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Spectroellipsometric Investigation of LPCVD Polysilicon: As Deposited and After Hydrogenation
C. Flueraru, M. Gartner, D. Dascalu, C. Rotaru
To cite this version:
C. Flueraru, M. Gartner, D. Dascalu, C. Rotaru. Spectroellipsometric Investigation of LPCVD Polysil- icon: As Deposited and After Hydrogenation. Journal de Physique III, EDP Sciences, 1996, 6 (2), pp.225-235. �10.1051/jp3:1996120�. �jpa-00249452�
Spectroellipsometric Investigation of LPCVD Polysilicon:
As Deposited and After Hydrogenation
C. Flueraru (*), M. Gartner (**), D. Dascalu and C. Rotaru
Institute of Microtechnology, PO Box 38-160, Bucharest 72225, Romania
(Received 15 May 1995, revised 26 September 1995, accepted 15 November 1995)
PACS.78.66.-w Optical properties of thin films, surface and layer structures
PACS.81.40.-z Treatment of materials and its effects on microstructure and properties PACS.73.61.Cw Elemental semiconductors
Abstract. Polycrystalline silicon deposited at 570 °C and 620 °C temperature, as-deposited
and after hydrogenation, was investigated by spectroellipsometry. The behaviour of refractive and absorption index versus wavelength is presented. The paper also includes evaluation of the
surface roughness and the crystallinity fraction of polysilicon via Bruggeman-Effective Medium Approximation. An attempt to evaluate the first two direct interband transitions from spec-
troellipsometric spectrum and comparison with other measurements is reported.
Rdsumd. On a 6tud16, par spectroellipsom4trie, du silicium polycristallin aprAs d6p6t h 570 °C et 620 °C, puis aprbs hydrOg6nation. Les comportements des indices de r6fractiOn et
d'absorption en fonction de la longeur d'onde sont pr6sent6s. Cet article contient l'6vaIuation de la rugosit6 de la surface et de la fraction cristalline du silicium polycristallin en utilisant
l'approximation du milieu effectif de Bruggeman. Un essai d'6valuation pour les deux premiAres
transitions interbande permet de calculer des spectres spectroellipsomdtriques la comparaison
avec d'autres mesures est aussi pr6sent6e.
1. Introduction
Polycrystalline silicon (polysilicon) is one of the most investigated materials due to its possible
use in new devices (thin film transistors, solar cells) and in electromechanical microsystems.
Its compatibility with silicon technology is an advantage but due to a very different area of ap-
plications, an effort in order to connect the technological parameters (deposition temperature,
pressure) with material characteristics (grain size, crystallinity fraction, surface roughness) is necessary. The most important parameters which can significantly influence the device proper- ties are surface roughness and grain size. Roughness can be characterized by an average height
of irregularities and it is a relative quantity depending on the ratio of the length scale of the
"mountains and valleys" to the wavelength of light. The present work is a complete analysis
(*)Author for correspondence (Fax: (40) 1 3124661)
(**) Permanent address: Institute of Physical Chemistry, Splaiul Independentei 202, 77208 Bucharest,
Romania
© Les #ditions de Physique 1996
Table I. The deposition temperature, annealing and thickness of the investigated poiysihcon.
Sample Temperature Annealing Polysilicon
thickness
IMT a 570 °C No 1000 I
IMT B 620 °C No 1054 I
IMT C 570 °C Yes 2100 I
IMT D 620 °C Yes 1557 I
of preliminary results published elsewhere [ii. The purpose of this paper is to investigate, by optical characterization, the dielectric constant of polysilicon thin film multilayer systems
as deposited and after annealing. By optical characterization, we mean the determination of
physical properties of a sample from its measured optical properties. The optical response of the system represented by a dielectric fonction is closely related to the electronic band structure of the material. Measurements of the first direct interband transitions have been performed by several optical techniques and calculated by theoretical (or semiempirical) methods. The
analysis focused on the temperature dependence of critical points in the band structure of silicon [2]. In this work an investigation of the first two direct interband transitions vers~s
crystalline fraction is presented for polysilicon.
2. Experimental Details
The substrate used was (100) p-type silicon wafer with a resistivity between 20-25 flcm. A silicon dioxide layer, with 10 000 10 300 I thickness,
was grown by thermal oxidation. The
undoped polysilicon was deposited by LPCVD (Low Pressure Chemical Vapor Deposition
p = 0.3 Torr) at temperatures of 570 °C and 620 °C with a thickness between 1000-2000 I.
The annealing was done at 400 °C for 3 h in H2 + N2 (25i~+75il). The thin film multilayer systems analysed in this paper are denoted in Table I.
