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In situ monitoring of MOVPE growth by combined spectroscopic ellipsometry and reflectance-difference spectroscopy
Thin Solid Films 364 (2000) 22±27 www.elsevier.com/locate/tsf
In situ monitoring of MOVPE growth by combined spectroscopic ellipsometry and re¯ectance-difference spectroscopy M. Ebert*, K.A. Bell, S.D. Yoo, K. Flock, D.E. Aspnes NC State University, Raleigh, NC 27695-8202 USA
Abstract Comprehensive characterization of epitaxial growth by metal organic vapor phase epitaxy (MOVPE) requires a combination of thin-®lm, near-surface-, and surface-sensitive techniques to determine layer thicknesses and compositions, composition of the most recently deposited material, and surface chemistry, respectively. These data can be obtained non-destructively by spectroscopic ellipsometry (SE) and re¯ectance-difference (-anisotropy) spectroscopy (RDS/RAS). Here we describe the ®rst uni®ed optical system, basically a rotating-polarizer ellipsometer (RPE) integrated into a modi®ed commercial rotating-sample MOVPE reactor, that performs both SE and RDS simultaneously with a single optical path. Data are obtained in parallel from 240 to 840 nm with a high-speed 16-bit photodiode array (PDA) at a repetition rate greater than 2 Hz and a precision of ^0.0001. We provide examples of its use, and show in particular that GaP intermixes with Si during the initial stages of heteroepitaxy. Capabilities of the presented con®guration and its potential for future investigations are discussed. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Real-time monitoring; Metalorganic vapor phase epitaxy; Growth control; Spectroscopic ellipsometry; Re¯ectance-difference spectroscopy; Silicon (Si); Gallium phosphide (GaP)
1. Introduction The goals of this work are to develop diagnostic equipment to implement non-destructive, sample-driven closedloop feedback control of III±V semiconductor growth by metalorganic vapor phase epitaxy (MOVPE), apply it to heteroepitaxy and the growth of graded-compositional devices in general, and better understand basic mechanisms of MOVPE. By being able to evaluate the properties of the most recently deposited material during deposition, it is possible to compare measured parameters with prede®ned target values and adjust these parameters as necessary, bypassing calculations involving reactor models or models of epitaxial growth [1±5]. We can also gain a better understanding of microscopic mechanisms of crystal growth, and attack from a new direction processes such as heteroepitaxy that are extremely important in technology but are still not well understood. MOVPE is considerably more complicated than physical deposition methods such as molecular beam epitaxy (MBE). Fig. 1 shows a schematic model of MOVPE, along with some approaches used to determine information about the * Corresponding author. Tel.: 1 1-919-515-1974; fax: 1 1-919-5151333. E-mail address: [email protected] (M. Ebert)
process. The ambient consists of the precursor species, carrier gas, and reaction byproducts. The surface reaction layer (SRL) consists of species physisorbed from the ambient that have not yet reacted with the surface, along with chemisorbed material that has partially reacted. The unreacted part can be accessed with p-polarized re¯ectometry [6], whereas the reacted part, which generally shows symmetry related to but lower than that of the substrate, can be accessed by RDS [7]. The near-surface region contains the most recently deposited material and is essentially the amount of material deposited between two consecutive optical measurements. It can be accessed by the analysis of kinetic ellipsometric (KE) data using virtual-interface theory [8]. Bulk properties such as compositions [1,2,4], layer thicknesses [3,9], temperatures [9,10], and strains [11] can be determined by ellipsometry. The ambient, including reaction byproducts, can be accessed by quadruple mass spectrometry (QMS). Current process control has generally focused on process modeling along with highly accurate measurements of process parameters such as temperature, pressure, and ¯ow rates and on accurate process modeling. The basic assumption is that a detailed knowledge of process parameters coupled with a detailed understanding of microscopic mechanisms will allow accurate deposition of materials and structures. This approach is necessarily very
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(99)0092 0-7
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Fig. 1. Regions involved in MOVPE growth and the techniques used to access them.
23
Fig. 2. Re¯ection from an isotropic substrate with an anisotropic overlayer. Quantities are de®ned in the text.
limited, since MOVPE growth processes are complex and sensitive to small variations. Furthermore, the growth chamber environment itself changes dynamically in time, e.g. by deposition of different coatings on the sample holder. This causes variations of local process parameters at the sample surface, which in turn can change the properties of the grown structures. In contrast, the sample-driven approach uses the actual properties of the sample to correct process parameters as necessary [4,5,12]. Therefore, within certain limits we gain independence from the performance characteristics of components such as mass ¯ow controllers or heaters, while at the same time obtaining information about the growth processes themselves. Furthermore, the only modeling necessary is that of the sample response to the probes being used to measure its properties. In most cases this is easier and more reliable than trying to model growth itself. Here, we access the ambient with QMS and sample parameters with RDS and SE. In particular, we describe the ®rst optical con®guration that obtains both RD and SE data simultaneously with a single optical beam. This minimizes modi®cations needed to existing growth systems while providing a large amount of useful information.
