11
TH. KLEINEFELD and W. VON DEE OSTFN: Biexcitons in Silver Bromide 293 phys. stat. sol. (b) 126, 293 (1984) Subject classification: 13.5.1 and 20.3; 22.5.1 Fachbereich Physik, Universitat-Gesamthochschule Paderbornl) Localized and Free Biexcitons in Silver Bromide TH. KLEINEFELD~) and W. VON DER OSTEN Recombination luminescence in AgBr at low temperature is studied for high power quasi-cw and pulsed excitation. The samples are nominally pure but vary systematically in iodine impurity content. Using time-resolving techniques several new luminescence transitions are detected and found to be correlated with iodine concentration. The results can be consistently explained as- suming that,, besides free excitons and free biexcitons, a biexciton bound to isoelectronic iodine is created and decays. The model is supported by energy positions and shape of the observed lines as well as by the dependence of luminescence intensity on excitation power and iodine concen- tration. To completely account for the observed spectra, the model also takes into account inter- valley exciton scattering by- X-phonons known to be an effective exciton relaxation process in AgBr. Die Rekombinationsstrahlung von AgBr bei tiefen Temperaturen und hohen Anregungsdichten wird fur quasi-Gleichlicht- und Pulsanregung untersucht. Die nominell reinen Proben variieren systematisch in ihrem Jod-Storstellengehalt. Mit Hilfe zeitauflosender Spektroskopie werden zahlreiche neue Emissionsiibergange gefunden, die mit dem Jodgehalt korreliert sind. Die Ergeb- nisse lassen sich konsistent unter Annahme eines an Jod gebundenen Biexzitons deuten, das neben freien Exzitonen und freien Biexzitonen erzeugt wird und zerfallt. Diese Vorstellung wird gestutzt durch Linienlagen und -form der beobachteten Emissionsiibergange sowie die Abhangigkeit der Emissionsintensitat von Anregungsleistung und Jodkonzentration. Zur vollstandigen Erklarung der Spektren muB die fiir AgBr bekannte Zwischental-St.reuung der Exzitonen mit X-Phononen berucksichtigt werden. 1. Introduction High density excitation effects in semiconducting materials have recently attracted considerable attention. At low temperatures and sufficiently high carrier concentra- tions in principle two different phenomena are observed : condensation of excitons into droplets of dense metallic electron-hole liquid (EHL) and formation of biexcitons or exciton molecules. Information on these excited states mostly originates from recom- bination luminescence under high intensity excitation which was extensively studied, both experimentally and theoretically, in various direct and indirect gap inaterials (for references see e.g. [l to 31). Regarding indirect gap semiconductors, silicon and germanium are examples where both EHL and biexciton were found with the biexciton state being less stable than the EHL (see e.g. [3 to 51). In AgBr that also exhibits an indirect edge the situation turned out to be more complex. Time-resolved luminescence spectroscopy a t high power levels in this material revealed emission lines at 2.669 eV and in the energy range 2.62 to 2.50 eV. While from analyzing its lineshape and dependence of emission inten- sity on excitation power the former line could undoubtedly be attributed to biexciton decay [6 to 81, the interpretation of the lower energy luminescence in terms of EHL 1j D-4790 Paderborn. FRG. 2, New address: Fachbereich Physik-Technologie, Universitat-Gesamthochschule Duisburg FRG.

Localized and Free Biexcitons in Silver Bromide

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Page 1: Localized and Free Biexcitons in Silver Bromide

TH. KLEINEFELD and W. VON DEE OSTFN: Biexcitons in Silver Bromide 293

phys. stat. sol. (b) 126, 293 (1984)

Subject classification: 13.5.1 and 20.3; 22.5.1

Fachbereich Physik, Universitat-Gesamthochschule Paderbornl)

Localized and Free Biexcitons in Silver Bromide

TH. KLEINEFELD~) and W. VON DER OSTEN

Recombination luminescence in AgBr a t low temperature is studied for high power quasi-cw and pulsed excitation. The samples are nominally pure but vary systematically in iodine impurity content. Using time-resolving techniques several new luminescence transitions are detected and found to be correlated with iodine concentration. The results can be consistently explained as- suming that,, besides free excitons and free biexcitons, a biexciton bound to isoelectronic iodine is created and decays. The model is supported by energy positions and shape of the observed lines as well as by the dependence of luminescence intensity on excitation power and iodine concen- tration. To completely account for the observed spectra, the model also takes into account inter- valley exciton scattering by- X-phonons known to be an effective exciton relaxation process in AgBr.

