Voltage-tunable photo- and electroluminescence of porous silicon

.__ __ B

CBS ELSEVIER

Voltage-tunable

JOURNAL

OF

LUMINESCENCE Journal

of Luminescence

70 (1996) 3 10-3 19

photo- and electroluminescence A. B&y*,

of porous silicon

J.C. Vial

Laboratoire de Spectronktrie Physique, Universitd Joseph Fourier de Grenoble and CNRS(UMR SSSS), BP 87, 140, avenue de la Physique, Britiment E45, Domaine Universitaire, 38402-Saint Martin d’H&es Cedex. France

Abstract Experimental results showing two electrically induced phenomena, namely the voltage-tunable electroluminescence (VTEL) and the voltage-induced quenching of porous silicon photoluminescence (QPL) are given. In both cases, a spectral shift as large as 300nm can be recorded for an external bias variation of only 0.5 V. This spectral shift is characterised by a blue-shift of the whole EL line in the case of the VTEL whereas it results from a progressive and selective quenching starting by the low-energy part of the luminescence line in the case of the QPL experiments. The origin of this spectral shift is discussed in relation with an electrically induced selective carrier injection into the silicon nanocrystallites accompanied with an enhancement of the non-radiative recombination taking place by an Auger relaxation process. Finally, it is shown that a partial oxidation of the porous silicon layer leads to a complete loss of the selectivity of these two phenomena. This result is qualitatively discussed by considering the voltage drop distribution between the substrate and the silicon nanocrystallites. The voltage drops are modified by the growth of the oxide layer on the nanocrystallite surface leading to a modification of the energy barriers at the crystallite boundaries. Keywords:

Photoluminescence;

Electroluminescence;

Porous

1. Introduction Porous silicon is a slightly disordered system compared for example to amorphous silicon, it is still monocrystalline at a nanometer scale and ordered at long distance. Nevertheless, a disorder is present in the crystallite size distribution, in the crystallite interconnections and in the surface passivation. These different kinds of disorder have different consequences on the luminescent properties of the material. The size distribution for example induces a confinement energy distribution and consequently a broadening of the optical transition. The disorder in crystallite interconnec* Corresponding

author.

0022-2313/96/$15.00 c 1996 Elsevier Science B.V. All rights reserved PII SOO22-23 13(96)00064-6

silicon; Auger effect

tions can induce a distribution of voltage drops within the porous layer when an external voltage is applied to the porous layer while inhomogeneity in passivation will induce a distribution of non-radiative recombination rates and consequently non-exponential luminescence decay shapes of the fluorescence. Since, the first experimental results concerning the intense visible photoluminescence [l], evidences for the inhomogeneous nature of the luminescence spectrum including the well-known blue line-shift observed upon increasing porosity and the photoluminescence decay time dependence on the wavelength of detection [2] have been shown. Recently, it has also been shown that a selective laser excitation within the inhomogeneous profile gives rise to a tunable and narrowed

A. Bsiesy, J.C. Vial J Journal of Luminescence

emission [3]: it is an illustration of the well-known (at least for insulators) “fluorescence narrowing” (FLN) phenomenon. The aim of this paper is to show that the new and spectacular effects consisting of a selective voltage-induced PL quenching as well as the observation of a voltage-tunable electroluminescence can be seen as an illustration of a selective electro-excitation of the inhomogeneously broadened optical transition. In addition, we will show that a unique model, which can account for most of the experimental observations, is related to the saturation of the optical transition due to the carrier accumulation in quantum crystallites leading to a reduction of the absorption coefficient or to a strong enhancement of the non-radiative Auger recombination rates. Finally, spectral narrowing being affected by slight modifications of the material (partial oxidation for example), we propose to take into account a distribution of voltage drops within the porous layer and thereby explain the behaviour of a large variety of porous silicon.

