In situ spectroelUpsometrlc study of the nucleation and growth of amorphous silicon

A detailed in situ spectroellipsometric analysis of the nucleation and growth of hydrogenated amorphous silicon (a:Si:H) is presented. Photoe1ectronic quality a-Si:H films are deposited by plasma-enhanced chemical vapor deposition on smooth metal (NiCr alloy) and crystalline silicon (c-Si) substrates. The deposition of a-Si:H is analyzed from the first monolayer up to a final thickness of 1.2 Jim. In order to perform an improved analysis, real time ellipsometric trajectories are recorded, using fixed preparation conditions, at various photon energies ranging from 2.2 to 3.6 eV. The advantage of using such a spectroscopic experimental procedure is underlined. New insights into the nucleation and growth mechanisms of a-Si:H are obtained. The nucleation mechanism on metal and c-Si substrates is very accurately described assuming a columnar microstructural development during the early stage of the growth. Then, as a consequence of the incomplete coalescence of the initial nuclei, a surface roughness at the 10-15 A scale is identified during the further growth of a-Si:H on both substrates. The bulk a-Si:H grows homogeneously beneath the surface roughness. Finally, an increase of the surface roughness is evidenced during the long term growth of a-Si:H. However, the nature of the substrate influenced the film growth. In particular, the film thickness involved in the nucleation-coalescence phase is found lower in the case of c-Si (67 ± 8 A) as compared to NiCr (118 ± 22 A). Likewise films deposited on c-Si present a smaller surface roughness even if thick samples are considered ( > 1 /-lm). More generally, the present study illustrates the capability of in situ spectroellipsometry to precisely analyze fundamental processes in thin-film growth, but also to monitor the preparation of complex structures on a few monolayers scale.


I. INTRODUCTION
A detailed knowledge ofthe growth mechanisms ofhydrogenated amorphous silicon (a-Si:H) is of considerable interest from a fundamental point of view and also for improving device performances.However the more conventional in situ surface probes are incompatible with the plasma-enhanced chemical vapor deposition (PECVD) generally used to prepare photoelectronic quality a-Si:H.On the contrary, when coupled to a plasma chamber, spectroellipsometry is a nondestructive technique which does not perturb the growth processes.In situ ellipsometry has proved very powerful in analyzi.ng the evolution of a-Si:H microstructure during growth.I -3 In situ ellipsometry at fixed wavelength, combined with the fast time resolution provided by the photoelastic modulation, is particularly wen adapted to perform detailed kinetic studies of a-Si:H. 2 I> Moreover the spectroscopic facility allows precise descriptions of the film morphology evolution.
The previous spectroelIipsometry experiments revealed that the growth of a-Si:H is influenced by the deposition conditions and the nature of the substrate.In particular, transparent conducting oxide and glass substrates were found to be reduced by the silane plasma during the early stage of the growth.s ,,, In contrast, a nucleation mechanism was observed when depositing a-Si:H, from a rf discharge, on metallic or crystalline silicon (c-Si) substrates. 4 s ,7 In the case of metallic substrates, optical models based on hemispherical nucleation were used to qualitatively reproduce the shape of the real time trajectories. 4A surface roughness, at the 10-50 A scale, is then generally observed during the bulk a-Si:H growth.Using metallic substrates, the presence of this surface roughness was attributed to the incomplete coalescence of the initial nuc1ei. 4As a matter of fact, the thickness of the surface roughness was found roughly equal to the internuclei distance. 4Such a growth model, displayed in Fig. 1, qualitatively reproduces the behavior of the ellipsometric trajectories up to a final thickness of 1000 A.4 The presence of a strong ion bombardment during growth induces the complete coalescence of the nuclei. 3,8 More recently, the growth of a-Si:H on c-Si and metal were carefully compared in a kinetic ellipsometry experiment performed at a single photon energy (3.4 e V). 9 The nucleation of a-Si:H on metal was found consistent with an hemispherical nucleation model while the nucleation on c-Si was described using a cylindrical geometry. 9his paper describes the results of a detailed study ofthe nucleation and growth of photoelectronic quality a-Si:H deposited by PECVD on smooth, homogeneous metal and c-Si substrates.In order to perform an improved analysis of the growth mechanism, real time eUipsometric trajectories are recorded, using fixed preparation conditions, at various photon energies ranging from 2.2 to 3.6 eV.The present study gives new insights into the nucleation-coalescence mechanism of a-Si:H.Furthermore, it allows a precise description of the a-Si:H growth from the deposition of the first monolayers up to a final thickness of more than 1 pm.More generany, this analysis iHustrates the capability of in situ spec-troeHipsometry to analyze fundamental processes and to monitor the growth of complex structures on a few monolayers scale.