Die Rekombinationsstrahlung von AgBr bei tiefen Temperaturen und hohen Anregungsdichten wird fur quasi-Gleichlicht- und Pulsanregung untersucht. Die nominell reinen Proben variieren systematisch in ihrem Jod-Storstellengehalt. Mit Hilfe zeitauflosender Spektroskopie werden zahlreiche neue Emissionsiibergange gefunden, die mit dem Jodgehalt korreliert sind. Die Ergeb- nisse lassen sich konsistent unter Annahme eines a n Jod gebundenen Biexzitons deuten, das neben freien Exzitonen und freien Biexzitonen erzeugt wird und zerfallt. Diese Vorstellung wird gestutzt durch Linienlagen und -form der beobachteten Emissionsiibergange sowie die Abhangigkeit der Emissionsintensitat von Anregungsleistung und Jodkonzentration. Zur vollstandigen Erklarung der Spektren muB die fiir AgBr bekannte Zwischental-St.reuung der Exzitonen mit X-Phononen berucksichtigt werden.

1. Introduction High density excitation effects in semiconducting materials have recently attracted considerable attention. A t low temperatures and sufficiently high carrier concentra- tions in principle two different phenomena are observed : condensation of excitons into droplets of dense metallic electron-hole liquid (EHL) and formation of biexcitons or exciton molecules. Information on these excited states mostly originates from recom- bination luminescence under high intensity excitation which was extensively studied, both experimentally and theoretically, in various direct and indirect gap inaterials (for references see e.g. [l to 31).

Regarding indirect gap semiconductors, silicon and germanium are examples where both EHL and biexciton were found with the biexciton state being less stable than the EHL (see e.g. [3 to 51). In AgBr that also exhibits an indirect edge the situation turned out to be more complex. Time-resolved luminescence spectroscopy a t high power levels in this material revealed emission lines a t 2.669 eV and in the energy range 2.62 to 2.50 eV. While from analyzing its lineshape and dependence of emission inten- sity on excitation power the former line could undoubtedly be attributed to biexciton decay [6 to 81, the interpretation of the lower energy luminescence in terms of EHL

1j D-4790 Paderborn. FRG. 2, New address: Fachbereich Physik-Technologie, Universitat-Gesamthochschule Duisburg

FRG.

Page 2: Localized and Free Biexcitons in Silver Bromide

294 TH. KLEINEFELD and W. VON DER OSTEN

renders more difficult [9, 101. This difficulty arises from the fact that this band is found to be composed by contributions of differ-nt origin and that it exhibits a complex structure if studied with sufficiently high spectral resolution [lo, 111. Also the binding energy of 55 to 60 meV derived from analyzing the luminescence in terms of EHL considerably deviates from theoretical predictions (30 nieV) even if the strong electron-LO coupling for AgBr is taken into account [9, 10, 121.

In this paper we describe in detail our results on recombination luminescence obtained in nominally pure AgBr crystals under high power quasi-cw and pulsed excitation. Some preliminary results were already published previously [13]. In particular, we consider the effect of ubiquitous iodine impurities in these crystals onto luminescence that we observe. The correlation between the intensity of some lumines- cence transitions in the highly excited spectra with iodine content leads us to propose that a biexciton bound to iodine impurity to a large part may be responsible for the recombination luminescence observed. Following Sections 2 and 3, in which experi- mental details and results are described, in Section 4 free and bound biexciton recom- bination is discussed with regard to energy positions, lineshapes and exciton kinetics. From the analysis binding energies and radius for both the free and bound biexcitons are derived. Finally in Section 5 a few remarks are made concerning multi-exciton complexes found in other materials.