2. Experimental N-type porous silicon layers are formed by anodisation of low-doped (8 x 1Ol4 cme3) monocrystalline (100) silicon substrate in an HF-electrolyte. The electrolyte is composed of 2 volumes of DI water, 5 volumes of ethanol and 3 volumes of HF 50% (wt%). The anodisation is performed under illumination with a tungsten lamp. The light intensity, the current density and the anodisation time are 40 m W/cm2, 5 mA/cm2 and 30 s respectively. The resulting layer is 0.1 pm thick (measured with a profilometer) with a porosity of about 80%. In these conditions, no macroporous structure is obtained. The photoluminescence is excited using the blue line (A = 458 nm) of an Argon laser. The porous layer is cathodically-polarised in 1M sulphuric acid (H2SO4) aqueous solution. A saturated calome1 electrode (SCE) is used as a reference potential. In order to generate an electroluminescence signal, the ammonium persulphate ((NH,),S,O,) can be added to the solution. It will be shown that the reduction of the persulphate ion (S20i2), taking place on the cathodically biased porous layer, provides very energetic holes [4] which, when injected

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in the porous layer skeleton, can recombine radiatively with the electrons that the material may provide. A visibile electroluminescence signal is then generated and detected by using a Princeton Optical Multichannel Analyzer allowing the recording of a whole spectrum in less than 0.1 s.

3. Results Fig. 1 shows the PL spectral evolution recorded as a function of the cathodic bias. From the rest potential to a polarisation of - 1 V no modification is observed. Upon increasing the cathodic potential, a strong and progressive decrease of the PL intensity is observed leading to a complete quenching of the emitted light at - 1.5 V. This quenching is accompanied by a blue shift of the PL peak wavelength. It can be seen that this blue shift is due to the fact that the red part of the spectrum (low luminescence energy) is quenched first. Consequently, the increasing polarisation leads to the narrowing of the line width in such a way that it is possible to observe a clear green luminescence once the red-orange part of the spectrum has been quenched. This electrically induced selective PL quenching is more clearly evidenced on the left part of Fig. 2 where the normalised PL intensity, recorded

?

d

2 ,”

‘G

E

E 2 500

600

700

Wavelength

800

3

(run)

Fig. 1. PL spectral evolution under cathodic polarisation. (a) From rest potential to - 1 V, (b) - 1.05 V, (c) - 1.1 V, (d) - 1.15 V and (e) - 1.2 V.

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qf Luminescence

70 (19%) 31 O&3I9

.t3

Potential (VISCE)

Potential (Vl’at-band)

Fig. 2. Right part: PL intensity as a function of the applied voltage (SCE) for various luminescence 1.77, 1.68, 1.59, 1.51, 1.44 and 1.35 eV). Left part: Numerical simulation, using expression (3) stated a function of the applied voltage (versus the flat band potential) for the same luminescence energies as shift between numerical and experimental spectra for a given PL energy is simply due to different

at different luminescence energies, is represented as a function of the cathodic polarisation. It obviously appears that the low luminescence energy (e.g. 1.3 eV) is totally quenched before any important modification of the high luminescence energy. Furthermore, a cut-off voltage can be assigned to each luminescence energy. Fig. 2 shows then that there is a linear dependence between the applied voltage cut-off and the luminescence energy. In addition, it must be noted that this PL quenching is totally reversible upon the applied bias. During a reverse scan of the cathodic bias, there is an increase of the PL intensity and a red shift of its peak wavelength position leading finally to the initial PL spectrum. This reversibility indicates that the PL quenching is not related to a chemical modification of the material which would lead to an irreversible behaviour. Intense visible electroluminescence can be generated under the same cathodic biasing conditions. However, in order to generate electroluminescence, a radiative recombination must take place between electrons and holes inside the silicon nanocrystallites. In the case of n-type silicon material, electrons are supplied by the cathodically (negatively)-biased substrate whereas holes can be provided by the electrochemical reduction of a strong oxidising

energies (from left to right: 2, 1.88, in the text, of the PL intensity as the experimental ones. The voltage potential reference.