Using a spectroscopic ellipsometer ,ve measured the change of the polarization state of an incident light beam upon its reflection from the sample surface. A typical configuration con-
tains a source, dispersing optics, polarizer, a compensator, the sample, an analyser and the detector. The light from a xenon arc lamp passes through a monochromator and several optical elements, reflects off the sample at the angle of incidence, and passes through an analyzer to the photodetector.
The fundamental equation of ellipsometry is
tgilexpj~/l)
=
~~
Rs
where 4l and /h are the measured ellipsometric parameters, Rp and Rs are reflection coeffi- cients of the sample for light polarized parallel and perpendicular to the plane of incidence, respectively. Spectroellipsometric measurements were made at an angle of incidence of 75° in the UV-VIS spectral range (280-700 nm) at 10 nm intervals.
Table II. The composition and thickness of thin film multilayer systems resulting from the best fit between experimental and simulated values.
Sample Temperature Annealing Composition Thickness
IMT A 570 °C No Si substrate
Si02 10 300 I
asi 1 000 I
Si02 30 I
No Si substrate
Si02 10 300 I
csi(45.4i~) + asi(42.6i~) + voids(12i~) 960 I csi(75.6i~) + asi(14.4i~) + voids(10i~) 94 I Si02 (85.6i~) + voids(14.4i~) 34 I
IMT C 570 °C Yes Si substrate
Si02 10 300 I
asi(80i~) + csi(20i~) 2 100 I
Si02 30 I
IMT D 620 °C Yes Si substrate
Si02 10 300 1
csi(60i~) + asi(30i~) + voids(10i~) 1477 I csi(80i~) + asi(10i~) + voids(10i~) 80 I
Si02(56i~) + voids(44i~) 70 I
3. Results and Discussions
The experimental tg4l and cos /h values were compared ~vith the same simulated values obtained
using the Bruggeman Effective Medium Approximation (EMA) [3] ~A<ith the layer thickness and the volume fraction of crystalline and amorphous silicon, as fitting parameters. The ratio
between the crystalline phase and the total volume is called the crystallinity fraction. The data
were analysed using a FORTRAN program developed at the Pennsylvania State University.
The program calculates tg4l and cos /h values for an assumed input optical model of the sample
and then optimizes the mean-square difference between measured and calculated tg4l and cos /h values by varying designated model parameters.
In the Bruggeman EMA each composite layer was modelled as a simple physical mixture of amorphous silicon, crystalline silicon and voids (or Si02). This approximation requires that the grains of each constituent in the composite material are randomly mixed, and that the
grain size is smaller than wavelength of light.
On the other hand, the light has to penetrate the sample until the substrate in order to obtain a complete description of the polysilicon layer. At the same time, the grain size must be large enough for a correct macroscopic evaluation of the optical parameters.
Table II presents the parameters resulting from the best fit.
The quality of fit is judged by the Mean Square Difference (MSD) [4]
N ~/~
MSD =
j~~ ~ i~ 11 lltg~YU tg~Yi)~ + (CDS/~U CDS /~i)~l
~=i
s(eV)
4.43 3.45 2.82 2.39 2.07
o-f
0.4
~~ ~ cosA
o
280 3fo 440 520 loo (So
~ (nm)
Fig. 1. Measured and best fitted ellipsometric spectra for IMT A sample.
s(eV)
4.43 3.45 2.82 2.39 2.07 1.83
tg~p cosA
o o
250 360 440 600
~ (nm)
Fig. 2. Measured and best fitted ellipsometric spectra for IMT B sample.
where N is the total number of measurements, p is the number of unknown model parameters and subscripts m, c represent measured and calculated data.
The experimental results and simulated values of tg4l and cos/h are presented in Figures
1 to 4. The silicon layer deposited at 570 °C is completely amorphous. The increase of the
deposition temperature yields an increase of the crystalline silicon fraction. Therefore islands of crystalline silicon are included in an amorphous silicon matrix. The voids are associated ~A.ith
defects (dislocations, microt~vins,...). The hydrogenation leads to an increase of the crystalline fraction via solid phase crystallisation process. The transformation from the amorphous to
crystalline phase is explained by the random nucleation and growth theory [5]. According to the classical theory, there exists a critical nucleus size above which it tends to grow and belo~A.
which it tends to disappear. The activation energies for the growth rate are usually 2.3 3.7 eV and for the nucleation rate are 4.8 5.9 eV [5]. In this study, the nucleation process is unlikely due to the low temperature annealing. So, the crystallisation takes place by an increase of grain size.
s (eV)
4 43 3.45 2.82 2.39 2.h7 1.83
0.6 4
tg y cosA
280 360 440 520 j00 680
~ (nm)
Fig. 3. Measured and best fitted ellipsometric spectra for IMT C sample.
s (eV)
4.43 3.45 2.82 2.39 2.07 1.83
1-s i
tg if C°SA
280 3f0 440 520 f00 (So
~ (nm)
Fig. 4. Measured and best fitted ellipsometric spectra for IMT D sample.
