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Real-time optical diagnostics for epitaxial growth
surface science
ELSEVIER
Surface Science307-309 (1994) 1017-1027
i .i iiiii !i i ii i iiiii ; ii iiiii i ii iii ii iiii J i
Invited paper
Real-time optical diagnostics for epitaxial growth D.E. Aspnes Department of Physics, North Carolina State University, Raleigh, NC 27695-8202, USA
(Received 20 August 1993)
Abstract
Various optical diagnostics are being developed to meet new challenges in epitaxial growth. Layer thicknesses and compositions, the primary parameters needed for growth control, can be obtained with bulk-oriented probes such as reflectometry and ellipsometry. New derivative algorithms for determining near-surface dielectric properties and compositions from kinetic ellipsometric and complex-reflectometric data have made possible closed-loop feedback control of alloy structures, including compositionally graded structures. New information about the kinetics and chemistry of growth is being obtained by surface-oriented probes such as laser light scattering (LLS), surface photoabsorption (SPA), and reflectance-difference (-anisotropy) spectroscopy (RDS/RAS). Examples are provided, and likely directions of further progress discussed.
1. Overview
Epitaxial growth technology is facing increasingly difficult challenges. Developing applications involving high temperatures and blue light emission require new materials such as carbides, nitrides, and I I - V I semiconductors [1,2]. Reduced-dimensional structures require new growth approaches such as selective-area epitaxy [3]. Although complexity is increasing and tolerances becoming more stringent, economic pressures are requiring improved yields, higher throughputs, and reduced times to market, all of which require greater uniformity over large wafers and the possibility of scale-up to multiwafer production levels. To meet these challenges growth technology is evolving from physical to chemical deposition methods, i.e., from molecular beam epitaxy (MBE) to organometallic chemical vapor deposi-
tion (OMCVD), chemical beam epitaxy (CBE), and related approaches [4]. However, chemical beam methods are rather sensitive to growth conditions, and the addition of new reactants can significantly alter growth rates and alloy compositions by modifying surface reactions, sticking coefficients, etc. [4]. The above trends are ensuring that in the not-too-distant future acceptable yields will be achieved only by obtaining accurate information about samples during growth. While the ultimate goal is closed-loop feedback control, the more modest and currently achievable target of realtime monitoring will already have a substantial impact by allowing conditions to be modified on-line to meet composition and thickness specifications, and by providing records through which causes of downstream failures of complex processes or devices can be identified and elimi-
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0899-6
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D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
nated. For vertical-cavity surface-emitting lasers the future has already arrived, since these devices cannot be fabricated reliably without growth"rate information obtained in principle during growth [5] or in practice during mid-growth interruptions [6]. Because growth is a surface process, information can be obtained in principle with any of the well-developed electron- or ion-beam methods, for example reflection high-energy electron diffraction (RHEED) as used with MBE [7]. However, for reactive ambients a n d / o r pressures above the ultrahigh vacuum (UHV) range such methods cannot be used. As a result, considerable attention has recently been directed toward developing optical approaches, which can be used in any transparent ambient. Optical probes have not previously been a significant factor in surface science because photons interact only weakly with material and optical spectra are not easily interpreted. In the visible-near ultra-violet (UV), whereo optiocal penetration depths are about 100 A, the 1-A-thick surface region will contribute only about 1% to the total reflected optical signal. In the infrared (IR), where penetration depths are about 1 ~m, sensitivity is correspondingly reduced. Nevertheless, the twin challenges of sensitivity and interpretability are being met by the development of new and the refinement of existing optical methods, by the generation of spectral databases on surfaces prepared and independently characterized in UHV, and by improved methods of calculating optical spectra from first principles. Near IR-visible-near UV optical surface-diagnostic techniques now in relatively common use include laser light scattering (LLS) [810], second-harmonic generation (SHG) [11] and its generalization, sum-frequency generation [12], IR absorption spectroscopy (IRAS) [13], surface differential reflectance (SDR) in its normal incidence [14] and p-polarized Brewster-angle (surface photoabsorption (SPA)) [9,15-19] forms, the ellipsometric equivalent of SDR [20], and reflectance-difference/reflectance-anisotropy spectroscopy (RDS/RAS) [21-29]. These approaches achieve surface sensitivity, and in some cases specificity, by using spectral
dependence to identify or symmetry to enhance the surface contributions to the overall optical signal. In LLS the measured property is the diffusive scattering that occurs if the surface becomes rough. SHG deals with second-harmonic light that is generated when an intense photon beam interacts with the sample. In RDS the measured property is the sample anisotropy. SHG and RDS are surface specific because the surface has a different symmetry from that of the bulk. IRAS achieves surface specificity because IRAS data are obtained in spectral regions where the substrate is transparent. SDR and SPA deal quantitatively with the changes that occur in reflectance when surface conditions are changed. SPA achieves higher sensitivity through the use of p-polarized light at pseudo-Brewster incidence. SHG, RDS, and IRAS are true surface spectroscopies because they can obtain information about surfaces under steady-state conditions, although most early and much recent RDS data were obtained in the SDR mode. The current sensitivities of SDR, SPA, and RDS are now significantly better than 0.01 monolayer (ML). While surface analysis is necessary for understanding growth mechanisms, the most important sample parameters for control purposes are layer thicknesses and compositions. These are bulk properties not directly related to surface conditions, and consequently must be measured by bulk-oriented probes such as spectroreflectometry (SR) [5,6] and spectroellipsometry (SE) [30-37] that return information integrated over the penetration depth of light. SR determines the scalar reflectances R s = ] r S] 2, Rp = [ rp ] 2, or R = I r n I 2, where r s, rp, and r n are the complex reflectances for s-polarized, p-polarized, and normally incident light, respectively. SE determines the complex reflectance ratio p r p / r s. p data clearly contain more information than R data, but SE instrumentation is more complicated. Both SR and SE require optical access to the sample through windows in the growth chamber. Problems of window deposits and strain can be overcome with proper design [38]. Layer thickness is encoded interferometrically in R and p through the component back-reflected from the interior boundary of the film, =
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
and can be obtained from the evolution of these data with increasing thickness as discussed below. The phase information in p allows SE to deal with film thicknesses down to the sub-.A range, whereas SR is best suited for relatively thick films. The simplicity and extensive development of SR over the last 20 years by the optical-coatings industry [39] is leading to similar applications in growth technology [5,6]. Composition is encoded in the dielectric response. For control purposes the composition of interest is not the average value of the film as obtained by conventional analysis, but the nearsurface value Eo of the most recently deposited material. The problem of determining e o has recently been solved with the development of virtual-interface (V-l) or derivative algorithms [40] that extract Eo from kinetic ellipsometric (KE) or complex reflectometric (KCR) data obtained quasicontinuously during deposition or etching. These algorithms are remarkable in that they require no information whatsoever about the underlying sample structure. By eliminating the forward error propagation and instability limitations of the conventional Fresnel approach, they have also enabled optical closed-loop feedback-control technology, as has recently been demonstrated [33]. The surface/near-surface optical diagnostics field, termed Epioptics by McGilp [41], is expanding so rapidly that a thorough review ,would be a substantial undertaking. RDS basically did not exist six years ago, SPA three years ago, and V-I analysis two years ago. Recent work has clearly demonstrated that optical methods are very effective for real-time analysis and control of epitaxial growth, and further development can be expected particularly regarding SHG, SFG, IRAS, and Raman scattering [42]. Although not an optical technique in the conventional sense, X-ray scattering is now also providing real-time growth information [43]. In the present review I discuss only a few of these many developments and refer to expanded treatments given by Pickering [44] and Richter [45]. To organize the topic I divide the parameters associated with growth into three categories: primary, secondary, and tertiary. The primary prop-
1019
erties are layer thickness and composition, especially near-surface composition, because if these cannot be prepared according to specification there is no point in continuing. Secondary properties are sample characteristics that are determined by surface properties: doping levels, interface widths, and spontaneous bulk ordering of alloys, etc. Tertiary parameters are those that deal with the growth environment itself, for example sample temperature, chamber pressure, types and fluences of reactants, etc. Tertiary parameters have received the most attention not only because they must be known reasonably well but also because they are relatively easy to measure (although not easy to measure accurately). However, the nonlinearity of chemical processes ensures that growth control would not be a solved problem even if all tertiary parameters were known perfectly. Eventually these nonlinearities, the extreme example of which is atomic layer epitaxy, may be exploited for selective area epitaxy and to achieve uniformity over a set of wafers in a production reactor [4]. Also, if thickness and composition could be controlled directly small drifts in growth conditions could be compensated as they occur. Accordingly, I concentrate on primary properties and surface analysis.