agent in the aqueous electrolyte. The persulphate ion is well-known to be an oxidising agent whose reduction provides energetic hole injection [4]. In these conditions, very efficient and rather stable EL can be observed on n-type porous silicon [S, 61. The electrical current and the i-integrated EL evolution as a function of the cathodic polarisation are carefully analysed in Ref. [7]. The EL spectra show a large reversible shift upon the cathodic bias. Fig. 3 presents several spectra recorded at different voltages during a typical scan. A quite important peak shift, from 880 nm at - 1 V to 610 nm at - 1.6 V, is observed. The EL peak energy is proportional to the external voltage. On the other hand, the FWHM of the EL is found to be narrower (0.25 eV) than that of the PL signal (0.6 eV). In order to evidence the spectral shift, the EL lines of Fig. (3) have been resealed. If these lines are represented with the same scale and compared to the PL line, it appears that the PL line is the envelope of all the emitted EL spectra as shown by Fig. 4a. In the frame of the quantum confinement model, the PL line is attributed to a distribution of the silicon crystallites size which constitute the porous layer. In these conditions, the result of Fig. 4 seems to suggest that, in the case of EL, the

A. Bsiesy, J.C. Vial 1 Journal of Luminescence

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,,,,,,,,,,,,,,,,,“,,,,,,,,,,,,

400

600

Wavelength

DO 0

800

(nm)

I’

Fig. 3. EL spectra obtained in 0.2 M (NH,) zS208 for different cathodic bias: (a) ~ 1 V, (b) - 1.2 V, (c) - 1.5 V, (d) - 1.6 V.

luminescence of only a class of silicon nanocrystallites can be excited whereas the high-energy optical excitation enables the luminescence of all the quantum-size crystallites (PL). To our knowledge, this electrically induced selective excitation of the electroluminescence is a behaviour which is unique in the field of semiconductors at least concerning the tunability large amplitude. Another strong indication of this selective character can be provided by the VTEL evolution as a function of the layer porosity. Figs. 4(a) and 4(b) show the PL of samples with porosities of 80% and 85% respectively. As the porosity increases, the PL line is blue-shifted by about 60 nm. This results from a shift of the silicon nanocrystallite size distribution towards smaller values [l]. The EL spectra obtained during a cathodic scan are also represented in Fig. (4). It clearly appers that for the 85% porosity sample the EL spectra are also enveloped by the PL line. The same relationship between the EL energy maximum and the applied polarisation is also obtained. Finally, one must note that the spectral position of the EL is determined by the increase of the cathodic bias but could be also affected by the simultaneously increasing current. In order to check the dominant factor, variations in the cathodic current, independently of the voltage, were easily obtained by changing the concentration of the electroactive species. Fig. 5 shows that when

50

Wavelength

(nm)

Fig. 4. Comparison of PL and EL spectra for two samples of different porosity. The bold lines refer to the PL spectra. The non-normalised EL spectra are represented using a fine line. For the sake of comparison, the scale of the PL intensity is adjusted to the same peak intensity as that of the EL.

the S20S2 concentration is doubled, the cathodic current is increased, but no difference is obtained in the potential dependence of the EL peak wavelength. As already mentioned, in the case of the cathodic EL of n-type porous layer, electrons are provided by the silicon bulk whereas holes are supplied by the electrolyte. Bright visible EL can also be generated on p-type porous layers under anodic polarisation. In this case, holes are supplied by the silicon bulk and electrons by the oxidation of surface silicon atoms. The energy of the resulting EL is also found to be voltage tunable. The EL energy tunability can thus be investigated under both polarities (anodic and cathodic) and on the same sample provided highly doped n-type porous silicon is used. Oxidation or reduction currents can be,

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it will be shown that the analysis of this experimental result allows to clarify the origin of the voltage-induced tunability of the EL energy.