which is calculated from r~ and f (angle of incidence) in the two-phase (substrate-ambient) model. The effect of the surface anisotropy can be signi®cant. For example the magnitude of the E2 peak in k12l for a Si(110) sample differs by as much as ^ 2.5% relative to its average value depending on u . For rotating samples, that are not synchronized to the polarizer, this variation appears as noise. The optical anisotropy of the surface is generally measured by RDS, which determines the relative difference Dr~=~r between the normal-incidence complex re¯ectances r~x and r~y for light linearly polarized along the two principal axes x and y of the anisotropic overlayer in the plane of the surface, where
2. Theory
r~x 2 r~y Dr~ 2 r~ r~x 1 r~y
We consider the re¯ection of an incident polarized beam from a sample that consists of an optically biaxial overlayer of thickness d on an optically isotropic substrate. This simulates a surface of lower symmetry on cubic substrate material as illustrated in Fig. 2. In standard Jones-matrix notation ~ r is the re¯ected electric ®eld E ! ! ! r~pp r~ps Eip Erp ~ Er 1 r~sp r~ss Ers Eis where i and r represent incident and re¯ected beams, s and p refer to the polarization state, and r~pp , r~ps , r~sp , and r~ss are the complex Fresnel re¯ection coef®cients of the sample. The quantity r~ determined by a rotating-polarizer ellipsometer is
r~
r~pp 1 r~sp tanA r~ 0 1 Dr~ r~ss 1 r~ps cotA
2
where r~ 0 is the complex re¯ectance ratio of the bare substrate and Dr~ depends on the sample azimuth u , as given in Ref. [13]. r~ is often expressed as the pseudodielectric function h1~ i h11 i 1 ih12 i
3
Here, we must consider the more general situation where light is incident at an angle f other than zero. We suppose that the polarizer and sample rotate at angular frequencies v pol and v sam, respectively. The time dependence of the intensity reaching the detector then has the form I t I0 vsam t1 1 a2 cos 2vpol t 1 b2 sin 2vpol t
4
where a 2 and b 2 are the usual RPE coef®cients and I0(v samt) is given in Ref. [13]. Since the surface anisotropy is small, we can expand I0(v samt) to ®rst order, which yields the additional frequency components 2 vsam ^ vpol . Thus if vsam 3vpol we can determine both r~ and D~r=r~ in a single polarizer rotation and avoid overlapping harmonics. The detected intensity then has the form
24
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Fig. 3. MOVPE growth reactor with sample holder, rotating spindle, optical components, and location of the QMS gas sampling point.
I t I0 a2 cos 2vpol t 1 b2 sin 2vpol t 1 a6 cos 6vpol t 1 b6 sin 6vpol t
5
where a 6 and b 6 are the normalized Fourier coef®cients due to the optically anisotropic overlayer. The quantities a 2 and b 2 yield the ellipsometric angles C and D according to the usual expressions s 1 1 a2 tanA 6 tanc 1 2 a2
b2 cosD q 1 2 a22
are quartz Rochon prisms. N2-purged nominal strain-free quartz windows provide optical access to the sample. The 0.2 m spectrograph uses a 250 mm entrance slit and a focusing 200 groove/mm grating, which is coupled to a 1024element photodiode array (PDA) to cover a spectral range of 240 to 840 nm. Multiple-internal-re¯ection artifacts in the PDA are eliminated by optically contacting a 2-mmthick quartz window directly to the detector surface. The PDA can be read every 6 ms, a timing interval established by reading 32 sets of data per polarizer rotation at a rotation rate of 5.5 Hz. The data are processed through a 16bit A/D converter in a controller that functions as the interface between the PDA and the computer. The computer Fourier analyzes the data and transmits the d.c., second, and sixth harmonics of the polarizer rotation frequency via a TCP/IP communications link to a second computer. The second computer performs the calculations necessary to evaluate k1l, Dr~=r~, and ultimately sample properties such as temperatures, ®lm thicknesses, and compositions as well as providing a means for displaying the data. While processing is taking place, the ®rst computer collects the data from the next polarizer rotation. The time between successive readings can be as short as 400 ms/ spectrum. With a slit width of 250 mm, beam wobble generated by sample runout is generally a signi®cant problem, because
7
Since a 2 and b 2 are independent of the surface anisotropy
r~ tanc´expiD
8
is the usual complex re¯ectance ratio. The real and imaginary parts of the non-normal-incidence anisotropy D~r =~r which originate mostly from Ärpp are calculated from q Dr~ 9 2 a26 1 b26 Re r~ 71:48
and Dr~ 21 a6 tan Im b6 r~ 71:48
10
3. Instrumentation We achieved our design goal of unifying SE and RDS in a single optical path with the system shown in Fig. 3. The ellipsometer part is similar to the system previously described by Collins and co-workers [14]. The source is a high pressure Xe short-arc lamp. The polarizer and analyzer
Fig. 4. Schematic of the dynamic wobble-adjustment mechanism.
