Photo-oxidation effects in porous silicon luminescence

PHYSICAL REVIEW B 69, 205317 共2004兲

Photo-oxidation effects in porous silicon luminescence R. R. Koropecki,1,2 R. D. Arce,1 and J. A. Schmidt1,2 1

Instituto de Desarrollo Technolo´gico para la Industria Quı´mica, Universidad Nacional del Litoral–Consejo Nacional de Investigaciones Cientı´ficas y Tećnicas, Guëmes 3450, 3000 Santa Fe, Argentina 2 ´ Departamento de Fısica, Facultad de Ingenierıá Quı´mica, UNL, Santiago del Estero 2829, 3000 Santa Fe, Argentina 共Received 23 October 2003; revised manuscript received 5 February 2004; published 26 May 2004兲 We investigate the photoluminescence 共PL兲 evolution of porous silicon samples when exposed to air in darkness and under illumination. Oxygen incorporation is monitored through ir spectroscopy. Fourier transform infrared measurements show that samples exposed to air in darkness exhibit low oxidation rates whereas its PL spectra remain unchanged. On the other hand, samples exposed to air under illumination show a remarkable change in its PL together with a drastic increase in the oxidation rate. A well defined PL peak starts to grow at the expense of a peak located at lower energies, which is present in the PL spectra of the as-prepared samples. The set of PL spectra obtained during the evolution shows an isostilbic point that suggests the existence of two emitting components kinetically correlated. The application of the factor analysis technique confirms this asseveration and enables us to obtain the spectrum of each single emitting component. The oxidation behavior, together with the shape and evolution of the PL spectra, are explained in terms of the quantum wires hypothesis combined with an oxidation mechanism with significant nucleation. The whole set of results demonstrates that quantum size effects may rule the photo-oxidation of the porous silicon structure, and gives strong support to a quantum confinement model for porous silicon PL. DOI: 10.1103/PhysRevB.69.205317

PACS number共s兲: 78.55.Mb, 68.65.⫺k, 81.07.Bc

I. INTRODUCTION

The origin of the visible photoluminescence 共PL兲 in porous silicon 共PS兲 has been a subject of extensive discussion during the last decade. The different models proposed to explain this phenomenon may be grouped into several categories: hydrogenated amorphous silicon model,1 surface hydride model,2 defect models,3 siloxene model,4 surface states models,5 and quantum confinement model.6 In this last model the quantum confinement effect leads to an increase of the Si band gap, together with a relaxation of the momentum conserving rule. These two facts easily explain the shift and the size dependence of the PS photoluminescence. A large number of additional experiments have contributed to make this model the most extensively accepted today.7 However, some results contradict also the standard quantum confinement model.7 In fact, it is still difficult to decide which model is the most suitable to describe the properties of PS.8 Probably, the behavior of PS has to be described with some combination of the previously mentioned models. Since the early experiments it is known that PS alters its properties when exposed to air. Oxidation seems to be, at least partially, the origin of these changes. Taking these facts into account, intentional oxidation has been considered as a mechanism to stabilize the properties of PS. Intentional oxidation is usually performed at high temperatures in order to accelerate the process. However, increasing the temperature may stimulate undesired processes, such as hydrogen evolution. There is evidence that light exposure notably increases the oxidation rates, saturating the oxidation process at room temperature. Several authors have reported that PL is affected by oxidation. These reports are contradictory to some extent, since some authors report a redshift of the PL peak during oxidation,9,10 while other authors report a blueshift.8,11 In this work we report changes in the photoluminescence 0163-1829/2004/69共20兲/205317共6兲/$22.50

