D. E. Aspnes
Department of Physics, NC State University, Raleigh, NC 27695-8202 USA
Tel: (919)515-4261; Fax: (919)515-1333; Email: email@example.com
The drive toward higher performance and increasing complexity in semiconductor devices, together with the trend toward chemical-beam deposition methods such as organometallic chemical vapor deposition (OMCVD) and chemical beam epitaxy (CBE), have provided strong incentives to develop a better understanding of growth processes and better methods of monitoring and even controlling epitaxial growth. Optical probes are of interest here because they are nondestructive, noninvasive, and function in relatively high-pressure ambients, including those encountered in OMCVD, where standard surface-analysis probes cannot be used.
The field is currently experiencing rapid progress owing to several recent developments. The first is the emerging use of photodiode-array (PDA) and charge-coupled device (CCD) detectors, which allow parallel acquisition and analysis of optical spectra over the quartz-optics range, typically 200 to 1000 nm on time scales of less than 1 s [1,2]. Spectral capabilities are required for the simultaneous determination of several parameters, for example thickness, composition, and temperature. If this information is to be useful, it must be made available on a time scale equivalent to that required to deposit a single monolayer (ML), which is about 0.3 nm. The second is the vertical-cavity surface-emitting laser (VCSEL). During the nearly 8 hours required to grow these devices, growth conditions tend to drift, particularly in molecular beam epitaxy (MBE), making some form of monitoring essential [2,3]. Fortunately, most VCSEL layers are so thick that optical monitoring can be done in the simplest possible way, by normal-incidence reflectometry, thereby minimizing the cost and complexity of the monitoring equipment and modifications needed to growth chambers . The third is the development of the virtual-interface (V-I) algorithm , which for laminar samples allows the dielectric response e, and therefore the composition, of the outermost deposited material to be determined from real-time optical data without any knowledge of the underlying materials or structure. This also eliminates the feed-forward instability of conventional Fresnel analysis, allowing sample-driven closed-loop feedback control of epitaxy to compositional precisions of 2 to 3% for thicknesses of the order of 1 ML . These are typical requirements for quantum-well structures in the active gain regions of semiconductor lasers. The fourth is the rapid development of theoretical approaches that can accurately calculate the optical responses of surfaces and interfaces, thereby allowing surface-optical spectra to be interpreted in microscopic terms . The fifth, a consequence of all the above, is the development of integrated tools that can in principle take the above advances into production [2,3,7-9].
Growth is a surface process, but as is well known optical probes are relatively insensitive to surface conditions. This can be appreciated by noting that surfaces are about 0.1 nm thick, whereas the minimum penetration depth of light in any material is typically about 10 nm. Thus about 99% of the information in a reflected beam relates to the bulk and only 1% to the surface. However, in the last few years various optical techniques such as spectroscopic reflectometry (SR), spectroscopic ellipsometry (SE), surface photoabsorption (SPA), reflectance-difference (-anisotropy) spectroscopy (RDS/RAS), p-polarized reflection spectroscopy (PRS), laser light scattering (LLS), and second-harmonic generation (SHG) have either been refined or invented to overcome the intrinsic insensitivity of optical probes to surface conditions and to meet other challenges presented by monitoring and control needs .
True surface-sensitive probes can operate with the surface under steady-state conditions, and include RDS, LLS, and SHG. These enhance surface sensitivity by taking advantage of the lower symmetry of the surface relative to the bulk to allow the two contributions to be separated. Thus RDS measures optical anisotropy, taking advantage of the fact that growth surfaces are usually optically anisotropic while the bulk is not. LLS responds to steps and other irregularities that scatter light out of the specular beam. SHG relies on the inversion symmetry of materials such as Si and Ge, which eliminates any contribution to SHG from the bulk. Relatively surface-sensitive probes identify surface contributions by the change in the optical response as surface conditions are changed, and thus are less specific than the true surface-sensitive probes. These include SPA and PRS, which use p-polarized light near the pseudo-Brewster and Brewster angles, respectively, to suppress as much as possible the bulk contribution. These can provide information about material whose symmetry is equivalent to that of the bulk, for example physisorbed species on the surface.
