Characterisation of porous silicon layers by spectroscopic ellipsometry

LUMINESCENCE

Journal of Luminescence 57 (1993) 205—209

JOURNAL OF

Characterisation of porous silicon layers by spectroscopic ellipsometry U. ~ a

H. Münder”, M. Thönissen” and W. Theil3c

Instutur für Festkorperphysik der TU, PN6-1, Hardenbergstr. 36, 10623 Berlin, Germany Inst itul für Schicht- und Jonentechnik der KFA, Posfach 1913, 52425 Jülich, Germany 1. Phvsikalisches Institut der RWTH, Sommerfeldstr. 28, 52074 Aachen, Germany

The influence of the microscopic structure of porous silicon layers on the dielectric function is determined by spectroscopic ellipsometry. The investigated layers were formed on high and low p-type doped substrates. Their microscopic structure was changed by varying the current density in the electrochemical formation process. The measured dielectric function was found to be extremely sensitive on the microscopic structure. New features occur in the measured dielectric function which are characteristic for the silicon skeleton in the porous silicon layers.

1. Introduction The dielectric function of a semiconductor in the visible and UV spectral range depends on its electronic structure. Consequently, all parameters which modify the electronic structure change the dielectric function. For example the mean diameter of crystals in nanocrystalline silicon layers [1] or strain of stressed crystals [2,3] influence the dielectric function. Both parameters can shift the spectral position of features in the dielectric function due to van Hove singularities in the joint density of states, the so-called optical gaps. Moreover, size effects lead to a broadening of these gaps. The optical response of inhomogenous films such as porous silicon layers (PSL) which are composed of the silicon skeleton, the pores (vacuum), and possibly oxidised silicon is given by an effective dielectric function written as . It depends on the mdividual dielectric functions, the microstructure (topology) and the porosity. The extraction of these parameters from the measured is difficult and up to now could only be done approximately. The Correspondence to: Dr. U. Rossow, Institut fur Festkorperphysik der TU, PN6-l, Hardenbergstr. 36, 10623 Berlin, Germany. 0022-2313/93/S06.00 © 1993 SSDI 0022-23l3(93)E0106-8

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advantage of optical investigations of the microscopic structure (here by spectroscopic ellipsometry) compared to electron microscopy is that the samples can be measured as-grown and nondestructively. In this paper, we will discuss the influence of various formation conditions as well as doping levels and therefore different microscopic structures of the layers on the dielectric function.

2. Experimental For the investigations, a spectroscopic ellipsometer of the rotating analyser type [4] was used in the spectral range from 1.8 to 5.5 eV. The measured raw data were directly converted into effective dielectric functions <~> which are also called pseudodielectric functions [4,5]. The investigated PSL were formed electrochemically (50% HF and ethanol (1: 1)) from p-doped substrates with resistivities in the range from 0.01 to 8 ~ cm. For a given substrate doping level, the current density was varied in order to obtain different porosities and therefore different microstructures. The thicknesses of the layers were about 5 pm and hence there is no substrate contribution to the dielectric function above 3 eV. To avoid any

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ENERCY (eV) Fig. I. The influence of increasing current density and consequently porosity on Im for PSL formed on highly p-type doped silicon substrates (0.01 ~ cm). The used current densities 2 are 9 (30%), 31 (40%), 94 (50%), 141 (60%) and 219 mA/cm (75%). A,B: main features ofthe dielectric function (also the peak or shoulder at —‘4.2 eV).

oxidation, freshly prepared samples were kept in a nitrogen atmosphere until the layers were measured,

3. Results The porosity for highly doped substrates (0.01 Q cm) was varied by using different current densities. With increasing porosity, the amount of large nanocrystals (>10 nm) is reduced which is confirmed by Raman studies [6]. Due to the increasing porosity, it is expected that the absolute values of lm should decrease. In addition, the shape of Im should change due to the decreasing mean diameter of the nanocrystals. Both can be observed in the spectra shown in Fig. 1. The dielectric function has three main features labeled A, B and a peak or shoulder at -.~4.2eV. The last two features can be assigned to the well known E~+ E1 (3.4 eV) and E2 (4.2 eV) gaps of bulk single crystalline silicon [1,5]. A new structure A is visible below the E~+ E1 gap which shifts to higher energies with increasing porosity. The structure B with a constant energetic position slightly below 3.4 eV vanishes for porosities >50%. The shape of the dielectric function for such high porosities resembles those found for microcrystalline silicon [7,8]. 2, When lowering the current density to 0.9 mA/cm

Fig. 2. A comparison of Im(e> for PSL with 75% porosity formed on different p-type doped substrates with resistivities as indicated. For the low-doped samples, Fabry—Perot interferences are observable for photon energies below about 2.5 eV. Besides these interferences, there remains only a broad feature C with a spectral position near the E 2 gap of bulk crystalline silicon.

the feature A occurs at about 2.5 eV well separated from the feature B (1 eV lower in energy). The shape of Im near the feature B is then very similar to that of the E~+ E~feature of bulk single crystalline silicon. For the formation of PSL, three differently p-type doped substrates were used (8,0.2 and 0.01 ~ cm). As already shown, highly doped samples exhibit a dielectric function similar to microcrystalline silicon. By lowering the doping concentration, a different shape of the dielectric function is found (Fig. 2). No feature remains at the spectral position of the bulk single crystalline E~+ E1 gap. Instead, a broad structure labeled C occurs at a spectral position close to the E2 gap of crystalline silicon.