As can be seen (Tab. II) for the IMT B sample it is necessary to introduce a layer associated with surface roughness. If the irregularities of the surface are of the order or exceed the wave£
length of light, the scattering theory has to be used. In this work, we focus on the microscopic roughness, for which the mean height of irregularities is much less than the wa,relength of light.
The layer associated with the roughness consists of mixtures ranging from silicon (amorphous
or crystalline) to mostly voids. Microscopic roughness can be evaluated via a density deficit of the thin layer. It is widely accepted that the surface of an as-deposited layer at low temper-
ature (570 °C) is smother that at medium temperature (620 °C). This result is in agreement
with electrical evaluation for surface roughness [6]. One observes the conservation of surface
roughness after annealing which is also confirmed by other authors [7]. For sample IMT D, it is also necessary to take into account a thin layer of polysilicon due to surface roughness. One
observes that for the smooth surface cases, the native Si02 has no voids. This microscopic roughness is below the resolution level of a scanning electron microscope an it can only be
checked with a Atomic Force Microscope. Because this type of roughness has a small effect
on light scattering, only the two techniques, spectroellipsometry and atomic force microscopy,
Table III. The calculated MSD for the best fit.
Sample N p MSD
IMTA 31 6 0.162
IMTB 31 9 0.196
IMTC 22 6 0.172
IbfTD 22 9 0.207
could be used for these measurements. The present surface roughness investigation are in good agreement with atomic force microscopy measurements [ii.
Incorporation of hydrogen improves the electrical and optical properties of polysilicon films.
Hydrogenation has been reported to i-educe the density of dangling bonds in grain boundaries [8]. An other effect of hydrogenation is a useful improvement of the SilSi02 interface in metal-
oxide-semiconductor electronic devices [9]. On the other hand, the surface morphology of
polj,silicon is preserved b~hydrogenation (cf. Tab. III). There are two explanations: I) Kamins [10] has proposed that it may be the presence of a native oxide on the surface of the film
that preserves the morphology because the Si-O bond energy is 185 kcal/mol and Si-Si bond
energy is 42 kcal/mol; and it) Hendricks and Mavero [11] have proposed that the morphology is
preserved because grain gro,vth during annealing involves small atomic movements, less than for surface modification. During annealing two reactions are thermally activated (passi,,ation and
depassivation), but the reaction barrier for passivation is smaller than that for dePassi;anion.
The follo,ving reaction occurs in the same way [8].
H+H-H2+4.5eV
It means that the temperature in the sample is higher than the furnace's temperature. In
this ~A>ay the increase of crystallinity fraction after annealing for the sample IMT C could
be explained. on the other hand the hydrogen, due to its low dimensions, strains the Si-Si bonds. In classical theory the amorphous silicon is described as a continuous random net,vork
and Si atoms are fourfold coordinated. Due to the presence of many bonding constraints,
the continuous random net~v.ork is overcoordinated. The hydrogen can reduce the net~A<ork coordination by breaking up Si bonds. Therefore, there are two phenomena which occur
simultaneously: the sample heating which leads to increase of grain size and the terminating
of the Si-Si bonds that leads to a decrease of grain size.
The values of refractive and absorption index obtained from ellipsometric spectra for all
polysilicon samples versus wavelength (photon energy) are represented in Figure 5 to 8.
When the crystallinity fraction increases, the shape of these cur,<es transforms from the shape of refractive and absorption index of amorphous silicon to that of monocrystaline silicon. The results presented in Figure 5 to 8 could be used in connection with technological conditions, to
design a polysilicon layer with the required optical constants. The maximum value of refractive index versus the crystallinity fraction in polysilicon has a parabolic behaviour (Fig. 9). ThP best empirical fit is
Max(n)
= 1.89f~ 0.309 f + 5.21
,vhere f is the crystalline fraction. In this multilayer analysis, the fitting parameters are the thickness and the volume fraction of the chosen constituent materials. This means, a change
in thickness of only one layer will modify the simulated spectrum. The question about the existence and the uniqueness of the solution for the best fit is very- important. From a physical point of vie,,<, the solution ob,>iously exists. The non-uniqueness of the solution occurs for the
s (eV)
4.43 3.45 2.82 2.39 ' 2.07 1.83
n k
250 360 440 520 f00 j80
~ (nm)
Fig. 5. The refractive and absorption index is plotted versus wavelength for IMT A sample.
s (eV)
4.43 3.45 2.52 2.39 2.07 1.53
6
s 4
n k
3
280 360 440 520 600 680
~
~ (nm)
Fig. 6. The refractive and absorption index is plotted versus wavelength for IMT B sample.
s (eV)
4.43 3.45 2.82 2.39 2.07 1.53
6 s 4
n k
3 2
0
280 360 440 520 600 680
~ (nm)
Fig. 7. The refractive and absorption index is plotted versus wavelength for IMT C sample.
s (eV)
4 43 3.45 2.52 2.39 2 07 1.53
6 6
s 4
n k
i i
o
280 360 440 520 600 (So
~ (nm)
Fig. 8. The refractive ~nd absorption index is plotted versus wavelength for IMT D sample.
investigated physical mechanisms which are potential sources for multiple stationary solutions.
