Real time spectroscopic ellipsometry for characterization of nucleation, growth, and optical functions of thin films

Thin Solid kTIms, 233 (1993) 244 252

244

Real time spectroscopic ellipsometry for characterization of nucleation, growth, and optical functions of thin films R. W. C o l l i n s , I l s i n A n , H. V. N g u y e n

a n d Y i w e i Lu

Materials Research Laborator) and Department ~[ Physics, The Pennsylvania State University, ~hliversity Park, PA 16802 (USA)

Abstract We have exploited the unique capabilities of a rotating-polarizer multichannel spectroscopic cllipsometer in real time studies of the evolution of microstructure and optical functions for various thin film materials. With a 16 ms acquisition time for ~ 50 point spectra from 1.3 to 4.3 eV, the precision of the ellipsometer is (0.04 ~', 0.1T') in (~, A) for a Si surface at 2.5 eV. Real time investigations of aluminum prepared by physical vapor deposition and hydrogenated amorphous semiconductors prepared by plasma-enhanced chemical vapor deposition are highlighted here. We focus on capabilities that elude a real time discrete-wavelength approach. For aluminum, this includes determining (i) the optical functions of small A1 particles ( < 50 A diameter) in the nucleation regime for comparison with those of bulk AI, and (ii) an electron mean free path that characterizes the effect of defects on the optical functions of the particles. For the amorphous semiconductors, this includes determining (i) the optical gap from real time measurements, and (ii) the monolayer-scale coalescence behavior that correlates well with the device suitability of the material.

1. Introduction Real time ellipsometry at one or more discrete wavelengths has been demonstrated as an effective method of monitoring the deposition of thin films [1-3]. Information on the time evolution of the dielectric function at the discrete wavelength(s) and the thickness of the film can be inferred from the ellipsometry angles ( ~ , A) collected in real time during film growth. Because the evolution of the dielectric function in turn provides information on the development of void volume fraction through an effective medium theory ( E M T ) [4], such measurements have been applied extensively to the study of nucleation phenomena. In these studies, the film is described in terms of one- and two-layer optical models, allowing one to distinguish between growth modes including atomic layer-by-layer growth, clustering ( V o l m e r - W e b e r ) , and layer-by-layer growth to a critical thickness followed by clustering (StranskiKrastanov) [5]. An approximate scale for nucleation can be determined for the last two modes, for example the thickness at which a bulk density film develops. Recently, the problem of determining the evolution of the near-surface optical properties from the time dependence of ( ~ , A) at one wavelength has been solved [6]. This information has been obtained in real time and applied to control the near-surface alloy composition of A1GaAs during preparation. In this way, any desired band gap profile can be generated through the thickness of the material. The overall accuracy of the approach

0040-6090/93/$6.00

relies on having an atomically abrupt interface between the film and the ambient vacuum, without any surface structural changes during growth. Thus, the approach appears generally suitable for epitaxial films. Despite its successes, discrete wavelength ellipsometry is unsatisfactory in m a n y complex situations. For example, during the nucleation of a thin film, changes of interest in electronic structure and microstructure may occur simultaneously as thin film nuclei increase in size. These processes are impossible to distinguish on the basis of experimentally observable changes in the dielectric function at discrete wavelengths. In another example, the band gap of a semiconductor may not be defined uniquely by the optical properties at a few wavelengths, or the interpretation may be complicated by a surface roughness layer whose thickness varies with time during growth. In this case, a full spectroscopic capability is needed to extract the band gap from real time observations. In this review, we describe the applications of a recently developed real time multichannel ellipsometer that can collect (ud, A) spectra from 1.3 to 4.3 eV with a minimum demonstrated acquisition time of 16 ms [7]. In the first application, the optical and electronic properties of aluminum thin films have been determined in the nucleation regime, where the film consists of isolated particles [8, 9]. In previous studies, it has been proposed that the optical properties of A1 clusters are influenced by finite size effects whereby the mean free path of the electrons increases linearly with the particle diameter

~" 1 9 9 3

Elsevier Sequoia. All rights reserved

245

R. W. Collins et al. / Real time spectroscopic ellipsometry

[10]. Such ideas can be tested for the first time in our experiments. In the second application, the evolution of microstructure for hydrogenated amorphous silicon (a-Si:H) [11] and silicon-carbon alloys (a-SiC:H) [12] in the coalescence stage has been studied. Using an analysis procedure that accounts for surface microstructure, the optical gap of the bulk film after coalescence can also be determined from the real time observations.