II. EXPERIMENTAL DETAILS
A capacitively coupled conventional glow-discharge reactor operating at 13.56 MHz was used for deposition of photoelectronic quality a-Si:H films.loThe substrates were placed on the grounded anode, the anode-to-cathode distance being fixed to about 40 mm.The reactor was always evacuated down to a base pressure of the order of 10-4 Pa.The substrate temperature was fixed to 300 DC.The standard deposition conditions were fixed as foHows: pure silane with a total pressure of20 Pa and 30 sccm flow rate, rfpowerof20 W. The average deposition rate estimated from kinetic ellipsometry measurements was: 1.45 ± 0.15 A s-t.The a-Si:H films were deposited on metal and c-Si covered with native oxides.Metallic substrates consist ofNiCr 400-A.thick films evaporated at 250°C on glass.During the plasma ignition procedure, the substrate is isolated from the discharge by an automatic shutter.Thus real time ellipsometry data acquisition is started after plasma stabilization.
Two fused silica windows allow the reflection on the substrate of the beam of a fast spectroscopic phase modulated ellipsometer (SPME) described in detail elsewhere,II.12with an angle of incidence of 69.5".Let us briefly recall that spectroellipsometry measures, as a function of the photon energy, the complex ratio between the parallel (p) and perpendicular (s) reflection coefficients of the electric field p = Yp/r, = tan W exp(i.6.).In the case of a homogeneous material with a sharp interface with ambient, p is directly related to the dielectric function of the sample E = £1 + iE 2 , otherwise a multilayer calculation is necessary.13For kinetic studies, the photon energy was fixed and N points Pi were recorded at regular intervals .6.t.Various photon energies ranging from 2.25 to 3.54 eV were used corresponding to a light penetration in a-Si:H decreasing from a few thousand angstroms to about 100 A. As a consequence substrate the ellipsometric measurements were integrated during variable time intervals ranging from 0.5 s (UV light) up to 1.5 s (2.25 eV), each individual real time trajectory corresponding typically to N = 3000 points.The experimental conditions corresponding to the various kinetic ellipsometry trajectories are summarized in Table 1.
The experimental CIJI,.6.) trajectories will be systematically compared to some theoretical computations based on various types of nucleation and growth models.In the models described below, the index of a substrate is deduced from the ellipsometric measurement performed immediately before the a-Si:H growth.The refractive index of the bulk a-Si:H corresponds to the value determined by fitting the real time trajectory to the growth model assuming a constant surface roughness (see Fig. 1 ). 4 The index of the mixed layers are the result of a Bruggeman effective medium approximation (EMA) assuming spherical or cylindrical inclusions.t4,15