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
the sample position tends to depend on the rotation rate of the spindle. A dynamic adjustment capability is therefore essential. We solved this problem with the mechanical assembly shown in Fig. 4. Here, the sample tilt is adjusted in two orthogonal directions by two micrometer screws that are coupled to a wobble stick inside the spindle shaft via thrust bearings and levers. Only one direction is shown in the ®gure for simplicity. With this assembly, sample runout can be reduced to less than ^0.028, which is suf®cient to eliminate artifacts that are related to beam wobble. In practice we adjust runout by minimizing the v sam component, the third harmonic of v pol, in the re¯ected beam. We have also found that further noise reduction can be achieved by orienting the image of the longitudinal axis of the lamp such that it is perpendicular to the spectrograph slit. This con®guration minimizes the effect of arc wander for lamps that show a radial instability of the position of the arc at the contacts. 4. Results and discussion 4.1. Si(110) To test the performance of our system, we measured a Si(110) sample at room temperature. Results are shown in Fig. 5. The top part shows k1Äl data obtained on the present system, along with data obtained on the same sample with our bench ellipsometer for comparison. The bottom part shows Dr~=~r data obtained on the same sample at f 71:48 and compares it to anisotropy data obtained at normal incidence with our RD spectrometer. The agreement between the upper sets of data is good within the accessible optical range. The differences at short wavelengths are probably due to stray light in the
Fig. 6. Surface temperature of a Si(110) sample during heating and cooling, from real-time analysis of SE data.
spectrograph. The same comments apply to the RD results shown at the bottom of the ®gure. The different absolute values of the RD data as well as the different signs of the imaginary parts are due to the different angles of incidence. The RD spectrum illustrates a good noise-to-signal ratio, which at 550 nm is 0.014 and 0.2% on a diode-to-diode and spectrum-to-spectrum basis, respectively. As an example of determining sample properties in real time, we show in Fig. 6 the temperature of a Si(110) sample monitored as a function of time for different power inputs to the sample heater. Here, the data were averaged over eight rotations for a total acquisition time of 2.0 s/spectrum. Standard growth conditions were used, i.e. the sample was maintained in 100 Torr N2. Heating was done by a graphite element located beneath the susceptor. The resulting spectra were analyzed in reciprocal space for the energy Eg of the (E0 0 , E1) critical-point complex near 3.4 eV at room temperature using recently developed algorithms [15]. The temperature was calculated using the relation T 2
Fig. 5. Top: Comparison of k1l data of a Si(110) sample measured by the in situ combined SE/RDS spectrometer and our reference bench ellipsometer. Bottom: Same, for RDS data. Lineshape differences in the bottom part are due to different angles of incidence.
25
Eg T 2 Eg 228C 0:473 meV
8C
11
where Eg(228C) is the room-temperature value of Eg and the temperature coef®cient of 0.473 meV/8C was obtained from Ref. [16]. This is an approximation to the Varshni equation [17], but one that is valid here since the non-linear component is small. The noise seen in Fig. 6 corresponds to a temperature uncertainty of ^2.58C at 3708C. The variation is qualitatively as expected, showing a shorter time constant for higher heater power and higher sample temperature, where radiative transfer of heat to and from the susceptor is more ef®cient. The time constant at low temperatures is surprisingly long, a result of poor heat transfer and the relatively large thermal mass of the susceptor. Comparison of the extracted surface temperature with that measured by the thermocouple located beneath the susceptor indicates thermocouple errors of as much as 608C, as previously reported for MBE [9]. We found that our thermocouple read low at
26
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Table 1 Growth data for GaP/Si heteroepitaxy Pressure (Torr)
Temperature (8C)
Total N2 ¯ow (slm)
PH3 ¯ow (sccm)
TMG ¯ow (sccm)
V/III Ratio
Ê /s) Growth rate (A
60
807
10.15
600
0.06
10000
1
low temperatures and high at high temperatures instead of being in error by an approximated constant amount. 4.2. GaP heteroepitaxy on Si(100) To assess capabilities under actual operating conditions, we investigated the heteroepitaxial growth of GaP on onaxis (^0.58) Si(100) n-type, 1±10 V cm, wafers. Best results were obtained when the sample was heated above 10008C, as measured by the thermocouple, for 15 min under 200 sccm PH3 ¯ow. The temperature was then lowered to 8078C for growth. To establish a high V/III ratio, PH3 ¯ow was increased to 600 sccm before TMG was introduced into the chamber. The TMG ¯ow was 0.06 sccm. Flow rates and settings are summarized in Table 1. Under these condiÊ /s. tions the growth rate was about 1 A The quality of the grown material was veri®ed by comparing its measured dielectric function to that of wellcharacterized reference data, as described in Ref. [18]. The comparison showed that the grown material had a slightly Ê of surface roughness. smaller broadening parameter and 7 A Results from data taken during growth are shown in Fig. 7. The open circles are the trajectory of k12l vs. k11l at 345.1 nm with time (thickness) as the running variable. This trajectory represents the response of only one of the 250 pixels of the complete set of spectra, which were acquired here every 7 s. The arrow indicates the time at which the TMG ¯ow was initiated. The approximate 5 min delay
before the onset of nucleation is due to a pressure difference between the vent and run lines of our MOVPE system. Once the pressures are balanced, response times are a fraction of a second. To interpret these data, we ®rst consider two plausible possibilities: layer-by-layer growth and island formation. The trajectory shown as diamonds was calculated assuming a continuous GaP layer of increasing thickness. The triangles show the trajectory for island growth modeled as an overlayer of 10% GaP and 90% voids. Our data lie outside the range delimited by these trajectories, which shows that growth is proceeding via another path. The next most reasonable hypothesis is that GaP and Si are intermixing, which is consistent with SIMS and TEM results obtained by other groups [19±21]. The calculation was done assuming that the resulting mixtures can be described as a Bruggeman effective-medium mixture of the dielectric responses of the individual constituents. Using this assumption and tailoring the relative fractions of GaP and Si in each layer, we ®nd excellent agreement as shown in Fig. 7. This implies that the separate GaP and Si regions are large enough to preserve their own dielectric identities, that is, the scale of the intermixing is of the order of or larger than about 2 nm. This suggests that the apparent intermixing might actually be due to faceting. Although SIMS data also show intermixing [19,20], SIMS data cannot distinguish between interdiffusion on an atomic scale and actual interpenetration of the two materials. The above interpretation is consistent with the TEM micrographs [21]. 5. Summary
Fig. 7. Trajectory of k12l vs. k11l at 345.1 nm during GaP/Si(100) heteroepitaxy, along with calculations of various models. Open circles: data; diamonds: calculated trajectory for laminar growth of GaP on Si; triangles: calculated trajectory for island growth represented as a layer of 10% GaP and 90% voids; squares: calculated best-®t trajectory, which was generated by the model shown at right.
