1016 cm-3

•

1666 J. Appl. Phys. 66 (6),15 September 1984 0021-8979/64/161666-03$02.40 ® 1964 American institute of PhysiCS 1666 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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ference in density of states in the two materials is sufficiently small that (Ee - Ef ) is the same on both sides ofthe barrier. In these circumstances the diffusion potential Vd is given by the conduction band discontinuity .JEe : e Vd = .JEe. Sever­al schemes have been proposed for calculating .JEe, though at present none has been demonstrated to be universally cor­rect and it is probable that in practice the band offsets may be influenced by interface charge.s We require flEe for a small change in alloy composition so rather than use the Anderson model, .JEe = XI - X 2' with interpolated values of electron affinity X taken from various sources, we have used Harri­son's LCAO calculations of valence band energies ( - Ev) which have been shown to give reasonable agreement with photothreshold data.9 With these values for - Ev and val­ues for the room temperature band gap we calculated - Ee for the compounds GaP, GaAs, InP, and InAs and using the interpolation scheme ofHaynes5 we calculated - Ee for the two alloy compositions of interest, giving flEe = 0.083, with the sense of the discontinuity as shown in Fig. 1. The calcu­lated band gap difference, flEs = 0.125 eV, agrees with data of Moon et al., 10 so although the absolute value of - Ev may only be accurate to -0.2 eV the above value of flEe is a reasonable estimate of difference between the two alloys. We then assumed tbat the band bending is apportioned approxi­mately equally on each side of the barrier so that the band bending in material (2) is Vd2 = 0.041 eV which for a doping level of 2.1 X 1016 cm -3 (the 650 ·C grown sample of Ref. 7) gives a band bending distance d of 540 A.

R.egarding this heterobarrier as describing the bound­ary of a cluster of overall dimension t, it can be seen that provided t>d the band bending region will have little effect on the conduction band positions on each side of the cluster boundary. However, since the cluster size is about 100 A the band bending within each cluster will be negligible, and the band diagram through a cluster will take the form shown schematically in Fig. 2(a) with the conduction bands separat­ed by an energy /JEe . By reference to work on quantum well structures the band diagram of Fig. 2(a) is generally held to be a correct representation of the band diagram for atomical­ly abrupt interfaces. 1 I Crystal growth within the miscibility gap is more likely to produce graded interfaces, which will smear out the conduction band discontinuity so that the spa­tial variation of Ee takes the form illustrated in Fig. 2(b). Although the abrupt discontinuity is now lost, we suggest that the conduction band energy nevertheless varies over a range -flEe becausethechangesinEe cannot be accommo­dated by diffusion potentials Vd generated by space-charge dipole layers within each "cluster" when the cluster size is very small, t !2<d. We make a final realistic modification to the model by supposing that there are fluctuations in the amplitude and scale of the composition modulation causing variations in the local amplitude of modulation of Ee. These potential fluctuations arise directly from alloy clustering, analogous to intentionally grown quantum well structures, and will be present in the absence of any impurities.

In a two-dimensional analogue to the three-dimension­al sample the sheet representing the spatial variation of Ee will have peaks and troughs, with the troughs separated by saddle regions between the peaks of height flE., somewhat

1867 J. Appl. Phys., Vol. 56, No.6, 15 September 1984

(0 )

( b)

FIG. 2. Conduction band diagram through a sequence of clusters with dif­ferent compositions (1) and (2) and with t<d (see Fig. 1). In (a) the interfaces between clusters are atomically abrupt whereas in (b) the interfaces are graded and there are random tluctuations in the cluster compositions.

less than flEe. When kT~ flEs the thermal electron distri­bution will extend above these saddles and the electrons will form an extended "sea" with peaks in the Ee sheet protrud­ing above this sea. These will contribute to carrier scattering, possibly in a similar manner to "space-charge" scattering introduced by Wiesberg12 giving J.L ex: T - 112, as for "alloy" scattering. As the temperature is reduced current transport in the saddle regions will have an increased influence on the mobility. The probability of quantum mechanical tunneling depends upon the shape of the potential barrier but rough estimates suggest that thermal emission over the saddle re­gion will make the dominant contribution to the current. Consequently when kT </JEs( <flEe), the probability of thermal emission over the barriers separating "lakes" of electrons will become the current limiting process. As the temperature is reduced further, thermal emission over the higher saddle regions will become less probable and the cur­rent flow will become inhomogeneous. Eventually conduc­tion will be restricted to a number of critical percolation paths through the sample, linking the "easy" low potential saddles between electron "lakes". Thus in the region where kT < flEs we predict a mobility component which decreases with decreasing temperature and a current distribution which is macroscopically inhomogeneous. We may also ex­pect J.L to fall with decreasing electron concentration. A simi­lar model has been used to describe conduction at low tem­peratures at the Si/Si02 interface,13 which is a true two-dimensional sheet.