Despite the emphasis on surface analysis, the primary parameters of interest remain layer thicknesses and compositions. These are bulk properties that, given the finite penetration depth of light, can be accessed by SR and SE in a manner impossible with surface probes alone. In SR the quantity of interest is the relative loss of intensity upon reflection, whereas in SE it is the relative change of polarization state. Since the intensity is real and the polarization state complex, SR and SE bear the same relationship as wattmeters and impedance bridges. Consequently, SR is considerably simpler than SE, requiring minimal equipment. SR can also be used at normal incidence. However, the phase information that SE provides is indispensable for acquiring information about sub-ML-thick layers and hence for monitoring and controlling growth at the ML level.
Whatever the application a spectral capability is essential since the spectral dependence of its dielectric response is a characteristic signature of a material. In addition, the availability of a range of wavelengths allows analysis to be tailored to capability, for example near-surface compositions where absorption is high and layer thicknesses where it is low.
Fig. 1. Schematic diagram of OMCVD growth, illustrating the different regions relevant for monitoring and control together with probes that can access these regions.
The potential effectiveness of the different probes discussed above and of various control strategies can be appreciated by considering the four regions associated with epitaxy: the ambient, surface reaction layer (SRL), the near-surface region (NSR), and the bulk, as illustrated in Fig. 1. The ambient consists of the carrier gas (if any) and the species that provide the constituent elements to the growth surface, including possibly thermally cracked and pre-reacted species. The ambient can be accessed by a number of probes, for example mass spectrometry, ultrasonic attenuation, thermocouples (TC), laser-induced fluorescence (LIF), infrared and ultraviolet absorption spectroscopy (IRAS and UVAS), coherent Raman anti-Stokes scattering (CARS), etc. The SRL contains both weakly (physisorbed) and strongly (chemisorbed) bound fractions. The unreacted fraction can be accessed by SPA and PRS, and at the nuisance level by SR and SE. The reacted fraction, which is in registry with the underlying substrate, can be accessed in addition by symmetry-sensitive probes such as reflection high energy electron diffraction (RHEED), grazing-incidence X-ray scattering (GIXS), LLS, RDS, and SHG. The NSR consists of the most recently deposited material and is accessible through the V-I analysis of kinetic ellipsometric (KE) and in principle kinetic complex reflectometric (KCR) data, which yields the dielectric response of the NSR. Deeper-lying material is accessed by SR and SE.
With respect to control, the ambient is in dynamic equilibrium with the unreacted part of the SRL, which in turn is in dynamic equilibrium with the reacted part, which in turn is in dynamic equilibrium with the NSR. Although information about all regions can be used to advantage, it is clear that for control purposes the weakest link is to the ambient, since its properties are separated from those of the material being grown by the largest number of intermediate steps. The strongest link is to the NSR itself. Control approaches based on the SRL, for example those using RDS  and PRS  lie in between. NSR control [5,12,13] bypasses the need to accurately model the intervening processes and automatically corrects for small changes as they occur. NSR control is also portable, in that it is unaffected by the idiosyncrasies of a particular reactor.
Fig. 2. RD spectra of (001) GaAs for different reconstructions and ambient conditions (after ref. 14).
As an example of monitoring surface reconstructions, Fig. 2 shows RD spectra obtained on (001) GaAs growth surfaces in both UHV and atmospheric-pressure H2 . The former data were obtained with the sample in an MBE chamber and the latter in an OMCVD reactor. The main points are first, the four different surface reconstructions each exhibit a distinctive spectral dependence, which allows them to be distinguished under growth conditions, and second, the same reconstructions are obtained on (001) GaAs whether the surface is in UHV or atmospheric-pressure H2.