We describe an optical monitoring system integrated with a modi®ed commercial MOVPE reactor that can obtain SE and RD spectra simultaneously with a single optical beam over a spectral range of 240 to 840 nm at a repetition rate of greater than 2.0 Hz. Through various design features noise is less than 0.02 and 0.2% from diode-to-diode and spectrumto-spectrum, respectively, which is suf®cient to allow sample-driven closed-loop control of MOVPE growth. Implications regarding applications to new materials systems or changes in existing systems can be appreciated by the fact that we were able to grow good material as measured by SE starting from a previously untried system in only ten runs. We have also demonstrated our realtime monitoring capabilities by determining the surface temperatures of a Si(110) substrate and by showing that the ®rst
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
stage of heteroepitaxy of GaP on Si probably occurs by facet formation and the interpenetration of the two materials. Although preliminary, these results hold considerable promise for revealing further details about epitaxial growth processes and for controlling MOVPE growth in realtime. Acknowledgements We gratefully acknowledge support of this work by the Of®ce of Naval Research under contract no. N000 014-93-10255 and an Award for International Cooperation by the Max-Planck-Gesellschaft. We also would like to thank Dr. N. Dietz for helpful discussions. References [1] D.E. Aspnes, W.E. Quinn, S. Gregory, Appl. Phys. Lett. 57 (1990) 2707. [2] D.E. Aspnes, W.E. Quinn, M.C. Tamargo, et al., J. Vac. Sci. Technol. A 10 (1992) 1840. [3] B. Johs, C. Herzinger, P. He, S. Pittal, J. Woollam, T. Wagner, Mater. Sci. Eng. B 44 (1997) 1. [4] M. Zorn, T. Trepk, P. Kurpas, M. Weyers, J.T. Zettler, W. Richter, J. Cryst. Growth 195 (1998) 1.
27
[5] B. Johs, C. Herzinger, J.H. Dinan, et al., Thin Solid Films 313±314 (1998) 490. [6] N. Dietz, K. Ito, Thin Solid Films 313 (1998) 1. [7] D.E. Aspnes, E. Colas, A.A. Studna, R. Bhat, M.A. Koza, V.G. Keramidas, Phys. Rev. Lett. 61 (1988) 2782. [8] D.E. Aspnes, J. Vac. Sci. Technol. A 14 (1996) 960. [9] G.N. Maracas, C.H. Kuo, S. Anand, R. Droopad, G.R.L. Sohie, T. Levola, J. Vac. Sci. Technol. A 13 (1995) 727. [10] P. Lautenschlager, M. Garriga, L. Vina, M. Cardona, Phys. Rev. B 36 (1987) 4821. [11] C. Pickering, Thin Solid Films 313±314 (1998) 406. [12] D.E. Aspnes, W.E. Quinn, M.C. Tamargo, et al., Appl. Phys. Lett. 60 (1992) 1244. [13] K. Hingerl, D.E. Aspnes, I. Kamiya, L.T. Florez, Appl. Phys. Lett. 63 (1993) 885. [14] I. An, H.V. Nguyen, A.R. Heyd, R.W. Collins, Rev. Sci. Instrum. 65 (1994) 3489. [15] D.E. Aspnes, S.D. Yoo, Phys. Status Solid i (b) 215 (1999) 715. [16] G.E. Jellison Jr., F.A. Modine, Phys. Rev. B 27 (1983) 7466. [17] Y.P. Varshni, Physica 34 (1967) 149. [18] K.B. Bell, M. Ebert, S.D. Yoo, K. Flock, D.E. Aspnes, J. Electron. Mater. (1999) (submitted). [19] T. Soga, Y. Kohama, K. Uchida, M. Tajima, T. Jimbo, M. Umeno, J. Cryst. Growth 93 (1988) 1. [20] S.W. Choi, G. Lucovsky, K.J. Bachmann, J. Vac. Sci. Technol. B 10 (1992) 1070. [21] T. Soga, T. Jimbo, M. Umeno, J. Cryst. Growth 163 (1996) 165.
