SEMICONDUCTORS
VOLUME 32, NUMBER 7
JULY 1998
Effect of 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 December 1, 1997; accepted for publication December 23, 1997! Fiz. Tekh. Poluprovodn. 32, 879–881 ~July 1998!
The spectral characteristics of the refractive index and the extinction coefficient in the range 0.6–2.0 eV for amorphous silicon films prepared by electron-beam evaporation with variation of the substrate temperature, deposition rate, and annealing temperature in air are presented. The results obtained are discussed on the basis of the changes in the Penn gap energy as a function of the indicated preparation and treatment conditions. © 1998 American Institute of Physics. @S1063-7826~98!02307-2#
Hydrogenated amorphous silicon ~a-Si:H! is of interest mainly because it holds promise for the fabrication of inexpensive large-area film solar cells.1 At the same time, investigators are devoting more and more attention to ‘‘hydrogenfree’’ amorphous silicon ~a-Si! as a promising, highrefractive-index material for passive interference elements in near-IR fiber optics.2,3 Figure 1 shows typical spectral dependences of the refractive index n and the extinction coefficient k of a-Si films prepared by electron-beam evaporation in vacuum ~see, for example, Ref. 4 for the technological details!. The optical constants were determined by the method of Ref. 5. Just as in most published data,6 in our case the values and variance of the refractive index of a-Si films ~curve 1! are higher than for crystalline silicon ~c-Si! and a-Si:H in the experimental frequency interval. This fact can be explained by recalling that in amorphous silicon, besides destruction of the long-range order, there is a high concentration of matrix defects: dangling bonds, pores, extraneous impurities, etc. In the present paper we examine the influence of pores on the optical properties of a-Si films prepared with different substrate temperatures (T s ) and deposition rates (V s ) and annealed in air. Depending on pore size, two cases can be studied. 1. If the pores are sufficiently large compared with the interatomic distance and slightly greater than or comparable to the wavelengths of visible light, then electromagnetic light waves undergo multiple scattering, and the optical properties of the material can be described within the effective-medium theory. According to Ref. 7, in the case when only pores are present in the material the following equation holds:
2. In the special case where the pores are very small ~less than 1 nm!, they can be treated as elements of a uniform network. Then the overall effect of the pores is to decrease the average strength of interatomic bonds 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 with the plasma frequency v p and the Penn gap energy \ v g by n 20 511 ~ 2/3!~ v 2p / v 2g ! .
To a good approximation, the energy \ v g corresponds to the maximum of the spectrum k( v ), while
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 the cluster bonds on the surface of a pore, C is the average coordination number, and the superscript 0 denotes a parameter of the fully coordinated material. The quantity f varies from 0 to 1, depending on the pore size. In the case of small pores ~less than 2–3 coordination spheres! f .0.25, and the value of n for such a medium will likewise be greater than for a fully coordinated material.
~1!
where x v is the relative volume of the pores, «ˆ m ( v ) and «ˆ v ( v ) are the complex permittivities of the medium and the pores, and «ˆ ( v ) is the effective complex permittivity of the system. 1063-7826/98/32(7)/3/$15.00
~3!
where e and m are the electron charge and mass, r is the density of the material, A is the molecular mass, and L A is Avogadro’s number. For c-Si, n V 54. The quantity \ v p is called the energy of a plasmon, which is a collective excitation of the electron gas localized mainly in dense regions of the random network and penetrating only very little into the pores, which in turn produce the density deficit in a-Si. Therefore, the plasmon energy can serve as a measure of the microscopic density of an amorphous semiconductor. According to the data of Ref. 9, pores with diameter not exceeding 0.5 nm are characteristic for a-Si films. Then the pores can be treated as a cluster of atoms removed 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 ~ v ! 12«ˆ ~ v !# 50,
~2!
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© 1998 American Institute of Physics
Semiconductors 32 (7), July 1998
FIG. 1. Spectral dependences of the refractive index n ~1, 2! and the extinction coefficient k (18 , 28 ) of a-Si films produced by electron-beam evaporation with substrate temperatures T s 5250 ~1, 18 ) and 20 (2, 28 ) °C.
On the basis of these arguments we can say that in our case the a-Si films produced by electron-beam evaporation with T s 5250 °C ~Fig. 1! contain pores with diameters comparable to the first or second coordination radius and are accordingly characterized by a high refractive index. Variation of the preparation conditions, specifically, decreases in T s from 250 to 20 °C and in V s by approximately a factor of 2 ~Figs. 1 and 2!, produces a qualitatively identical change in n in films — a decrease in n near the absorption edge. The dispersion of the refractive index also decreases under these conditions. As a result, the difference in the behavior of the curves 1 and 2 in the two figures is very substantial in the short-wavelength region. For example, for photon energy \ v .1.9 eV the difference between the refractive indices is ;1 ~Fig. 1!, whereas for \ v .1.0 eV this difference is ;0.4. For \ v ,0.8 eV the refractive index is virtually independent of these deposition conditions.