2. Experimental The crystals used in our experiments originated from the following sources: the Bul- garian Academy of Sciences in Sofia (Bulgaria), the University of North Carolina in Chapel Hill (USA), and from our own crystal growth facility. They were selected out of a number of nominally pure samples that usually contain small amounts of iodine. The iodine content was estimated from the integrated intensity of the well-known bound exciton luminescence band attributed to iodine impurity [14, 151 and using an intentionally doped sample with 1000 ppm as calibration point. The range of concen- trations covered was cI = 0.1 to 500 ppm. All measurements were performed a t 1.9 K with the samples immersed in pumped liquid helium.

Two types of experimental techniques were used allowing for measurements in different time regimes and differing in excitation power densities. One method em- ployed uv excitation from a high power argon ion-laser (excitation wavelength AL = 360 nm ( E L = 3.4 ev)) . The beam was chopped with a frequency of 22 kHz, which compared to the short decay time of the relevant states under investigation corresponds to quasi cw-excitation. By focussing the laser onto the sample, power densities up to 150 kW/cin2 were obtained. A digital lock-in technique described in detail previously [lo] was applied to separate luminescence components with different time behaviour. The time resolution in this case was about 100 ns.

The excitation source in the other technique applied was a narrow band dye-laser pumped by a pulsed frequency-tripled Nd-YAG laser. The power densities available for excitation in this case reached 150 kW/cm2 up to several MW/cm2. Special photon counting electronics were used for efficient sampling of data and simultaneously provided a time-resolution of about 2.5 ns [16]. The experiment was computer control- led. Time-resolved spectra with 0.1 nm (= 0.5 meV) maximum spectral resolution were obtained within several hours of measuring time.

The volume power density Pv generated by an exciting laser beam of wavelength jlL and power density Y s a t the sample surface is given by Pv = P,a(AL) exp { -%(AL) . . x}, where x is the coordinate inside the crystal parallel to the laser beam and cy is the absorption coefficient. According to the strong dependence of &(AL) in AgBr, P, may be varied by changingAL and keeping the number of incident photons almost constant.

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Localized and Free Biexcitons in Silver Bromide 295

For small penetration depths P,,(lI,) -.(A,). To make the results obtained a t dif- ferent excitation wavelengths comparable, the surface power densities given in the following are corrected for a wavelength of 360 nm where 01 = 500 cm-l in AgBr. The maximum surface power density of 2MW/cm2 reached in the experiments corresponds to 5 x l O l 9 photons/cmz s.

3. Experimental Results Typical luminescence spectra obtained for quasi-cw excitation with the uv lines of the argon-ion laser (excitation photon energy E L = 3.4 eV) are represented in Fig. 1. The spectra are obtained by employing the digital lock-in technique (Section 2 ) and are shown time-resolved corresponding to decay times z 2 100 ns. The long-lived component is due to the well-known recombination of the iodine bound exciton (BX, z = 18 ps) consisting of a narrow zero-phonon line a t 2.641 eV (Izp) and multi- phonon structure [la, 151. The fast component of the spectrum, besides the free exciton (FX) and several weakly bound exciton transitions near FX, contains a strong emission band with a characteristic double peak structure a t around 2.59 eV (lines BXX,) plus another weak and narrow line a t 2.636 eV (line BXX,). The lines BXX, and BXX, obviously occur a t high excitation powers only, with a slightly sublinear increase of intensities up to 150 kW/cm2.

