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Dynamics of multiphonon processes in luminescence spectra of oxygen-bound excitons in ZnTe: O
JOURNALOF
LUMINESCENCE ELSEVIER
Journal of Luminescence 58 (1994) 206 209
Dynamics of multiphonon processes in luminescence spectra of oxygen-bound excitons in ZnTe: 0 Y. Burkia, W. Czajaa, V. Capozzil~~*, P. Schwendimannc alnstitut de Physique Appliquèe, Ecole Politechnique Fèdèrale, CH-1015 Lausanne, Switzerland bDi•partimento di Fisica, Univers,tà degli studi di Ban, 1-70126 Ban, Italy ‘Defense Technology and Procurement Agency, System Analysis Division, CH-3003 Bern, Swit~erland
Abstract Photoluminescence (PL) spectra of oxygen-bound exciton transitions in ZnTe: 0 have been measured for temperatures ranging from 2 to 300 K and both for band-to-band excitation and for excitation resonant with the oxygen-bound exciton state. The temperature dependence of both optical and acoustical phonon contributions to the PL spectra is presented and discussed.
We present some results on the photoluminescence (PL) of the isoelectronic trap oxygen in ZnTe. Besides their relevance in their own right these results allow us to understand better the gain spectra recently observed in ZnTe : 0 and discussed in Ref. [1]. Bound exciton luminescence, which persists up to room temperature, is one of the most surprising features observed in this material. As will turn out in the following, the analysis of luminescence relies heavily on the formalism used earlier when discussing luminescence from the isoeiectronic trap AgBr : I [2]. The comparison between theory and experiment is satisfying for both traps. This indicates that the model of [2] is suited for the discussion of the optical properties of different isoelectronic traps. We consider two different excitation modes: a resonant mode corresponding to excitation via the 587 nm line of a rhodamine 6G dye laser into the excited states of the oxygen-
*
Corresponding author,
bound exciton and band-to-band excitation which is obtained with an Ar laser at 478 nm. These two excitation wavelengths are chosen in order to characterize the excitation mechanism which leads to optimum gain in ZnTe: 0 [1]. We shall refer to these two excitation modes explicitly when different behavior in the luminescence spectra related to the different excitation modes arises. Otherwise, all resuits refer to band-to-band excitation, which is easier to perform. Let us sketch briefly the model used for the fit of the ‘experimental curves; for mathematical details, we refer to [2]. It consists of two electronic levels (ground state and excited state), which are coupled to an electromagnetic field by the usual dipole coupling. The excited electronic state is also coupled to both the optical and the acoustical phonon modes of the crystal. This coupling, which is linear in the phonon amplitudes, accounts for the perturbation of the lattice due to the presence of the excited state. In the case of ZnTe: 0, longitudinal and transverse optical as well as acoustical
0022-2313/94/$07.00 C 1994 Elsevier Science B.V. All rights reserved SSDI 0022-2313(93)E0139-O
V. Burki el a!.
3000
/ Journal of Luminescence 58
‘ .
207
(1994) 206 209
2500
2000
:: 620
630
640
650
660
670
680
690
Wavelength (nm) Fig. 1. Fit (dotted line) of the luminescence spectra (solid line) for different temperatures from 2 to 60K.
phonons couple to the excited state. In the calculations the electron phonon interaction is diagonalized exactly, whereas the interaction with photons is treated by first-order perturbation theory. We evaluate the luminescence spectrum through the transition probability from the excited state dressed by the electron phonon interaction to the ground state of the system, which consists of phonon states and of the electronic ground state, The transition probability is averaged over a thermal distribution of the phonons in order to account for the temperature dependence of the luminescence spectrum. Moreover, it is integrated over the one-phonon density of states, which weights the different phonon contributions. This latter quantity is obtained from experiments, i.e. from neutron scattering data. As a result, the luminescence
spectrum is obtained as a function of temperature. The Huang Rhys factors for the different phonon modes, which are related to the amplitude of the different peaks in the spectrum and therefore to the strength of the electron phonon coupling, are obtained through a fit to the experimental spectra at low temperature (2 K). We assume that there is no relaxation within the excited state and that the vibrational states are the same for the crystal ground state and for the oxygen-bound exciton state. This assumption is reasonably confirmed by the experimental data. The results of the fit for luminescence are presented in Fig. 1. We begin by considering the luminescence spectrum at 2K in Fig. 1. The fit is rather satisfying, except for some inaccuracies in the position of the
