- Email: [email protected]
Optical investigation of porous silicon membranes
LUMINESCENCE
Journal of Luminescence 57 (1993) 51—55
JOURNALOF
Optical investigation of porous silicon membranes E. Massone, A. Foucaran and J. Camassel Groupe d’Etude des Semiconducteurs, Universitè de Montpellier 2 and CNRS, 34095 Monlpe/lier Cedex 5, France
We present a systematic investigation of the optical properties oftwo different series ofp + - and n + -porous silicon membranes. Collecting first PL on both sides of the membranes, we discuss the samples homogeneity. Next, we collect transmission spectra and, on 70 sm thick samples, resolve small absorption features at about 2.3 eV. This indicates, for these series of samples, a Stokes-shift ofthe PL spectra of about 0.6 eV and corresponds with about 30% dispersion in the width of the corresponding confining systems.
1. Introduction Since the pioneering work of Canham [1] and Lehman and Gosële [2], porous silicon (PS) layers have been widely investigated for possible applications in silicon-compatible optoelectronic circuits. This is because light-emitting diodes (LEDs), where PS would act as the active part of the device, would be fully compatible with the standard microelectronic technology and are highly desirable. As a consequence, many investigations of the electroluminescence of PS layers have been done and a first prototype PS-LED has been recently reported [3]. It was made of four successive layers of different materials stacked in the following way. First was a monocrystalline p-type silicon substrate, second an active film of PS, third a microcrystalline n-type SiC layer and finally, an ITO semi-transparent electrode. The efficiency was poor and the light emission was only observed in the forward bias under 620 mA (20 V). Obviously, very much work has to be done in order to achieve a more efficient recombination of the electron—hole pairs in the forthcoming years.
First, one has to decide whether the recombination band is intrinsic or not. Toward this end, a detailed understanding of the optical properties of PS has to be reached. Up to now, quantum size effects are the most popular belief hut quantum size effects, for “standard” semiconductor systems (like GaAs/GaAIA5 or InGaAs/InP), always show a finite Stokes-shift of the PL line with respect to the quantized absorption features. This comes directly from the finite roughness of the quantum wells [4] and similar effects should be found for PS. In this work, we investigate the near-band-edge absorption spectrum of two different series of PS membranes. On our best (thinner) samples, we resolve a small absorption feature at about 2.3 eV. Comparing with the energetic position of the maxima of the PL lines, for the same series of samples, we find a typical value for the Stokes-shift of about 0.6 eV. Discussing these results in terms of a statistic distribution of the confining thicknesses, we show that they correspond with a typical dispersion of about 30%.
2. Anodization procedure Correspondence to: J. Camassel, cc074-GES, UM2-Sciences Ct Techniques, 34095 Montpellier Cedex 5, France. 0022-2313/93/$06.00 © 1993 SSDI 0022-2313(93) E0077-B
—
All membranes investigated in this work have been prepared by electrochemical anodization of