BXX, ' b

A & 2.6

energy (el0 - energy (el4 ___c

Fig. 1 Fig. 2

Fig. 1. Time-resolved luminescence spectrum for quasi-cw excitation ( E L = 3.4 eV, P = = 150 kW/cm2). Components with decay times t 2 100 ns shown separately in a) and b). Inset represents BXX, line enlarged in intensity scale. Estimated iodine content of sample cI = 0.1 ppm. For assignments see text. Narrow transitions near FX due to weakly bound excitons not discussed in this paper. a ) t > 100 ns, b) t < 100 ns

Fig. 2. Luminescence spectra obtained for pulsed excitation at EL = 2.82 eV. Power densities are a) P = 1.8 and b) 0.36 MW/cm2. Estimated iodine content GI = 1.0 ppm. For assignments see text

Page 4: Localized and Free Biexcitons in Silver Bromide

296 TH. KLEINEFELD and W. %-ox DER OSTEN - cI =01 ppm

I0 f i

f

Fig. 3

0 I 2 3 $ @ml -----

Fig. 4

Fig. 3. Dependence of BXX, band intensity on FX band intensity for pulsed excitation in samples of different iodine content. Integrated intensities in arbitrary units but in scale relative t o each other for the three samples. Range of excitation powers P = 0 to 1.8 MW/cm2

Fig. 4. Integrated intensity of BXX, band in arbitrary units vs. iodine concentration for quasi-cw excitation a t constant excitation power of 100 kW/crn2

The BXX, double peak is generally superimposed by another fast decaying lumines- cence band of unknown origin that is not necessarily due to a high excitation effect. This band (“&-line”) was reported previously by us and others [lo, 111 and consists of a narrow zero-phonon line a t 2.595 eV and pronounced LO(r) phonon structure. In Fig. 1 (lower spectrum) this band is noticeable as a weak shoulder only. As found earlier, i t predominates the fast spectrum a t low excitation levels down to 250 W/cm2. Due to its different dependence on excitation intensity being sublinear, a t high excita- tion powers i t does not contribute much to the total intensity of the BXX, band.

The BXX, line is weak but clearly observed in the time-unresolved total spectrum. However, due to its small intensity and narrow halfwidth (about 1.5 meV), its inten- sity in the fast spectrum shows some variations that partly originate from the sub- traction of spectra necessary to separate the different time components. To some extent this line is sample dependent.

Fig. 2 shows luminescence observed in AgBr under pulsed laser excitation for two different power densities in the MW/cm2 regime. The excitation photon energy chosen was E L = 2.82 eV which in view of the small absorption coefficient of AgBr a t this energy (01 = 20 cm-1) guarantees volume excitation of the sample. According to the pulsed excitation (pulse width 10 ns), the iodine bound exciton luminescence is suppressed. Due to its small intensity and narrow halfwidth the BXX, line could not be detected in the pulsed-excited spectra. Like in the cw-excited spectrum of Fig. 1, both the free exciton (FX) and the strong BXX, recombination luminescence are observed. Although structure is indicated in the BXX, band maximum, the signal-to- noise ratio in this series of measurements, that covered a large range of photon energies and different excitation powers, is insufficient to definitely identify it with the double peak detected for cw-excitation. Measurements in a limited spectral range with improved signal-to-noise ratio and high spectral resolution, however, clearly prove the occurrence of the double peak also in the pulsed-excited spectra (see e.g. Fig. 7). Compared to Fig. 1, pulsed laser excitation leads to the occurrence of another strong band (FXX) a t the low-energy side of the FX luminescence. This band was attributed before to the decay of the free biexciton (exciton molecule) mainly on the basis of its

Page 5: Localized and Free Biexcitons in Silver Bromide

Localized and Free Biexcitons in Silver Bromide 297

lineshape and its superlinear (although not quadratic) dependence of its intensity on excitation [6 to 81.

We tried to measure the decay times of all observed luminescence bands and found for the FX and FXX bands that in all samples they were below the time resolution (2.5 ns) of our multichannel photon counting system. The decay of the BXX, band is well described by an exponential function with a lifetime of zBxx, = 7.9 ns at 1.9 K.