4. Discussion

Cathodic Potential (V/SCE) Fig. 5. Cathodic current and EL peak wavelength obtained for a (NH4)2S208 concentration of 0.2 M (a,*) and 0.1 M (b,A), as a function of the cathodic bias

2 E

1.8

-B 1.6 5 = 1.4 W -1

ti 1.2

Y

12 2 Polarisation

The origin of the bright and visible porous silicon EL can be easily related to an efficient radiative recombination between holes and electrons injected into the silicon nanocrystallites. However, the voltage-induced tunability of the EL energy is somewhat less straightforward. In order to investigate this tunability, one must keep in mind that the inhomogeneous broadening of the luminescence line represents a distribution of confinement energies, i.e. of nanocrystallite sizes. In these conditions, the EL energy tunability should result from a selective carrier supply of the crystallites vis a vis of their dimensions. Larger silicon nanocrystallites are first charged at a low bias whereas the smaller ones are charged at higher biases. More quantitatively, the carrier confinement effect leads to a rising of the energy levels of the electrons in a given nanocrystallite of a quantity E above the Fermi level of the non-confined n-type silicon as shown by scheme 7(a). The probability of electron injection on a confined electronic level E will then be proportional to the electron concentration: n(E) For confinement high enough to bring the optical transitions is the visible range and at room temperature this concentration n is very low since it follows the FermiiDirac statistic 1

(V/SCE) n(E)

Fig. 6. EL peak energy as a function and anodic (b) polarisation.

of the applied

cathodic

1 + exp (E/kT)

’

(a)

these conditions, obtained for fairly low polarisations. Fig. 6 shows that, under cathodic or anodic polarisation conditions, there is the same proportionality factor between the emitted EL energy and the applied voltage. Moreover, the extrapolation of these two linear regimes to a luminescence energy of 1.1 eV (the silicon band gap energy) leads to a polarisation gap of 1.1 V. In the following section,

in

x

The increasing polarisation leads to an upward shift of the energy bands in the non-confined silicon due to the Fermi level pinning at the silicon bulk surface which is under carrier accumulation conditions. Consequently, an increase AI of the applied voltage induces a modification of the carrier concentration n corresponding to a given confinement energy E: 1 n(E)

z

1 + exp(E - qAT//kT)’

(2)

A. Bsiesy. J.C. Vial/Journal

si

of Luminescence

I

I

crystallite

Si crystallite

si

Si Substrate

Eg=l.lev

315

70 (1996) 310-319

1

Substrate

I Y.

Cathodic

Anodic

Fig. 7. Energy band diagram of a silicon nanocrystallite under polarisation showing the electrons (a) and holes (b) Fermi level shift for a nV of voltage variation. The dotted energy levels correspond to a luminescent crystallite at the silicon band gap energy.

AI/ can be large enough to allow electron injection at E and the EL emission at the energy hv = 2E + Eg is therefore enabled. In this description, the confinement energies of electrons and holes are assumed to be the same. In the anodic EL regime, the symmetric situation occurs. The hole confinement energy being raised by a quantity E above the Fermi level of holes, the hole concentration at E is initially very low. The Fermi level is then shifted downward in the valence band where the concentration of holes p(E) at a given energy E is increased as the anodic bias is raised. One ends up with an expression of p(E) similar to expression (2). This model suggests that the EL tunability is a consequence of the voltage-induced Fermi level shift through the carrier confinement energy distributions which triggers the EL emission either by electrons (cathodic EL) or by holes (anodic EL) injection. This mechanism can be even further confirmed if one assumes that the carrier confinement energy distributions can be extended to the silicon band gap energy. This is performed on Fig. 6 by