A. Nucleation of a~Si:H
The nucleation models are displayed in Fig. 2. The most simple assumption corresponds to the uniform growth of a homogeneous material with a constant index.In the hemispherical nucleation model, a hexagonal network of hemispherical nuclei of a-Si:H is created with an average distance d between them.The radius oftlle nuclei increases continuously until the hemispheres come into contact.It results in a density deficient layer of growing thickness, the void volume fraction of the film decreasing from I = 1 down to 0.39.• 16 In a different way, the third model assumes a columnar microstructural development during the nucleation phase. 9In this latter case, the a-Si:H nuclei are located on a hexagonal network separated by an average distance d = 60 A. In d being fixed, the free parameters of this last model are the initial and final radii r, and r f and the final cylinder height d n' The real time trajectories recorded at 3.1 and 3.54 eV during the deposition of a-Si:H on NiCr substrates are compared in Figs.3(a) and 3(b) to the nucleation models described above.In both cases, the experimental trajectories strongly depart from the uniform growth assumption (long dashes) confirming previous resuIts. 45 . 7In contrast the ('l', Ll) SPME trajectory, recorded at 3.1 e V [Fig. 3 (a) J is in rather good agreement with the hemispherical nucleation assumption corresponding to d = 80 A (short dashes).A similar conclusion was recently deduced from an ellipsometrk study at 3.4 eV of the early stage of the growth of a-Si:H on Mo and Cr substrates. 9Nevertheless, the experimental results obtained at 3.54 eV [Fig.3(b) J can rule out the hemispherical nucleation model.At 3.54 eV the experimental trajectory is only compatible with the columnar nucleation model, a very good fit with the cylindrical nucleation also being obtained at 3.1 eV (solid lines).The fitted three parameter values ri,rf' and d" are presented, as functions of  be estimated from the spectroscopic data: r = 20 + 4 Ar f = 29 ± 1 A, and d n = 60 ± 20 A. The high rf-valu~ shows that the cylinders almost come into contact at the end of the nucleation phase.
The beginning of the growth of a-Si:H deposited on c~Si substrate, recorded at 3.4 eV, is displayed in Fig. 4. Figures 3 and 4 correspond to similar preparation conditions.The experimental (111,.:1)trajectory of Fig. 4 describes a wen-defined loop.7 This apparent difference of the eIlipsometric trajectory shapes can probably be attributed to the best time resolution provided by the SPME technique.As already pointed out, the experimental ('V,Il) trajectory, shown in Fig. 4, clearly departs from the uniform growth and the hemispherical nucleation assumptions.5 In contrast, the first few seconds of the growth, and the first part of the loop are in very good agreement with the columnar nucleation assumption, confirming the conclusion of a previous ellipsometric experiment.9 Moreover, the results of Table II show that the nucleation phase on c-Si substrate is very weakly affected by variations of the preparation conditions.Then, as a first conclusion it can be inferred that similar nucleation mechanisms are observed in the early stage of the growth of a-Si:H on c-Si and metal substrates.However lower values of d n (35 A) and larger values of'i (26 A..) are obtained on c-Si, as compared to the NiCr substrate.

B. Coalescence and bulk a-Si:H growth
The remaining problem is the optical description of the coalescence of the initial columnar microstructure, the presence of a small roughness at the top surface of a-Si:H being well established.-----l-----'-------'---  The coalescence model described above has been compared to the experimental trajectories recorded, at various photon energies, during the deposition of 800-4500 A thick a-Si:H on NiCr substrates.The results are displayed in Figs.7 and 8.An extremely good agreement is obtained with the growth model displayed in Fig. 5, whatever the photon energy.In particular, Figs.8(a)-(c) illustrate the influence of the parameter de on the fit, in the case of a linear decrease of 11 during the coalescence (a = 1).The precision on the value of de can be estimated from Fig. 7 to about 25 A at a fixed wavelength.The beginning of the coalescence phase is indicated on each (\fJ ,a) trajectory displayed in Fig. 7. Finally in the case of metallic substrate, the following average value can be estimated from the spectroscopic data recorded in Table II: de = (60 ± 20)A.
Because of the presence of a well-defined loop in the experimental ('l',a) trajectory at the end of the nucleation phase (see Fig. 4), the data recorded in the case of the c-Si substrate are very sensitive to the coalescence mechanism of a-Si:H.Thus a slight modification of the simple coalescence model presented in Fig. 5 --------r-------~--------_r--------

c. Evolution of the surface roughness
As already pointed out, the pseudodielectric function € of a-Si:H can be estimated from the spectroellipsometric data by assuming a sharp interface with ambient.The long term evolutions of the imaginary part 1: 2 , obtained with NiCr substrates, are presented in Fig. 10.A slight decrease of the spectrum together with a slight shift towards lower energies are observed.This behavior is characteristic of an increase of the surface roughness with increasing film thickness.I -3 In the same way, a continuous shift of the convergence point of the ('1',11) trajectory is observed when depositing a-Si:H on c-Si substrate (region D-E in Fig. 11).This shift can be interpreted as a surface roughness evolution during film growth.Using this assumption, the increase of the surface roughness 254-------~----~------~------~------ can be estimated to be 5-10 A for an increase in thickness of 1.0 p.m at low deposition rates (less than 3 A s -1 ).In particular, for the standard conditions, the increase of surface roughness is estimated to 6 A. Likewise a 3-4 A increase of the surface roughness was observed in a previous experiment.I7 Furthermore the comparison of the' E z spectra corresponding to the thicker films 0.2 ,um) in Fig. 12 reveals a larger surface roughness in the case of the NiCr substrate.This surface roughness difference can also be estimated by the fit of the kinetic trajectories to the constant surface roughness model (displayed in Fig. 1) if the total film thickness is such that the surface roughness evolution can be neglected.In this way, the surface roughness thickness can be estimated to (14 ± 2) A during the growth of the first 3- in the case of coSio