Most important in interpreting the spectra observed under high intensity excitat,ion is their correlation with iodine content cI present in all samples. In Fig. 3, the depend- ence of the BXX, integral intensity in crystals with different cI is represented as a function of the FX integrated intensity which is assumed to be proportional to excitation power. As shown for pulsed excitation, t,he BXX, band tends to saturate a t higher excitation powers, and a similar result is obtained for quasi-cw excitation. For both modes of excitation, a t constant excitation power, the BXX, intensity is found to exhibit a characteristic dependence on cI. It is illustrated in Fig. 4 for 100 kW/cm2 quasi-cw excitation, with the maximum of Isxx, occurring slightly shifted to higher cI for increased values of excitation power. Qualitatively, a similar behavionr is observed for the BXX, line (in t,he ew-excited spectra) suggesting the BXX, and BXX, line to be of the same origin.

4. Discussion 4.1 Free biexciton Tecombination

In a free biexciton (FXX) two free excitons (FX) are bound essentially by Coulonib and exchange interaction [17].3) A likely process for FXX radiative recombination is one in which one exciton remains in a real indirect FX state while the other recombines via a virtual indirect F X state. This process gives rise to a luminescence line that with regard to the FX emission is shifted to lower energy by about the FXX binding energy E:xx. According to Cho [18], the FXX recombination lineshape in case of an indirect gap material is given by

In this expression, int,egration has to be carried out over all F X and FXX states with respective wave vectors k and K. E~~ and gFxX are the kinetic energies of the exciton

I I I 1 t i FXX FX

Fig. 5. F X and FXX recombination luminescence observed for pulsed excitation (E, = 2.8 eV, P = 1.8 MW/cm2). Points: experimental data. Full line: fits according to (1 ) and ( 2 ) . 6 X X binding energy indicated with regard t o the FX

eneryy ieVJ - . +

s, In case of indirect FX, in principle two FXX states with different resulting wave vector are to be expected. In AgBr, where two indirect FX with k = kL may be combined, these are FXX states with K = 0 and K = Kx corresponding to the center and X-point of the Brillouin zone, respectively.

Page 6: Localized and Free Biexcitons in Silver Bromide

298 TH. KLEINEFELD and W. VON DER OSTEN

and biexciton which in case of AgBr may be written as E F ~ = h2(k - k#/2M* and E~~~ = h2jK - 2kL)2/4M*, respectively ( M * effective single exciton mass). EFX, , ,

and E are the energies of the indirect exciton gap, the momentum conserving (TO(L)-) phonon, and the photon. The exponential describes the population of FXX states with T representing the temperature of the FXX gas. According to [18], the matrix element is of the form -

M = M , [C (f K - k ) + ~ ( k - +K)] , (21 the overlap function c(k‘) = co/(k’2 + x : ) ~ , where x,, = l /a , is the reciprocal average distance a, of the two holes in the FXX (FXX “radius”). M , is a constant. Numerical integration of (1) allows to fit the FXX lineshape to the experimental data as shown in Fig. 5. From the fit the radius and the binding energy (corresponding to the transi- tion K = 2kL -+ k = kL) with regard to the F X state are obtained for the FXX. The derived values listed in Table 1 are in reasonable agreement with previous results

Table 1 Free (FXX) and bound (BXX,) biexciton parameters in AgBr determined from fitting (1) and (6) to the experimental data (see Fig. 5, 7 and text)

FXX BXX,

binding energy Eb (meV) 6.9 , 0.2 83 + 1 radius q, (nm) 0.28, 1 2.5 f 2 temperature T (K) 20 , 3 -

IS, 71. The temperatmure of the FXX syst,ein resulting from the fit is T F ~ X = (20 + 3 ) K . A ,

Compared to earlier measurements, due to different experimental conditions (lower temperature, lower excitation photon energies) the FX and FXX luminescence lines are well separated in our spectra. This allows to individually f i t the F X line, that formally may be described by a Maxwellian distribution [19,201. The temperature obtained in this way from the fit is T F X = (12 & 1) K, which is different from the FXX temperature in contrast to previous analyses [6, 71, where TFxX = T F ~ was generally assumed.