2. Thickness and composition Determining the thickness and composition of an evolving layer from kinetic data is a quite different problem than that of determining layer thicknesses and compositions of finished samples. Consequently, it is not surprising that alternative analytic approaches might be possible. In the standard Fresnel method, eo is determined from the most recent data point and the calculated parameters of all preceding layers. In V-I analysis Eo is determined from the two most recent data points, or a suitable average. While both approaches yield the same value of eo under ideal conditions, they differ in their treatment of fluctuations, with important practical consequences. By considering the outermost layer to be an independent entity, the V-I approach localizes fluctuation effects instead of allowing them to accumu-
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D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
Et
Eo
l
:
Eb
of the sample can be written in terms of r v, e o, and layer thickness d as EaEi
Er :
LAYER
r = ErIE i -
Z r v + roa 1 + Zrvroa'
(1)
d
AMBIENT
Fig. 1. Schematic diagram of reflectance involving a virtual interface.
late. This eliminates instabilities in the solution and permits the analysis of arbitrarily thin layers, including layers with graded compositions. Also, thickness resolution is established during analysis and is limited only by the signal-to-noise level of the data. Since the difference between Fresnel and V-I approaches has not been discussed previously I consider it here in more detail. I suppose a set of complex reflectances [ri] measured at thickness increments Ad. Each increment is analyzed according to the model shown in Fig. 1, which illustrates a wave E i incident on a layer of dielectric function Eo. Let the layer be uniform to a depth d of at least Ad, and suppose that an interface (possibly virtual) exists at d. At the substrate side of this interface some fraction E t of E i is transmitted and some fraction E b is reflected by the underlying structure. Scatteringmatrix theory [46] shows that the virtual reflectance r~ = E J E t is completely determined by the underlying structure and consequently is independent of d. In Fresnel analysis the interface is assumed to be real, with d = Ad and the dielectric function of the underlying layer not necessarily equal to e o. r v is calculated from the known thicknesses and previously evaluated dielectric functions of the underlying layers. Given r v, the value of e of the previous layer, Ad, and the most recent value of ri, one now solves the Fresnel equations for Eo and then calculates the next value of r v. The process is then repeated. In V-I analysis the interface is assumed to be virtual, with Eo the same on both sides of the boundary. In this model the complex reflectance
where roa is the complex reflectance of the overlayer-ambient boundary, Z = exp(2ik o ±d), and c k o ± / t o = no± = e o - (E a sinZ~b)1/2, where c a is the ambient dielectric function and th is the angle of incidence. Eq. (1) applies to either s- or ppolarized light as long as the appropriate expression is used for roa. Given the values of r~ corresponding to d = 0 and Ad, respectively, one now solves Eq. (1) for both r v and e o and discards r v. In the limit that Ad ~ 0 this is equivalent to obtaining e o from the instantaneous value and derivative of r. Thus the Fresnel and V-I approaches represent sequential and local, respectively, solutions for c o. In the former approach the r v are assumed to be exact and any fluctuation or roundoff error is accommodated in Eo. However, this error in e o then propagates into the next calculated value of r v, resulting in an instability if Ad is too small. In contrast, in the V-I solution errors are apportioned between r v and e o in any given layer. Consequently, the solution is stable for arbitrarily small Ad. It is clear from the above discussion that neither the Fresnel nor the V-I approach can be used with scalar data. While R is relatively easy to measure, the technology needed to measure r to sufficient accuracy does not exist. Unfortunately, although p is complex the above analysis is not strictly applicable to it because it involves both r s and rp, each of which must be described by its own virtual reflectance r~s and rvv. However, in the ellipsometric case approximate solutions that are accurate to better than 0.1% in epitaxial growth applications can be obtained by assuming that rvs and rvp result from the same virtual substrate with dielectric function ev. In this virtual-substrate approximation (VSA), it can be shown [40] that at any point ri, ev is just the pseudodielectric function ( e ) calculated from p in the two-phase (substrate-ambient) model. The VSA also simplifies interface analysis because it
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027 i
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allows the outermost layers to be treated with a mathematically simpler model. Using Eq. (1) it is now possible to discuss the determination of thickness and composition in general. In semiconductor epitaxy, where all values of E are similar, I r v I is relatively small. T h e n to first order in r v the trajectory of r with increasing d in the complex r plane (and that of r-related optical functions such as p and (E) in their respective complex planes) is approximately an exponential spiral. Several examples are shown in Fig. 2, which presents (E) data obtained as a function of increasing time (film thickness) for three AlxGa l_xAs layers of different AI compositions x grown sequentially by CBE on a G a A s substrate. Each of the three spirals begins at the dielectric function of the underlying material and converges to the dielectric function of the deposited layer when the layer becomes optically thick. For A l ~ G a l _ x A s material, x and E2 are related at a sample t e m p e r a t u r e of 600°C and a photon energy of 2.6 eV by the empirical expres-
1021
sion [31] e2(X)= e2(0 ) -- 1 6 . 9 3 x - 0.33x 2, where 62(0) is the measured imaginary part of the dielectric function of GaAs. Note that reflectance data are one-dimensional projections of these spirals and as such are generally shown as explicit functions of thickness (time), where the spirals take the form of interference oscillations. Consider first the situation where e o is known and d is to be determined. In the VSA any spiral can be calculated a priori since it supposes that a layer of dielectric function e o is being deposited on a uniform substrate of dielectric function ( e ) , the pseudodielectric function calculated from p for the point chosen to represent d = 0. If the layer is optically absorbing no two cycles will overlap and thicknesses can be determined simply by locating the data directly on the spiral. This type of procedure has recently been used to control deposition rates by Jobs et al. [34] and to establish removal rates of Si-related materials by Duncan et al. [35] With SR the situation is more complicated because a knowledge of the initial value of reflectance is not sufficient to define the interference pattern. Either the substructure must be known explicitly or sufficient data must be obtained to define the p a r a m e t e r r v needed with e o to calculate the spiral. For this reason reflectance methods are usually restricted to films with d ~ A. An additional complication with SR is that thickness sensitivity vanishes at any local extremum. Suppose now the deposition rate is known but e o is not. Here, d can be obtained trivially by integrating the deposition rate, and e o at any point from a V-I analysis of K C R or K E data. The data of Fig. 3 illustrate one application. These data are compositions x calculated in real time from Eo for a 200 .A wide A l x G a l _ x A s parabolic quantum well grown by closed-loop feedback control [33]. These values were compared to target values shown as the solid line. Compositional discrepancies were corrected by adjusting the flow of the Al-containing species, triisobutyl aluminum (TIBAI), to the growth surface. The results are noteworthy not only because they represent the first (and so far only) demonstration of closed-loop feedback control of composition but also because x was determined by
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
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is in stage 1, SPA is now moving into stage 2, and RDS is in stage 3. As the sensitivity of SHG and Raman scattering is still improving and samples at growth temperature are not sufficiently transparent to allow conventional multiple-internal-reflection IRAS, I discuss only the first three.
~i I
I
100
Fig. 3. Compositional data for a 200-,~-wide parabolic quantum well grown by closed-loop feedback control. Top: data and target values; middle: difference; bottom: control voltage (after Ref. [33]).
analysis of the outermost 3 ,~ of depositing material [33]. In the most general case neither composition nor deposition rate are known. If the VSA is valid five parameters must be determined. In this case the second derivative (curvature) must be established as well. From Fig. 2 this requires measurements over thicknesses of some 10 s of ,~. In fact, without knowing the convergence point (scale) of the spiral, it is not possible to determine eo because the magnitude of the first derivative is needed in the calculation. If the VSA is not valid then all 7 parameters must be determined by curve fitting, as has also recently been noted by Urban and Tabet [47].
While LLS has long been used as a means of visually assessing surface morphology during MBE growth, recent efforts have been directed toward more quantitative analysis. Pidduck and coworkers used LLS to investigate step flow in Si CVD [8]. Horikoshi et al. used LLS to detect the onset of Ga droplet formation in GaAs homoepitaxy, thereby identifying when saturation coverage had been achieved [9]. Celii et al. recently used LLS to determine the critical thickness of InxGa l_xAs layers grown on GaAs, taking advantage of the connection between surface roughness and misfit dislocations [10]. Data are shown in Fig. 4. The,sample consisted of a superlattice of 46 A layers of In0.16Ga0.84 interleaved with 170 ~, thick layers of GaAs on a GaAs substrate. Growth proceeded pseudomorphically up to the sixth layer, when the surface began to roughen as shown by the increase of scattered light. Roughness continued to increase during subsequent growth. TEM micrographs showed that the associated dislocations were forming ridges 8-10 ,4, high in the (110)
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3. Surface analysis All optical surface-analysis probes have followed a common developmental path, beginning with kinetic studies at a single wavelength, progressing to spectral kinetic measurements, then if the technique permits to detailed spectral analyses of surfaces under steady-state conditions. LLS
'? 20
25
30
35
40
45
Growli'l Time (ram)
Fig. 4. LSS data for the |noA6Gao.s4As superlattice shown in the inset. Misfit dislocations generated when the critical thickness is reached at the onset of the sixth InGaAs layer cause increased scattering (after Ref. [10]).