of PS when oxidation takes place under blue light illumination. The experiments are performed at room temperature in air atmosphere. Infrared spectroscopy is used to detect oxygen incorporation and modifications in the hydrogen bonding structure. The evolution of the PL spectra shows the existence of an isoemissive point. Factor analysis technique is applied in order to investigate the kinetics involved during the evolution of the PL spectra. Our results clearly show that instead of a continuous shift of the PL peak, the lightinduced oxidation leads to the growth of a new luminescence peak at the expense of another one located at a lower energy. Although the photoinduced growth or decrease of PL peaks have been reported for porous silicon samples prepared under different conditions, up to our knowledge there is no previous report on the concomitant occurrence of both processes. The behavior of ir and PL spectra strongly suggests that PL evolution is related to photo-oxidation effects. All these results seem to be a manifestation of discrete changes in the size of the PS structure. In spite of the fact that our results correspond to samples prepared under specific conditions, they can be considered as striking evidence of the importance of quantum confinement effects, both in the oxidation of the PS structure and in the concomitant evolution of the PL spectrum.

II. EXPERIMENTAL PROCEDURE

The porous silicon layers were prepared by electrochemical anodization using slightly p-type boron doped 共100兲 silicon wafers with resistivities of 7–17 ⍀ cm. An aluminum contact was evaporated on the back side of the wafers. The anodization was done using a constant current density of 20 mA/cm2 for 40 min in ambient conditions of temperature and illumination. The electrolyte was a solution of HF (48%):C2 H5 (OH) in a proportion 1:2 by volume. The anod-

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R. R. KOROPECKI, R. D. ARCE, AND J. A. SCHMIDT

ization cell was made of Teflon, with a platinum wire as cathode contact. After the anodization, the porous silicon surface was rinsed with ethyl alcohol and dried under N2 flow. As soon as the etching process finished, the samples were kept in darkness, except when exposed to controlled amounts of radiation to study photoinduced effects. The weight of one of the samples was measured before and after the etching. After that, the porous part of the sample was removed by using a 1N Na共OH兲 solution, and the sample was weighted again. A (94⫾2)% porosity and a thickness of around 35 ␮m were determined from these measurements by using the gravimetric method. PL spectra were measured using a Hitachi model F2000 fluorimeter, setting the excitation light at 400 nm. An interference filter centered at 400 nm was intercalated in the excitation beam of the spectrometer to avoid undesired stray light from the excitation monochromator, which can be efficiently scattered. As a result, the intensity of the excitation beam was 4 mW/cm2. A sample holder was designed in order to maintain the sample surface at an angle of 70° with respect to the excitation beam. The sample was exposed to the excitation beam for a cumulated time between 0 and 100 min in 14 steps, taking a PL spectrum after each step. Between the successive spectra the sample remained in the sample compartment, carefully avoiding all sample handling during the experiment. In another experiment, the PL spectrum of an as-prepared sample was recorded, then the sample was stored in darkness at room temperature during one week, and the PL spectrum was measured again. No changes in the PL spectrum were detected after this procedure, although oxidation of the sample was indeed observed through the evolution of the ir spectra. In a different experiment, series of ir spectra were taken with a conventional Fourier transform infrared 共FTIR兲 spectrometer after different periods of light exposure. In this case, the light was supplied by a conventional halogen lamp filtered with a 400 nm interference filter. The intensity of the irradiation beam was 0.7 mW/cm2 at normal incidence, providing conditions of intensity and wavelength similar to those employed in the PL evolution study.

III. RESULTS AND DISCUSSION

Figure 1 shows the evolution of the PL spectra for an as-prepared sample when exposed to blue light illumination. As it can be observed, the band peaking around 1.9 eV decreases during the light exposure, whereas a band peaking around 2.12 eV rises. Note that all the spectra intersect in a point at 1.93 eV, i.e., the emission remains unchanged at this energy throughout the experiment. This kind of points, named isostilbic points,12 are commonly met when PL spectra are taken in a solution in which a chemical reaction involving only two emitting components, a reactant and a product, is in progress; or in a solution in which the two emitting components are in equilibrium and their relative proportions are controlled by the concentration of some other component. The nature of the isostilbic point is similar to its