A s known from resonance Raman scattering with the indirect F X as intermediate state [20 ] , the occurrence of the Maxwellian lineshape for the FX reconibination does not necessarily imply thermal equilibriuni between the exciton system and the lattice. As was shown in these experiments, a t low temperature the lineshape is rather deter- niined by various exciton relaxation processes involving acoustic and optical phonons. Due to the lack of any phonon absorption processes a t low temperatures (lattice temperature = temperature of coolant = 1.9 K), thermal equilibrium cannot be established within the F X lifetime being of the order of nanoseconds in AgBr [21]. Also, a t the low excitation densities in these experiments, there are no exciton- exciton collisions to establish thermal equilibrium among the excitons.

The difference in T F X and TFXX following from the analysis of the present high excit,ation experiments indicates t8hat thermal equilibrium does also not exist between the FX and FXX systems. This suggests that even at the high excitation densities in our experiment exciton collisions are not sufficiently effective for thernialization. Consequently a temperature of the F X and the FXX gas cannot be defined, and T may rather be regarded as distribution parameter for the kinetic energies of the cor- responding particles.

Page 7: Localized and Free Biexcitons in Silver Bromide

Localized and Free Biexcitons in Silver Bromide 299

4.2 Bound biexeiton recombination

Based on energy positions, lineshapes and dependence on iodine content the lumines- cence lines BXX, and BXX, that appear a t high excitation powers (Fig. 1 and 2) can be consistently interpreted as due to recombination of a bound biexciton (BXX). The BXX is created by successive binding of two FX to an impurity trap that, on the basis of our results, is suggested to be isoelectronic iodine. Due to localization in real space the BXX state of energy EBsX is spread out in k-space.

For the decay of the BXX we consider two different processes. In the first one a bound single exciton (BX) is left behind, while the other exciton recombines via a virtual indirect FX state plus eniission of a momentum-conserving L-point phonon. From the energy difference between final and initial states for this process the energy hv, of the emitted photon is given by

hvO = EBXX - EBX - hWT0 9 (3) where EBX and h o ~ o are the energies of the single exciton bound to iodine and the TO(L) phonon, respectively. Since only discrete energy amounts are involved in (3), this process results in a narrow recombination line. We attribute the BXX, line (at 2.636 eV) to this process.

The other decay channel leads to the double peak BXX,. In this case we assume that both excitons become unbound so that one exciton remains in a real (indirect) Fx state while the other decays via a virtual exciton state. This process is schemati- cally illustrated in Fig. 6. As indicated there, the decay via the virt,ual exciton state may proceed in two different ways. One possibility is by means of emission of a momentum-conserving ~ TO(L) phonon. The energy of the emitted photon in this case will be

L' wave vector

Fig. 6

I I > 256 2 60 i

energy ieW - Fig. 7

Fig. 6. Schematic representation of the decay of the iodine BXX (dashed arrows) leaving behind two FX. Energy shown vs. wave vector. Full and dashed bands correspond to real and virtual states. Full arrows represent emitted photons and phonons

Fig. 7. BXX, recombination luminescence. Experimental curves shown are (a) for quasi-cw excitation ( E L = 3.4 eV, P = 150 kW/cm2) and (b) for pulsed excitation ( E L = 2.8 eV, P = = 1.8 MW/cm2). The calculated spectrum (full line) represents recombination involving TA(X) and LA(X) scattering. Dashed line corresponds t o calculation including LO(F) emission. Base lines of spectra shifted with regard to each other.

Page 8: Localized and Free Biexcitons in Silver Bromide

300 TH. KLEINEFELD and W. VON DER OSTEN

where EBX,0 is the F X gap energy (see Fig. 6). On the other hand, the exciton may be scattered by an intervalley X-phonon into a virtual PX state a t a different point in the Brillouin zone (L + L*). As known from resonant Raman measurements [ZO], this process is highly efficient for exciton relaxation and involves TA(X) or LA(X) phonons. Energy conservation in this situation is analogous to (4), however, with the rcsulting photon energy hvi being reduced with regard to hv, by the energy ho, of the X-phonon involved. Due to the variable energy term E ~ X in (4), both decay processes are expected to give rise to slightly broadened peaks. On the basis of their energetic distance from each other (equal to about l A w T A ( X ) ) and their widths, the BXX, lines (at 2.59 eV) are attributed to these decay channels.