In situ monitoring of MOVPE growth by combined spectroscopic ellipsometry and re¯ectance-difference spectroscopy M. Ebert*, K.A. Bell, S.D. Yoo, K. Flock, D.E. Aspnes NC State University, Raleigh, NC 27695-8202 USA
Abstract Comprehensive characterization of epitaxial growth by metal organic vapor phase epitaxy (MOVPE) requires a combination of thin-®lm, near-surface-, and surface-sensitive techniques to determine layer thicknesses and compositions, composition of the most recently deposited material, and surface chemistry, respectively. These data can be obtained non-destructively by spectroscopic ellipsometry (SE) and re¯ectance-difference (-anisotropy) spectroscopy (RDS/RAS). Here we describe the ®rst uni®ed optical system, basically a rotating-polarizer ellipsometer (RPE) integrated into a modi®ed commercial rotating-sample MOVPE reactor, that performs both SE and RDS simultaneously with a single optical path. Data are obtained in parallel from 240 to 840 nm with a high-speed 16-bit photodiode array (PDA) at a repetition rate greater than 2 Hz and a precision of ^0.0001. We provide examples of its use, and show in particular that GaP intermixes with Si during the initial stages of heteroepitaxy. Capabilities of the presented con®guration and its potential for future investigations are discussed. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Real-time monitoring; Metalorganic vapor phase epitaxy; Growth control; Spectroscopic ellipsometry; Re¯ectance-difference spectroscopy; Silicon (Si); Gallium phosphide (GaP)
1. Introduction The goals of this work are to develop diagnostic equipment to implement non-destructive, sample-driven closedloop feedback control of III±V semiconductor growth by metalorganic vapor phase epitaxy (MOVPE), apply it to heteroepitaxy and the growth of graded-compositional devices in general, and better understand basic mechanisms of MOVPE. By being able to evaluate the properties of the most recently deposited material during deposition, it is possible to compare measured parameters with prede®ned target values and adjust these parameters as necessary, bypassing calculations involving reactor models or models of epitaxial growth [1±5]. We can also gain a better understanding of microscopic mechanisms of crystal growth, and attack from a new direction processes such as heteroepitaxy that are extremely important in technology but are still not well understood. MOVPE is considerably more complicated than physical deposition methods such as molecular beam epitaxy (MBE). Fig. 1 shows a schematic model of MOVPE, along with some approaches used to determine information about the * Corresponding author. Tel.: 1 1-919-515-1974; fax: 1 1-919-5151333. E-mail address: [email protected] (M. Ebert)
process. The ambient consists of the precursor species, carrier gas, and reaction byproducts. The surface reaction layer (SRL) consists of species physisorbed from the ambient that have not yet reacted with the surface, along with chemisorbed material that has partially reacted. The unreacted part can be accessed with p-polarized re¯ectometry [6], whereas the reacted part, which generally shows symmetry related to but lower than that of the substrate, can be accessed by RDS [7]. The near-surface region contains the most recently deposited material and is essentially the amount of material deposited between two consecutive optical measurements. It can be accessed by the analysis of kinetic ellipsometric (KE) data using virtual-interface theory [8]. Bulk properties such as compositions [1,2,4], layer thicknesses [3,9], temperatures [9,10], and strains [11] can be determined by ellipsometry. The ambient, including reaction byproducts, can be accessed by quadruple mass spectrometry (QMS). Current process control has generally focused on process modeling along with highly accurate measurements of process parameters such as temperature, pressure, and ¯ow rates and on accurate process modeling. The basic assumption is that a detailed knowledge of process parameters coupled with a detailed understanding of microscopic mechanisms will allow accurate deposition of materials and structures. This approach is necessarily very
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(99)0092 0-7
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Fig. 1. Regions involved in MOVPE growth and the techniques used to access them.
23
Fig. 2. Re¯ection from an isotropic substrate with an anisotropic overlayer. Quantities are de®ned in the text.
limited, since MOVPE growth processes are complex and sensitive to small variations. Furthermore, the growth chamber environment itself changes dynamically in time, e.g. by deposition of different coatings on the sample holder. This causes variations of local process parameters at the sample surface, which in turn can change the properties of the grown structures. In contrast, the sample-driven approach uses the actual properties of the sample to correct process parameters as necessary [4,5,12]. Therefore, within certain limits we gain independence from the performance characteristics of components such as mass ¯ow controllers or heaters, while at the same time obtaining information about the growth processes themselves. Furthermore, the only modeling necessary is that of the sample response to the probes being used to measure its properties. In most cases this is easier and more reliable than trying to model growth itself. Here, we access the ambient with QMS and sample parameters with RDS and SE. In particular, we describe the ®rst optical con®guration that obtains both RD and SE data simultaneously with a single optical beam. This minimizes modi®cations needed to existing growth systems while providing a large amount of useful information.