FIG. 1. Evolution of the PL spectra during illumination with 400 nm light. Each of the spectra corresponds to an illumination time plotted in Fig. 2. The arrows indicate the sense of the evolution.

equivalent in absorption spectroscopy, named isosbestic point.12 In order to study the behavior of the PL spectra during photon irradiation we apply principal factor analysis 共PFA兲 to the whole set of PL spectra. The PFA method is well described in the literature, so we will use the common nomenclature for this technique without going into specific details.13 We will mention, however, that the method is very reliable to determine the number and the characteristics of the independent components giving rise to the evolution of a series of spectra involving a linear behavior. The validity of this method follows from the assumption that the measured spectrum of a sample, which is evolving in time, is a unique linear combination of the spectra resulting from n fundamental emission modes, each one arising from a different physical species 共or physical environment兲 which does not change during the evolution. For the kth measured spectrum, E k (ប ␻ i ) 共emission intensity at energy ប ␻ i ) we have n

E k共 ប ␻ i 兲 ⫽

兺

j⫽1

c k j f j共 ប ␻ i 兲,

共1兲

where f j (ប ␻ i ) is the unknown spectrum of the fundamental emission mode of species j at energy ប ␻ i , c k j is its concentration at the kth sample measurement, and n denotes the number of fundamental spectra. Defining ‘‘data’’ and ‘‘fundamental’’ matrices S and F by Ski ⫽E k (ប ␻ i ) and F ji ⫽ f j (ប ␻ i ), respectively, we note that Eq. 共1兲 can be viewed as one representation of S in a vector space. To be more specific, for l ប ␻ i ’s and t measured spectra during the evolution, there are an infinite number of t⫻n matrices K and n⫻l matrices ␴ such that S⫽K␴ .

共2兲

By hypothesis, the only physically meaningful such decomposition of S is that in Eq. 共1兲, which remain to be determined. The notion of an abstract vector space implies the existence of a set of basis vectors ␴ I forming the columns of matrix ␴ in Eq. 共2兲. One such set is furnished by the eigen-

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PHOTO-OXIDATION EFFECTS IN POROUS SILICON . . .

TABLE I. Results from factor analysis 共only the 5 first eigenvalues are reported here兲. Factor no.

Eigenvalue

IND function

RE

Eigenvalue error

1 2 3 4 5

80.8700 3.19530 2.43⫻10⫺2 1.40⫻10⫺3 6⫻10⫺4

1.8101⫻10⫺4 2.0753⫻10⫺5 9.8014⫻10⫺6 1.0094⫻10⫺5 1.1585⫻10⫺5

3.0590⫻10⫺2 2.9884⫻10⫺3 1.1860⫻10⫺3 1.0094⫻10⫺3 9.3835⫻10⫺4

1.0975⫻10⫺2 1.1717⫻10⫺2 1.1410⫻10⫺2 1.1405⫻10⫺2 1.2333⫻10⫺2

vectors Q i of the Hermitian t⫻t covariance matrix Z⬅STS (ST is the transpose matrix of S兲, such that14 ZQ i ⫽␭ i Q i .