1023
D.E. Aspnes/ Surface Science307-309 (1994) 1017-1027 49O%
151
/
-///
470"C
,
,
/
%
s / o
£g. io
,o
TMG
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flow d u r a t i o n
,'o (s)
Fig. 5. SPA data obtained by exposing an AsH3-stabi]ized (001) GaAs surface to TMG during OMCVD at several sub-
An example of an SPA application involving spectral measurements is given in Fig. 6 [19]. These data were obtained by exposing a AsH 3stabilized (100) GaAs substrate in an OMCVD growth environment to GaC1 and triethylgallium (TEG). The T E G was used to generate a reference spectrum for a Ga-terminated surface. Because the GaCl-exposed surface exhibits essentially the same spectral response for both (011) (shown) and (011) orientations of the plane of incidence, the data indicate that the GaC1- and TEG-exposed surfaces are equivalent, possibly even identical, and that the GaCl-exposed surface is also terminated with Ga.
strate temperatures as indicated (after Ref. [16]). 3.3. R D S / R A S
direction. A similar anisotropy in the relaxation of InP films deposited on GaAs on Si was studied by Acher et al. using RDS [22]. 3.2. SPA
Another experimentally simple approach that has seen widespread application is SPA. Most work has involved single-wavelength kinetic studies, but spectral data has recently been reported [17-19]. Not surprisingly, spectral information has increased diagnostic power substantially. An example of a kinetics application illustrating control possibilities for A L E is shown in Fig. 5 [16]. This figure shows the SPA response of an AsH3-saturated (001) GaAs surface that is exposed to trimethylgallium (TMG) at different temperatures during OMCVD at approximately 4 - 6 kPa pressure. A well-defined interruption is seen in the 470°C data, indicating self-limiting growth appropriate to ALE. Differences of substrate temperatures of only 20°C, which are difficult to measure on an absolute scale, are clearly seen thereby allowing A L E conditions to be established precisely. Kobayashi and Kobayashi also demonstrated a correlation between the change in SPA signal during H 2 purging and the sheet hole density, showing a connection between surface conditions and dopant incorporation. This was interpreted as being due to attached methyl groups [16].
RDS has become an established technique for obtaining information about the electronic structure of I I I - V growth surfaces as well as kinetic information about surface-reactant interactions. Because it can be used to analyze growth surfaces under steady-state conditions it avoids the "which-surface" ambiguity inherent in methods that depend on a change of surface conditions. Recent attention has focused on the R D equivalent of R H E E D oscillations and the determination of microscopic mechanisms of OMCVD growth through detailed measurements of surface reconstructions that occur during growth. The most thoroughly investigated surface is (001) GaAs, which has been studied under a wide range of U H V and atmospheric pressure (AP)
0.2
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300 400
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500 600
i
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700 800
WAVELENGTH ( nm )
Fig. 6. SPA spectra obtained by exposing an AsH3-stabilized (100) GaAs surface to GaC1 and TEG during OMCVD (after Ref. [19]).
1024
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
(001)GaAs- UHV/H2 .... UHV
.002
--
(4x2)/-like 590/550°C
H2
o
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Fig. 7. RD spectra for (001) GaAs surfaces prepared in UHV by MBE (dashed curves) and in AP H 2 by OMCVD (solid lines) (after Ref. [23]).
conditions by Kamiya and coworkers [23,24]. From R D data taken on surfaces prepared by M B E and independently characterized by R H E E D , Kamiya et al. were able to demonstrate that (001) G a A s surfaces in U H V and in AP H 2 were virtually identical and to identify typical coverages in OMCVD under growth conditions. Representative results are shown in Fig. 7 [23]. The similarity between R D spectra obtained with the (001) G a A s surface in the two different ambients is striking. Theoretical calculations showed that the structures observed near 1.9 and 2.6 eV are due to transitions involve G a - G a and A s - A s surface dimers, respectively, and that these features could be used to track the relative surface concentrations of these surface species [48]. These data also showed that, under typical O M C V D growth conditions, the (001) G a A s surface was terminated by 2 layers of As and not one, as commonly supposed. When the As-press u r e / sample temperature phase diagram was established [23], it was found that the O M C V D
region was an extension of the M B E region. This not only provided further evidence of the essential similarity of the surfaces in the two environments, but also showed that under typical OMCVD growth conditions the (001) G a A s surface is c(4 × 4)-like, that is, terminated by 2 outer layers of As instead 1 as in MBE. It also showed that these higher As coverages were a consequence of the vastly higher As partial pressures encountered in O M C V D , which at any given temperature push the equilibrium point to higher As coverages. Recent data obtained during growth have yielded similar results [29,45]. An example of R D oscillations is given in Fig. 8 [28]. Recent work has established conditions where these oscillations are maximized at both low [26] and high [28] reactor pressures. The oscillations of Fig. 8 were obtained during OMCVD at a reactor pressure of 104 Pa, an A s H 3 partial pressure of 70 Pa, a substrate temperature of 502°C, and a photon energy of 2.65 eV, which corresponds to the R D peak of surface As dimers. Each oscillation interval accurately represents growth of 1 M L of material, as shown by postgrowth destructive analysis. Consequently, these oscillations provide growth-rate information for
- i - ~ - X
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=
T~
"7
~."~0.42
Pa
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.
Pa
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0 10 20 30 40 50 60 TIME (s) Fig. 8. RD oscillationsobservedduring OMCVD growth on (001) OaAs at H 2 and AsH 3 pressures of 100 mbar and 70 Pa, respectively, and a sample temperature of 502°C. TMG pressures are as indicated (after Ref. [28]).
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
states on the (2 x 1) reconstruction of (001) Ge [27]. Because these results involve a simpler material, they may stimulate further theoretical analysis of surface optical anisotropy effects. Also, Aspnes et al. used a sampling approach to obtain the first spectra of (001) GaAs surfaces in an ALE-like exposure sequence [25]. During AsH 3 exposure the surface was found to be c(4 × 4)-like, consistent with the (001) GaAs phase diagram but not with any of the conventional models of ALE growth.
0.2
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Energy [eV] Fig. 9. T h i n lines: R D c h a n g e s p e c t r a •(RDS) c a l c u l a t e d for 4~ = 75 ° for various c o m b i n a t i o n s of initial and final recons t r u c t i o n s on (001) G a A s as i n d i c a t e d . H e a v y line: S P A a n i s o t r o p y f r o m the d a t a of Ref. [18] (after Ref. [49]).
OMCVD analogous to that provided by RHEED for MBE. The mechanism giving rise to the RD oscillations is not understood, although it is clearly a cooperative phenomenon involving oscillating As-As surface coverage probably between partial single and double layers. Similar oscillations have been observed with tertiarybutylarsine (TBAs) [28]. Deppert et al. have used these oscillations to measure growth-rate nonlinearities at the onset of growth by low pressure OMCVD [26]. Hingerl et al. recently derived relations that connect measured SPA anisotropies to RD spectra, allowing RD databases to be used in the interpretation of SPA results [49]. Fig. 9 compares RD change spectra, the calculated difference between RD spectra measured under steady-state conditions for two different reconstructions, to the anisotropy of SPA data calculated from results reported by Nishi et al. [18]. The best agreement is obtained by modeling the difference as a change of surface reconstruction from c(4 × 4) under AsH 3 to a Ga-rich phase under triethylgallium (TEG), as expected from reported conditions. These results open the possibility of more detailed analyses through a combination of SPA and RDS. Although not pertaining directly to epitaxial growth, Wormeester et al. recently used ellipsometry to determine the RD response of surface
4. Future directions
The field of real-time optical characterization will clearly continue to expand not only through the development of new and refinement of existing techniques but also with respect to applications to new materials systems. Rapid data acquisition will be required, especially for applications involving multinary systems where single-wavelength data are insufficient. Parallel and serial versions of rapid-scan ellipsometers have been developed and explored by Collins and coworkers [32,37] and Duncan and coworkers [35], respectively. When optical multichannel detection is adapted to SPA and RDS, it will be possible to assess surface reconstructions in OMCVD at a glance, as is now done with RHEED in MBE. Although the present technological obstacles are formidable, it may prove attractive to develop normal-incidence complex reflectometry as an alternative to SE for the real-time analysis of very thin films, since in this case the derivative approach is exact. At the same time growth chambers must evolve to meet the specific needs of optical measurements. These requirements include not only optical access to the sample through transparent, strain-free, and deposition-free windows, but also the development of runout-corrected and vibration-free sample mounts and manipulators as recently discussed by Maracas and coworkers [36]. Ellipsometric data obtained with rotating samples will contain an RD-like component that can be analyzed for surface coverage using standard RD databases [49].