Elsevier Science Publishers B.V. All rights reserved
52
E. Massone ci a!.
/
Optica/ investigation of porous silicon membranes
2cm2 pieces of silicon, cleaved from {1 00}oriented 4 in. wafers of + and ~ + -type commercially available material. The corresponding resistivities were in the range 0.05—0.08 Qcm for ~ + and 0.01—0.001 ~1cm for n~samples. Ohmic contacts were provided by ion implantation, thermal annealing and evaporation of either an aluminium film for the p + substrates or a gold film for the n + ones. Starting from commercial wafers (with an initial thickness of 270 pm), we cleaved square pieces of 1.5 x 1.5 cm2. They were used to grow different (final) thicknesses of membranes, in the range 70—270 pm, by using an in situ two steps procedure. First, an initial (let say 200 pm thick) layer of PS was anodized and etched off in a NaOH solution. Next, a second (final) anodization was done. In this way, reasonable compromises could be achieved between membrane thickness and mechanical resistance over an effective diameter of 1 cm. All pttype samples were anodized in day light, The n ~-type anodizations were carried out under different illumination conditions (with a 100 W tungsten lamp, an unfocalised He—Ne laser beam and, finally, in the dark). Excepting this point, the anodization conditions were identical for all samples. We used a (vertical) teflon single cell where the wafers were mounted at bottom. Only 0.8 cm 2 of the front surface was exposed to the electrolyte. A current density of 20 mA cm2 was used, with an electrolyte solution made of a one-to-one by volume mixture of 98% ethanol and 40% HF. Because of our in situ two-step procedure, the gravimetric porosity was difficult to control for the thinner membranes. It was then determined from additional samples, anodized for the same time under similar conditions. In this case, assuming homogeneous profiles, the resulting (gravimetnc) porosities were in the ranges of —~ 40% for ~ and 55% for n~-type samples. These values appear somewhat suspicious. Indeed no PL should be found for such low porosity p + or + -type material and, with this respect, our ~
3. Samples homogeneity
-
-
gravimetric data should mainly be considered as qualitative,
Because we wanted to compare the energetic positions of the interband absorption edge with the maxima of the PL emission bands, we first checked for the samples homogeneity. This was simply done by using the 4880 A line of an Ar~ion laser to collect PL spectra on both sides of the membranes. In the following, we systematically call “front” side the polished surface of the silicon wafer, where the anodization was started (silicon to electrolyte interface), and “back” side the rough (back) surface of the sample, where the ohmic contacts were made. In Fig. 1, we display two different series of spectra, for two different samples in the case where the homogeneity of PL is good. Both samples were p~-type but with different thicknesses (70 and 120 pm, respectively). Every time, the PL signal had the usual width (—~0.45 eV) but, due to the poorer surface preparation, the PL spectra collected on the back sides of the samples were systematically weaker. As a matter of fact, the ratio of front side to back side intensities can reach more than one order of magnitude. Actually, it is not clear how the roughness of the back face can simply explain such
_______________________________________ —F ,~
-
~
-
fl±tyfle
‘
ront Side (xl) Back Side
e70~tm
~
.7
(x 10)
•~
~
(a)
•..:~ —
.~
——
P+type 120
Front Side (xl) Back Side
—
(x 40) -~ .~
~
(b 5000
) 6000
7000
8000
9000
Wavelength (A) Fig. I. Comparison of PL spectra collected on both sides of the homogeneous membranes.
E. Massone et a!.
-
-
Optical investigation of porous silicon membranes
53
than the regions near the substrate, we find just the opposite. This behaviour is not understood but
p+type
FrontSide
—
/
BackS
cannot be explained by the usual effect of a chemical dissolution of silicon in HF, which would occur in addition anodic reaction [6] when the etch time exceedstoathe critical value.
~0pm
(a)
Finally, we show in Fig. 2(b), the typical behaviour observed on a series of three n + membranes.
n+type —
Front
Even if they were grown under different light or dark conditions, every time no PL feature could be recorded on the back side of the samples. As a consequence, no valuable comparison between the PL and absorption spectra has been attempted.
a
x 5000
6000
7000
8000
9000
Wavelength (A) Fig. 2. Same as Fig. I, but for samples in which the homogeneity is poor.