共3兲

Note that, from Eq. 共1兲, there would be exactly n nonzero eigenvalues ␭ if there were no experimental errors. The presence of errors introduces unphysical additional eigenvalues. The difference between the ‘‘pure’’ data and the raw experimental data is evaluated through the experimental real error 共RE兲.13 This parameter depends on the number of eigenvectors considered to reproduce the experimental data. The right value of RE is the one obtained considering only eigenvectors which are not related with experimental noise. In the present case, the right RE is evaluated from a set of spectra obtained after irradiating the sample until no evolution is detected within the typical measurement times. It is expected that the spectra obtained under such conditions are identical within the experimental error. The RE calculated assuming only one independent factor for this set of spectra is 3⫻10⫺3 . This value should be equal to the RE corresponding to the whole set of evolving spectra. Another criterion to determine the actual number of significant factors is the use of the factor indicator function 共IND function兲, empirically defined by Malinowski,13 which should have a minimum for the right number of factors. The main results of the principal components analysis are summarized in Table I. Although the IND function has a minimum for three factors, it is known that, when the experimental error is not uniformly distributed, this criterion overestimates the number of significant factors. In fact, since the RE is equal or larger than 3⫻10⫺3 only for the first two factors, this criterion indicates that only two independent factors are present. Moreover, only the two main eigenvalues of the covariance matrix are significantly larger than its error. The ␹ 2 function criterion also leads to the existence of only two independent components. In order to obtain the set of spectra with physical significance, we perform a transformation taking into account the nature of the process, called target transformation.13 The main hypothesis involved in this transformation is to take the first spectrum as a pure component, which is a very reasonable assumption. As a result of this procedure, we also obtain the temporal evolution of the concentrations of the emitting components. The concentrations of the principal components as a function of the cumulated illumination time are shown in Fig. 2共a兲. Note that the concentration of both components can be

well fitted with exponential functions, a behavior that points towards a first-order kinetics. The spectra of these components are shown in Fig. 2共b兲. As expected, the emission yield is the same for the two components at the energy of the isostilbic point. Each one of the experimental spectra can be reproduced as the sum of these two independent components weighted by the corresponding concentrations. Therefore, the factor analysis 共FA兲 results undoubtedly prove the existence of two emitting components kinetically correlated, a result already suggested by the existence of an isostilbic point. Moreover, the FA gives the spectrum of each emitting species and the evolution of its concentrations. If we accept a pure quantum confinement model, the origin of the two PL components can be attributed to the emission from quantum wires of different sizes. As a first step we

FIG. 2. Results from factor analysis applied to the set of spectra of Fig. 1. 共a兲 Evolution of the concentrations. The solid lines result from the fitting with an exponential decay for the first component, and with an exponential growth for the second one. 共b兲 Principal components spectra. The arrow indicates the crossing point which generates the isostilbic point 共IP兲 of the set of spectra.

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model the luminescence spectra following the procedure used in Ref. 15. For this purpose we consider square silicon columns, with an elliptical conduction band E c (k) characterized by two effective electronic masses, m t and m l , and a spherical valence band E v (k) characterized by a heavy-hole effective mass m h . The confinement gap is derived assuming an infinitely deep confining potential for the wires. Using the Van Roosbroeck–Shockley relation16 and a proper expression for the absorption coefficient, the spontaneous recombination rate R ph is evaluated for a single wire of width L:15 R ph 共 ប ␻ ,L 兲 ⫽B