208
V. Burki et al.
Journal of Luminescence 58 (1994) 206 209
acoustical phonon peaks. This indicates that we are working with an approximate description of the material. In fact, from group theoretical arguments a selection rule for ZnTe acoustical phonons follows which allows only phonon combinations with total momentum k 0 to couple to the electronic transitions. Thus, the optical phonons are allowed in one-phonon processes and are well reproduced in Fig. 1, whereas the acoustic phonons can assist only in combinations of at least two with vanishing total momentum. However, since the optical phonon branches in ZnTe are rather fiat, a large number of combinations of optical and acoustic phonons are possible. These will be responsible for the temperature dependence to be discussed laterandjustifytherathergoodfitfortemperatures lower than 60 K. However, the model only partially accounts for the selection rules characteristic of the material because the one-phonon density of states is used in the calculations. This fact partially explains the shift of one of the acoustic phonon peaks in the theoretical curve in Fig. I and influences the behavior of the PL spectra at higher temperatures. An important feature of ZnTe: 0 which is not shown in Fig. 1 is the separation between absorption and luminescence spectra which share only the zero phonon line (ZPL) and are mirror images of each other [4]. This property indicates that the excited states of the crystal ground state seen in luminescence and that of the oxygen-bound exciton state are the same as in absorption. This characteristic explains some peculiarities of the temperature dependence of the PL spectra of ZnTe which will be discussed later, The general features of the luminescence spectra as a function of the temperature are also well described by the model in the temperature range between 2 and 60 K. In particular, the slow disappearance of the phonon fine structure with increasing temperature is well reproduced. We notice also that the ZPL and the longitudinal optical (LO) replica disappear more rapidly than the structure related to acoustical phonons. This feature is also well reproduced in spite of the imprecise fit of the relative peak strengths. These features of the luminescence spectra show that the acoustic phonon contributions to the luminescence —
become more and more important with increasing temperature and become dominant for T ? 60K. It is interesting to note that in spite of the inaccurate handling of two-phonon processes in the model [2], the fit remains reasonable. We also note that above 60 K, a shift of the spectral position of the maximum of the luminescence intensity appears. The plot of the integrated intensities of the ZPL and of the first phonon replica are shown in Fig. 2. Both follow an exponential law, exp( yT2), with the experimental value for y given by y = = I x 10 ~K 2, This result is in good agreement with that of [3] which predicts. on the basis of multiphonon processes, that the total intensity of the ZPL and of the LO phonon replicas have the following temperature dependence: dE ~
~~tl3k ?
where E is the energy and I the intensity. This relation is obtained from the model of [2] by cxplicitly performing the integration over the expression for the luminescence intensity which is also presented in [2]. We note that it is derived assuming that the acoustic phonons can be treated in a Debye approximation. The value of Yi given above coincides with that found from the temperature dependence of the absorption [3]. Its value is comparable with that obtained for AgBr:I [1] once the material parameters are properly scaled. This indicates that the model used here gives a good description of the temperature dependence of the integrated luminescence of different isoelectronic traps. The integrated luminescence of the unstructured part of the spectra which is related to the acoustical phonons shows a more complicated behavior which is not shown here [5]. In the case of resonant excitation, the overall intensity is fitted by two exponential curves whose exponents y~and Y2 have the same value as for the absorption [5] and the low temperature part of which (T < 60K) follows (1). For band-to-band excitation the temperature dependence shows a different behavior. For values of the temperature between 2 and 60 K it decreases as predicted by (1), whereas it increases
V. Burki et al.
/ Journal of Luminescence 58
(1994) 206 209
209
10~
~
8 ,~
102
TL 10’
0
500
1000
1500
2000
2500
3000
3500
4000
2(K2)
T
Fig. 2. Temperature dependence of the integrated luminescence intensity of the zero phonon line (a) and of its first longitudinal optical replica (b).
for temperatures greater than 60K, and at room temperature the same efficiency as for 10K is obtained. While for resonant excitation the behavior of the luminescence is directly related to that of the absorption, the band-to-band excitation is more difficult to analyze. We notice however that in the temperature region below 60K both excitation regimes are well described by (1). Finally, for both excitations it is shown that the overlap between absorption and luminescence spectra remains negligible independent of the temperature [5].