a large difference. More investigations, using a series of wafers initially polished on both sides, has to be done. The main point in Fig. 1 is the very good agreement observed between the two spectra collected on the front and back sides. Whatever is the true (real) porosity of the sample, this supports the basic assumption of a constant value through the bulk of the membranes and, in the next part, will support a quantitative analysis of the energy difference which separates the weak absorption edge from the strong PL maximum. It should be noticed that not all membranes exhibit the same basic behaviour. For instance, we show in Fig. 2 two counter examples. The solid line in Fig. 2(a) corresponds with the PL spectrum collected on the front side of a 70 pm p~membrane. While it exhibits a broad peak centered at 7300 A, the luminescence signal collected on the back side (broken line) is shifted to shorter wavelengths by 300 A. Such in-depth inhomogeneity has been already reported [5] for p-type substrates etched off for more than 1 h. However, the observations of Ref. 5 are not fully consistent with our data. While the authors of Ref. 5 find that the regions near the surface exhibit a shorter wavelength luminescence
4. Absorption features For completeness, we display in Figs. 3 and 4 the full series of absorption spectra collected for the different ~ and nt-type PS membranes. The most significant features are as follows. (i) Depending on the membrane thickness (p + type samples), different ranges of absorption coefficients can be found. While the thinner samples (70 and 120 pm) agree well with a consistent value of the absorption coefficient of the order of 550 cm at about 2.5 eV, the thicker one (270 pm) would give results about four times lower. This confirms -
-
500
p+type E 400 .i~ ~
-
\
300
n200
. -.
—
—
d7Ojtm d=70~tm
—
\.~
0
~
~
~~
1d=27O~m
0 5000
‘.
6000
7000
8000
9000
Wavelength (A) Fig. 3. Comparison of absorption spectra collected on the series of p + membranes investigated in this work.
54
E. Massone ci a!.
50
Optical investigation of porous silicon membranes
E___
light
~
5000
/
6000
7000
8000
900(1
Wavelength (A) Fig. 4. Same as Fig. 3, but now for n~material.
200 100 0
13
~p+
~
1.5
1.7
1.9
2.1
type 2.3
2.5
Energy (eV)
that the membranes are certainly not homogeneous above a critical thickness. The critical thickness should be intermediate between 120 and 270 pm but, up to now, no attempt has been made to determine the correct value. Moreover, it should be a function of doping and anodization conditions. (ii) Comparing p + and n + -PS membranes with identical thickness (270 pm) we find that, in both cases, the same overall absorption intensity is found (c 150 cm 1 at —~ 2.5 eV). In the case of the n + material, however, a clear additional shoulder develops around 2 eV. While being only weakly sensitive to the preparation conditions, we believe that it comes from even more significant inhomogeneities in the n + -type material. -
5. Discussion In Fig. 5, comparing the PL and absorption spectra collected for our best (homogeneous) samples (see Fig. 1), we find the following points: (i) There is a wide range of energetic overlap between the PL lines (which extend from 1.4 to 2.3 eV) and the near-band-edge absorption tails, This results in no obvious (easily identified) Stokesshift. This is a first strong discrepancy with the case of more standard low-dimensional systems [4]. (ii) Looking more in detail to the absorption spectra displayed in Fig. 3, we identify a broad shoulder, around 5500 A, which resolves consistently
Fig. 5. Comparison of PL and absorption spectra collected on the same samples. These data evidence a small absorption edge at 2.3 eV in the case of the thinner membrane with a Stokes-shift of about 0.65 eV of the maximum of PL.
on the two samples with 70 pm thickness. This could correlate with the lower interband transition. (iii) To support this assumption, we refer to the spectroscopic ellipsometry data reported, in the 1.5—5 eV range, by Ferrieu et al. [7]. The interesting point is that, for ~ + -PS layers of 31% porosity, they demonstrated a clear damping of interference fringes which were complete (at room temperature) above 2.5 eV. This confirms on a completely independent way that, in similar material, there is indeed a finite absorption edge located slightly below 2.5 eV (even if the corresponding energy position could not be resolved in the work of Ref. [7]). In this work, we propose to associate the lowest (fundamental) interband transition (for our 70 pm thick pt-PS membrane) with the small structure experimentally found around 2.3 eV. Because we cannot resolve any corresponding phonon structure, we propose that it should be associated with a zero-phonon transition. Finally, because the maximum of the PL line resolved on the same sample was around 1.65 eV (7500 A), we find a Stokes shift which should be of the order of 0.6 eV. Finally, coming back to the standard views of confinement energies and Stokes shift in quantum wells and quantum wires [4,8—10],we can attempt
E. Massone et a!.
/ Optical
investigation of porous silicon membranes
to analyse these data in more detail. In the simplest approximation, we write the confinement energy E~: E~=
K
—
—.