which is calculated from r~ and f (angle of incidence) in the two-phase (substrate-ambient) model. The effect of the surface anisotropy can be signi®cant. For example the magnitude of the E2 peak in k12l for a Si(110) sample differs by as much as ^ 2.5% relative to its average value depending on u . For rotating samples, that are not synchronized to the polarizer, this variation appears as noise. The optical anisotropy of the surface is generally measured by RDS, which determines the relative difference Dr~=~r between the normal-incidence complex re¯ectances r~x and r~y for light linearly polarized along the two principal axes x and y of the anisotropic overlayer in the plane of the surface, where
2. Theory
r~x 2 r~y Dr~ 2 r~ r~x 1 r~y
We consider the re¯ection of an incident polarized beam from a sample that consists of an optically biaxial overlayer of thickness d on an optically isotropic substrate. This simulates a surface of lower symmetry on cubic substrate material as illustrated in Fig. 2. In standard Jones-matrix notation ~ r is the re¯ected electric ®eld E ! ! ! r~pp r~ps Eip Erp ~ Er 1 r~sp r~ss Ers Eis where i and r represent incident and re¯ected beams, s and p refer to the polarization state, and r~pp , r~ps , r~sp , and r~ss are the complex Fresnel re¯ection coef®cients of the sample. The quantity r~ determined by a rotating-polarizer ellipsometer is
r~
r~pp 1 r~sp tanA r~ 0 1 Dr~ r~ss 1 r~ps cotA
2
where r~ 0 is the complex re¯ectance ratio of the bare substrate and Dr~ depends on the sample azimuth u , as given in Ref. [13]. r~ is often expressed as the pseudodielectric function h1~ i h11 i 1 ih12 i
3
Here, we must consider the more general situation where light is incident at an angle f other than zero. We suppose that the polarizer and sample rotate at angular frequencies v pol and v sam, respectively. The time dependence of the intensity reaching the detector then has the form I t I0 vsam t1 1 a2 cos 2vpol t 1 b2 sin 2vpol t
4
where a 2 and b 2 are the usual RPE coef®cients and I0(v samt) is given in Ref. [13]. Since the surface anisotropy is small, we can expand I0(v samt) to ®rst order, which yields the additional frequency components 2 vsam ^ vpol . Thus if vsam 3vpol we can determine both r~ and D~r=r~ in a single polarizer rotation and avoid overlapping harmonics. The detected intensity then has the form
24
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Fig. 3. MOVPE growth reactor with sample holder, rotating spindle, optical components, and location of the QMS gas sampling point.
I t I0 a2 cos 2vpol t 1 b2 sin 2vpol t 1 a6 cos 6vpol t 1 b6 sin 6vpol t
5
where a 6 and b 6 are the normalized Fourier coef®cients due to the optically anisotropic overlayer. The quantities a 2 and b 2 yield the ellipsometric angles C and D according to the usual expressions s 1 1 a2 tanA 6 tanc 1 2 a2
b2 cosD q 1 2 a22
are quartz Rochon prisms. N2-purged nominal strain-free quartz windows provide optical access to the sample. The 0.2 m spectrograph uses a 250 mm entrance slit and a focusing 200 groove/mm grating, which is coupled to a 1024element photodiode array (PDA) to cover a spectral range of 240 to 840 nm. Multiple-internal-re¯ection artifacts in the PDA are eliminated by optically contacting a 2-mmthick quartz window directly to the detector surface. The PDA can be read every 6 ms, a timing interval established by reading 32 sets of data per polarizer rotation at a rotation rate of 5.5 Hz. The data are processed through a 16bit A/D converter in a controller that functions as the interface between the PDA and the computer. The computer Fourier analyzes the data and transmits the d.c., second, and sixth harmonics of the polarizer rotation frequency via a TCP/IP communications link to a second computer. The second computer performs the calculations necessary to evaluate k1l, Dr~=r~, and ultimately sample properties such as temperatures, ®lm thicknesses, and compositions as well as providing a means for displaying the data. While processing is taking place, the ®rst computer collects the data from the next polarizer rotation. The time between successive readings can be as short as 400 ms/ spectrum. With a slit width of 250 mm, beam wobble generated by sample runout is generally a signi®cant problem, because
7
Since a 2 and b 2 are independent of the surface anisotropy
r~ tanc´expiD
8
is the usual complex re¯ectance ratio. The real and imaginary parts of the non-normal-incidence anisotropy D~r =~r which originate mostly from Ärpp are calculated from q Dr~ 9 2 a26 1 b26 Re r~ 71:48
and Dr~ 21 a6 tan Im b6 r~ 71:48
10
3. Instrumentation We achieved our design goal of unifying SE and RDS in a single optical path with the system shown in Fig. 3. The ellipsometer part is similar to the system previously described by Collins and co-workers [14]. The source is a high pressure Xe short-arc lamp. The polarizer and analyzer
Fig. 4. Schematic of the dynamic wobble-adjustment mechanism.