ប␻ 关 ប ␻ ex ⫺E g 共 L 兲兴 ⫺1/2关 ប ␻ ⫺E g 共 L 兲兴 ⫺1/2 L2

再

⫻exp ⫺

冎

b ប ␻ ⫺E g 共 L 兲 c , kT

共4兲

were B is a constant, ប ␻ ex and ប␻ are the excitation and the emission energies, respectively, and E g (L) is the confinement gap. The PL line shape is obtained by integrating Eq. 共4兲 over all the wire widths contributing to the emission, weighted by the probability distribution for the widths of the wires. A Gaussian distribution P ␴ ,L 0 (L), centered at an average width L 0 and with a standard deviation ␴, is assumed at this stage. By using a computer code we fit each of the two principal components of Fig. 2共b兲, with L 0 and ␴ as adjustable parameters. From the fit of the first component we obtain a mean wire width L 01⫽2.77 nm and a standard deviation ␴ 1 ⫽0.24 nm, and L 02⫽2.42 nm, ␴ 2 ⫽0.12 nm for the second component. The values that we have obtained for L 0 are within the range of sizes typically measured from electron microscopy.17 Different models based on quantum confinement15,18,19 give values of L 0 and ␴ similar to the ones that we have obtained. When PS is illuminated with photons having enough energy, a photo-oxidation effect takes place. This effect has been detected by ir spectroscopy on samples prepared under identical conditions and irradiated using the same photon flux and energy as in the PL evolution experiment. Figure 3共a兲 shows the evolution of the ir spectra during the irradiation. It can be observed that a broad band located at ⬃1100 cm⫺1 evolves during the irradiation, which can be assigned to stretching modes of Si– O– Si bridges. The broad band growing at ⬃850 cm⫺1 has no clear assignation,20,21 although it is known to be related to Si– O bonds, eventually associated with a H neighbor. As it can be observed in Fig. 3共b兲, oxidation also takes place in darkness, but in a much lower scale. In both cases the oxidation of PS samples becomes detectable due to the existence of structures with large surface area. It is known that the presence of charged carriers is needed for oxidation to proceed.22 In the case of oxidation in darkness, carriers are only generated through a thermal process. The density of carriers generated in this way becomes significant only in regions where the scale of the microstructure is large enough to preclude quantum confinement enlargement of the gap. When the samples are irradiated with high energy photons, electron-hole pairs are also created in smaller structures, like quantum wires, in spite of the enlarged gap. Therefore, dark oxidation takes

FIG. 3. Infrared spectra after different air exposure times: 共a兲 under illumination, 共b兲 in darkness. The spectra for 96 min and 24 h were vertically displaced for clarity.

place only in large scale microstructure regions, and not in quantum wires, whereas light-assisted oxidation also occurs in quantum wires. Since quantum wire oxidation is required for the PL spectra to evolve, the preceding argument explains why ir spectra evolve in darkness but PL spectra do not, while both spectra evolve under illumination. The concurrence of these effects strongly suggests that PL evolution is related to a photo-oxidation process governed by quantum size effects. We propose a possible model, based on quantum confinement effects, to explain the evolution of the luminescence spectra under blue light illumination. In this model we associate photoinduced changes in luminescence to quantum wire photo-oxidation, which leads to a reduction in the size of the quantum wires. No polarization effects are taken into account. When oxidation proceeds, there will be gap fluctuations along the wires due to different confinement widths. In fact, the oxide layers behave as infinite energy barriers and the effective size of the oxidized wires will be smaller. If the scale of the longitudinal fluctuations is small, there will be an average confinement width and the emission peak will shift in a continuous way towards higher energies. However, if the scale of the fluctuations is large compared to the effective Bohr radius, the system will behave as the superposition of at least two systems of quantum wires, with different confinement widths. As we only detect two peaks in the PL spectra, and taking into account the differences between fitted widths

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PHOTO-OXIDATION EFFECTS IN POROUS SILICON . . .

of the two principal components, differ in around one lattice parameter, we assume that only a monolayer of oxide is formed. The relative height of the peaks will change according to the proportion of wires with different widths. This behavior will take place if the first stages of oxidation proceed with nucleation, forming a limited number of monolayer islands over the wires. If nucleation is large, the emission from the island regions will be intense enough to be detected when the mean size of the islands is relatively large, so it is reasonable to consider that only two main widths of quantum wires differing in a monolayer will be present. Based on our model we perform a computer simulation of the process. The oxidation rate of the wires is assumed to be proportional to the density of electrons in excess in the conduction band, ⌬n. This density is related to the absorption coefficient as15 ⌬n⫽ 共 1⫺R 兲 ␣ 共 ប ␻ ex ,L 兲

Ie ␶ L 2, ប ␻ ex

共5兲

where R is the reflectivity of the sample, ␶ is the lifetime of the carriers, and ␣ (ប ␻ e ,L) is the absorption coefficient of quantum wires of width L, for a given excitation photon energy. As indicated in Ref. 15, the absorption coefficient depends on L as

␣ 共 ប ␻ ex ,L 兲 ⬀

1 关 ប ␻ ex ⫺E g 共 L 兲兴 ⫺1/2. L2

共6兲

Therefore, the oxidation rate is W 共 L 兲 ⬀ 关 ប ␻ ex ⫺E g 共 L 兲兴 ⫺1/2,

共7兲

and the surface area S no (L) of nonoxidized quantum wires with diameter L evolves as