IV. DISCUSSION
The present study is focused on the nucleation and growth of a-Si:H, prepared by PECVD, on smooth homogeneous substrates which do not lead to a chemical interaction with the silane plasma (or the a-Si:H film) during the deposition of the first few monolayers.However in the case of metallic substrates, a nucleation mechanism in the early stage of the growth and the presence of a roughness at the free surface during the further growth were established by in situ ellipsometry a few years ago. 8Likewise, previous studies revealed the presence of a nucleation mechanism during the early stage of the growth of a-Si:H on coSio 4, 7 These previous ellipsometric studies generally consist of the analysis of real time ellipsometric trajectories recorded at only one 1 ,7 or two 4 ,8 photon energies.Moreover very simple optical models were sometimes used.For instance, the nucleation-coalescence mechanism of a-Si:H was often described by a linear decrease of the void volume fraction with increasing film thickness deposition.1,5,7 Although this approach to fitting allows one to parametrize some real time trajectories, it is not informative from a fundamental point of view.
In contrast, the present study of the growth of a-Si:H on the NiCr substrate is based on a set of seven real time trajectories recorded at various photon energies, each individual trajectory consisting of about 3000 ('II ,b.) measurements, By varying the photon energy, the light can probe different film thicknesses.Furthermore the spectroscopic analysis allows a precise description of the deposition mechanisms, in particular the growth model and the free parameters values must be independent of the wavelength of the light.Let us recall for example that, in the case of the metallic substrate, the data recorded at 3.1 e V are compatible with two different nucleation mechanisms.However, the same fit performed at different photon energies allows to rule out the hemispherical nucleation model (see Fig. 3), In the present experiment the various trajectories were recorded independently.Therefore, some discrepancies between the fitted parameters at different wavelengths of Table II can be partly attributed to an incomplete reproducibility of the preparation conditions from run to run.A better experimental system would anow simultaneously recording of several real time trajectories.Thus an improvement of the in situ spectroellipsometry analysis can be expected from a new device which combines the fast data acquisition of the phase modulated technique and the real time spectroscopic facility.IS The present study reveals that the nucleation mechanism on NiCr and c-Si substrates is accurately described assuming a columnar microstructural development during the early stages of the growth of a-Si:H.The disklike geometry corresponding to the deposition of the first monolayers can probably be understood from a thermodynamic standpoint, as already suggested. 9In the two cases substrate/oxide/ a-Si:H considered here, the sum of the a-Si:H surface and the oxide/a-Si:H interfacial free energies must be less than the oxide surface energy.Thus the free energy of the system is minimized by a two-dimensional growth process that maxi-mizes interface area.Then, as a consequence of the incomplete coalescence of the initial nuclei, a surface roughness on a 10-15 A scale can be identified during the further growth of a-Si:H on both surfaces.Finally, an increase of this surface roughness is evidenced when dealing with the deposition of rather thick films.This growth mechanism is found to be little affected by the preparation conditions (see Table II).The identification on the real time trajectories of these four stages of the growth can have important practical consequences for growth monitoring.In particular, because the index of a-Si:H is close to the value corresponding to c-Si, small amplitUde variations of \II and I:i are observed during the real time evolution.As a consequence the four stages described above can very clearly identified in Fig. 11.
Nevertheless, although the same nucleation and growth model can account for the deposition of a-Si:H on both substrates, the results presented in Table II and the behavior displayed in Fig, 12 reveal a slight influence of the nature of the substrate on the film growth even if 1.2-flm thick samples are considered.Furthermore, the nuclei density being fixed to the same value in both cases (d = 60 A), the values shown in Table II are very sensitive to relative behaviors, The film thickness involved in the nucleation-coalescence phase is found to be lower in the case of c-Si: 67 ± 8 A as compared to NiCr: 118 ± 22 A. The initial surface coverage for c-Si: r i = 26 ± 1 A is slightly larger than for NiCr: r i = 20 ± 4 A, Moreover, in the c-Si case the exponent a defined by Eq. ( 1) is found to be 0.4 ± 0,1, indicating a faster coalescence kinetic process than in the NiCr case.In summary, these results show that the growth of a-Si:H on NiCr departs more clearly from the uniform behavior, this substrate corresponding further to the more sensitive surface roughness (see Fig. 12).These behaviors can probably be attributed to different substrate surface morphologies, the NiCr film evaporated on glass probably being less smooth than the c-Si substrate.In the same way, the a-Si:H surface roughness is partly related to the substrate morphology, This last trend was clearly identified when depositing a-Si:H on rough substrates like transparent conducting oxides.6 This strong influence of the substrate was attributed to the low surface diffusion length of the precursors of a-Si:H.3,9