By monitoring surface reconstructions, the optical equivalent of RHEED oscillations, and optical interferences that result from finite layer thicknesses, Zettler et al. have developed RDS into a sophisticated monitoring probe for Aixtron horizontal-flow OMCVD reactors . This and a similar development of normal-incidence reflectometry by Breiland et al. [2,3] for Emcore vertical-flow reactors provide two examples where monitoring and growth capabilities have been integrated into single production tools.
Fig. 3. Locus of <e> with thickness for Al xGa1-xAs layers of increasing Al composition deposited sequentially on GaAs (after ref. 15).
The added complexity of SE relative to SR has inhibited the development of combined deposition/analysis tools similar to those mentioned above, although applications to in situ (as opposed to real-time) monitoring are developing rapidly. The issues involved, and the advantages of having complex rather than real quantities available for analysis are illustrated by the data of Fig. 3 . Here, the locus of the real <e1> and imaginary <e2> of the ellipsometrically determined pseudodielectric function <e> obtained during the sequential deposition of AlxGa1-xAs layers of different compositions x on a GaAs substrate are plotted in the complex <e> plane with thickness (time) as the running variable. These data were obtained at a photon energy of 2.6 eV, where the dielectric function of AlxGa1-xAs is changing particularly rapidly with x. They form a sequence of approximately exponential spirals, with each spiral beginning at the dielectric function of the optically thick material prior to a change of composition and ending at the dielectric function of the new layer when it becomes optically thick. If reflectance had been measured the result would have been a plot of reflectance vs. time, with the spirals appearing as (one-dimensional) interference oscillations.
Several points can be made. First, the thickness corresponding to one circuit of a spiral is determined by the refractive index and is here about 50 nm. The data points are about 0.2 nm apart, hence monolayer sensitivity is easily achieved. Second, the convergence rate depends on the absorption coefficient. Thus material containing a higher percentage of Al is more transparent. Third, and most important for control purposes, a line connecting any point on an exponential spiral to its focus makes a constant angle with the tangent at that point, and if material is being deposited at a constant rate, the spacing between adjacent points is proportional to the distance between the points and the focus. Thus if the angle, the proportionality constant, and the growth rate are known, the focus, and hence the material composition of the NSR, can be obtained by a simple geometric construction involving in principle no more than two data points. Aside from generalizations that improve accuracy and allow application to compositionally graded material, this is the principle on which the V-I algorithm is based.
Other conclusions can also be drawn. First, the thickness of the NSR is determined by the number of points that must be averaged to calculate the derivative to sufficient accuracy. Thus this thickness of the NSR is not an intrinsic parameter but is determined by instrument performance. Second, since the value and derivative are both needed to determine the dielectric function of the NSR, additional information such as the deposition rate must be obtained either independently or through the determination higher derivatives, such as curvature, which in turn requires the measurement of many more data points. Thus deposition rates are more effectively determined at wavelengths where e varies relatively slowly with x. Finally, it is clear that this type of analysis cannot be done with scalar data, so an ellipsometer is required.
The simplest control application of V-I analysis is to hold material composition constant. Many examples can now be cited, but we note only one, which involved maintaining the composition of AlxGa1-xAs buffer layers for high-electron-mobility transistors to within 0.1% of a target value in a multiwafer production OMCVD reactor . This was an impressive result considering that for each revolution of the susceptor the optical beam sampled 6 different wafers and the dead spaces between.
Sample-driven closed-loop feedback control of the growth of compositionally graded materials requires the analysis of very thin layers, and the precision is therefore less. So far, only three examples have been reported. The original Bellcore work involved a 20 nm wide AlxGa1-xAs quantum well grown with composition controlled to better than 3% by analysis of 1 ML of material . Mantese et al. reported the growth of linear ramp structures of GexSi1-x on Si . Ebert et al. described the growth of parabolic quantum wells of InxGa1-xP on GaAs . The latter work was done on a modified Emcore reactor using an integrated multiwavelength optical probe that combined both SE and RDS functions in a single optical path, and hence could follow surface reconstructions and material growth simultaneously.