FIG. 2. Effect of the deposition rate on the spectral dependences 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.
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FIG. 3. Spectral dependences of the refractive index n ~1–4! and the extinction coefficient k (18 – 48 ) of a-Si films prepared with T s 5250 °C and annealed in air for 1 h at 20, 100, 150, and 250 °C ~1–4 or 18 – 48 , respectively!.
Turning now to the frequency dependences of the extinction coefficient ~curves 18 and 28 in Figs. 1 and 2!, we can see that variations of T s and V s affect the behavior of k( v ) differently. Decreasing the substrate temperature ~Fig. 1! shifts the absorption edge toward longer wavelengths, while decreasing V s ~Fig. 2! shifts the absorption edge of amorphous silicon toward higher energies. This fact suggests that the mechanism leading to a decrease in the refractive index as T s decreases is different from the mechanism in the case when V s decreases. Evidently, as T s decreases, the pore sizes in a-Si increase. In turn, this results in a decrease of n, which approaches the refractive index of c-Si, while for very large pores ~50–100 nm! n achieves values which are lower than in the crystalline material. Since the Penn energy gap decreases in the process, the maximum of the function k( v ) and therefore the absorption edge shift toward longer wavelengths, as we observe on the experimental curves presented ~Fig. 1!. In this case the decrease in \ v g is explained by a decrease in the average coordination number. Decreasing the deposition rate should decrease the porosity of the film, and according to Eq. ~4! the refractive index should increase in this case. On the other hand, for low deposition rates the amount of extraneous impurities, such as oxygen, hydrogen, carbon, and so on, entering the film is larger. If we agree with Ref. 9 and assume that the pores in the original a-Si are approximately 0.5 nm in diameter, then it is difficult to imagine that the pore size will decrease further as the deposition rate decreases. Therefore, it is unlikely that a decrease in deposition rate will affect the optical characteristics of a-Si via a decrease in the pore size. To isolate the effect of extraneous impurities, we thought it would be useful to consider the combined effect of the deposition rate and the subsequent annealing of a-Si in air, since in the latter case extraneous impurities should enter the film from the atmosphere. According to the experimental data, the annealing of a-Si in air, just as a decrease in the
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Semiconductors 32 (7), July 1998
deposition rate ~Figs. 2 and 3!, decreases the refractive index and shifts the absorption edge toward higher energies. On this basis we believe that the character of the change produced in the optical properties of a-Si by variation of the preparation and heat-treatment conditions is described well within the Penn model. The Penn energy gap is determined both by the presence and the behavior of extraneous impurities in the film and by the structure of the short-range order in amorphous silicon. Thus, the diffusion of oxygen into the bulk of the material results in saturation of the dangling bonds and the formation of Si–O bonds instead of Si–Si bonds. Since the Si–O bond is energetically stronger than the Si–Si bond, the Penn energy gap \ v g increases and the maximum of k( v ) shifts toward shorter wavelengths. On the other hand, ‘‘healing’’ of the network, i.e., a decrease in the number of dangling bonds, increases the coordination number, while relaxation of an already fully connected network ~a decrease in the spread of bond lengths and bond and dielectric angles! increases the Penn energy gap.
*!E-Mail:
[email protected] 1
A. Madan and M. Shaw, The Physics and Applications of Amorphous Semiconductors ~Academic Press, Boston-San Diego-N.Y.-LondonSydney-Tokyo-Toronto, 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 on the Structure and Properties of Crystalline and Amorphous Materials @in Russian#, Nizhni Novgorod State University, Nizhni Novgorod, 1996, p. 28. 4 A. V. Ershov, A. I. Mashin, and A. F. Khokhlov, Vysokochist. Veshchestva 2, 35 ~1995!. 5 A. S. Valeev, Opt. Spektrosk. 15, 500 ~1963! @Opt. Spectrosc. 15, 269 ~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 J. D. Joannopoulos and G. Lucovsky ~Eds.!, The Physics of Hydrogenated Amorphous Silicon, Vol. 2: Electronic and Vibrational Properties, ~Springer-Verlag, Berlin–New York, 1984; Mir, Moscow, 1988, 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 M. E. Alferieff