4. Discussion The spectra taken for highly p-doped PSL seem to have two main contributions besides the E2 structure. The feature B can be related to the known E~+ E1 feature of bulk crystalline silicon broadened due to size effects. On the other hand, a new feature A occurs whose origin is still not clear.shift In in Ref. is reported thatwhen the feature not the[9] energetic position varyingdoes the

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Characterisalion of porous silicon layers

angle of incidence. Therefore the authors conclude that anisotropy does not induce this feature A and explained the feature by depolarisation of light (due to a light scattering process). However, we found that by heating the PSL to temperatures of 600°Ca red shift of the feature A occurs of nearly the same amount as it is the case for the E~+ E1 gap of dense crystalline silicon [10]. The reflectivity near the feature is increased, while for scattering or depolarisation no increase is expected. Moreover, such sharp features in the dielectric function are unlikely to stem from scattering of the light, since the (columnar) structure is irregular [11]. Consequently, depolarisation effects can be ruled out. Because the feature A shifts with temperature by the same amount as the E~+ E1 gap and is not affected by varying the angle of incidence, a possible layered structure of the PSL can also be ruled out. By simulating reflectance spectra obtained on PSL, it has been shown that the topology significantly influences the dielectric function. The influence of the topology, e.g. the percolation of the crystals in the PSL, can only correctly be described using the Bergman effective medium theory [12]. Within this model, effective dielectric functions can be calculated for various topologies, if the volume fractions and dielectric functions of the phases of the PSL are given. For all topologies, the calculated values of the effective dielectric functions, however, are restricted to a certain area of the complex c-plane. This area is enclosed by rigorous bounds [13]. The bounds have been calculated (see Fig. 3) for a PSL with porosity of 30% using the bulk dielectric function of silicon [5]. The values of the dielectric function near the maximum of the feature A for the 30% porosity sample (7.6 + i 13.2), however, do not fit in this area, Therefore, the feature A is not induced by the topology of the PSL. Consequently, the feature A is likely to be induced by electronic transitions. We must assume that the electronic structure of the silicon skeleton differs from that of the dense bulk material as discussed in a previous paper [14]. The most p05sible reasons for a change in the electronic structure are size effects in nanocrystals, transitions between localised states in small nanocrystals, strain effects

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0.010 0005 0000 7 8 9 Real part Fig. 3. Rigorous bounds for PSL with 30% porosity. The shaded area shows possible Im values for a photon energy of 3 eV. .

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or surface effects. In the case of size effects, a small blue shift of the bulk features is expected [1] in contrast to the large red shift of A relative to the bulk silicon E~+ E1 feature. Various effects, however, could cause a shift of the gaps to lower energies [7]. Hydrostatic tensile stress is one example. The shift in the E~+ E1 gap due to stress is 4 meV/kbar [7]. The feature A was in the investigated samples shifted up to 1 eV relative to E~+ E~ which would correspond to a stress value of 250 kbar. Such high stress values are in disagreement to Raman and X-ray diffraction results [15] and thus an explanation only by a stress effect can be ruled out. On the other hand, at the surface such stress values are not unlikely. Due to relaxation, reconstruction or contamination large stress can be built up. This can cause electronic states at the silicon surface which allow direct transitions to occur below the E~+ E1 gap [16]. Another reason for a red shift of the E~+ E1 gap is that the exciton binding energy is increased in the small crystals compared to that in bulk materials. However, it is also possible that the feature A is induced by transitions between “localised” states in nanocrystals. In this case, features occur in the dielectric function below the E~+ E1 gap as calculated for chains with diameters in the nanometer range [17]. In this case, however, large anisotropy is found depending on the orientation of the electric field vector of the incident light with respect to the chain axis. However, since no anisotropy is reported by Ref. [9] and