⳵ S no ⫽⫺W 共 L 兲 S no , ⳵t

共8兲

S no 共 L,t 兲 ⫽S 0 exp关 ⫺W 共 L 兲 t 兴 ,

共9兲

where S 0 is the total surface area before oxidation of wires having width L. Each time a wire of width L oxidizes a new wire having a width L⫺a appears. Therefore, as the oxidation proceeds the distribution of wire widths evolves as P 共 L,t 兲 ⫽ P ␴ ,L 0 共 L 兲 exp关 ⫺W 共 L 兲 t 兴 ⫹ P ␴ , 共 L 0 ⫺a 兲共 L 兲兵 1⫺exp关 ⫺W 共 L 兲 t 兴其 ,

共10兲

where P ␴ ,(L 0 ⫺a) is a Gaussian centered at (L 0 ⫺a) with standard deviation ␴. A first-order kinetics should be expected for the evolution of the PL spectra provided that the dependence of W on L is not very strong. The overall recombination rate is obtained by using the above time-dependent distribution of wire widths in the following expression: dW ␴ ,L 0 共 ប ␻ 兲 ⫽

冋冕

⬁

L 0共 ␻ 兲

册

P 共 L,t 兲 ប ␻ R ph 共 ប ␻ ,L 兲 dL d 共 ប ␻ 兲 . 共11兲

FIG. 4. Simulated PL spectra for different light-exposure times. The lineshape results from the model of Ref. 15, while the evolution is a consequence of the time dependence of the distribution of wire sizes predicted by the photo-oxidation model described in this work.

The emission spectra simulated by using the above presented model is shown in Fig. 4. The parameters for the initial Gaussian distribution function P ␴ ,L 0 (L) were taken from the fit of the first component shown in Fig. 2共b兲, i.e., L 0 ⫽2.77 nm and ␴ ⫽0.24 nm. We have also taken a⫽L 01 ⫺L 02⫽0.35 nm. As can be observed, our model reproduces quite well the main characteristics of the measured evolution, including the isostilbic point, even when the parameter ␴ was not allowed to change. Moreover, the evolution of the height of the peaks in Fig. 4 follows the same exponential behavior shown by the concentrations of the principal components of Fig. 2. Therefore, a model based on quantum confinement can reproduce the main experimental behavior. The importance of quantum effects on the photo-oxidation process is also revealed.

IV. CONCLUSIONS

Photoluminescence measurements on porous silicon are reported, which show a singular evolution when the samples are exposed to air under illumination. The initial photoluminescence band, peaking at ⬃1.9 eV, decreases with the exposure time, whereas a new peak at 2.12 eV rises. The whole set of spectra show an isostilbic point at 1.93 eV, a result that has not been reported before. The existence of such an isoemissive point, together with results from factor analysis applied to the whole set of spectra, confirm the existence of only two emitting components, kinetically correlated. The spectra of each one of these components can be adjusted within the frame of a model based on quantum confinement effects. Moreover, the evolution under photo-oxidation of the luminescence spectra can also be explained by a quantum confinement model, assuming layer by layer photooxidation, with significant nucleation, of the quantum wires. The fact that oxidation takes place in darkness, but photolu-

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minescence does not evolve without illumination, emerges naturally from this model. The preceding results, although cannot be considered as a proof for the quantum confinement model, give strong support to it, suggesting that size effects play an important role not only in the photoluminescence but also in the photo-oxidation mechanisms of porous silicon.

1

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ACKNOWLEDGMENTS

This work was partially supported with grants of ANPCyT 共PICT 12-06950兲 and CAI⫹D 2000-84-6-1. J.A.S. acknowledges support from the Alexander von Humboldt Foundation and the Fundacioń Antorchas.

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