Using E~= 1.05 eV, S dL
References [1] L.T. Canham, AppI. Phys. Lett. 57 (1990) 1046. [2] V. Lehmann and V. Gosële, AppI. Phys. Lett. 58 (1991) 856.
—,
where K depends only on the geometry of the confining system; n has been shown to vary from 1.5 [9] to 2 [8,10] and L is the quantifying dimension. Assuming that the Stokes shift S between absorption and luminescence comes only from stastic fluctuations in the dimensions of the confining systems, we get S nE~dL =
55
=
0.65 eV, n
=
2, we get
30%,
which means that the geometry of our PS material is still far from perfect control.
[3] T. Futagi, T. Matsumoto, M. Katsuno, Y. Ohta, H. Mimura and K. Kitamura, Jap. J. AppI. Phys. 31(1992) L616. [4] F. Young, M. Wilkinson, E.J. Austin and K.P. Donnel, Phys, Rev. Lett. 70 (1993) 323. [5] MA. Tiscler, R.T. Collins, J.H. Stathis and J.C. Tsang, AppI. Phys. Lett. 60 (1990) 639. [6] R. Herino, G. Bomchil, K. Barla, C. Bertrand and J.L. Ginoux, J. Electrochemical Soc. 134 (1987) 1994. [7] F. Ferrieu, A. Halimaoui and D. Bensahel, Solid State Commun. 84 (1992) 293. [8] J. Camassel, E. Massone, S. Lyapin, J. Allegre, P. Vincente, A. Foucaran, A. Raymond and J.L. Robert, in: Proc. 21st ICPS, Beijing, in press. [9] G. Fishman, I Mihalcescu and R. Romestain, unpublished. [10] N.S. Averkiew, V.M. Asnin, A.B. Churilov, 1.1. Markov, N.E. Mokrousov, A. Yu. Silov and V.1. Stepanov, unpublished.
Journal of Luminescence 57 (1993) 51—55
JOURNALOF
Optical investigation of porous silicon membranes E. Massone, A. Foucaran and J. Camassel Groupe d’Etude des Semiconducteurs, Universitè de Montpellier 2 and CNRS, 34095 Monlpe/lier Cedex 5, France
We present a systematic investigation of the optical properties oftwo different series ofp + - and n + -porous silicon membranes. Collecting first PL on both sides of the membranes, we discuss the samples homogeneity. Next, we collect transmission spectra and, on 70 sm thick samples, resolve small absorption features at about 2.3 eV. This indicates, for these series of samples, a Stokes-shift ofthe PL spectra of about 0.6 eV and corresponds with about 30% dispersion in the width of the corresponding confining systems.
1. Introduction Since the pioneering work of Canham [1] and Lehman and Gosële [2], porous silicon (PS) layers have been widely investigated for possible applications in silicon-compatible optoelectronic circuits. This is because light-emitting diodes (LEDs), where PS would act as the active part of the device, would be fully compatible with the standard microelectronic technology and are highly desirable. As a consequence, many investigations of the electroluminescence of PS layers have been done and a first prototype PS-LED has been recently reported [3]. It was made of four successive layers of different materials stacked in the following way. First was a monocrystalline p-type silicon substrate, second an active film of PS, third a microcrystalline n-type SiC layer and finally, an ITO semi-transparent electrode. The efficiency was poor and the light emission was only observed in the forward bias under 620 mA (20 V). Obviously, very much work has to be done in order to achieve a more efficient recombination of the electron—hole pairs in the forthcoming years.