2. Experimental apparatus The rotating-polarizer multichannel ellipsometer is described in detail in refs. 7, 13-15. It consists of (i) a collimated Xe source, (ii) a quartz Rochon polarizer rotating at a frequency of 10-35 Hz, (iii) the sample in a high vacuum chamber with stress-balanced windows [16], (iv) a calcite Glan-Taylor analyzer, (v) a prism spectrograph and (vi) a 1024-pixel Si photodiode array with controller. Four raw spectra in the integrated irradiance are collected, one for each of the four quadrants of the rotating polarizer optical cycle. The controller provides the capability of pixel grouping, so that the array can operate as a 1024/N pixel detector (N even). The operational parameters of the system can be set according to the desired precision and/or speed [7]. For a polarizer frequency of 12.5 Hz, 80 optical cycles can be accumulated and averaged to obtain a single pair of 128-point (ud, A) spectra in 3.2 s. Under these conditions, the standard deviation in (u,,, A) at 2.5eV is (0.003 °, 0.007°), as obtained on a stable Cr surface [(~, A ) ~ ( 3 0 °, 110°)]. At the opposite extreme, for a polarizer rotation frequency of 31.3 Hz, a single optical cycle provides a pair of 64-point (ud, A) spectra with a 16 ms acquisition time. In this case, the standard deviation in (q~, A) at 2.5eV is (0.04 °, 0.12°), as obtained from spectra collected during plasma etching of 500 A amorphous silicon on single-crystal Si [(ud, A) (20 °, 120°)]. The repetition period for the acquisition of successive spectra depends on the desired speed and/or duration of the process under study. If high speed is the only consideration, the repetition period can be reduced to the acquisition time. In this mode, the raw spectra cannot be transferred to permanent memory, processed, or displayed in real time. As a result, the total observation period is limited by the memory available in the detector controller. In our present system configuration, 250 full sets of 64-point spectra completely fill the 256-kByte memory. With a minimum repetition period of 16 ms, this results in a total observational period of 4 s, however, memory expansion is available if warranted by the application. At the other extreme, if high speed repetition is not necessary, then raw data reduc-

tion, video display, and permanent storage can be performed in real time. For a 128-point pair of (ud, A) spectra, this typically adds 4 - 5 s to the repetition time. 3. Results and discussion 3.1. Aluminum in the nucleation regime

We have undertaken a detailed study of aluminum thin films in the nucleation regime [8, 9]. The films were prepared by evaporation and by magnetron sputtering onto c-Si wafers coated with ~ 100 A, thick thermallygrown oxide. The repetition period for full spectra in (W, A) ranged from 1.25 s for high rate evaporation (280A, min -~) to 6.0s for low rate sputtering ( 5 0 W power: 16A, min-I). From 8 to 20 optical cycles were averaged, resulting in acquisition times of 320-800 ms. After deposition, selected films were dissolved in dilute HC1, and the bare substrates were studied by e x situ spectroscopic ellipsometry (SE). In all cases, the substrate oxide thickness and optical properties were unchanged from those measured before film growth. This demonstrates the absence of any measurable chemical reaction between SiO 2 and AI at the nominal substrate temperature of 25 °C [17]. Any such reaction would complicate the interpretation of nucleation. Figure 1 shows the effective dielectric function (points) of an evaporated AI film, obtained from real time (q', A) spectra collected in 320 ms, ~70 s after the onset of growth. The average deposition rate was 43 A, min -1, estimated from subsequent real time SE analysis. The effective dielectric function (el, e2) and thickness, d = 50/~, were determined from a singlelayer model for the film, neglecting possible optical anisotropy. In this analysis, d was chosen in an attempt to minimize artifacts in the deduced (~l, ~2) of the film that arise from the E l - E o structure in the Si substrate dielectric function [18]. SE was also undertaken vs. angle of incidence on a thin evaporated A1 film (23 A,), measured statically in an inert atmosphere just after preparation. All spectra could be simulated closely with a unique dielectric function; this result supports the assumption of optical isotropy. The physical origins underlying this result are discussed below. In Fig. 1, the broad dispersion and absorption features in ~ and ~2 are characteristic of the dipolar plasmon-polariton resonance in metal particles. To interpret these results, we start with a general anisotropic form of the Maxwell-Garnett EMT, appropriate for spheroidal particles [19]: ell (to) = 1 + { Q / [ F , +

(ep(to)

--

1)-l]},

[ei(to)]-1 = 1 -- {Q/[F± + (ep(to) - 1) -l]}

(la) (lb)

where eli and el are the principal components of the effective dielectric function parallel and perpendicular

246

R. W. Collins et al. 25

I

I

I

E v a p o r a t e d AI Rate: 43 ~/min

20

I

Real time spectroscopic ellipsometry

I

d=50 Fit

o

/

~,

15 ~

10 5 0 -5 1.0

"'

0.8

~

0.6

I

I

I

I

I

I

I

I

m~ 0 . 4 Z < ~ 0.2 0.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 PHOTON E N E R G Y (eV) Fig. 1. Effective dielectric function for a 50 A thick aluminum particle film (points) extracted from SE data collected in 320 ms during evaporation (43 ~ min-~). Also shown is a best fit using a MaxwellGarnett type E M T (lines). Normal-incidence transmittance spectra calculated from the effective dielectric functions and thickness are shown in the lower panel, assuming a free-standing film (points = experimental data; line = fit) (after ref. 9).