We suggest that this model may account for the mobil­ity data of Quillec et 01. 7 Since .ilEs may be -kT at room temperature we would not expect percolation to be domi­nant in these particular samples and this is confirmed by the

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I ,j

i I I 'I

: i I i " I i ,<

mobility decreasing with temperature above 77 K. However their samples do show a lower mobility for growth in the miscibility gap region, which we propose is due to Ec modu­lation, and the reduction in mobility is larger at 77 than 300 K. The data in Fig. 2 of Ref. 7 also shows that f.Ln (77 K) ceases to increase with decreasing carrier density below 3X 1015 cm- 3 for samples grown in the miscibility gap. These unexplained features are consistent with our model. The absence of broadening of the luminescence3 suggesting recombination in the low gap regions is also consistent with our model.

Further evidence for the influence of percolation con­duction is provided by our unpUblished measurements of f.tn (T) in epitaxial layers of Gao.s 1110.5 P. This material was grown by MBE, lattice matched to GaAs (Ref. 14) under similar conditions to material in which evidence for cluster­ing was observed by TEM.4 Of four samples with n-3X 1016 cm-3 three had a mobility which increased by -30% from 100 to 300 K. For this material we have esti­mated that iJ.Ec = 0.11 eV for a variation of ± 10% in the composition and so the current is more likely to be limited to percolation paths than in the quaternary alloy considered above. Again, this material exhibited no broadening of the luminescence. IS Conduction via percolation paths may lead to high local current densities and this may have an effect on device degradation. Electrical injection GalnP /GaAs DR lasers made by both vapor epitaxy16 and MBE17 have very short operating lifetimes of only a few minutes whereas no such rapid degradation has been found in similar optically pumped structures grown by MBE.ls High local power dissi­pation in the cladding regions could explain the failure of the electrical devices.

The essential features of our model are that the compo­sition fluctuations which occur for growth within the misci­bility gap cause spatial modulation of Ec on a scale suffi­ciently small that band bending within the clusters is negligible. If current transport is dominated by thermal emission over the barrier regions separating minima in Ec '

1868 J. Appl. Phys., Vol. 56, No.6, 15 September 1984

then when kT becomes small compared with the amplitude of modulation of Ec the current flow becomes nonuniform and is eventually restricted to percolation paths. We there­fore expect an increase in carrier mobility with increasing temperature. We suggest that the effects of the spatial vari­ation of Ec should be considered in detailed calculations of the mobility of III-V alloys to provide a more thorough test of our proposed model, and possibly a better understanding of electon scattering in these alloys.

The thoughts in this paper were originally stimulated by comments of G. B. Scott on the possible failure mecha­nisms of GalnP injection lasers. The MBE GaInP material was grown by J. S. Roberts.

J B. deCremoux, P. Hirtz, and J. Ricciardi, GoAs and Related Compounds, Vienna 1980, edited by H. W. Thim (lOP London, 1981), p. 115.

2B. deCremoux, J. Phys. (Paris) Colloq. 43, C5 (1982). 3p. Henoc, A Izrael, M. Quillec, and H. Launois, Appl. Phys. Lett. 40, 963 (1982).

4J. P. Gowel'S, Appl. Phys. A31, 23 (1983). 51. R. Haynes, A. R. Adams, and P. D. Green, GalnAsP Alloy Semiconduc­tors, edited by T. P. Pearsall (Wiley, Chichester, 1982), p. 189.

6M. A. Littlejohn, J. R. Hauser, and T. H. Glisson, Solid-State Electron. 21, 107 (1978).

7M. Quillec, J-L. Benchimol, S. Slempkes, and H. Launois, Appl. Phys. Lett. 42, 886 (.1983).

8See for example H. Kroemer, Swf. Sci. 132, 543 (1983). 91N. A. Harrison, Electronic Structure and the Properties of Solids (Free­man, San Francisco, 1980). J~. L. Moon, G. A. Antypas, and L. W. James, J. Electron. Mater. 3, 635

(1974). IlSee for example, R. Dingle, Festkiirperproblerne XV, 21 (1975). 12L. R. Weisberg, J. Appl. Phys. 33,1817 (1962). I3E. Arnold, Swf. Sci. 58, 60 (1976). J·P. Blood, J. S. Roberts, and 1. P. Stagg, J. Appl. Phys. 53, 3145 (19821. '51. S. Roberts, G. B. Scott, andJ. P. Gowel'S, 1. Appl. Phys. 52, 4018 (19811. J6C. J. Neuse, G. H. Olsen, and M. Ettenberg, Appl. Phys. Lett. 29, 54

(1976). 171. S. Roberts and G. B. Scott (unpublished). 'SO. B. Scott, J. S. Roberts, and R. F. Lee, Appl. Phys. Lett. 37, 30 (1980).

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