First, one has to decide whether the recombination band is intrinsic or not. Toward this end, a detailed understanding of the optical properties of PS has to be reached. Up to now, quantum size effects are the most popular belief hut quantum size effects, for “standard” semiconductor systems (like GaAs/GaAIA5 or InGaAs/InP), always show a finite Stokes-shift of the PL line with respect to the quantized absorption features. This comes directly from the finite roughness of the quantum wells [4] and similar effects should be found for PS. In this work, we investigate the near-band-edge absorption spectrum of two different series of PS membranes. On our best (thinner) samples, we resolve a small absorption feature at about 2.3 eV. Comparing with the energetic position of the maxima of the PL lines, for the same series of samples, we find a typical value for the Stokes-shift of about 0.6 eV. Discussing these results in terms of a statistic distribution of the confining thicknesses, we show that they correspond with a typical dispersion of about 30%.
2. Anodization procedure Correspondence to: J. Camassel, cc074-GES, UM2-Sciences Ct Techniques, 34095 Montpellier Cedex 5, France. 0022-2313/93/$06.00 © 1993 SSDI 0022-2313(93) E0077-B
—
All membranes investigated in this work have been prepared by electrochemical anodization of
Elsevier Science Publishers B.V. All rights reserved
52
E. Massone ci a!.
/
Optica/ investigation of porous silicon membranes
2cm2 pieces of silicon, cleaved from {1 00}oriented 4 in. wafers of + and ~ + -type commercially available material. The corresponding resistivities were in the range 0.05—0.08 Qcm for ~ + and 0.01—0.001 ~1cm for n~samples. Ohmic contacts were provided by ion implantation, thermal annealing and evaporation of either an aluminium film for the p + substrates or a gold film for the n + ones. Starting from commercial wafers (with an initial thickness of 270 pm), we cleaved square pieces of 1.5 x 1.5 cm2. They were used to grow different (final) thicknesses of membranes, in the range 70—270 pm, by using an in situ two steps procedure. First, an initial (let say 200 pm thick) layer of PS was anodized and etched off in a NaOH solution. Next, a second (final) anodization was done. In this way, reasonable compromises could be achieved between membrane thickness and mechanical resistance over an effective diameter of 1 cm. All pttype samples were anodized in day light, The n ~-type anodizations were carried out under different illumination conditions (with a 100 W tungsten lamp, an unfocalised He—Ne laser beam and, finally, in the dark). Excepting this point, the anodization conditions were identical for all samples. We used a (vertical) teflon single cell where the wafers were mounted at bottom. Only 0.8 cm 2 of the front surface was exposed to the electrolyte. A current density of 20 mA cm2 was used, with an electrolyte solution made of a one-to-one by volume mixture of 98% ethanol and 40% HF. Because of our in situ two-step procedure, the gravimetric porosity was difficult to control for the thinner membranes. It was then determined from additional samples, anodized for the same time under similar conditions. In this case, assuming homogeneous profiles, the resulting (gravimetnc) porosities were in the ranges of —~ 40% for ~ and 55% for n~-type samples. These values appear somewhat suspicious. Indeed no PL should be found for such low porosity p + or + -type material and, with this respect, our ~
3. Samples homogeneity
-
-
gravimetric data should mainly be considered as qualitative,
Because we wanted to compare the energetic positions of the interband absorption edge with the maxima of the PL emission bands, we first checked for the samples homogeneity. This was simply done by using the 4880 A line of an Ar~ion laser to collect PL spectra on both sides of the membranes. In the following, we systematically call “front” side the polished surface of the silicon wafer, where the anodization was started (silicon to electrolyte interface), and “back” side the rough (back) surface of the sample, where the ohmic contacts were made. In Fig. 1, we display two different series of spectra, for two different samples in the case where the homogeneity of PL is good. Both samples were p~-type but with different thicknesses (70 and 120 pm, respectively). Every time, the PL signal had the usual width (—~0.45 eV) but, due to the poorer surface preparation, the PL spectra collected on the back sides of the samples were systematically weaker. As a matter of fact, the ratio of front side to back side intensities can reach more than one order of magnitude. Actually, it is not clear how the roughness of the back face can simply explain such
_______________________________________ —F ,~
-
~
-
fl±tyfle
‘
ront Side (xl) Back Side
e70~tm
~
.7
(x 10)
•~
~
(a)
•..:~ —
.~
——
P+type 120
Front Side (xl) Back Side
—
(x 40) -~ .~
~
(b 5000
) 6000
7000
8000
9000
Wavelength (A) Fig. I. Comparison of PL spectra collected on both sides of the homogeneous membranes.