extrapolating the linear regimes of the tunable EL energy to a luminescence energy of 1.1 eV. This means that it is assumed that one can find silicon nanocrystallites in the porous skeleton with the appropriate dimensions so as to give rise to an EL emission at the silicon band gap energy. The case of this particular crystallite is represented on scheme 7(a) and 7(b). In order to generate EL from this crystallite in the cathodic range, the external voltage is such that the Fermi level is at the bottom of the conduction band (EL energy = 1.1 eV). This voltage value can be called I/,. Similarly, in the anodic range, EL at 1.1 eV can be obtained at a voltage value 1/2 which corresponds to a Fermi level position at the top of the valence band. Scheme 7 then shows that a gap of 1.1 V between 1/1 and 1/2 should be expected. This is in a very good agreement with the experimental results of Fig. 6. Finally, another rather simple way to interpret the results of Fig. 6 is to consider that a voltage scan which covers the cathodic and the anodic polarisations leads to a continuous shift of the Fermi level from the highest electron confinement

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energy to the highest hole confinement energy through the silicon energy band gap. EL at different energies is then recorded except “during the shift of the Fermi level through the forbidden energy gap”. It is now clear that the VTEL experiments allow to clarify the origin of the porous silicon luminescence energy tunability. As shown by Figs. 1 and 2, this tunability can also be found in the voltageinduced quenching of the porous silicon PL(QPL). There is a close relationship between the QPL and the VTEL results since they both take place in the same polarisation range and are characterised by a similar energy selectivity. Moreover, Fig. 3 shows that the increasing voltage enables high energy electroluminescence but leads also to the quenching of the lower electroluminescence energy in such a way that the EL line width shows only a slight increase upon the spectral shift. The EL and the PL signals thus present a similar quenching character which presumably rises from a common mechanism. The mechanism of this PL and EL quenching is still to be investigated. This investigation is based on the comparison of the simultaneous evolution of the PL and the EL signals. Although this simultaneous recording presents some experimental complications, its use in unavoidable if one seeks confidence in the voltage scale. The comparison of different experiments, generally performed on different sample and/or in different electrolytes, leads to voltage scale variation principally due to a different ohmic voltage drops and to the sample modifications between two successive experiments. The simultaneous evolution of the PL and the EL intensity for a given luminescence wavelength (j_ = 700 nm.), as a function of the applied voltage, is represented by Fig. 8. It shows that the EL sets on and that the PL cuts off at exactly the same “onset” or “cut-of’ voltage (I’,). Since no EL can be observed in the absence of carriers in the silicon nanocrystallites, this result gives a strong experimental evidence that the PL quenching is triggered by the carrier injection into these crystallites. Moreover, the behaviour represented on Fig. (8) is independent of the luminescence energy. However, one can note that the PL cut-off voltage (I’,) is proportional to the PL energy. Just as in the case of

70 (1996) 3 I O-3 19

Cathodic polarisation

(-V/SCE)

Fig. 8. EL and PL voltage evolution at a luminescence energy of 1.77 eV. Note that the voltage scale corresponds to the absolute value of the cathodic polarisation.

the VTEL, higher voltages are thus necessary to enable carrier injection on the more confined silicon crystallites. The voltage-evolution of the PL intensity can be well fitted, as shown in the right part of Fig. (2), by expression (3) using a FermiiDirac law to give the carrier injection probability at a given voltage. It includes two parameters: V,, the PL cut-off potential and n, an ideality factor (17 n?2), which describes the sharpness with which the PL quenching takes place:

IPL = I,

11

1 (3)

vo--. I + expr

I

Note that in this description the variable is the voltage (the confinement energy E was used in the EL description) and that the confinement energy is included in V,. This expression is, in fact, directly deduced from expression (2) and in terms of carrier injection it simply means that a crystallite will emit light only if the carrier injection probability is negligeable. This shows that the PL quenching is triggered by the carrier injection into the silicon crystallites but the quenching mechanism is still to be clarified. A first possible explanation is the decrease of the number of the optically active sources as a result of the electron accumulation (driven by the cathodic bias) in the Si nanocrystallites which can make