To further support this model we have analyzed the lineshape of the BXX recom- bination in more detail. Since the BXX decay is similar to that of the FXX, we modified (1) neglecting the dependence on biexciton wave vector and taking into account the localization of the biexciton state by using zero kinetic energy. The energy dependence of the recombination intensity then may be written as

I ( E ) I s dk 1kI2 8 @BXX - EFX, 0 - &EX - AUTO - E } 9 (5)

where we assume the same overlap function c(k') as for the FXX decay. Carrying out the integration one obtains

where I , is a constant, EBXX,l is the energy of the onset of the luminescence band (at 2.593 eV), and xol is the BXX radius.

Fig. 7 illustrates the fi t according to our model in comparison to the experimental lineshape observed for both cw and pulsed excitation. Applying (6) the high energy peak of the BXX, band is well reproduced. For the fit a BXX binding energy of 83 meV (with regard to the FX) and a BXX radius of 2.5 nm are used (see Table 1). The lineshape of the low energy BXX, peak can be computed correspondingly taking into account intervalley scattering. In calculating the contribution of these processes to the luminescence band, we used the ratio of scattering probabilities for TA(X) and LA(X) scattering cTAlcLA = 1.68 as determined from resonant Raman scattering [20]. Also higher order intervalley processes 2TA(X) and TA(X) + LA(X) were included, for which the scattering probabilities are known to be large. As seen from Fig. 7, by inclusion of these processes the low-energy peak is either well reproduced both with respect to peak position and width, the full calculated line representing the linear superposition of all contributions. As suggested by the structure of the experi- mental lineshape a t lower energies, interaction with LO(I') phonons also plays a role in the recombination process. The dashed line is an improved fit where we took a linear coupling to LO(I') phonons into account using a coupling constant S" with S = 0.3 (n number of phonons involved).

A strong argument supporting our model in which the observed luminescence is attributed to the iodine BXX decay is the energy difference between the BXX, line position and the onset of the BXX, band. The experimental value from our spectra is hv, - hv, = 43.5 meV. On the other hand, this quantity can be determined inde- pendently as difference between the exciton gap energy (EFx, 0 = 2.6845 eV) and the zero-phonon transition energy (EBX = 2.6415 eV) of the iodine bound single exciton as obvious from subtracting (3) and (4) (eFX = 0 in (4)). The value obtained in this way agrees within 1 meV.

Page 9: Localized and Free Biexcitons in Silver Bromide

Localized and Free Biexcitons in Silver Bromide 301

Comparison of the BXX binding energy of 83 meV with that of the iodine bound single (Ekx = 43 meV [14]) shows that in the iodine BXX the two excitons are bound with about equal strength. The weak (integrated) intensity of the BXX, line relative to the BXX, band indicates that the BXX decay into two FX is more probable than the process in which a single BX is left behind.

4.3 Exciton kinetics

Starting from the ideas developed above, some of the characteristic features of the observed free and bound exciton and biexciton transitions can be described by means of a kinetic model in which the interaction of the various states is represented in form of rate equations. In particular, the model is able to explain the absence of the iodine- bound single exciton (BX) recombination in the pulsed excited spectra (Fig. 2 ) ) the saturating behaviour of the iodine BX and BXX (Fig. 3)) and the dependence of the BXX, intensity on iodine content (Fig. 4). The relevant generation and decay processes for the various excitons and biexcitons are summarized schematically in Fig. 8. Correspondingly for the time derivations of the various intensities nt the following relations exist

nFXX nBXX TFXX TBXX

f - f - 7

zi are the lifetimes of the different exciton states, I, represents the laser excitation intensity creating free excitons, and A, ... E,, are the conversion Coefficients for creation of the various particles as evident from Fig. 8. In deriving (8) and (10)) we assumed E, = 0 according to the small probability of the BXX recombination process in which an iodine BX is left behind (see Section 4.2).