to the substrate, Q is the A1 volume fraction and e.p is the intrinsic dielectric function of the A1 particles. Fll and F L are parameters that depend on the assumed interparticle interaction and must approximately satisfy Fl = Fll + Q to maintain consistency with the observed isotropy. In order to fit the spectra of Fig. 1 to eqn. (la) (or equivalently to eqn. (lb)) using linear regression analysis (LRA), the A s h c r o f t - S t u r m formulas [20] are applied to parameterize ep(Og) as the sum of an intraband (or Drude) (eD) and two interband (or parallel-band) contributions (eps.]]~ and ePS-200): Gp ~- GD ~- CPB-II1 -~- ~PB-20OIn the LRA, the Drude optical mass and the interband onset energies are fixed at bulk values. Thus, m o p t = 1.55me, 2JU200] = 1.47 eV, and 2[U, 11[ = 0 . 5 0 e V , where me is the electron mass and IUK ] is the Fourier coefficient of the pseudo-potential for interband transitions of wavevector K. We assume, however, that the relaxation times zj for the three transitions ( j = D, PB-111, and PB-200) are reduced from bulk values Z/, bulk according to (L) ' = (Z/, bulk) 1 ~_ (1)j/2), where the electron velocities are equated to the Fermi velocity and 2 is a common value of the mean free path [21]. 2 accounts for the possibility of electron scattering at surfaces or internal

particle defects. With this approach, we can represent ~:p(¢O) in the LRA with one variable parameter, 2. We can now fit the spectra of Fig. 1 to ell of eqn. (la) using the three free parameters, Q, Fjl and 2. Figure 1 includes the best LRA fit (solid line) to the experimental (e~, e2) spectra for the 50/~ thick film, obtained with Q = 0.58, Fii = 0.0435 and 2 = 8.5/~. For comparison to ref. 10, transmittance spectra are also shown in Fig. 1 (bottom), calculated from (e~, ~:2) assuming a free-standing film. Excellent agreement is obtained between the experimental and fitted results. The large best-fit value of Q in the fit of Fig. 1 implies that the particles are flattened and cover a large substrate area, as expected just prior to coalescence. For both evaporated and sputtered AI films, Q, FII and 2 were obtained vs. film thickness from similar fits in the nucleation regime. Figure 2 shows 1 - Q vs. thickness for the evaporated film of Fig. 1. Over the same range of d, Fll decreases from 0.12 to 0.040, signifying an increase in the particle interaction. The simplest Maxwell Garnett type EMT, derived assuming that spherical metal particles interact via the Lorentz local field [22], leads to an isotropic effective dielectric function given by eqn. (la) and (lb) with interaction parameters of the form [23] FII = ( l - Q ) / 3 and Fj = (1 + 2Q)/3. Values of Fll and Q, obtained in the LRA vs. film thickness, clearly do not obey the former equation. Thus, we must resort to a more complex form for the interaction parameters. We apply standard formulas for FII and F~, derived assuming static dipole interactions between identical 1.0

~ ! ~ . ~ .

I

I

I

Z 0 S .<

0.8

0.6 Ld _~ 0 >

0.4

c~ 0 >

0.2

20

4O

60

80

1 O0

NUCLEI SPACING (b,)

0.0

0

I

I

I

L

I

10

20

30

40

50

THICKNESS

60

(A)

Fig. 2. Void volume fraction vs. film thickness deduced from a linear regression analysis o f real time SE data using one-layer models for the films. Results are shown for a-Si:H prepared by P E C V D from pure Sill 4 at a plasma power flux of 52 m W cm 2 and a substrate temperature of 250 ~'C, on native oxide-covered c-Si (open circles) and on Cr (solid circles). Triangles show corresponding results for the evaporated AI film of Fig. 1. The broken lines are model calculations assuming that hemispherical nuclei form on a square grid, increase in radius, and make contact.

247

R. W. Collins et al. / Real time spectroscopic ellipsometry

spheroidal particles and their images in the substrata [24]. Substituting Ftl and Q into such formulas yields F± and the axial ratio of the particles y = b/c, where b and c = d/2 are the semiaxes parallel to and perpendicular to the film surface respectively. Assuming that the particles are distributed on a square grid, we find that F± = F n + Q holds to within 3% for all A1 films over a wide range of thicknesses ( 2 0 - 6 0 ,~). This result occurs because the anisotropy due to dipole interactions cancels that due to the spheroidal particle shape. This provides a physical basis for the experimental observations and also supports the theoretical formalism. In addition, we find reasonable trends in 7, deduced in conjunction with F l , in that (i) 7 is larger for sputtered than for evaporated films in the early stage of nucleation and (ii) 7 increases with thickness for all films, converging to ~2.5 prior to coalescence. This value is in reasonable agreement with results from earlier transmission electron microscopy studies of AI particles on SiO2/Si substrates [25]. The mean free path 2 deduced by LRA is of greater interest than the morphology and particle interactions because it provides insights into the electronic properties of the particles. Figure 3 shows 2 vs. thickness for two evaporated and two sputtered A1 films over the thickness range before coalescence. Surprisingly, 2 falls within the narrow range of 7.5 _+ 2 ,~ (considering the confidence limits for each point), although the film thickness increases by a factor of 5. If electron scattering at surfaces were to limit the mean free path, then 2 would be proportional to the particle size (i.e. the minor semiaxis d/2 in this case). As a result, we conelude that the limitation on the mean free path arises from electron scattering, not at surfaces, but by defects