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D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
Various problems remain to be solved before a full control technology can be realized. These include the optimization of loop performance consistent with system stability, the achievement of accuracy as well as precision, and the development of multiwavelength measurement and processing capabilities that can establish thickness as well as composition. In this regard thickness and composition may well be determined by separate Fresnel and derivative analyses, respectively, carried out simultaneously at different wavelengths. Such approaches will require considerable computing power, but computer technology appears to be able to keep ahead of demands. The near-term future should also see substantial advances in capabilities and applications of SHG, SFG, IRAS, and Raman scattering. It is necessary to develop these approaches because the ability to establish surface chemistry with visible-near UV linear optical techniques is limited. Nonlinear and IR interactions with surface species are weak, making this a genuine challenge. However, new high intensity sources such as free-electron lasers may make such measurements feasible. Approaches dealing with lateral inhomogeneity by the use of small spot sizes [30], imaging [50], or direct analysis [51] also need to be developed to deal with the increasingly important phenomenon of selective-area epitaxy. 5. Acknowledgments
It is a pleasure to acknowledge the contributions of my collaborators in the growth-control and RDS work discussed in Sections 2 and 3: I. Kamiya, H. Tanaka, R. Bhat, M.J.S.P. Brasil, L.T. Florez, S. Gregory, J.P. Harbison, R.E. Nahory, M.A.A. Pudensi, W.E. Quinn, S.A. Schwarz, and M.C. Tamargo. The experimental work described in Sections 2 and 3 was done when all authors were at Bellcore, where I. Kamiya was supported by ONR Contract N-00014-90-J-1267. 6. References [1] See, e.g., Proc. Mater. Res. Soc. 162 (1990); R.F. Davis, J. Vac. Sci. Technol. A 11 (1993) 829.
[2] R.M. Park, M.B. Troffer, C.M. Rouleau, J.M. DePuydt and M.A. Haase, Appl. Phys. Lett. 57 (1990) 2127; R.P. Vaudo, D.B. Eason, K.A. Bowers, K.J. Gossett, J.W. Cook, Jr. and J.F. Schetzina, J. Vac. Sci. Technol. B 11 (1993) 875. [3] G.J. Davies, P.J. Skevington, C.L. French and J.S. Foord, J. Cryst. Growth 120 (1992) 369; R.A. Hamm, A. Feygenson, D. Riner, Y.L. Wang, H. Temkin, R.D. Yadvish and M.B. Panish, Appl. Phys. Lett. 61 (1992) 592; R. Matz, H. Heinecke, B. Baur, R. Primig and C. Cremer, J. Cryst. Growth 127 (1993) 230. [4] S.M. Bedair, B.T. McDermott, Y. Ide, N.H. Karam, H. Hashemi, M.A. Tischler, M. Timmons, J.C.L. Tarn and N. EI-Masry, J. Cryst. Growth 93 (1988) 182; C.R. Abernathy, J. Vac. Sci. Technol. A 11 (1993) 869; L. Niinist6 and M. Leskel~i, Thin Solid Films 225 (1993) 130. [5] H. Sankur, W. Southwell and R. Hall, J. Electron. Mater. 20 (1991) 1099. [6] K. Bacher, B. Pezeshki, S.M. Lord and J.S. Harris, Jr., Appl. Phys. Lett. 61 (1992) 1387; S.A. Chalmers and K.P. Killeen, Appl. Phys. Lett. 62 (1993) 1182. [7] B.A. Joyce, P.J. Dobson, J.H. Neave, K. Woodbridge, J. Zhang, P.K. Larsen and B. BSlger, Surf. Sci. 186 (1986) 423. [8] A.J. Pidduck, D.J. Robbins, A.G. Cullis, D.B. Gasson and J.L. Glasper, J. Electrochem. Soc. 136 (1989) 3083; A.J. Pidduck, D.J. Robbins, D.B. Gasson, C. Picketing and J.L. Glasper, J. Electrochem. Soc. 136 (1989) 3088; C. Picketing, Thin Solid Films 206 (1991) 275; C.M. Rouleau and R.M. Park, J. Vac. Sci. Technol. A 11 (1993) 1792. [9] Y. Horikoshi, H. Yamaguchi, F. Briones and M. Kawashima, J. Cryst. Growth 105 (1990) 326. [10] F.G. Celii, E.A. Beam III, L.A. Files-Sesler, H.-Y. Liu and Y.C. Kao, Appl. Phys. Lett. 62 (1993) 2705. [11] T. Stehlin, M. Feller, P. Guyot-Sionnest and Y.R. Shen, Opt. Len. 13 (1988) 389; M.E. Pemble, D.S. Buhaenko, S.M. Francis, P.A. Goulding and J.T. Allen, J. Cryst. Growth 107 (1991) 37; P.V. Kelly, J.D. O'Mahoney, J.F. McGilp and Th. Rasing, Appl. Surf. Sci. 56-58 (1992) 453. [12] R. Superfine, P. Guyot-Sionnest, J.H. Hunt, C.T. Kao and Y.R. Shen, Surf. Sci. 200 (1988) L445; Y.R. Shen, Nature 337 (1989) 519. [13] Y.J. Chabal, G.S. Higashi, K. Raghavachari and V.A. Burrows, J. Vac. Sci. Technol. A 7 (1989) 2104; P.E. Gees and R.F. Hicks, J. Vac. Sci. Technol. A 10 (1992) 892. [14] S. Selci, F. Ciccacci, G. Chiarotti, P. Chiaradia and A. Cricenti, J. Vac. Sci. Technol. A 5 (1987) 327; D. Eres and J.W. Sharp, Appl. Phys. Lett. 60 (1992) 2764. [15] Y. Horikoshi, M. Kawashima and N. Kobayashi, J. Cryst. Growth 111 (1991) 200; A. Usui, Thin Solid Films 225 (1993) 53.
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027 [16] N. Kobayashi and Y. Kobayashi, Thin Solid Films 225 (1993) 32. [17] N. Kobayashi and Y. Horikoshi, J. Appl. Phys. Jpn. 29 (1990) L702. [18] K. Nishi, A. Usui and H. Sakaki, Appl. Phys. Lett. 61 (1992) 31. [19] K. Nishi, A. Usui and H. Sakaki, Thin Solid Films 225 (1993) 47. [20] D. Gautard, J.L. Laport, M. Cadoret and C. Pariset, J. Cryst. Growth 71 (1985) 125; M. Gendry, J. Durand, M. Erman, J.B. Theeten, L. Nevot and B. Pardo, Appl. Surf. Sci. 44 (1990) 309; S. Andrieu and F. Arnaud d'Avitaya, J. Cryst. Growth 112 (1991) 146. [21] D.E. Aspnes, J.P. Harbison, A.A. Studna and L.T. Florez, Phys. Rev. Lett. 59 (1987) 1687; G. Paulsson, K. Deppert, S. Jeppesen, J. J6nsson, L. Samuelson and P. Schmidt, J. Cryst. Growth 111 (1991) 115; B.A. Joyce, J. Zhang, T. Shitara, J.H. Neave, A. Taylor, S. Armstrong, M.E. Pemble and C.T. Foxon, J. Cryst. Growth 115 (1991) 338; V.L. Berkovits, V.N. Bessolov, T.N. L'vova, E.B. Novikov, V.I. Safarov, R.V. Khasieva and B.V. Tsarenkov, J. Appl. Phys. 70 (1991) 3707. [22] O. Acher, S.M. Koch, F. Omnes, M. Defour, M. Razeghi and B. Dr6villon, J. Appl. Phys. 68 (1990) 3564. [23] I. Kamiya, D.E. Aspnes, H. Tanaka, L.T. Florez, J.P. Harbison and R. Bhat, Phys. Rev. Lett. 68 (1992) 627. [24] I. Kamiya, D.E. Aspnes, L.T. Florez and J.P. Harbison, Phys. Rev. B 46 (1992) 15894. [25] D.E. Aspnes, I. Kamiya, H. Tanaka and R. Bhat, J. Vac. Sci. Technol. B 10 (1992) 1725. [26] K. Deppert, J. J6nsson and L. Samuelson, Thin Solid Films 224 (1993) 133. [27] H. Wormeester, D.J. Wentink, P.L. de Boeij, C.M.J. Wijers and A. van Silfhout, Phys. Rev. B 47 (1993) 12664. [28] F. Reinhardt, W. Richter, A.B. Miiller, D. Gutsche, P. Kurpas, K. Ploska, K.C. Rose and M. Zorn, J. Vac. Sci. Technol. B 11 (1993) 1427. [29] I. Kamiya, H. Tanaka, D.E. Aspnes, M. Koza and R. Bhat, Appl. Phys. Lett. 63 (1993) 3206. [30] M. Erman and J.B. Theeten, J. Appl. Phys. 60 (1986) 859. [31] D.E. Aspnes, W.E. Quinn and S. Gregory, Appl. Phys. Lett. 56 (1990) 2569. [32] Y.-T. Kim, R.W. Collins and K. Vedam, Surf. Sci. 233 (1990) 341; I. An, Y.M. Li, H.V. Nguyen and R.W. Collins, Rev. Sci. Instrum. 63 (1992) 3842. [33] D.E. Aspnes, W.E. Quinn, M.C. Tamargo, M.A.A. Pudensi, S.A. Schwarz, M.J.S.P. Brasil, R.E. Nahory and S. Gregory, Appl. Phys. Lett. 60 (1992) 1244.