E. Massone et a!.
-
-
Optical investigation of porous silicon membranes
53
than the regions near the substrate, we find just the opposite. This behaviour is not understood but
p+type
FrontSide
—
/
BackS
cannot be explained by the usual effect of a chemical dissolution of silicon in HF, which would occur in addition anodic reaction [6] when the etch time exceedstoathe critical value.
~0pm
(a)
Finally, we show in Fig. 2(b), the typical behaviour observed on a series of three n + membranes.
n+type —
Front
Even if they were grown under different light or dark conditions, every time no PL feature could be recorded on the back side of the samples. As a consequence, no valuable comparison between the PL and absorption spectra has been attempted.
a
x 5000
6000
7000
8000
9000
Wavelength (A) Fig. 2. Same as Fig. I, but for samples in which the homogeneity is poor.
a large difference. More investigations, using a series of wafers initially polished on both sides, has to be done. The main point in Fig. 1 is the very good agreement observed between the two spectra collected on the front and back sides. Whatever is the true (real) porosity of the sample, this supports the basic assumption of a constant value through the bulk of the membranes and, in the next part, will support a quantitative analysis of the energy difference which separates the weak absorption edge from the strong PL maximum. It should be noticed that not all membranes exhibit the same basic behaviour. For instance, we show in Fig. 2 two counter examples. The solid line in Fig. 2(a) corresponds with the PL spectrum collected on the front side of a 70 pm p~membrane. While it exhibits a broad peak centered at 7300 A, the luminescence signal collected on the back side (broken line) is shifted to shorter wavelengths by 300 A. Such in-depth inhomogeneity has been already reported [5] for p-type substrates etched off for more than 1 h. However, the observations of Ref. 5 are not fully consistent with our data. While the authors of Ref. 5 find that the regions near the surface exhibit a shorter wavelength luminescence
4. Absorption features For completeness, we display in Figs. 3 and 4 the full series of absorption spectra collected for the different ~ and nt-type PS membranes. The most significant features are as follows. (i) Depending on the membrane thickness (p + type samples), different ranges of absorption coefficients can be found. While the thinner samples (70 and 120 pm) agree well with a consistent value of the absorption coefficient of the order of 550 cm at about 2.5 eV, the thicker one (270 pm) would give results about four times lower. This confirms -
-
500
p+type E 400 .i~ ~
-
\
300
n200
. -.
—
—
d7Ojtm d=70~tm
—
\.~
0
~
~
~~
1d=27O~m
0 5000
‘.
6000
7000
8000
9000
Wavelength (A) Fig. 3. Comparison of absorption spectra collected on the series of p + membranes investigated in this work.
54
E. Massone ci a!.
50
Optical investigation of porous silicon membranes
E___
light
~
5000
/
6000
7000
8000
900(1
Wavelength (A) Fig. 4. Same as Fig. 3, but now for n~material.