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these entities transparent to the excitation wavelength. This is the so-called Burstein blue-shift [S] of the optical transition. This explanation is used in the case of the nanocrystalline TiO, films [9]. According to this model, in the absence of an external bias, the confined electronic levels of a Si nanocrystallite are unoccupied and the excitation absorption is possible giving rise to the observed orange-red PL. Once the electronic levels are occupied due to the electron flow coming from the substrate, it is no more possible to photogenerate any electron-hole pair, the excitation is no longer absorbed and this crystallite becomes optically inactive. This voltage-induced absorption bleaching may well apply in our case. However, in the case of the EL signal quenching, the Burstein effect cannot be invoked since no optical absorption is involved in the EL excitation process. An alternative explanation might be related to the fact that under carrier injection conditions, an electrically injected electron as well as an optically generated electron-hole pair, may be simultaneously present in a silicon crystallite. In these conditions, theoretical calculations [lo] have shown that an Auger process becomes very likely since the estimated relaxation time is 1O-9 s, several orders of magnitude shorter than the radiative recombination rate (10e5 s). Consequently, an efficient non-radiative relaxation of the optically generated electron-hole pair takes place leading to the PL quenching. Concerning the EL voltage evolution, it can be seen as the result of two opposed processes. The first, related to carrier injection, leads to the EL build up whereas the second provokes its quenching. This EL quenching takes place by an Auger process if two electrons and one hole are simultaneously injected into the silicon crystallite. The first regime can be simply represented by the following expression:

cf Luminescence 70

317

(1996) 310-319

ready mentioned, related to the injection of a second electron. Expression (3) can thus apply but in order to correctly fit the EL evolution, a cut-off voltage I/’ slightly different from I/, should be considered. This difference means that the injection of a second electron requires a higher voltage, probably due to Coulomb charging effect. It has been shown that the porous silicon luminescence tunability is related to carrier injection into the silicon nanocrystallites determined by the applied polarisation. In these conditions the voltage distribution at the different interfaces (substrate- or electrolyte-nanocrystallite) should play an important role. Consequently, it seems interesting to study the influence of a partial oxidation of the porous material on its luminescence tunability since it is a simple way to induce a voltage-drop modification. The oxidation can be performed either by an anodic process in an aqueous solution or by a thermal treatment (30 mn. at 300 “C) in an oxygen ambient. Both processes give comparable results. Fig. 9 shows the EL tunability behaviour before (Fig. 9(a)) and after (Fig. 9(b)) a partial oxidation of about 50% of the porous silicon atoms. Such treatment leads not only to a loss of the tunability but also to a loss of the energy selectivity; a large and constant width of the EL line (about 0.5 eV instead of 0.25 eV on the non-oxidised samples) is obtained on the partially oxidised samples. This means that the luminescence of all the silicon nanocrystallites is observed regardless of the

$‘ 0)

1.9 - Acal .

1.8 3 k17*****.. Ef

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.

.

.

@I

l

.

.

I

1 IEL =

IO V,-V'

i 1 + expr

I

. I .

(4)

Expression (4) is the complementary of expression (3) since, in this case the carrier injection provokes an intensity increase. The EL quenching is, as al-

1.4 1 -1.5

, -1.4 Cathodic

I -1.3 -1.2 Polarisation

/ -1.1

(V/SIZE)

Fig. 9. Evolution of the EL energy as a function of the applied polarisation for a non-oxidised (a) and for a partially oxidised (b) porous layer.

A. Bsiesy, J.C. Vial /Journal

600

Fig. 10. Comparison ween a non-oxidised layer.

700 Wavelength

800 (nm)

of the voltage-induced (a) and a partially

900

PL quenching betoxidised (b) porous

applied polarisation. The partial oxidation leads also to a loss of the selectivity of the voltage-induced PL quenching as illustrated by Fig. 10. These results show that the partially oxidised porous silicon has the same behaviour as a porous layer contacted with a solid electrode where no luminescence tunability has been evidenced [ll]. A tentative explanation of this effect is the oxide-induced modification of the voltage drop between the silicon bulk and the silicon nanocrystallites. In these conditions and due to the oxide growth, carriers are no more preferentially injected into a specific class of silicon nanocrystallites.