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[34] B. Johs, J.L. Edwards, K.T. Shiralagi, R. Droopad, K.Y. Choi, G.N. Maracas, D. Meyer, G.T. Cooney and J.A. WooUam, Proc. Mater. Res. Soc. 222 (1992) 75. [35] W.M. Duncan and S.A. Henck, Appl. Surf. Sci. 63 (1993) 9; S.A. Henck, W.M. Duncan, L.M. Lowenstein and S.W. Butler, J. Vac. Sci. Technol. A 11 (1993) 1179. [36] G.N. Maracas, J.L. Edwards, K. Shiralagi, K.Y. Choi, R. Droopad, B. Johs and J.A. Woollam, J. Vac. Sci. Technol. A 10 (1992) 1832; G.N. Maracas, J.L. Edwards, D.S. Gerber and R. Droopad, Appl. Surf. Sci. 63 (1993) 1. [37] H.V. Nguyen, I. An and R.W. Collins, Phys. Rev. B 47 (1993) 3947. [38] A.A. Studna, D.E. Aspnes, L.T. Florez, B.J. Wilkens and R.E. Ryan, J. Vac. Sci. Technol. A 7 (1989) 3291. [39] H.A. Macleod, Opt. Acta 19 (1972) 1; E. Pelletier, Proc. SPIE 401 (1983) 74; R. Herrmann and A. Z611ner, Proc. SPIE 401 (1983) 83; C.J. van der Laan, Appl. Opt. 25 (1986) 753. [40] D.E. Aspnes, J. Opt. Soc. Am. A 10 (1993) 974. [41] J.F. McGilp, J. Phys.: Condensed Matter 2 (1990) 7985. [42] P.V. Kelly, J.D. O'Mahony, J.F. McGilp and Th. Rasing, Appl. Surf. Sci. 56-58 (1992) 453; N. Esser, M. K6pp, P. Haier, A. Kelnberger and W. Richter, J. Vac. Sci. Technol. B 11 (1993) 1481; V. Wagner, D. Drews, M. van der Emde, N. Esser, D.R.T. Zahn, J. Geurt and W. Richter, J. Appl. Phys., in press. [43] D.W. Kisker, P.H. Fuoss, K.L. Tokuda, G. Renaud, S. Brennan and J.L. Kahn, Appl. Phys. Lett. 56 (1990) 2025; P.H. Fuoss, D.W. Kisker, F.J. Lamelas, G.B. Stephenson, P. Imperatori and S. Brennan, Phys. Rev. Lett. 69 (1992) 2791. [44] C. Pickering, in: Handbook of Crystal Growth, Vol. III, in press. [45] W. Richter, Philos. Trans. R. Soc. London A 344 (1993) 453. [46] D.Y.K. Ko and J.R. Sambles, J. Opt. Soc. Am. A 5 (1988) 1863. [47] F.K. Urban III and M.F. Tabet, J. Vac. Sci. Technol. A 11 (1993) 976. [48] Y.C. Chang and D.E. Aspnes, Phys. Rev. B 41 (1990) 12002; Y.C. Chang, S.F. Ren and D.E. Aspnes, J. Vac. Sci. Technol. A 10 (1992) 1856. [49] K. Hingerl, D.E. Aspnes, I. Kamiya and L.T. Florez, Appl. Phys. Lett. 63 (1993) 885. [50] D. Beaglehole, Rev. Sci. Instrum. 59 (1988) 2557. [51] M. Haverlag and G.S. Oehrlein, J. Vac. Sci. Technol. B 10 (1992) 2412.
ELSEVIER
Surface Science307-309 (1994) 1017-1027
i .i iiiii !i i ii i iiiii ; ii iiiii i ii iii ii iiii J i
Invited paper
Real-time optical diagnostics for epitaxial growth D.E. Aspnes Department of Physics, North Carolina State University, Raleigh, NC 27695-8202, USA
(Received 20 August 1993)
Abstract
Various optical diagnostics are being developed to meet new challenges in epitaxial growth. Layer thicknesses and compositions, the primary parameters needed for growth control, can be obtained with bulk-oriented probes such as reflectometry and ellipsometry. New derivative algorithms for determining near-surface dielectric properties and compositions from kinetic ellipsometric and complex-reflectometric data have made possible closed-loop feedback control of alloy structures, including compositionally graded structures. New information about the kinetics and chemistry of growth is being obtained by surface-oriented probes such as laser light scattering (LLS), surface photoabsorption (SPA), and reflectance-difference (-anisotropy) spectroscopy (RDS/RAS). Examples are provided, and likely directions of further progress discussed.