200 100 0
13
~p+
~
1.5
1.7
1.9
2.1
type 2.3
2.5
Energy (eV)
that the membranes are certainly not homogeneous above a critical thickness. The critical thickness should be intermediate between 120 and 270 pm but, up to now, no attempt has been made to determine the correct value. Moreover, it should be a function of doping and anodization conditions. (ii) Comparing p + and n + -PS membranes with identical thickness (270 pm) we find that, in both cases, the same overall absorption intensity is found (c 150 cm 1 at —~ 2.5 eV). In the case of the n + material, however, a clear additional shoulder develops around 2 eV. While being only weakly sensitive to the preparation conditions, we believe that it comes from even more significant inhomogeneities in the n + -type material. -
5. Discussion In Fig. 5, comparing the PL and absorption spectra collected for our best (homogeneous) samples (see Fig. 1), we find the following points: (i) There is a wide range of energetic overlap between the PL lines (which extend from 1.4 to 2.3 eV) and the near-band-edge absorption tails, This results in no obvious (easily identified) Stokesshift. This is a first strong discrepancy with the case of more standard low-dimensional systems [4]. (ii) Looking more in detail to the absorption spectra displayed in Fig. 3, we identify a broad shoulder, around 5500 A, which resolves consistently
Fig. 5. Comparison of PL and absorption spectra collected on the same samples. These data evidence a small absorption edge at 2.3 eV in the case of the thinner membrane with a Stokes-shift of about 0.65 eV of the maximum of PL.
on the two samples with 70 pm thickness. This could correlate with the lower interband transition. (iii) To support this assumption, we refer to the spectroscopic ellipsometry data reported, in the 1.5—5 eV range, by Ferrieu et al. [7]. The interesting point is that, for ~ + -PS layers of 31% porosity, they demonstrated a clear damping of interference fringes which were complete (at room temperature) above 2.5 eV. This confirms on a completely independent way that, in similar material, there is indeed a finite absorption edge located slightly below 2.5 eV (even if the corresponding energy position could not be resolved in the work of Ref. [7]). In this work, we propose to associate the lowest (fundamental) interband transition (for our 70 pm thick pt-PS membrane) with the small structure experimentally found around 2.3 eV. Because we cannot resolve any corresponding phonon structure, we propose that it should be associated with a zero-phonon transition. Finally, because the maximum of the PL line resolved on the same sample was around 1.65 eV (7500 A), we find a Stokes shift which should be of the order of 0.6 eV. Finally, coming back to the standard views of confinement energies and Stokes shift in quantum wells and quantum wires [4,8—10],we can attempt
E. Massone et a!.
/ Optical
investigation of porous silicon membranes
to analyse these data in more detail. In the simplest approximation, we write the confinement energy E~: E~=
K
—
—.
Using E~= 1.05 eV, S dL
References [1] L.T. Canham, AppI. Phys. Lett. 57 (1990) 1046. [2] V. Lehmann and V. Gosële, AppI. Phys. Lett. 58 (1991) 856.
—,
where K depends only on the geometry of the confining system; n has been shown to vary from 1.5 [9] to 2 [8,10] and L is the quantifying dimension. Assuming that the Stokes shift S between absorption and luminescence comes only from stastic fluctuations in the dimensions of the confining systems, we get S nE~dL =
55
=
0.65 eV, n
=
2, we get
30%,
which means that the geometry of our PS material is still far from perfect control.
[3] T. Futagi, T. Matsumoto, M. Katsuno, Y. Ohta, H. Mimura and K. Kitamura, Jap. J. AppI. Phys. 31(1992) L616. [4] F. Young, M. Wilkinson, E.J. Austin and K.P. Donnel, Phys, Rev. Lett. 70 (1993) 323. [5] MA. Tiscler, R.T. Collins, J.H. Stathis and J.C. Tsang, AppI. Phys. Lett. 60 (1990) 639. [6] R. Herino, G. Bomchil, K. Barla, C. Bertrand and J.L. Ginoux, J. Electrochemical Soc. 134 (1987) 1994. [7] F. Ferrieu, A. Halimaoui and D. Bensahel, Solid State Commun. 84 (1992) 293. [8] J. Camassel, E. Massone, S. Lyapin, J. Allegre, P. Vincente, A. Foucaran, A. Raymond and J.L. Robert, in: Proc. 21st ICPS, Beijing, in press. [9] G. Fishman, I Mihalcescu and R. Romestain, unpublished. [10] N.S. Averkiew, V.M. Asnin, A.B. Churilov, 1.1. Markov, N.E. Mokrousov, A. Yu. Silov and V.1. Stepanov, unpublished.