References [1] Y. Burki, P. Schwendimann, W. Czaja and H. Berger, Europhys. Lett. 13 (1990) 555; Y. Burki, P. Schwendimann, W. Czaja and V. Capozzi, Europhys. Lett. 16 (1991) 163. [2] A. Testa, W. Czaja, A. Quattropani and P. Schwendimann, J. Phys. C 20 (1987) 1253. [3] V. Slusarenko, V. Burki, W. Czaja and H. Berger, Phys. Stat. Sol. B 161 (1990) 897. [4] RE. Dietz, D.G. Thomas and J.J. Hopfield, Phys. Rev. Lett. 8 (1962) 391 [5] Y. Burki, W. Czaja, V. Capozzi and P. Schwendimann, J. Phys.: Condens. Matter, to be published.
LUMINESCENCE ELSEVIER
Journal of Luminescence 58 (1994) 206 209
Dynamics of multiphonon processes in luminescence spectra of oxygen-bound excitons in ZnTe: 0 Y. Burkia, W. Czajaa, V. Capozzil~~*, P. Schwendimannc alnstitut de Physique Appliquèe, Ecole Politechnique Fèdèrale, CH-1015 Lausanne, Switzerland bDi•partimento di Fisica, Univers,tà degli studi di Ban, 1-70126 Ban, Italy ‘Defense Technology and Procurement Agency, System Analysis Division, CH-3003 Bern, Swit~erland
Abstract Photoluminescence (PL) spectra of oxygen-bound exciton transitions in ZnTe: 0 have been measured for temperatures ranging from 2 to 300 K and both for band-to-band excitation and for excitation resonant with the oxygen-bound exciton state. The temperature dependence of both optical and acoustical phonon contributions to the PL spectra is presented and discussed.
We present some results on the photoluminescence (PL) of the isoelectronic trap oxygen in ZnTe. Besides their relevance in their own right these results allow us to understand better the gain spectra recently observed in ZnTe : 0 and discussed in Ref. [1]. Bound exciton luminescence, which persists up to room temperature, is one of the most surprising features observed in this material. As will turn out in the following, the analysis of luminescence relies heavily on the formalism used earlier when discussing luminescence from the isoeiectronic trap AgBr : I [2]. The comparison between theory and experiment is satisfying for both traps. This indicates that the model of [2] is suited for the discussion of the optical properties of different isoelectronic traps. We consider two different excitation modes: a resonant mode corresponding to excitation via the 587 nm line of a rhodamine 6G dye laser into the excited states of the oxygen-
*
Corresponding author,
bound exciton and band-to-band excitation which is obtained with an Ar laser at 478 nm. These two excitation wavelengths are chosen in order to characterize the excitation mechanism which leads to optimum gain in ZnTe: 0 [1]. We shall refer to these two excitation modes explicitly when different behavior in the luminescence spectra related to the different excitation modes arises. Otherwise, all resuits refer to band-to-band excitation, which is easier to perform. Let us sketch briefly the model used for the fit of the ‘experimental curves; for mathematical details, we refer to [2]. It consists of two electronic levels (ground state and excited state), which are coupled to an electromagnetic field by the usual dipole coupling. The excited electronic state is also coupled to both the optical and the acoustical phonon modes of the crystal. This coupling, which is linear in the phonon amplitudes, accounts for the perturbation of the lattice due to the presence of the excited state. In the case of ZnTe: 0, longitudinal and transverse optical as well as acoustical
0022-2313/94/$07.00 C 1994 Elsevier Science B.V. All rights reserved SSDI 0022-2313(93)E0139-O
V. Burki el a!.
3000
/ Journal of Luminescence 58
‘ .
207
(1994) 206 209
2500
2000
:: 620
630
640
650
660
670
680
690
Wavelength (nm) Fig. 1. Fit (dotted line) of the luminescence spectra (solid line) for different temperatures from 2 to 60K.
phonons couple to the excited state. In the calculations the electron phonon interaction is diagonalized exactly, whereas the interaction with photons is treated by first-order perturbation theory. We evaluate the luminescence spectrum through the transition probability from the excited state dressed by the electron phonon interaction to the ground state of the system, which consists of phonon states and of the electronic ground state, The transition probability is averaged over a thermal distribution of the phonons in order to account for the temperature dependence of the luminescence spectrum. Moreover, it is integrated over the one-phonon density of states, which weights the different phonon contributions. This latter quantity is obtained from experiments, i.e. from neutron scattering data. As a result, the luminescence
spectrum is obtained as a function of temperature. The Huang Rhys factors for the different phonon modes, which are related to the amplitude of the different peaks in the spectrum and therefore to the strength of the electron phonon coupling, are obtained through a fit to the experimental spectra at low temperature (2 K). We assume that there is no relaxation within the excited state and that the vibrational states are the same for the crystal ground state and for the oxygen-bound exciton state. This assumption is reasonably confirmed by the experimental data. The results of the fit for luminescence are presented in Fig. 1. We begin by considering the luminescence spectrum at 2K in Fig. 1. The fit is rather satisfying, except for some inaccuracies in the position of the