1. Overview
Epitaxial growth technology is facing increasingly difficult challenges. Developing applications involving high temperatures and blue light emission require new materials such as carbides, nitrides, and I I - V I semiconductors [1,2]. Reduced-dimensional structures require new growth approaches such as selective-area epitaxy [3]. Although complexity is increasing and tolerances becoming more stringent, economic pressures are requiring improved yields, higher throughputs, and reduced times to market, all of which require greater uniformity over large wafers and the possibility of scale-up to multiwafer production levels. To meet these challenges growth technology is evolving from physical to chemical deposition methods, i.e., from molecular beam epitaxy (MBE) to organometallic chemical vapor deposi-
tion (OMCVD), chemical beam epitaxy (CBE), and related approaches [4]. However, chemical beam methods are rather sensitive to growth conditions, and the addition of new reactants can significantly alter growth rates and alloy compositions by modifying surface reactions, sticking coefficients, etc. [4]. The above trends are ensuring that in the not-too-distant future acceptable yields will be achieved only by obtaining accurate information about samples during growth. While the ultimate goal is closed-loop feedback control, the more modest and currently achievable target of realtime monitoring will already have a substantial impact by allowing conditions to be modified on-line to meet composition and thickness specifications, and by providing records through which causes of downstream failures of complex processes or devices can be identified and elimi-
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0899-6
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D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
nated. For vertical-cavity surface-emitting lasers the future has already arrived, since these devices cannot be fabricated reliably without growth"rate information obtained in principle during growth [5] or in practice during mid-growth interruptions [6]. Because growth is a surface process, information can be obtained in principle with any of the well-developed electron- or ion-beam methods, for example reflection high-energy electron diffraction (RHEED) as used with MBE [7]. However, for reactive ambients a n d / o r pressures above the ultrahigh vacuum (UHV) range such methods cannot be used. As a result, considerable attention has recently been directed toward developing optical approaches, which can be used in any transparent ambient. Optical probes have not previously been a significant factor in surface science because photons interact only weakly with material and optical spectra are not easily interpreted. In the visible-near ultra-violet (UV), whereo optiocal penetration depths are about 100 A, the 1-A-thick surface region will contribute only about 1% to the total reflected optical signal. In the infrared (IR), where penetration depths are about 1 ~m, sensitivity is correspondingly reduced. Nevertheless, the twin challenges of sensitivity and interpretability are being met by the development of new and the refinement of existing optical methods, by the generation of spectral databases on surfaces prepared and independently characterized in UHV, and by improved methods of calculating optical spectra from first principles. Near IR-visible-near UV optical surface-diagnostic techniques now in relatively common use include laser light scattering (LLS) [810], second-harmonic generation (SHG) [11] and its generalization, sum-frequency generation [12], IR absorption spectroscopy (IRAS) [13], surface differential reflectance (SDR) in its normal incidence [14] and p-polarized Brewster-angle (surface photoabsorption (SPA)) [9,15-19] forms, the ellipsometric equivalent of SDR [20], and reflectance-difference/reflectance-anisotropy spectroscopy (RDS/RAS) [21-29]. These approaches achieve surface sensitivity, and in some cases specificity, by using spectral
dependence to identify or symmetry to enhance the surface contributions to the overall optical signal. In LLS the measured property is the diffusive scattering that occurs if the surface becomes rough. SHG deals with second-harmonic light that is generated when an intense photon beam interacts with the sample. In RDS the measured property is the sample anisotropy. SHG and RDS are surface specific because the surface has a different symmetry from that of the bulk. IRAS achieves surface specificity because IRAS data are obtained in spectral regions where the substrate is transparent. SDR and SPA deal quantitatively with the changes that occur in reflectance when surface conditions are changed. SPA achieves higher sensitivity through the use of p-polarized light at pseudo-Brewster incidence. SHG, RDS, and IRAS are true surface spectroscopies because they can obtain information about surfaces under steady-state conditions, although most early and much recent RDS data were obtained in the SDR mode. The current sensitivities of SDR, SPA, and RDS are now significantly better than 0.01 monolayer (ML). While surface analysis is necessary for understanding growth mechanisms, the most important sample parameters for control purposes are layer thicknesses and compositions. These are bulk properties not directly related to surface conditions, and consequently must be measured by bulk-oriented probes such as spectroreflectometry (SR) [5,6] and spectroellipsometry (SE) [30-37] that return information integrated over the penetration depth of light. SR determines the scalar reflectances R s = ] r S] 2, Rp = [ rp ] 2, or R = I r n I 2, where r s, rp, and r n are the complex reflectances for s-polarized, p-polarized, and normally incident light, respectively. SE determines the complex reflectance ratio p r p / r s. p data clearly contain more information than R data, but SE instrumentation is more complicated. Both SR and SE require optical access to the sample through windows in the growth chamber. Problems of window deposits and strain can be overcome with proper design [38]. Layer thickness is encoded interferometrically in R and p through the component back-reflected from the interior boundary of the film, =
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
and can be obtained from the evolution of these data with increasing thickness as discussed below. The phase information in p allows SE to deal with film thicknesses down to the sub-.A range, whereas SR is best suited for relatively thick films. The simplicity and extensive development of SR over the last 20 years by the optical-coatings industry [39] is leading to similar applications in growth technology [5,6]. Composition is encoded in the dielectric response. For control purposes the composition of interest is not the average value of the film as obtained by conventional analysis, but the nearsurface value Eo of the most recently deposited material. The problem of determining e o has recently been solved with the development of virtual-interface (V-l) or derivative algorithms [40] that extract Eo from kinetic ellipsometric (KE) or complex reflectometric (KCR) data obtained quasicontinuously during deposition or etching. These algorithms are remarkable in that they require no information whatsoever about the underlying sample structure. By eliminating the forward error propagation and instability limitations of the conventional Fresnel approach, they have also enabled optical closed-loop feedback-control technology, as has recently been demonstrated [33]. The surface/near-surface optical diagnostics field, termed Epioptics by McGilp [41], is expanding so rapidly that a thorough review ,would be a substantial undertaking. RDS basically did not exist six years ago, SPA three years ago, and V-I analysis two years ago. Recent work has clearly demonstrated that optical methods are very effective for real-time analysis and control of epitaxial growth, and further development can be expected particularly regarding SHG, SFG, IRAS, and Raman scattering [42]. Although not an optical technique in the conventional sense, X-ray scattering is now also providing real-time growth information [43]. In the present review I discuss only a few of these many developments and refer to expanded treatments given by Pickering [44] and Richter [45]. To organize the topic I divide the parameters associated with growth into three categories: primary, secondary, and tertiary. The primary prop-
1019
erties are layer thickness and composition, especially near-surface composition, because if these cannot be prepared according to specification there is no point in continuing. Secondary properties are sample characteristics that are determined by surface properties: doping levels, interface widths, and spontaneous bulk ordering of alloys, etc. Tertiary parameters are those that deal with the growth environment itself, for example sample temperature, chamber pressure, types and fluences of reactants, etc. Tertiary parameters have received the most attention not only because they must be known reasonably well but also because they are relatively easy to measure (although not easy to measure accurately). However, the nonlinearity of chemical processes ensures that growth control would not be a solved problem even if all tertiary parameters were known perfectly. Eventually these nonlinearities, the extreme example of which is atomic layer epitaxy, may be exploited for selective area epitaxy and to achieve uniformity over a set of wafers in a production reactor [4]. Also, if thickness and composition could be controlled directly small drifts in growth conditions could be compensated as they occur. Accordingly, I concentrate on primary properties and surface analysis.
2. Thickness and composition Determining the thickness and composition of an evolving layer from kinetic data is a quite different problem than that of determining layer thicknesses and compositions of finished samples. Consequently, it is not surprising that alternative analytic approaches might be possible. In the standard Fresnel method, eo is determined from the most recent data point and the calculated parameters of all preceding layers. In V-I analysis Eo is determined from the two most recent data points, or a suitable average. While both approaches yield the same value of eo under ideal conditions, they differ in their treatment of fluctuations, with important practical consequences. By considering the outermost layer to be an independent entity, the V-I approach localizes fluctuation effects instead of allowing them to accumu-
1020
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
Et
Eo
l
:
Eb
of the sample can be written in terms of r v, e o, and layer thickness d as EaEi
Er :
LAYER
r = ErIE i -
Z r v + roa 1 + Zrvroa'
(1)
d
AMBIENT
Fig. 1. Schematic diagram of reflectance involving a virtual interface.
late. This eliminates instabilities in the solution and permits the analysis of arbitrarily thin layers, including layers with graded compositions. Also, thickness resolution is established during analysis and is limited only by the signal-to-noise level of the data. Since the difference between Fresnel and V-I approaches has not been discussed previously I consider it here in more detail. I suppose a set of complex reflectances [ri] measured at thickness increments Ad. Each increment is analyzed according to the model shown in Fig. 1, which illustrates a wave E i incident on a layer of dielectric function Eo. Let the layer be uniform to a depth d of at least Ad, and suppose that an interface (possibly virtual) exists at d. At the substrate side of this interface some fraction E t of E i is transmitted and some fraction E b is reflected by the underlying structure. Scatteringmatrix theory [46] shows that the virtual reflectance r~ = E J E t is completely determined by the underlying structure and consequently is independent of d. In Fresnel analysis the interface is assumed to be real, with d = Ad and the dielectric function of the underlying layer not necessarily equal to e o. r v is calculated from the known thicknesses and previously evaluated dielectric functions of the underlying layers. Given r v, the value of e of the previous layer, Ad, and the most recent value of ri, one now solves the Fresnel equations for Eo and then calculates the next value of r v. The process is then repeated. In V-I analysis the interface is assumed to be virtual, with Eo the same on both sides of the boundary. In this model the complex reflectance