within the particles. The exact origin of these defects is not entirely clear at present. Transmission electron diffraction studies of A1 films evaporated onto thermally grown SiO2 substrates reveal a crystalline structure for similar-sized A1 particles; however, our nearly constant value of 2 suggests that the particles are not single crystals [25]. Possibly they are aggregates of a few nano-crystalline grains with a defective intergranular phase that shortens the electron lifetime. The nearly constant mean free path with thickness also implies that the intrinsic dielectric function ep of the A1 particles is independent of size and shape, yet significantly different from that of bulk AI, as shown in Fig. 4. Results for both bulk AI (solid lines) and A1 particles (broken lines) in this figure were calculated from the Ashcroft-Sturm formulas. The particle dielectric function was deduced with 2 set to 8.5/~, the best fit value for the film of Fig. 1. Three observations can be made from Fig. 4. First, reduction in 2 leads to an enhancement in e2p for the particle film (except near 1.47 eV, the onset of the (200)

70

i

6O 50

i

• o • A

12

i

i

i

..... CD

3O

/

....... E'pB

20 10

8

'<

6

"-.~,

~

-,,

-

....... ..-..-._ ~ ~ ~ ' ~ " I

--- . . . -

I

i

0

+

{

AI ~D + E'p{

(x=8.s ~1

/~\ ,,\

E v a p o r a t i o n @ high r a t e E v a p o r a t i o n @ low r a t e S p u t t e r i n g @ 1 0 0 Watts S p u t t e r i n g @ 50 Watts

10 =<

i

--EBulk ..... E'p =

40

0 2O 14

~' '"A

",/"A Co

i

21U2oo1=1.47 eV /

~1 --20

-40 -60

4 2

-80

0 0

I 10

20

I 30

I 40

I 50

I 60

70

d (~)

Fig. 3. Electron mean free path as a function of thickness obtained from a linear regression analysis of the effectivedielectricfunctions of aluminum particle films. The effectivedielectric functions were deduced from real time SE results for two evaporated and two sputtered films. The error bars are the 90% confidencelimits (after ref. 9).

r

i

2

3

4

PHOTON ENERGY (eV)

Fig. 4. Intrinsic dielectric function of aluminum particles (dashed lines; 2 = 8.5/~) for comparison with that of bulk aluminum (solid lines), both calculated from the Ashcroft-Sturm formulas. For the particle film, the dielectric function is decomposed into its intraband (eD) and total interband (eva=ePB_lll-I-e P B . 2 0 0 ) parts (dot-dashed lines).

248

R. W. Collins et al. / Real time ,Vwctroscopic eUipsometry

interband peak) as well as a much weaker decrease in ~:~p with decreasing photon energy. Both trends are attributed to changes in eD, the intraband contribution to Cp. Second, the reduction in 7 broadens beyond recognition the peak due to the (200) interband contribution. As a result, it is impossible to determine if a shift in the onset energy has occurred, for example due to quantum size effects. Thus, a previous claim that the absence of this feature in AI particles is due to a quantum size effect must be re-examined [26]. Third, the width of the absorption feature in the effective ~2 of Fig. 1 is proportional to ~2p at the resonance energy [27]. A decomposition of 'f;2p in Fig. 4 ( d o t - d a s h e s ) shows that the intraband and interband contributions are equal, implying that both are needed to achieve the fit in Fig. 1. 3.2. Nucleation and coalescence in hydrogenated amorphous silicon and silicon -carbon alloys

Real time SE has also been applied to the study of nucleation and coalescence of tetrahedrally-bonded amorphous semiconductors prepared by plasmaenhanced chemical vapor deposition (PECVD) [11, 12, 28]. Because the bulk optical properties of a m o r p h o u s semiconductors cannot be expressed in terms of a small number of wavelength-independent parameters, an analysis of real time SE data must extract the dielectric function and the microstructure simultaneously. In earlier work, we have developed and justified one- and two-layer modelling procedures to solve this problem [29]. First we shall review and discuss these procedures, and then compare results obtained for films prepared under different conditions. To start the analysis, we propose a two-layer model for the film to explain the SE data. The bottom ( " b u l k " ) layer exhibits a low void volume fraction and simulates the material that forms only after initial nuclei make contact. The top layer exhibits a high void fraction and simulates the initial particles and intervening void space present during nucleation, as well as the surface roughness arising from the nucleation process after the bulk layer has formed. This top layer is simulated with the Bruggeman E M T as a mixture of void and the material that constitutes the bulk layer. In the next step, we select one spectrum in the bulk film growth regime where both layers are present and guess their thicknesses, assuming that the roughness layer is a 50/50 mixture in the EMT. The two guesses are used to invert the (qJ, A) spectra mathematically in order to deduce the dielectric function of the bulk layer (which also describes the top layer component in the EMT). With this trial dielectric function, the full real time SE data can be interpreted by L R A to deduce the time evolution of the two layer thicknesses and the top layer void volume fraction. At this point, however, the