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
the sample position tends to depend on the rotation rate of the spindle. A dynamic adjustment capability is therefore essential. We solved this problem with the mechanical assembly shown in Fig. 4. Here, the sample tilt is adjusted in two orthogonal directions by two micrometer screws that are coupled to a wobble stick inside the spindle shaft via thrust bearings and levers. Only one direction is shown in the ®gure for simplicity. With this assembly, sample runout can be reduced to less than ^0.028, which is suf®cient to eliminate artifacts that are related to beam wobble. In practice we adjust runout by minimizing the v sam component, the third harmonic of v pol, in the re¯ected beam. We have also found that further noise reduction can be achieved by orienting the image of the longitudinal axis of the lamp such that it is perpendicular to the spectrograph slit. This con®guration minimizes the effect of arc wander for lamps that show a radial instability of the position of the arc at the contacts. 4. Results and discussion 4.1. Si(110) To test the performance of our system, we measured a Si(110) sample at room temperature. Results are shown in Fig. 5. The top part shows k1Äl data obtained on the present system, along with data obtained on the same sample with our bench ellipsometer for comparison. The bottom part shows Dr~=~r data obtained on the same sample at f 71:48 and compares it to anisotropy data obtained at normal incidence with our RD spectrometer. The agreement between the upper sets of data is good within the accessible optical range. The differences at short wavelengths are probably due to stray light in the
Fig. 6. Surface temperature of a Si(110) sample during heating and cooling, from real-time analysis of SE data.
spectrograph. The same comments apply to the RD results shown at the bottom of the ®gure. The different absolute values of the RD data as well as the different signs of the imaginary parts are due to the different angles of incidence. The RD spectrum illustrates a good noise-to-signal ratio, which at 550 nm is 0.014 and 0.2% on a diode-to-diode and spectrum-to-spectrum basis, respectively. As an example of determining sample properties in real time, we show in Fig. 6 the temperature of a Si(110) sample monitored as a function of time for different power inputs to the sample heater. Here, the data were averaged over eight rotations for a total acquisition time of 2.0 s/spectrum. Standard growth conditions were used, i.e. the sample was maintained in 100 Torr N2. Heating was done by a graphite element located beneath the susceptor. The resulting spectra were analyzed in reciprocal space for the energy Eg of the (E0 0 , E1) critical-point complex near 3.4 eV at room temperature using recently developed algorithms [15]. The temperature was calculated using the relation T 2
Fig. 5. Top: Comparison of k1l data of a Si(110) sample measured by the in situ combined SE/RDS spectrometer and our reference bench ellipsometer. Bottom: Same, for RDS data. Lineshape differences in the bottom part are due to different angles of incidence.
25
Eg T 2 Eg 228C 0:473 meV
8C
11
where Eg(228C) is the room-temperature value of Eg and the temperature coef®cient of 0.473 meV/8C was obtained from Ref. [16]. This is an approximation to the Varshni equation [17], but one that is valid here since the non-linear component is small. The noise seen in Fig. 6 corresponds to a temperature uncertainty of ^2.58C at 3708C. The variation is qualitatively as expected, showing a shorter time constant for higher heater power and higher sample temperature, where radiative transfer of heat to and from the susceptor is more ef®cient. The time constant at low temperatures is surprisingly long, a result of poor heat transfer and the relatively large thermal mass of the susceptor. Comparison of the extracted surface temperature with that measured by the thermocouple located beneath the susceptor indicates thermocouple errors of as much as 608C, as previously reported for MBE [9]. We found that our thermocouple read low at
26
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
Table 1 Growth data for GaP/Si heteroepitaxy Pressure (Torr)
Temperature (8C)
Total N2 ¯ow (slm)
PH3 ¯ow (sccm)
TMG ¯ow (sccm)
V/III Ratio
Ê /s) Growth rate (A
60
807
10.15
600
0.06
10000
1
low temperatures and high at high temperatures instead of being in error by an approximated constant amount. 4.2. GaP heteroepitaxy on Si(100) To assess capabilities under actual operating conditions, we investigated the heteroepitaxial growth of GaP on onaxis (^0.58) Si(100) n-type, 1±10 V cm, wafers. Best results were obtained when the sample was heated above 10008C, as measured by the thermocouple, for 15 min under 200 sccm PH3 ¯ow. The temperature was then lowered to 8078C for growth. To establish a high V/III ratio, PH3 ¯ow was increased to 600 sccm before TMG was introduced into the chamber. The TMG ¯ow was 0.06 sccm. Flow rates and settings are summarized in Table 1. Under these condiÊ /s. tions the growth rate was about 1 A The quality of the grown material was veri®ed by comparing its measured dielectric function to that of wellcharacterized reference data, as described in Ref. [18]. The comparison showed that the grown material had a slightly Ê of surface roughness. smaller broadening parameter and 7 A Results from data taken during growth are shown in Fig. 7. The open circles are the trajectory of k12l vs. k11l at 345.1 nm with time (thickness) as the running variable. This trajectory represents the response of only one of the 250 pixels of the complete set of spectra, which were acquired here every 7 s. The arrow indicates the time at which the TMG ¯ow was initiated. The approximate 5 min delay
before the onset of nucleation is due to a pressure difference between the vent and run lines of our MOVPE system. Once the pressures are balanced, response times are a fraction of a second. To interpret these data, we ®rst consider two plausible possibilities: layer-by-layer growth and island formation. The trajectory shown as diamonds was calculated assuming a continuous GaP layer of increasing thickness. The triangles show the trajectory for island growth modeled as an overlayer of 10% GaP and 90% voids. Our data lie outside the range delimited by these trajectories, which shows that growth is proceeding via another path. The next most reasonable hypothesis is that GaP and Si are intermixing, which is consistent with SIMS and TEM results obtained by other groups [19±21]. The calculation was done assuming that the resulting mixtures can be described as a Bruggeman effective-medium mixture of the dielectric responses of the individual constituents. Using this assumption and tailoring the relative fractions of GaP and Si in each layer, we ®nd excellent agreement as shown in Fig. 7. This implies that the separate GaP and Si regions are large enough to preserve their own dielectric identities, that is, the scale of the intermixing is of the order of or larger than about 2 nm. This suggests that the apparent intermixing might actually be due to faceting. Although SIMS data also show intermixing [19,20], SIMS data cannot distinguish between interdiffusion on an atomic scale and actual interpenetration of the two materials. The above interpretation is consistent with the TEM micrographs [21]. 5. Summary
Fig. 7. Trajectory of k12l vs. k11l at 345.1 nm during GaP/Si(100) heteroepitaxy, along with calculations of various models. Open circles: data; diamonds: calculated trajectory for laminar growth of GaP on Si; triangles: calculated trajectory for island growth represented as a layer of 10% GaP and 90% voids; squares: calculated best-®t trajectory, which was generated by the model shown at right.