where roa is the complex reflectance of the overlayer-ambient boundary, Z = exp(2ik o ±d), and c k o ± / t o = no± = e o - (E a sinZ~b)1/2, where c a is the ambient dielectric function and th is the angle of incidence. Eq. (1) applies to either s- or ppolarized light as long as the appropriate expression is used for roa. Given the values of r~ corresponding to d = 0 and Ad, respectively, one now solves Eq. (1) for both r v and e o and discards r v. In the limit that Ad ~ 0 this is equivalent to obtaining e o from the instantaneous value and derivative of r. Thus the Fresnel and V-I approaches represent sequential and local, respectively, solutions for c o. In the former approach the r v are assumed to be exact and any fluctuation or roundoff error is accommodated in Eo. However, this error in e o then propagates into the next calculated value of r v, resulting in an instability if Ad is too small. In contrast, in the V-I solution errors are apportioned between r v and e o in any given layer. Consequently, the solution is stable for arbitrarily small Ad. It is clear from the above discussion that neither the Fresnel nor the V-I approach can be used with scalar data. While R is relatively easy to measure, the technology needed to measure r to sufficient accuracy does not exist. Unfortunately, although p is complex the above analysis is not strictly applicable to it because it involves both r s and rp, each of which must be described by its own virtual reflectance r~s and rvv. However, in the ellipsometric case approximate solutions that are accurate to better than 0.1% in epitaxial growth applications can be obtained by assuming that rvs and rvp result from the same virtual substrate with dielectric function ev. In this virtual-substrate approximation (VSA), it can be shown [40] that at any point ri, ev is just the pseudodielectric function ( e ) calculated from p in the two-phase (substrate-ambient) model. The VSA also simplifies interface analysis because it
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027 i
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allows the outermost layers to be treated with a mathematically simpler model. Using Eq. (1) it is now possible to discuss the determination of thickness and composition in general. In semiconductor epitaxy, where all values of E are similar, I r v I is relatively small. T h e n to first order in r v the trajectory of r with increasing d in the complex r plane (and that of r-related optical functions such as p and (E) in their respective complex planes) is approximately an exponential spiral. Several examples are shown in Fig. 2, which presents (E) data obtained as a function of increasing time (film thickness) for three AlxGa l_xAs layers of different AI compositions x grown sequentially by CBE on a G a A s substrate. Each of the three spirals begins at the dielectric function of the underlying material and converges to the dielectric function of the deposited layer when the layer becomes optically thick. For A l ~ G a l _ x A s material, x and E2 are related at a sample t e m p e r a t u r e of 600°C and a photon energy of 2.6 eV by the empirical expres-
1021
sion [31] e2(X)= e2(0 ) -- 1 6 . 9 3 x - 0.33x 2, where 62(0) is the measured imaginary part of the dielectric function of GaAs. Note that reflectance data are one-dimensional projections of these spirals and as such are generally shown as explicit functions of thickness (time), where the spirals take the form of interference oscillations. Consider first the situation where e o is known and d is to be determined. In the VSA any spiral can be calculated a priori since it supposes that a layer of dielectric function e o is being deposited on a uniform substrate of dielectric function ( e ) , the pseudodielectric function calculated from p for the point chosen to represent d = 0. If the layer is optically absorbing no two cycles will overlap and thicknesses can be determined simply by locating the data directly on the spiral. This type of procedure has recently been used to control deposition rates by Jobs et al. [34] and to establish removal rates of Si-related materials by Duncan et al. [35] With SR the situation is more complicated because a knowledge of the initial value of reflectance is not sufficient to define the interference pattern. Either the substructure must be known explicitly or sufficient data must be obtained to define the p a r a m e t e r r v needed with e o to calculate the spiral. For this reason reflectance methods are usually restricted to films with d ~ A. An additional complication with SR is that thickness sensitivity vanishes at any local extremum. Suppose now the deposition rate is known but e o is not. Here, d can be obtained trivially by integrating the deposition rate, and e o at any point from a V-I analysis of K C R or K E data. The data of Fig. 3 illustrate one application. These data are compositions x calculated in real time from Eo for a 200 .A wide A l x G a l _ x A s parabolic quantum well grown by closed-loop feedback control [33]. These values were compared to target values shown as the solid line. Compositional discrepancies were corrected by adjusting the flow of the Al-containing species, triisobutyl aluminum (TIBAI), to the growth surface. The results are noteworthy not only because they represent the first (and so far only) demonstration of closed-loop feedback control of composition but also because x was determined by
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
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:~.
~,x
-0.05
' :' '.'
.
TARGET
0 0.05
•..,"'-~." ...>. %1
,,""
I
-100
I
d (,~)
,
f
~"'-"
i
"J~ 1
0
I
is in stage 1, SPA is now moving into stage 2, and RDS is in stage 3. As the sensitivity of SHG and Raman scattering is still improving and samples at growth temperature are not sufficiently transparent to allow conventional multiple-internal-reflection IRAS, I discuss only the first three.
~i I
I
100
Fig. 3. Compositional data for a 200-,~-wide parabolic quantum well grown by closed-loop feedback control. Top: data and target values; middle: difference; bottom: control voltage (after Ref. [33]).
analysis of the outermost 3 ,~ of depositing material [33]. In the most general case neither composition nor deposition rate are known. If the VSA is valid five parameters must be determined. In this case the second derivative (curvature) must be established as well. From Fig. 2 this requires measurements over thicknesses of some 10 s of ,~. In fact, without knowing the convergence point (scale) of the spiral, it is not possible to determine eo because the magnitude of the first derivative is needed in the calculation. If the VSA is not valid then all 7 parameters must be determined by curve fitting, as has also recently been noted by Urban and Tabet [47].
While LLS has long been used as a means of visually assessing surface morphology during MBE growth, recent efforts have been directed toward more quantitative analysis. Pidduck and coworkers used LLS to investigate step flow in Si CVD [8]. Horikoshi et al. used LLS to detect the onset of Ga droplet formation in GaAs homoepitaxy, thereby identifying when saturation coverage had been achieved [9]. Celii et al. recently used LLS to determine the critical thickness of InxGa l_xAs layers grown on GaAs, taking advantage of the connection between surface roughness and misfit dislocations [10]. Data are shown in Fig. 4. The,sample consisted of a superlattice of 46 A layers of In0.16Ga0.84 interleaved with 170 ~, thick layers of GaAs on a GaAs substrate. Growth proceeded pseudomorphically up to the sixth layer, when the surface began to roughen as shown by the increase of scattered light. Roughness continued to increase during subsequent growth. TEM micrographs showed that the associated dislocations were forming ridges 8-10 ,4, high in the (110)
100
~T~
.,o=.l
~
~°
3. Surface analysis All optical surface-analysis probes have followed a common developmental path, beginning with kinetic studies at a single wavelength, progressing to spectral kinetic measurements, then if the technique permits to detailed spectral analyses of surfaces under steady-state conditions. LLS
'? 20
25
30
35
40
45
Growli'l Time (ram)
Fig. 4. LSS data for the |noA6Gao.s4As superlattice shown in the inset. Misfit dislocations generated when the critical thickness is reached at the onset of the sixth InGaAs layer cause increased scattering (after Ref. [10]).
1023
D.E. Aspnes/ Surface Science307-309 (1994) 1017-1027 49O%
151
/
-///
470"C
,
,
/
%
s / o
£g. io
,o
TMG
~
flow d u r a t i o n
,'o (s)
Fig. 5. SPA data obtained by exposing an AsH3-stabi]ized (001) GaAs surface to TMG during OMCVD at several sub-
An example of an SPA application involving spectral measurements is given in Fig. 6 [19]. These data were obtained by exposing a AsH 3stabilized (100) GaAs substrate in an OMCVD growth environment to GaC1 and triethylgallium (TEG). The T E G was used to generate a reference spectrum for a Ga-terminated surface. Because the GaCl-exposed surface exhibits essentially the same spectral response for both (011) (shown) and (011) orientations of the plane of incidence, the data indicate that the GaC1- and TEG-exposed surfaces are equivalent, possibly even identical, and that the GaCl-exposed surface is also terminated with Ga.
strate temperatures as indicated (after Ref. [16]). 3.3. R D S / R A S
direction. A similar anisotropy in the relaxation of InP films deposited on GaAs on Si was studied by Acher et al. using RDS [22]. 3.2. SPA
Another experimentally simple approach that has seen widespread application is SPA. Most work has involved single-wavelength kinetic studies, but spectral data has recently been reported [17-19]. Not surprisingly, spectral information has increased diagnostic power substantially. An example of a kinetics application illustrating control possibilities for A L E is shown in Fig. 5 [16]. This figure shows the SPA response of an AsH3-saturated (001) GaAs surface that is exposed to trimethylgallium (TMG) at different temperatures during OMCVD at approximately 4 - 6 kPa pressure. A well-defined interruption is seen in the 470°C data, indicating self-limiting growth appropriate to ALE. Differences of substrate temperatures of only 20°C, which are difficult to measure on an absolute scale, are clearly seen thereby allowing A L E conditions to be established precisely. Kobayashi and Kobayashi also demonstrated a correlation between the change in SPA signal during H 2 purging and the sheet hole density, showing a connection between surface conditions and dopant incorporation. This was interpreted as being due to attached methyl groups [16].
RDS has become an established technique for obtaining information about the electronic structure of I I I - V growth surfaces as well as kinetic information about surface-reactant interactions. Because it can be used to analyze growth surfaces under steady-state conditions it avoids the "which-surface" ambiguity inherent in methods that depend on a change of surface conditions. Recent attention has focused on the R D equivalent of R H E E D oscillations and the determination of microscopic mechanisms of OMCVD growth through detailed measurements of surface reconstructions that occur during growth. The most thoroughly investigated surface is (001) GaAs, which has been studied under a wide range of U H V and atmospheric pressure (AP)
0.2
i
I
i
I
i
i
i
i
,
i
t
i
B
Ts = 520 °C
'~ ne~ m¢
0.1
t011]
TEC
0 ~'rm'l"rT
" " C~O
-0.i -o.2 I 200
[
I
i
I
300 400
i
I
i
'
500 600
i
i
700 800
WAVELENGTH ( nm )
Fig. 6. SPA spectra obtained by exposing an AsH3-stabilized (100) GaAs surface to GaC1 and TEG during OMCVD (after Ref. [19]).