Therefore, it cannot be expected to find a general proof for the uniqueness of the solution. In this study, the thickness of Si02 and polysilicon layers has been verified using other methods.
The values of El and e2, the real and imaginary part of complex permittivity versus wa;e- length, (photon energy) could easily be calculated with the aid of the refractive and absorption
index for each case.
The band structure of crystalline silicon presented several direct interband transitions related to critical points at different parts of the Brillouin zone. The lowest direct transition bet,,<een the conduction and valence bands appears for the (000) direction and it is assigned to E[ (r(~ ~ r[~,). This energy gap is degenerated along the A direction of the Brillouin zone, with the El transition (A( - A[). Due to the spin-orbit interaction, r[~ splits into r[ and r( (with
splitting energy /h[) and r]~ splits into Pi and Pi (with splitting energy /ho
= 0.044 el/ [2]).
In this way, the transition r(~ - r[~, has a fine structure and consists of the following energy
levels: E[(r( - r(), E[ + /h[ (Pi - Pi), E[ + /ho (Pi - r( forbidden transition) and
E[ + /h[ + /holpi
- r( [12]. In fact the splitting energies /ho and /h[ of crystalline silicon are very small and are neglected in our analysis. The El transition is degenerate due to spin orbit interaction in the El and El +/hi transitions. This spin-orbit splitting energy /h1 " 0.029 eV [2]
cannot be determinated via spectroellipsometric Spectrum. The energy of critical points could be found by a fitting procedure between the second derivative of the experimental data and [2]
d~e n(n 1)Ae~~(hoJ ECP + irl'~~~ n # 0
d(hoJ)~ Ae~~(hoJ ECP + ir)~~ n
= 0
where critical points are described by the amplitude A, energy ECP, broadening r, and exciton
phase angle # [2]. The E[ and El interband critical points are clearly resolved in the second- derivative spectrum d~e/d(hoJ)~. In this work, we are interested infinding the changes of critical
point energy with respect to hydrogenation. The other critical point parameters are presented
and discussed in reference [2].
The critical point energies can also be evaluated by a graphical method since the energy. for which the maximum and inflection point of real and imaginary part of complex permittivity
occurs, corresponds to the same value. So the E[ transition is associated [2,13] with the max- imum of e2 and the inflection point of El In the same way the El transition is associated with
Table IV. The comparison of the first two direct interband transitions for crystalline silicon.
Transition Type of transition Results (eV) References
r(~~ - r[~ 3.35
3.32
3.2
3.281
hi - A[ El 3.49
3.38
3.412
Table V. Results for the first two direct interband transitions for partially polycrystalline silicon Samples.
Sample E[ tran8ition (eV) El tran8ition (eV)
u8ing El u8ing e2 u8ing El u8ing e2
cry8talline Silicon 3.35 + 0.01 3.35 + 0.01 3.50 + 0.01 3.48 + 0.01
IMT B 3.30+0.01 3.36+0.01 3.51+0.01 3.45+0.01
IMT D 3.32 + 0.01 3.36 + 0.01 3.51 + 0.01 3.47 + 0.01
the fir8t maximum of El and the second point of inflection of e2. For a correct evaluation of the maximum and minimum points, the first derivate of both components of complex permit- tivity have been analysed. The comparison of our results with other references of crystalline
silicon investigation are presented in Table IV. It is widely accepted that the band structure of amorphous silicon is very distinct from that of crystalline silicon.
Similar investigations for IMT A and IMT C are not relevant because it is not possible to
kept the association between critical points and the shape of El and e2. For the IMT B and IMT D samples, the results are presented in Table V.
Values included in the second (first) column of the E[ (Ei transition are obtained as photon
energy for the maximum imaginary (real) part of the complex permittivity. The other column contains values of the same transition evaluated with the second-derivative of the real part of the complex permittivity for the E[ transition and the second derivative of the imaginary part of the complex permittivity for Ei transition, respectively. It is obvious that the decrease of the crystallinity fraction carries out important changes in the band structure behaviour. As
can be seen in Table V, the second-derivative spectrum of the real or imaginary part of the permittivity is more sensitive to the crystallinity fraction (Fig. 10).
This graphical method is limited by the experimental errors. As can be seen in Table V, both transitions (E[ and Ei) decrease by increasing the amorphous silicon fraction. Because the amorphous silicon does not have as well a defined band gap as the crystalline semiconductor,