most important result is the time evolution of the unbiased estimator of the mean square deviation, ~r [30], which is summed for the LRA fits to all spectra vs. time. In an iterative procedure, the initial thickness guesses are then adjusted, the trial dielectric function is recalculated and the LRA fits are repeated, in an attempt to minimize the sum of the a values. When the minimum sum is found, the resulting bulk layer dielectric function, as well as the time evolution of the structural parameters, are as close as possible to the correct solution, given the assumptions. A minor improvement can be made by adjusting the top layer volume fraction from the initial 50/50 assumption so that it stabilizes to a time-independent value in the bulk film growth regime. In fact, when a stable roughness void fraction is found, it is reasonable to fix its value in a final LRA. Such a simplification to the model is not valid in the nucleation regime, however, when the top layer is simulating the nucleating film whose void volume fraction varies with thickness. A number of checks must be made to ensure the validity of the two layer approach. First, it is assumed in the model that the dielectric function of the bulk layer is independent of thickness. This assumption may be in error if, for example, the composition of the layer exhibits a gradient with thickness. Problems of this nature are reflected in a gradual increase in ~ over time, even for the best fit, and a more complex optical model would be required to rectify them. Such behavior in a is cause for concern only for films prepared under certain conditions. Second, it is assumed that the dielectric functions of the nuclei and the roughness component in the E M T are identical with that of the bulk material. In the case of P E C V D a-Si:H on a Cr surface, a careful inversion of ( ~ , A) to obtain the effective dielectric function in the nucleation regime reveals that this is not precisely correct [28]. The particle films show an optical gap and peak in ~:~ that is blue-shifted by ~0.25 eV relative to bulk material. This is believed to result from excess H covering particle surfaces. Such an effect is probably also associated with the roughness component. Neglecting such a phenomenon leads to a slightly higher cr value in the early growth stages, but does not affect the two thicknesses and the deduced bulk film dielectric function. Figure 5 shows the two thicknesses l~s. time for P E C V D a-Si:H as an example of the high speed capabilities of the multichannel ellipsometer [7, 1 l]. The film in this case was prepared from pure Sill4 onto native oxide-covered crystalline silicon (c-Si) at 250 ~'C using a power flux of 520 m W cm 2 at the grounded substrate electrode. This is a factor of 10 higher than that typically used for optimum photoelectronic quality material, resulting in deposition at a relatively high rate of ~ 4 0 0 , ~ min -~. For this sample, (hu, A) spectra were

R. W. Collins et al.

30

I

/._25

I

v

l-layer

o

BULK

I

/

i

model I 2-layer

model~

20 bO (J3 I,I15 Z 010 m ~-

5 0

0

1

2

3

4

249

Real time spectroscopic ellipsometry

5

TIME (sec) Fig. 5. Surface and bulk layer thicknesses (solid and open circles respectively) obtained in a linear regression analysis of SE data collected during a-Si:H PECVD onto SiO2/c-Si at 250 °C. The plasma power flux at the substrate was set at 520 mW cm -2, leading to a deposition rate of 400/~ m i n - L The acquisition and repetition times for the SE spectra were both 64 ms. The layer thickness in a one-layer model is also shown for the nucleation regime (triangles) (after ref. 7).

collected with acquisition and repetition times of 64 ms, using raw data from two successive optical cycles. The results in Fig. 5 can easily be interpreted in terms of nucleation and coalescence. In the first 1.5 s of growth, the high void fraction surface layer increases rapidly in thickness as nuclei form and increase in size. After ~ 2 s, this layer saturates to a thickness of 17 ,~ just as the underlying bulk layer reaches monolayer thickness (2.5-3 ,~). At this point it appears that the particles have made contact and the substrate is covered. From this point onwards, the incoming flux contributes to an increase in the underlying bulk layer thickness, with the high void fraction layer riding on top of the surface as roughness. Interestingly, this roughness layer relaxes by ~ 4 • to a thickness of 13 ,~ as the underlying bulk layer builds to 30 ,~. This smoothening effect is quite reproducible, typically to within _+0.5/~ in this case, and shows that the real time SE can resolve surface phenomena during PECVD on a millisecond time scale and a submonolayer thickness scale. For times less than 2 s, Fig. 5 shows that the bulk layer is less than a monolayer in thickness. Thus, it is appropriate to use a one-layer model in this time range. As shown in Fig. 5, the film thickness for this model (triangles) is basically identical with the top layer thickness in the two-layer model (solid circles). For a-Si:H growth on native oxide-covered c-Si substrates, we find that the best fit void volume fraction in the one-layer model increases weakly from 0.4 and stabilizes at 0.5 just prior to the formation of the first bulk monolayer. (See Fig. 2 for a typical example.) This suggests that mono-