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the feature A does not vanish in annealing the PSL to temperatures above 800°C,it is more likely that the feature A is surface related. A comparison of the effective dielectric functions measured on differently doped PSL shows a dramatic change in lowering the doping level. In the spectra taken for low-doped samples, a loss of the E~+ E1 feature in the dielectric function is found. Instead a broad feature C occurs. This behaviour seems to be due to size effects because, for example, disorder or defects hardly affect the E~+ E1 feature but strongly affect the E2 [7]. The feature C can also not be explained by an amorphous structure of the PSL. The line shape of Im as well as the spectral position (below 3.8 eV for amorphous silicon) of the maximum is different. Moreover, the onset of absorption indicated by the Fabry-.Perot interferences is shifted to the blue compared to amorphous silicon. By annealing (low-doped substrates) the structure of the PSL changes and the line shape reveals that the silicon skeleton is then mainly amorphous [18,19]. Important to note is that, in accordance to all reflectivity and ellipsometry measurements (see, for example, Refs. [9,18] ), for low-doped samples Fabry—Perot interferences occur in the spectral range below 2.5 eV or even up to higher photon energies. Because all layers are thick (here about 5 pm), the existence of a direct gap in this spectral range is very unlikely. For Ill—V or Il—VI compound semiconductors the interferences die out above the direct gap for layers of comparable thickness. 5. Conclusions It has been shown that the measured dielectric functions are extremely sensitive against changes in the microscopic structure. The dielectric function of the silicon skeleton differs from that of bulk single crystalline silicon. A new feature occurs in the dielectric function for high-doped substrates. The ongin of this feature is still unclear but it seems to be related to the surfaces. For high-doped substrates and porosities, a dielectric function similar to the one of microcrystalline silicon is found. On the other hand, for the low-doped material a new shape of the dielectric function is found which does not

correspond to literature data of microcrystalline silicon. However, again an explanation of the observed structure cannot be given. Further studies are in progress to solve both questions. Consequently, unsatisfactory results are obtained in fitting the effective dielectric functions of porous silicon layers within the Bruggeman effective medium theory or using silicon bulk data.

Acknowledgements We would like to thank W. Richter, U. Frotscher, Th. Werninghaus, S. Frohnhoff and M. Berger for fruitful discussions and technical help.

References [I] S. Logothetidis, H.M. Polatoglou and S. Ves, Solid State Commun. 68 (1988) 1075. [2] J. Kircher, W. Bohringer, W. Dietrich, H. Hirt, P. Etchegoin and M. Cardona, Rev. Sci. Instrum. 63 (1992) 3733. [3] R. Zallen and W. Paul, Phys. Rev. 155 (1967) 703. [4] D.E. Aspnes and A.A. Studna, AppI. Opt. 14 (1975) 220. [5] D.E. Aspnes and A.A. Studna, Phys. Rev. B 27(1983)985. [6] H. Münder, M.G. Berger, S. Frohnhoff, M. Thbnisseri and H. Lüth, J. Lumin. 57 (1993) 5. [7] Thessaloniki, 5. LogothetidisGreece, and H.M. in: Proc. 20th eds.Polatoglou, E.M. Anastassakis andICPS, J.D. Joannopoulos (World Scientific, 1990) pp. 1795, 2067. [8] M. Fang and B. Drevillon, J. Appl. Phys. 70 (1991) 4894. [9] F. Ferrieu, A. l-lalimaoui and D. Bensahel, Solid State Commun. 84 (1992) 293. [10] P. Lautenschlager, P.B. Allen and M. Cardona, Phys. Rev. B 31(1985) 2163. [II] For indium islands on GaAs, for example, a much broader feature is observed: U. Resch-Esser, N. Blick, Y.S. Raptis, N. Esser, Th. Werninghaus, U. Rossow and W. Richter, in: Proc. ICFSI-4, Jülich,H.June 1993, H. to be published. [12] W. TheilJ, P. Grosse, Münder, LUth, R. Herino and M. Ligeon, Mater Res. Soc. Proc. 283 (1992) 215. [13] G.W. Milton, J. AppI. Phys. 52 (1981) 5286, 5294 (1981); B.U. Felderhof, Physica 126 A (1984) 430. [14] H. MUnder, MG. Berger, U. Rossow, U. Frotscher, W. Richter, R. Henna and M. Ligeon, Appi. Surf. Sc,. 63 (1993) 57. [15] H Münder, C. Andrzejak, M.G. Berger, U. Klemradt, H. Lüth, R. Herino and M. Ligeon, Thin Solid Films 221 (1992) 27.

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[16] W. Daum, H.J. Krause, U. Reichel and H. Ibach, in: Proc. ICFSI-4, Jülich, June 1993, to be published, [17] F. Buda, J. Kohanoff and M. Parrinello, Phys. Rev. Lett. 69 (1992) 1272. [18] H. Münder, M.G. Berger, S. Frohnhoff, H. Lüth, U. Rossow, U. Frotscher and W. Richter, Mater. Res. Soc. Proc. 283 (1992) 281.

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[19] U. Rossow, Th. Werninghaus, U. Frotscher, H. Münder and W. Richter, ‘Microstructure and electronic properties ofporous silicon layers investigated by spectroscopic ellipsometry’, in: Proc. 13th General Conf. of the Condensed Matter Division ofthe European Physical Society, Regensburg, 1993.