We describe an optical monitoring system integrated with a modi®ed commercial MOVPE reactor that can obtain SE and RD spectra simultaneously with a single optical beam over a spectral range of 240 to 840 nm at a repetition rate of greater than 2.0 Hz. Through various design features noise is less than 0.02 and 0.2% from diode-to-diode and spectrumto-spectrum, respectively, which is suf®cient to allow sample-driven closed-loop control of MOVPE growth. Implications regarding applications to new materials systems or changes in existing systems can be appreciated by the fact that we were able to grow good material as measured by SE starting from a previously untried system in only ten runs. We have also demonstrated our realtime monitoring capabilities by determining the surface temperatures of a Si(110) substrate and by showing that the ®rst
M. Ebert et al. / Thin Solid Films 364 (2000) 22±27
stage of heteroepitaxy of GaP on Si probably occurs by facet formation and the interpenetration of the two materials. Although preliminary, these results hold considerable promise for revealing further details about epitaxial growth processes and for controlling MOVPE growth in realtime. Acknowledgements We gratefully acknowledge support of this work by the Of®ce of Naval Research under contract no. N000 014-93-10255 and an Award for International Cooperation by the Max-Planck-Gesellschaft. We also would like to thank Dr. N. Dietz for helpful discussions. References [1] D.E. Aspnes, W.E. Quinn, S. Gregory, Appl. Phys. Lett. 57 (1990) 2707. [2] D.E. Aspnes, W.E. Quinn, M.C. Tamargo, et al., J. Vac. Sci. Technol. A 10 (1992) 1840. [3] B. Johs, C. Herzinger, P. He, S. Pittal, J. Woollam, T. Wagner, Mater. Sci. Eng. B 44 (1997) 1. [4] M. Zorn, T. Trepk, P. Kurpas, M. Weyers, J.T. Zettler, W. Richter, J. Cryst. Growth 195 (1998) 1.
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[5] B. Johs, C. Herzinger, J.H. Dinan, et al., Thin Solid Films 313±314 (1998) 490. [6] N. Dietz, K. Ito, Thin Solid Films 313 (1998) 1. [7] D.E. Aspnes, E. Colas, A.A. Studna, R. Bhat, M.A. Koza, V.G. Keramidas, Phys. Rev. Lett. 61 (1988) 2782. [8] D.E. Aspnes, J. Vac. Sci. Technol. A 14 (1996) 960. [9] G.N. Maracas, C.H. Kuo, S. Anand, R. Droopad, G.R.L. Sohie, T. Levola, J. Vac. Sci. Technol. A 13 (1995) 727. [10] P. Lautenschlager, M. Garriga, L. Vina, M. Cardona, Phys. Rev. B 36 (1987) 4821. [11] C. Pickering, Thin Solid Films 313±314 (1998) 406. [12] D.E. Aspnes, W.E. Quinn, M.C. Tamargo, et al., Appl. Phys. Lett. 60 (1992) 1244. [13] K. Hingerl, D.E. Aspnes, I. Kamiya, L.T. Florez, Appl. Phys. Lett. 63 (1993) 885. [14] I. An, H.V. Nguyen, A.R. Heyd, R.W. Collins, Rev. Sci. Instrum. 65 (1994) 3489. [15] D.E. Aspnes, S.D. Yoo, Phys. Status Solid i (b) 215 (1999) 715. [16] G.E. Jellison Jr., F.A. Modine, Phys. Rev. B 27 (1983) 7466. [17] Y.P. Varshni, Physica 34 (1967) 149. [18] K.B. Bell, M. Ebert, S.D. Yoo, K. Flock, D.E. Aspnes, J. Electron. Mater. (1999) (submitted). [19] T. Soga, Y. Kohama, K. Uchida, M. Tajima, T. Jimbo, M. Umeno, J. Cryst. Growth 93 (1988) 1. [20] S.W. Choi, G. Lucovsky, K.J. Bachmann, J. Vac. Sci. Technol. B 10 (1992) 1070. [21] T. Soga, T. Jimbo, M. Umeno, J. Cryst. Growth 163 (1996) 165.