The stationary solutions (dni/dt = 0 ) of (8) and (10) are

1

Fig. 8. Schematic representation of generation and re- combination mechanisms of free and bound single exci- tons (FX, BX) and free and bound biexcitons (FXX, BXX). zt are the lifetimes of the various states, A, ... E, are conversion coefficients for creation or annihilation

Page 10: Localized and Free Biexcitons in Silver Bromide

302 TH. KLEINEFELD and W. VON DER OSTEN

and

They qualitatively reflect the saturation behaviour of the BXX, luminescence intensity (Fig. 3) as well as of the iodine BX intensity observed previously [22] a t sufficiently high FX densities. In particular, (12) is consistent with our observation that for quasi-cw excitation (small nFX) saturation of the BXX, band occurs only for samples with small iodine concentration (eI = 0.1 ppm). In contrast, for pulsed excitation (high nFx) saturation is observed also for samples with higher cI.

The characteristic dependence of the BXX intensity on iodine content qualitatively follows from reducing (7) and (10) to the relevant terms. Making the reasonable assumption that

1. the number of FX (np) is predominantly determined by generation via photons and trapping a t iodine impurities, and

2 . the number of BXX created under our excitation conditions is relatively small (nBxx < cI), their stationary solutions by means of (8) may be written

and

Replacing n F X in (14) by (13) and assuming nnx - cI for small n B X according to (8) , the density of BXX is approximately obtained as

nnxx = ZBXXDO~FX~BXCI . (14)

The dashed line in Fig. 4 is a fit of (15) to the experimental data a t I, = const, the good agreement qualitatively supporting our model. Also (15) reproduces the shift of the maximum of the curve a t increased I , observed experimentally.

Finally, also the lack of iodine BX luminescence for pulsed excitation may be understood from the kinetic model developed above. The quasi-cw spectra (P < < 150 kW/cm2) already show saturation of the number of iodine BX, 80 that further increase of excitation power in the pulsed spectra does not significantly increase nnx- However, a t these high excitation densities a sufficient number of F X is created to convert existing BX to BXX states. Consequently, for pulsed laser excitation nnx decreases due to increasing n B x X . This results in suppression of the iodine BX lumincs- cence band and the observed predominance of the BXX luminescence (Fig. 2 ) .

5. Concluding Remarks

Although we cannot exclude that luminescencc due to EHL recombination contri- butes in the spectral range we have studied, the observed emission largely seems to be of different origin. The model of an iodine BXX developed above is in good accord- ance with all our experimental observations, but more specific measurements will have to be performed to further substantiate it. While multiexciton complexes bound a t various donors and acceptors in Ge and Si are frequently reported in the literature (see e.g. [23]), the most closely related case to the present example is the biexciton bound to nitrogen isoelectronic trap in GaP [24]. In this material, like in AgBr, additional recombination lines appear a t high excitation intensities. They are ascribed to recom-

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Localized and Free Biexcitons in Silver Bromide 303

bination of one of the two excitons comprising the BXX, leaving a single exciton bound to nitrogen in the ground state. Multi-particle transitions including the analogue to the BXX, line in AgBr were sought but the evidence for these processes was found to be not conclusive. To understand the relative strengths of the various decay processes in AgBr and Gap, in particular the weak intensity of the BXX, compared to the BXX, line in AgBr, the proposed model requires further development. In principle, however, we believe that isoelectronic iodine plays a similar role for AgBr as nitrogen in Gap. In particular, it will be difficult t o further purify the cryRtals and reduce the content of unintentionally present iodine in AgBr, which is required for further investigations of the EHL in this material.

Acknowledgements

The authors like to thank Dr. H. Stolz for many helpful discussions. The work was partly supported by the Minister for Wissenschaft und Forschung des Landes NRW.

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(Received February 28, 7.984)