V. SUMMARY AND CONCLUSIONS
We have presented a detailed in situ spectroellipsometry analysis of the nucleation and growth of photoelectronic quality a-Si:H deposited on smooth metal and crystalline silicon (c-Si) substrates, As compared to the previous in situ ellipsometric experiments, various kinetic real time trajectories recorded at different photon energies, using similar preparation conditions, have been used in the present study.The advantage of using such a spectroscopic experimental procedure has been underlined.New insights into the nucleation and growth mechanisms of a-Si:H have been obtained.The present study reveals that the nucleation mechanism on metal and c-Si substrates is accurately described assuming a columnar microstructural development during the early stages of the growth of a-Si:H.Then, as a consequence of the incomplete coalescence of the initial nuclei, a slight surface roughness is identified during the further growth of a~Si:H on both substrates while the bulk a~Si:H grows homogeneously beneath this surface roughness.Finally, an increase of the surface roughness is evidenced when dealing with the deposition of thick films.However, the nature of the substrate influenced the film thickness involved in the nucleation~coalescence phase is found to be lower in the case of c-Si: 67 ± 8 A as compared to NiCr: 118 ± 22 A-More generally, the growth of a-Si:H on NiCr departs more dearly from the uniform behavior.
Finally the present study illustrates the capability of in situ spectroellipsometry to provide a very precise description of a thin-film growth, but also to monitor the deposition of complex structures on a few monolayers scale.
FIG. L Schematic representation of the nucleation and growth model assuming a constant surface roughness.

4 .
FIG. 3. Real time examinations ofthe beginning of the growth of a-Si:H on NiCrsubslratc, (a) at 3.1 eV; (b) at 3.54eV.
FIG.6.Influence of the parameter a on the evolution of the overlayer void volume fraction}; during the coalescence period.

FIG. 7 .
FIG. 7. Real time examinations of the long term growth a-Si:H deposited in standard conditions on NiCr substrate, (a) at 3.1 eV, (b) at 2.82 eV, and (c) at 2.48 e V.The dashed lines illustrate the influence of the parameter de on the coalescence phase.
is necessary to fit the ('II ,a) trajectory corresponding to the c-Si substrate.The good fit of the loop displayed in Fig.9is obtained when taking into account a slight increase (0.1-0.2 A) of the cylinder radii at fixed height d n , before the coalescence phase.Further, Fig.9illustrates the infl.uence of the value of the exponent a defined by Eq. (1) on the fit.The results presented in TableIIshow that a and de are weakly affected by the preparation conditions, one obtains for the c-Si substrate: a = (004 ± 0.1) and de = (35 ± 5) A. A comparison between the results obtained with the two different substrates reveal a slight reduction of de and a significant decrease of a in the case of coSio This behavior can be interpreted as a fast coalescence in this last case.

FIG. 9 .
FIG. 9. Real time examination, at 3.40 eV, of the long term growth of a-Si:H on c-Si substrate.The dashed lines illustrate the influence of the parameter a on the coalescence phase.

PSIFIG. 11 .
FIG. 10.Spectroellipsometric measurements corresponding to three a-Si:H films with different thicknesses deposited on NiCr substrates: the measurements being performed at room temperature.

5 FIG. 12 .
FIG.12.Spectroellipsometric measurements on 1.2 J1.m thick a-Si:H samples deposited in standard conditions on c-Si and NiCr substrates: the measurements being recorded at deposition temperature.

TABLE I .
Experimental conditions corresponding to the various ellipso• metric trajectories.In each case, the kinetic trajectory is fitted to the growth models up to a final thickness d,,,, .

TABLE H .
Structural parameters related to the nucleation and coalescence phases.

Table n .
Compatible values are obtained from 2.25 to 3.54 eV evidencing the validity of the columnar model to account for the nucleation phase.In the case of a metallic substrate, the following average values can