layer a-Si:H discs form first on the oxide and possibly evolve into hemispherical structures prior to coalescence. This behavior is reproducible, yet distinctly different from that for a-Si:H growth on Cr and other metal substrates as shown in Fig. 2. The broken lines in Fig. 2 have been calculated assuming that hemispherical nuclei form on a square grid from the onset, increase in size, and make contact. The result for a-Si:H growth on Cr is consistent with a spacing between hemispheres of 40/~ with contact at a thickness of 22 A. We return to two important features in Fig. 5 that are of interest for films prepared under different conditions. First, the surface layer thickness when the first bulk monolayer forms provides information on the nucleation density. In fact, if the surface structure evolves into hemispherical clusters by this point (see discussion of Fig. 2), then the nucleation density is Nd ,~ {2ds(tb)}-2, where ds(tb) is the surface layer thickness at the time tb when the first bulk monolayer forms. Second, the amount of surface smoothening Ads, measured as the difference between the maximum ds near tb and the stabilized value at some specified bulk layer thickness, provides information on the ability of film precursors to relax the nucleation-induced surface morphology. This effect is expected to scale with the precursor surface diffusion length. Figure 6 shows Ads, measured in the first 50/~ of bulk film growth, for a-Si:H depositions on native SiO2/c-Si and Cr substrates performed v s . plasma power and substrate temperature [11]. Most depositions were per12

9

PP/c-Si PP/Cr

0

L

•

R/c-Si

R/Cr

v

t ~

o< -0 <3

6

(b)

(o) 0

P

I

I

I

0.0 0.2 0.4 0.6 0.8 rf

POWER FLUX

(w/c~ 2)

I

I

I

100

200

300

Ts(°C)

Fig. 6. Surface smoothening in the first 50 ,~ of bulk film growth for PECVD a-Si:H, plotted as a function of (a) rf plasma power flux at the substrate surface with a fixed substrate temperature of 250 °C, and (b) substrate temperature with a fixed rf plasma flux of 52 mW cm 2. These results were deduced from the decay of the surface roughness layer in analyses such as that in Fig. 5. PP = parallel-plate PECVD; R = r e m o t e He PECVD; C r = s p u t t e r e d Cr substrate; c-Si= native oxide-covered c-Si substrate. The solid lines are guides to the eye for the PP/c-Si depositions (after ref. 11).

250

R. W. Collins et al. / Real time s])ectroscopic ellipsometry

formed by parallel-plate PECVD, although selected remote He PECVD [31] films were also studied. A reduction in Ad, is a manifestation of a higher nucleation density and/or a larger ultimate roughness thickness. Although both effects occur in the a-Si:H films of Fig. 6 at the lower substrate temperatures and the higher plasma powers, the latter effect tends to be dominant. Not surprisingly, the conditions of maximum smoothening, i.e. lowest plasma power and ~ 250 °C substrate temperature, are those that provide optimum electronic grade material. Away from this optimum it has been proposed that precursor surface diffusion is reduced as a result of either the lower temperature or the reduction in surface H-coverage (at high plasma powers and temperatures) [32]. Our results support such proposals, and suggest that the conditions of lower precursor surface diffusion, leading to incomplete nuclei coalescence on the monolayer scale, also give rise to bulk defects that limit the electronic quality of the a-Si:H. We have also studied amorphous silicon carbon alloys (a-SiC:H), prepared from Sill4 and CH4 mixtures on SiO2/c-Si substrates at 250 ~'C by parallel-plate PECVD [12]. Figure 7 shows the peak d~ value near tb, as well as Ad~, measured in the first 50 A of bulk growth, for films prepared with a constant S i H 4 : C H 4 gas flow ratio of 3:2, but at different H2 dilution levels. H2 dilution has been shown to lead to improved electronic performance of a-SiC:H alloys [33]. We observe an apparent decrease in nucleation density and greater surface smoothening with increasing dilution. In fact, for films prepared at high H2 dilution, a weak smoothening effect continues for bulk layer thicknesses > 5 0 A, while films prepared at low dilution exhibit long term roughening tendencies. The behavior of Fig. 7 is expected, based on our intuition of the role of atomic H in the plasma. First, excess H may thwart the tendency of C-based precursors to form stable sp 2 hybridized bonds that might otherwise lead to a higher density of nuclei on the substrate. More generally, excess H may passivate substrate nucleation sites, or it may etch away unstable nuclei, increasing the critical (i.e. minimum stable) nucleus size. Once a continuous film has formed, the beneficial role of H may be similar: to maintain full H-coverage and to prevent sp a C bond formation at the surface. Through the real time studies of Figs. 6 and 7, with electronic property correlations, we identify process-property relationships on the monolayer scale of events. In addition to the microstructural parameters of Fig. 7, the dielectric functions of the a-SiC:H films are determined in the analysis. For a-SiC:H, the dielectric function provides information on H- and C-bonding and void volume fraction through tetrahedron models of the network [34]. In electronic device applications of amorphous semiconductors, however, the optical gap is one of the most important parameters. We have found that