1024
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
(001)GaAs- UHV/H2 .... UHV
.002
--
(4x2)/-like 590/550°C
H2
o
- .oo2
,y
.
j
(2x4)/-like
~586/500~C
Ar ~-~,
c(4x4)/-like 518/460°C
~
0 - .002
""~%/
I
d(4x4)/-like328/300°C
//~, /
.002
"
_.oo
2
3
4
E (eV)
5
Fig. 7. RD spectra for (001) GaAs surfaces prepared in UHV by MBE (dashed curves) and in AP H 2 by OMCVD (solid lines) (after Ref. [23]).
conditions by Kamiya and coworkers [23,24]. From R D data taken on surfaces prepared by M B E and independently characterized by R H E E D , Kamiya et al. were able to demonstrate that (001) G a A s surfaces in U H V and in AP H 2 were virtually identical and to identify typical coverages in OMCVD under growth conditions. Representative results are shown in Fig. 7 [23]. The similarity between R D spectra obtained with the (001) G a A s surface in the two different ambients is striking. Theoretical calculations showed that the structures observed near 1.9 and 2.6 eV are due to transitions involve G a - G a and A s - A s surface dimers, respectively, and that these features could be used to track the relative surface concentrations of these surface species [48]. These data also showed that, under typical O M C V D growth conditions, the (001) G a A s surface was terminated by 2 layers of As and not one, as commonly supposed. When the As-press u r e / sample temperature phase diagram was established [23], it was found that the O M C V D
region was an extension of the M B E region. This not only provided further evidence of the essential similarity of the surfaces in the two environments, but also showed that under typical OMCVD growth conditions the (001) G a A s surface is c(4 × 4)-like, that is, terminated by 2 outer layers of As instead 1 as in MBE. It also showed that these higher As coverages were a consequence of the vastly higher As partial pressures encountered in O M C V D , which at any given temperature push the equilibrium point to higher As coverages. Recent data obtained during growth have yielded similar results [29,45]. An example of R D oscillations is given in Fig. 8 [28]. Recent work has established conditions where these oscillations are maximized at both low [26] and high [28] reactor pressures. The oscillations of Fig. 8 were obtained during OMCVD at a reactor pressure of 104 Pa, an A s H 3 partial pressure of 70 Pa, a substrate temperature of 502°C, and a photon energy of 2.65 eV, which corresponds to the R D peak of surface As dimers. Each oscillation interval accurately represents growth of 1 M L of material, as shown by postgrowth destructive analysis. Consequently, these oscillations provide growth-rate information for
- i - ~ - X
2.65 a~V = 775 PTMG
=
T~
"7
~."~0.42
Pa
\
L <~
0 . 5 7 Pa
.
Pa
•
Pa I
0 10 20 30 40 50 60 TIME (s) Fig. 8. RD oscillationsobservedduring OMCVD growth on (001) OaAs at H 2 and AsH 3 pressures of 100 mbar and 70 Pa, respectively, and a sample temperature of 502°C. TMG pressures are as indicated (after Ref. [28]).
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
states on the (2 x 1) reconstruction of (001) Ge [27]. Because these results involve a simpler material, they may stimulate further theoretical analysis of surface optical anisotropy effects. Also, Aspnes et al. used a sampling approach to obtain the first spectra of (001) GaAs surfaces in an ALE-like exposure sequence [25]. During AsH 3 exposure the surface was found to be c(4 × 4)-like, consistent with the (001) GaAs phase diagram but not with any of the conventional models of ALE growth.
0.2
0.1
(2x4) - c(4x4)
<
<
d / (4x2) / - (2x4) ~0~2
%t 1.s
i
2.~
'
a.~
1025
'
4.~
'
5.s
Energy [eV] Fig. 9. T h i n lines: R D c h a n g e s p e c t r a •(RDS) c a l c u l a t e d for 4~ = 75 ° for various c o m b i n a t i o n s of initial and final recons t r u c t i o n s on (001) G a A s as i n d i c a t e d . H e a v y line: S P A a n i s o t r o p y f r o m the d a t a of Ref. [18] (after Ref. [49]).
OMCVD analogous to that provided by RHEED for MBE. The mechanism giving rise to the RD oscillations is not understood, although it is clearly a cooperative phenomenon involving oscillating As-As surface coverage probably between partial single and double layers. Similar oscillations have been observed with tertiarybutylarsine (TBAs) [28]. Deppert et al. have used these oscillations to measure growth-rate nonlinearities at the onset of growth by low pressure OMCVD [26]. Hingerl et al. recently derived relations that connect measured SPA anisotropies to RD spectra, allowing RD databases to be used in the interpretation of SPA results [49]. Fig. 9 compares RD change spectra, the calculated difference between RD spectra measured under steady-state conditions for two different reconstructions, to the anisotropy of SPA data calculated from results reported by Nishi et al. [18]. The best agreement is obtained by modeling the difference as a change of surface reconstruction from c(4 × 4) under AsH 3 to a Ga-rich phase under triethylgallium (TEG), as expected from reported conditions. These results open the possibility of more detailed analyses through a combination of SPA and RDS. Although not pertaining directly to epitaxial growth, Wormeester et al. recently used ellipsometry to determine the RD response of surface
4. Future directions
The field of real-time optical characterization will clearly continue to expand not only through the development of new and refinement of existing techniques but also with respect to applications to new materials systems. Rapid data acquisition will be required, especially for applications involving multinary systems where single-wavelength data are insufficient. Parallel and serial versions of rapid-scan ellipsometers have been developed and explored by Collins and coworkers [32,37] and Duncan and coworkers [35], respectively. When optical multichannel detection is adapted to SPA and RDS, it will be possible to assess surface reconstructions in OMCVD at a glance, as is now done with RHEED in MBE. Although the present technological obstacles are formidable, it may prove attractive to develop normal-incidence complex reflectometry as an alternative to SE for the real-time analysis of very thin films, since in this case the derivative approach is exact. At the same time growth chambers must evolve to meet the specific needs of optical measurements. These requirements include not only optical access to the sample through transparent, strain-free, and deposition-free windows, but also the development of runout-corrected and vibration-free sample mounts and manipulators as recently discussed by Maracas and coworkers [36]. Ellipsometric data obtained with rotating samples will contain an RD-like component that can be analyzed for surface coverage using standard RD databases [49].
1026
D.E. Aspnes / Surface Science 307-309 (1994) 1017-1027
Various problems remain to be solved before a full control technology can be realized. These include the optimization of loop performance consistent with system stability, the achievement of accuracy as well as precision, and the development of multiwavelength measurement and processing capabilities that can establish thickness as well as composition. In this regard thickness and composition may well be determined by separate Fresnel and derivative analyses, respectively, carried out simultaneously at different wavelengths. Such approaches will require considerable computing power, but computer technology appears to be able to keep ahead of demands. The near-term future should also see substantial advances in capabilities and applications of SHG, SFG, IRAS, and Raman scattering. It is necessary to develop these approaches because the ability to establish surface chemistry with visible-near UV linear optical techniques is limited. Nonlinear and IR interactions with surface species are weak, making this a genuine challenge. However, new high intensity sources such as free-electron lasers may make such measurements feasible. Approaches dealing with lateral inhomogeneity by the use of small spot sizes [30], imaging [50], or direct analysis [51] also need to be developed to deal with the increasingly important phenomenon of selective-area epitaxy. 5. Acknowledgments
It is a pleasure to acknowledge the contributions of my collaborators in the growth-control and RDS work discussed in Sections 2 and 3: I. Kamiya, H. Tanaka, R. Bhat, M.J.S.P. Brasil, L.T. Florez, S. Gregory, J.P. Harbison, R.E. Nahory, M.A.A. Pudensi, W.E. Quinn, S.A. Schwarz, and M.C. Tamargo. The experimental work described in Sections 2 and 3 was done when all authors were at Bellcore, where I. Kamiya was supported by ONR Contract N-00014-90-J-1267. 6. References [1] See, e.g., Proc. Mater. Res. Soc. 162 (1990); R.F. Davis, J. Vac. Sci. Technol. A 11 (1993) 829.
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