Fig. 4. Composition (top), compositional error (middle), and TME carrier- gas flow (bottom) during sample-driven closed-loop feedback control of the epitaxial growth of an InxGa1-x P parabolic quantum well as described in the text (after ref. 13).
Data for one of the InxGa1-xP structures are shown in Fig. 4 . This structure was grown at a deposition rate of 0.5 nm/s and is 100 nm wide. The upper part shows the target and measured compositions, the middle the difference, and the bottom the H2 setpoint, which is nominally proportional to the flow of the trimethylindium (TMI) precursor to the growth surface, and hence the In concentration of the sample. Here, the composition was held to within 3% by analysis of the outermost 4.5 nm of material. Consistent with previous results , the amount of TMI needed to achieve an In composition of x = 0.45 at the beginning of the run is different from that at the end. This could be a result either of a difference in the concentration of TMI (a solid) in the H2 carrier gas as a result of the variable flow rate through the bubbler, or an increased efficiency of In incorporation into the NSR as a result of the observed change of surface reconstruction with decreasing TMI flow. Either way, the hysteresis seen in Fig. 4 would be extremely difficult to model. Hence the accuracy of virtual reactor calculations, where one attempts to predict the properties of a sample through computation, must be limited at best.
The above provides only a few examples drawn from a rapidly growing field. While considerable progress has been made, further progress is required. So far, only ternary materials have been grown under sample-driven closed-loop feedback control of epitaxy; controlled growth of quaternary materials is needed. While precision is improving, further improvements may be needed to achieve this goal along with the capability of independently determining temperature, composition, strain, and bulk ordering, all of which affect dielectric properties in similar ways. Accuracy is a separate issue. Finally, while SR has been refined to where it can be used in production, this must still be done for SE. In the absence of a more complicated device structure than VCSELs, SE technology is currently being developed through rotating-compensator configurations as a means of improving both diagnostic power and accuracy .
Work at NC State University was done in collaboration with M. Ebert, K. A Bell, K. Flock, G. D. Powell, and S.-D. Yoo, and was supported by the ONR, DARPA, and an Award for International Cooperation from the Max Planck Gesellschaft.
1. I. An et al., Rev. Sci. Instr. 62, 1904 (1992).
2. K. P. Killeen and W. G. Breiland, J. Electron. Mater. 23, 179 (1994).
3. W. Breiland et al., J. Cryst. Growth 174, 564 (1997).
4. D. E. Aspnes, J. Opt. Soc. Am. 10, 974 (1993).
5. D. E. Aspnes et al., Appl. Phys. Lett. 60, 1244 (1992).
6. W. G. Schmidt et al., Phys. Rev. B61, R16335 (2000).
7. M. Ebert et al., Thin Solid Films 264, 22 (2000).
8. K. A. Bell et al., J. Electron. Mater. 29, 106 (2000).
9. K. Haberland et al., J. Electron. Mater. 29, 94 (2000).
10. J.-T. Zettler, Prog. Cryst. Growth and Char. of Mater. 35, 27 (1997).
11. V. Woods et al, J. Vac. Sci. Technol. A18, 1190 (2000).
12. L. Mantese et al., Appl. Surface Sci. 154-155, 229 (2000).
13. M. Ebert et al., phys. stat. sol. (in press).
14. I. Kamiya et al., Phys. Rev. 46, 15894 (1992).
15. D. E. Aspnes et al., Appl. Phys. Lett. 56, 2569 (1990).
16. A. G. Thompson et al., III-Vs Review 9, 12 (1996).
17. See, for example, the Proceedings of the Second International Conference on Spectroscopic Ellipsometry, published as Thin Solid Films 313-314 (1998).
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