40

i

i

f

/z' / /

i

i

i

[ S i H 4 ] + [ C H 4]

[SiH4]+[CH4]

=5.0 sccm

=2.5 sccm

3O v

•

o

ds(tb)

•

v

Ad s

O

o

%20 7D <:]

1

10

I

i

I

0

5

10

/ /

//'l

15

I

I

20

25

FLOW RATIO [ H 2 ] / ( [ S i H 4 ] + [ C H 4 ]

)

Fig. 7. Thickness of the surface roughness layer at the onset of bulk film growth dAtb) and the surface smoothening Ad~ in the first 50/~ of bulk film growth for a-SiC:H films vs. the H2:(SiH 4 + CH4) flow ratio. For depositions with H2:(SiH 4 + CH4) flow ratio < 15, the Sill 4 and CH 4 flows were fixed at 3 and 2 stand, cm3min ~ (sccm) respectively. For H2:(SiH 4 + CH4) > 15, the Sill 4 and CH 4 flows were fixed at 1.5 and 1 sccm. The partial pressure of Sill 4 + CH 4 was set at 0.08 Torr, the plasma power flux at 130 W c m 2 and the substrate temperature at 250 C (after ref. 12).

5

i

i

Sill 4 "• CH 4 4 f-

i

•

5

:

0

1.56

o

4

:

1

1.60

/-

3:2

i

E g (eV)

175

,lf~'-

//./

1

1.5

2.0

2.5

3.0

E(~V) Fig. 8. Optical gap deduced from real time observations (160 ms acquisition time) for - 150 ~ thick a-SiC:H films prepared under the same conditions as those in Fig. 7, but with a fixed H2:(SiH 4 + CH4) ratio of 20:5 (in seem) and a variable SiH4:CH 4 flow ratio. The optical gap is obtained by an extrapolation of the linear behavior in c2 '/2 to zero ordinate. These results are appropriate for a semiconductor temperature of 250 'C (after ref. 12).

the optical gap can be extracted with reasonable accuracy from the real time observations. Figure 8 provides results for ~ 150/~ thick a-SiC:H alloys vs. SiH4:CH4 gas flow ratio. Here the gap is obtained from an extrapolation of ~21/2 US. photon energy using the higher energy range where our data are most accurate [35]. It must be remembered that the gaps obtained in this way are appropriate for a deposition temperature of 250 °C, and

R. W. Collins et al. / Real time spectroscopic ellipsometry

are thus, typically, ~0.15 eV lower than the values at 25 °C.

4. Conclusions Real time spectroscopic ellipsometry has been developed to characterize the nucleation, coalescence, and optical properties of thin films. The ellipsometer uses a multichannel detection system in order to provide experimental spectra in (W, A) from 1.3 to 4.3 eV and to combine millisecond scale time resolution with submonolayer sensitivity to surface phenomena. We have reviewed applications in metal and semiconductor film growth, focusing on the electronic and microstructural characteristics that cannot be extracted with discrete wavelength ellipsometry. In concluding, we emphasize the limitations of the single wavelength approach. For A1 film growth, real time ellipsometry at one wavelength would not contribute much to an understanding of the nucleation and optical properties of the A1 particles. Basically, four free parameters are needed to analyze the data properly at each time, including the film thickness, a particle interaction parameter, the void volume fraction and the electron mean free path in the particles. Two effects combine to complicate interpretation in the early stages of growth. First, the variations in the void fraction and interaction parameter with thickness lead to effective optical functions that vary with time or particle film thickness. Furthermore, the required E M T is not simple, and a spectroscopic analysis is required to infer it. Second, the optical functions of the AI particles themselves, needed in the calculation of the effective optical functions of the film, differ greatly from those of bulk A1 due to a defective structure for the particles. In earlier research on a-Si:H and related materials, extensive single wavelength ellipsometry studies have been undertaken [36, 37]. In principle, (W, A) measurements can be numerically inverted to deduce the void fraction and thickness in a one-layer model of the nucleation stage, or the two thicknesses in a two-layer model for the later stages of growth, provided that the dielectric function of the bulk film material is known. This dielectric function can be estimated from (u?, A) values obtained after the film has become opaque. In practice, however, systematic errors in the dielectric function (e.g. due to surface roughness) or in the (ud, A) values make this approach unreliable for comparing results for different samples. A full spectroscopic analysis is required as demonstrated here, not only to increase confidence in the outcome of the analysis, but also to ensure that the chosen optical model is valid. Finally, in complex materials such as a-SiC:H, in which the energy position and slope of the absorption onset

251

both vary as a result of possible variations in C, H, or void content, the spectroscopic capability is needed for the optical gap determinations from real time observations. A real time approach to optical gap determination is important in many device applications in which a number of ultrathin films are combined in a device structure.

Acknowledgments The authors acknowledge support for this research from the National Science Foundation under Grant Nos. DMR-8957159 and DMR-8901031, the National Renewable Energy Laboratory under Subcontract No. XG-l-10063-10, and DuPont Corporation.

References 1 J. B. Theeten and D. E. Aspnes, Ann. Rev. Mater. Sci., 11 (1981) 97. 2 S. Gottesfeld, in A. J. Bard (ed.), Electroanalytical Chemistry: A Series o f Advances, Vol. 15, Marcel Dekker, New York, 1989, p. 143. 3 R. W. Collins, Rev. Sci. Instrum., 61 (1990) 2029. 4 D. E. Aspnes, Thin Solid Films, 89 (1982)249. 5 J. A. Venables, G. D. T. Spiller and M. Hanbucken, Rep. Prog. Phys., 47 (1984) 399. 6 D. E. Aspnes, W. E. Quinn and S. Gregory, Appl. Phys. Lett., 56 (1990) 2569. 7 I. An, Y. M. Li, H. V. Nguyen and R. W. Collins, Rev. Sci. Instrum., 63 (1992) 3842. 8 H. V. Nguyen, I. An and R. W. Collins, Phys. Rev. Lett., 68(1992) 994. 9 H. V. Nguyenand R. W. Collins, J. Opt. Soc. Am. A, 3 (1993) 515. 10 C. G. Granqvist and O. Hunderi, J. Appl. Phys., 51 (1980) 1751. 11 Y. M. Li, I. An, H. V. Nguyen, C. R. Wronski and R. W. Collins, Phys. Rev. Lett., 68 (1992) 2824. 12 Y. Lu, I. An, C. R. Wronski and R. W. Collins, unpublished data, 1993. 13 N. V. Nguyen,B. S. Pudliner, I. An and R. W. Collins, J. Opt. Soc. Am. A, 8 (1991) 919. 14 I. An and R. W. Collins, Rev. Sci. Instrum., 62 (1991) 1904. 15 I. An. Y. Cong, N. V. Nguyen, B. S. Pudliner and R. W. Collins, Thin Solid Films, 206 (1991) 300. 16 A. A. Studna, D. E. Aspnes, L. T. 'Florez, B. J. Wilkens, J. P. Harbison and R. E. Ryan, J. Vac. Sci. Technol. A, 7 (1989) 3291. 17 M. H. Hecht, R. P. Vasquez, F. J. Grunthaner, N. Zamani and J. Maserjian, J. Appl. Phys., 57 (1985) 5256. 18 H. Arwin and D. E. Aspnes, Thin Solid Films, 113 (1984) 101. 19 T. Yamaguchi, S. Yoshida and A. Kinbara, Thin Solid Films, 31 (1974) 173. 20 N. W. Ashcroft and K. Sturm, Phys. Rev. B, 3 (1971) 1898. 21 U. Kreibig, J. Phys. F, 4 (1974) 999. 22 J. C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. A, 203 (1904) 385; 205 (1905) 237. 23 D. N. Jarrett and L. Ward, J. Phys. D, 9 (1976) 1515. 24 T. Yamaguchi, H. Takahashi and A. Sudoh, J. Opt. Soc. Am., 68 (1978) 1039. 25 S. Roberts and P. J. Dobson, Thin Solid Films, 135 (1986) 137. 26 V. V. Truong, P. Courteau and J. Singh, J. Appl. Phys., 62 (1987) 4863.

252

R. W. Collins et al. / Real time spectroscopic ellipsometry

27 A. Meessen, J. Phys. Paris, 33 (1972) 371. 28 Y. M. Li, I. An, C. R. Wronski and R. W. Collins, J. Non-Cryst. Solids', 137& 138 (1991)787. 29 I. An, Y. M. Li, C. R. Wronski and R. W. Collins, Appl. Phys. Lett., 59 (1991) 2543. 30 D. E. Aspnes, Proc. Soc. Photo-Opt. lnstrum. Eng., 276 (1981) 188. 31 G. Lucovsky, D. V. Tsu, R. A. Rudder and R. J. Markunas, in J. L. Vossen and W. Kern (eds.), Thin Film Processes I1, Academic, New York, p. 565.

32 K. T a n a k a and A. Matsuda, Mater. Sci. Rep., 2 (1987) 139. 33 A. Matsuda and K. Tanaka, J. Non-Cryst. Soh~ts, 97& 98 (1987) 1367. 34 K. Mui and F. W. Smith, Phys. Rev. B, 35(1987) 8080; 38(1988) 10623. 35 G. D. Cody in J. 1. Pankove (ed.t, Semiconductors and Semimetals', Vol. 21B, Academic, New York, 1984, p. 11. 36 R. W. Collins, in H. Fritzsche (ed.), Amorphous Silicon and Related Materials', World Scientific, Singapore, 1988, p. 1003. 37 B. Drevillon, J. Non-Crvst. Solids, 114 (1989) 139.