5. Conclusion

This paper gives a description of two voltage induced selective effects on cathodically-biased n-type porous silicon. Despite the very different observed phenomena i.e. the tunable electroluminescence and the photoluminescence quen-

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70 (1996) 31 O-31 9

ching, we have pointed out the common features and have built a unique model where the distribution of carrier confinement associated to the voltage-selective carrier injection allows a quantitative description of both phenomena. To our knowledge, this is the first demonstration of spectral narrowing and tuning effects obtained on a so wide range by the mean of an electrical excitation of a solid. Furthermore, there are no objective reasons to say that similar results cannot be obtained on porous silicon contacted by a solid electrode since in spite of using a liquid contact, the tunability effects turned out to be only determined by the charge exchange between the silicon bulk and the porous skeleton. Research in this direction should consequently be motivated by the numerous technological applications that these tuning effects may lead to. Apart from the fact that they allow to understand the tuning effects, these experiments unexpectedly give information of a more fundamental character concerning the porous silicon luminescence. A remarkable example in this field is the experiment showing that the voltage selective injection (on cathodically and anodically biased samples) extrapolates the “gap” of silicon nanocrystallites for 0 applied volt to a value which is exactly the gap of the silicon bulk. For us, this is a strong confirmation that the origin of the porous silicon visible luminescence is not related to some chemical species [12, 131 or to surface states [14] but is simply arising from a radiative recombination of confined carriers. This experiment shows one typical way of using the voltage selective injection for spectroscopic purposes. There is no doubt that new tools using the voltage selective carrier injection will be soon discovered.

References [l] L. T. Canham, Appl. Phys. Lett. (1990) 1046. [Z] J. C. Vial, S. Billat, A. Bsiesy, G. Fishman, F. Gaspard, R. Herino, M. Ligeon, F. Madeore, 1. Mihalcescu, F. Muller and R. Romestain, Physica B (1993) 593. [3] P. D. J. Calcott, K. J. Nash, L. T. Canham, M. J. Kane and D. Brumhead, J. Phys. Condes. Matter (1993) L91. [4] R. Memming, J. Electrochem. Sot. (1969) 785. [S] P. M. M. C. Bressers, J. W. J. Knapen, E. A. Meulenkamp and J. J. Kelly, Appl. Phys. Lett. (1992) 108.

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[6] L. T. Canham, W. Y. Leong, M. I. J. Beale, T. 1. Cox and L. Taylor, Appl. Phys. Lett. (1992) 2563. [7] A. Bsiesy, F. Muller, M. Ligeon, F. Gaspard, R. Herino, R. Romestain and J. C. Vial, Phys. Rev. Lett. (1993) 637. [S] E. Burstein, Phys. Rev. (1954) 362. [9] B. O’regan, M. Gratzel and D. Fitzmaurice, Chem. Phys. Lett. (1991) 89. [lo] I. Mihalcescu, J. C. Vial, A. Bsiesy, F. Muller, R. Romestain, E. Martin, C. Delerue, M. Lannoo and G. Allan, Phys. Rev. B (1995) 17605.

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[ 1 l] H. Koyama, T. Oguro and N. Koshida, Appl. Phys. Lett. (1993) 3177. [12] M. S. Brandt, H. D. Fuchs, M. Stutzmann, J. Weber and M. Cardona, Solid State Commun. (1992) 307. [13] S. M. Prokes, 0. J. Glembocki, V. M. Bermudez, R. Kaplan, L. E. Friedersdorf and P. C. Searson (1992) 13788. [14] F. Koch, V. Petrova-Koch and T. Muschik, in: Light Emission from Silicon, eds., J.C. Vial, L. T. Canham and W. Lang (Elsevier, Amsterdam, 1993) p. 271.