208
V. Burki et al.
Journal of Luminescence 58 (1994) 206 209
acoustical phonon peaks. This indicates that we are working with an approximate description of the material. In fact, from group theoretical arguments a selection rule for ZnTe acoustical phonons follows which allows only phonon combinations with total momentum k 0 to couple to the electronic transitions. Thus, the optical phonons are allowed in one-phonon processes and are well reproduced in Fig. 1, whereas the acoustic phonons can assist only in combinations of at least two with vanishing total momentum. However, since the optical phonon branches in ZnTe are rather fiat, a large number of combinations of optical and acoustic phonons are possible. These will be responsible for the temperature dependence to be discussed laterandjustifytherathergoodfitfortemperatures lower than 60 K. However, the model only partially accounts for the selection rules characteristic of the material because the one-phonon density of states is used in the calculations. This fact partially explains the shift of one of the acoustic phonon peaks in the theoretical curve in Fig. I and influences the behavior of the PL spectra at higher temperatures. An important feature of ZnTe: 0 which is not shown in Fig. 1 is the separation between absorption and luminescence spectra which share only the zero phonon line (ZPL) and are mirror images of each other [4]. This property indicates that the excited states of the crystal ground state seen in luminescence and that of the oxygen-bound exciton state are the same as in absorption. This characteristic explains some peculiarities of the temperature dependence of the PL spectra of ZnTe which will be discussed later, The general features of the luminescence spectra as a function of the temperature are also well described by the model in the temperature range between 2 and 60 K. In particular, the slow disappearance of the phonon fine structure with increasing temperature is well reproduced. We notice also that the ZPL and the longitudinal optical (LO) replica disappear more rapidly than the structure related to acoustical phonons. This feature is also well reproduced in spite of the imprecise fit of the relative peak strengths. These features of the luminescence spectra show that the acoustic phonon contributions to the luminescence —
become more and more important with increasing temperature and become dominant for T ? 60K. It is interesting to note that in spite of the inaccurate handling of two-phonon processes in the model [2], the fit remains reasonable. We also note that above 60 K, a shift of the spectral position of the maximum of the luminescence intensity appears. The plot of the integrated intensities of the ZPL and of the first phonon replica are shown in Fig. 2. Both follow an exponential law, exp( yT2), with the experimental value for y given by y = = I x 10 ~K 2, This result is in good agreement with that of [3] which predicts. on the basis of multiphonon processes, that the total intensity of the ZPL and of the LO phonon replicas have the following temperature dependence: dE ~
~~tl3k ?
where E is the energy and I the intensity. This relation is obtained from the model of [2] by cxplicitly performing the integration over the expression for the luminescence intensity which is also presented in [2]. We note that it is derived assuming that the acoustic phonons can be treated in a Debye approximation. The value of Yi given above coincides with that found from the temperature dependence of the absorption [3]. Its value is comparable with that obtained for AgBr:I [1] once the material parameters are properly scaled. This indicates that the model used here gives a good description of the temperature dependence of the integrated luminescence of different isoelectronic traps. The integrated luminescence of the unstructured part of the spectra which is related to the acoustical phonons shows a more complicated behavior which is not shown here [5]. In the case of resonant excitation, the overall intensity is fitted by two exponential curves whose exponents y~and Y2 have the same value as for the absorption [5] and the low temperature part of which (T < 60K) follows (1). For band-to-band excitation the temperature dependence shows a different behavior. For values of the temperature between 2 and 60 K it decreases as predicted by (1), whereas it increases
V. Burki et al.
/ Journal of Luminescence 58
(1994) 206 209
209
10~
~
8 ,~
102
TL 10’
0
500
1000
1500
2000
2500
3000
3500
4000
2(K2)
T
Fig. 2. Temperature dependence of the integrated luminescence intensity of the zero phonon line (a) and of its first longitudinal optical replica (b).
for temperatures greater than 60K, and at room temperature the same efficiency as for 10K is obtained. While for resonant excitation the behavior of the luminescence is directly related to that of the absorption, the band-to-band excitation is more difficult to analyze. We notice however that in the temperature region below 60K both excitation regimes are well described by (1). Finally, for both excitations it is shown that the overlap between absorption and luminescence spectra remains negligible independent of the temperature [5].
References [1] Y. Burki, P. Schwendimann, W. Czaja and H. Berger, