SEMICONDUCTORS

VOLUME 32, NUMBER 11

NOVEMBER 1998

Influence of the deposition and annealing conditions on the optical properties of amorphous silicon A. I. Mashin, A. V. Ershov, and D. A. Khokhlov N. I. Lobachevski Nizhni Novgorod State University, 603600 Nizhni Novgorod, Russia

~Submitted September 15, 1997; accepted for publication May 26, 1998! Fiz. Tekh. Poluprovodn. 32, 1390–1392 ~November 1998!

The refractive index and extinction coefficient in the range 0.6–2.0 eV of amorphous silicon films deposited by electron-beam evaporation with variation of the substrate temperature, deposition rate, and anneal temperature in an air atmosphere are presented. The results are discussed in terms of variation of the Penn energy gap as a function of the deposition and treatment conditions. © 1998 American Institute of Physics. @S1063-7826~98!01911-5#

2. If the voids are very small ~less than 1 nm!, they can be treated as accessible elements of a uniform network. Then the overall influence of the voids is confined to decreases in the mean interatomic bonding force and the plasma frequency of the material, and the optical properties can be calculated within the Penn model. According to Ref. 8, the static refractive index n 0 is related to the plasma frequency v p and the Penn energy gap \ v g in the following manner:

The interest in hydrogenated amorphous silicon (a-Si:H) is due mainly to the prospects of using it to fabricate inexpensive film solar cells of large area.1 At the same time, researchers have been focusing increasingly greater attention on ‘‘hydrogen-free’’ amorphous silicon (a-Si) as a promising material with a large refractive index for nearinfrared fiber-optic passive interference elements.2,3 Figure 1 shows typical spectral curves of the refractive index n and the extinction coefficient k of a-Si films obtained by electron-beam evaporation in vacuum ~for the technological details, see, for example, Ref. 4!. The optical constants were determined according to the method in Ref. 5. As in the case of most of the literature data,6 in our case ~curve 1! the values and dispersion of the refractive index of the a-Si films are greater than those of crystalline silicon (c-Si) and a-Si:H in the frequency range investigated. This finding can be explained if it is recalled that amorphous silicon has not only a loss of long-range order, but also a high concentration of matrix defects: dangling bonds, voids, extrinsic impurities, etc. In this communication we examine the influence of voids on the optical properties of a-Si films obtained at various substrate temperatures (T s ) and deposition rates (V s ) and subjected to annealing in air. Two cases can be considered, depending on the void size. 1. If the voids are fairly large compared to the interatomic distance and slightly exceed or are comparable to the light wavelength, the electromagnetic light wave undergoes repeated scattering, and the optical properties of the material can be described within the effective-medium theory. According to Ref. 7, if there are only voids in the material, it satisfies the equality

n 20 511 ~ 2/3!~ v 2p / v 2g ! .

In this case the value of \ v g coincides to within good accuracy with the maximum of the k( v ) spectrum, and

v 2p 5 ~ 4 p e 2 /m !~ r L A /A ! n v ,

n511 ~ 2/3!~ v 2p / v 2g !~ r / r 0 ! 124 f ,

~4!

where f 5d ln C/d ln r is the fraction of cluster bonds on the void surface, C is the mean coordination number, and the superscript 0 denotes the parameter for the completely coordinated material. The value of f varies from 0 to 1 as a function of the void diameter. In the case of small voids ~less than 223 coordination spheres! f .0.25, and the value of n for such a medium will be greater than the value for the completely coordinated material.

~1!

where x v is the relative void volume, «ˆ m ( v ) and «ˆ v ( v ) are the complex dielectric constants of the medium and the voids, and «ˆ ( v ) is the effective complex dielectric constant of the system. 1063-7826/98/32(11)/3/$15.00

~3!

where e and m are the charge and mass of an electron, r is the density of the material, A is the molecular weight, and L A is Avogadro’s number. For c-Si n v 54. The quantity \ v g is called the plasmon energy. A plasmon is a collective excitation of the electron gas that is localized mainly in dense regions of the random network and penetrates only slightly into the voids, which, in turn, create the density deficit in a-Si. Thus, the plasmon energy can serve as a measure of the microscopic density of the amorphous semiconductor. According to the data in Ref. 9, a-Si films typically have voids with diameters no greater than 0.5 nm. A void can then be regarded as a cluster of atoms separated from the fully coordinated structure, and the expression ~2! can be written as10

~ 12x v !@ «ˆ m ~ v ! 2«ˆ ~ v !# / @ «ˆ m ~ v ! 12«ˆ ~ v !#

1x v @ «ˆ v ~ v ! 2«ˆ ~ v !# / @ «ˆ m ~ v ! 12«ˆ ~ v !# 50,

~2!

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© 1998 American Institute of Physics

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Semiconductors 32 (11), November 1998

Mashin et al.

FIG. 1. Spectral curves of the refractive index n ~1, 2! and the extinction coefficient k (18 , 28 ) of a-Si films obtained by electron-beam evaporation at the substrate temperatures T s 5250 ~1, 18 ) and 20 °C ~2, 28 ).

FIG. 3. Spectral curves of the refractive index n ~1–4! and the extinction coefficient k (18 – 48 ) of a-Si films deposited at T s 5250 °C and annealed in air for 1 h at 20 ~1, 18 ), 100 ~2, 28 ), 150 ~3, 38 ) and 250 °C ~4, 48!.

On the basis of these arguments, it can be assumed that in our case the a-Si films obtained by electron-beam evaporation at T s 5250°C ~Fig. 1! have voids, whose diameter is comparable to the first or second coordination radius and, accordingly, are characterized by a large refractive index. Variation of the deposition conditions, or, more specifically, a decrease in the substrate temperature T s from 250 to 20 °C and the deposition rate V s by a factor of roughly 2 ~Figs. 1 and 2!, leads to qualitatively identical variation of n for the films, i.e., to lowering of its value near the absorption edge. The refractive index dispersion also decreases under these conditions. As a result, the difference in the behavior of curves 1 and 2 in both figures is very significant in the shortwavelength region. For example, while the difference between the refractive indices for a photon energy \ v .1.9 eV is ;1 ~Fig. 1!, the difference for \ v .1.0 eV amounts to ;0.4. When \ v ,0.8 eV, the value of the re-

fractive index scarcely depends on the deposition conditions indicated. Inspection of the spectral curves of the extinction coefficient ~Figs. 1 and 2, curves 18 and 28! reveals that variations in T s and V s influence the behavior of k( v ) differently. For example, a decrease in the substrate temperature T s ~Fig. 1! leads to displacement of the absorption edge toward longer wavelengths, while a decrease in V s ~Fig. 2! causes displacement of the absorption edge of amorphous silicon toward higher energies. This finding allows us to assume that the mechanisms for the decreases in the refractive index in response to the lowering of T s and V s are different. Lowering T s clearly leads to an increase in the diameters of the voids in a-Si. This, in turn, leads to lowering of n, bringing it closer to the values for c-Si, and for very large voids (;502100 nm) it leads to refractive index values that are smaller than in crystalline silicon. Since the width of the Penn gap also decreases in that case, the maximum on the k( v ) curve and, therefore, the absorption edge shift toward longer wavelengths, as we observe on the experimental curves presented ~Fig. 1!. The decrease in \ v g in this case is attributed to a decrease in the mean coordination number. A decrease in the deposition rate should lead to a decrease in the film porosity, and in this case, according to ~4!, there should be an increase in the refractive index. On the other hand, at low deposition rates a large quantity of extrinsic impurities, such as oxygen, hydrogen, carbon, etc., enters the film. If we follow Shevchik and Paul9 and assume that the diameter of the voids in the original a-Si is ;0.5 nm, it is difficult to imagine a further decrease in their diameter as the deposition rate is lowered. Thus, an influence of lowering the deposition rate on the optical characteristics of a-Si through a decrease in the void diameter is unlikely. In order to reveal the influence of extrinsic impurities, it would be useful to jointly examine the influences of the deposition rate and the subsequent annealing of a-Si in air, since the penetration of extrinsic impurities into the film from the atmosphere should be expected in the latter case.

FIG. 2. Influence of the deposition rate on the spectral curve of the refractive index n ~1, 2! and the extinction coefficient k (18 , 28 ) of a-Si films. Film deposition rate V s , nm/s: 1, 18 — 0.53; 2, 28 — 0.30.

Mashin et al.

Semiconductors 32 (11), November 1998

According to the experimental data, annealing a-Si in air, like a decrease in the deposition rate ~Figs. 2 and 3!, leads to a decrease in the refractive index and displacement of the absorption edge toward higher energies. Taking into account the foregoing statements, we believe that the character of the variation of the optical properties of a-Si in response to variation of the deposition conditions and to heat treatment is described well within the Penn model. The magnitude of the Penn gap is determined both by the presence and character of the behavior of extrinsic impurities in the film and by the short-range structure of amorphous silicon. For example, the diffusion of oxygen into the bulk of the material leads to saturation of the dangling bonds and the formation of Si–O bonds instead of Si–Si bonds. Since a Si–O bond is energetically stronger than a Si–Si bond, the Penn gap \ v g increases and the maximum on the k( v ) curve shifts toward shorter wavelengths. On the other hand, ‘‘lightening’’ the network, i.e., lowering the number of dangling bonds, leads to an increase in the coordination number, and relaxation of the already completely connected network ~a decrease in the spread of bond lengths, bond angles, and dihedral angles! increases the Penn gap.

1

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A. Madan and M. P. Shaw, The Physics and Applications of Amorphous Semiconductors ~Academic Press, Boston, 1988; Mir, Moscow, 1991!, p. 670. 2 K. Hamada, M. Wada, H. Shimizu, M. Kume, F. Susa, T. Shibutani, N. Yoshikawa, K. Itoh, G. Kano, and I. Teramoto, IEEE J. Quantum Electron. QE-21, 623 ~1985!. 3 A. V. Ershov, N. B. Zvonkov, A. I. Mashin, and D. A. Khokhlov, in Proceedings of the Russian Conference ‘‘Structure and Properties of Crystalline and Amorphous Materials,’’ Nizhni Novgorod, 1996 @in Russian#, NizhniŽ Novgorod State University, NizhniŽ Novgorod ~1996!, p. 28. 4 A. V. Ershov, A. I. Mashin, and D. A. Khokhlov, Vysokochist. Veshchestva 2, 35 ~1995!. 5 A. S. Valeev, Opt. Spektrosk. 15, 500 ~1963! @Opt. Spectrosc. ~USSR! 15, 301 ~1963!#. 6 M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, Phys. Rev. B 1, 2632 ~1970!. 7 D. R. Penn, Phys. Rev. 128, 2093 ~1962!. 8 The Physics of Hydrogenated Amorphous Silicon, Vol. 2: Electronic and Vibrational Properties, J. D. Joannopoulos and G. Lucovsky @Eds.# ~Springer-Verlag, Berlin–New York, 1984; Mir, Moscow, 1987!, p. 447. 9 N. J. Shevchik and W. Paul, J. Non-Cryst. Solids 16, 55 ~1974!. 10 J. C. Philips, Phys. Status Solidi B 44, K1 ~1971!. Translated by P. Shelnitz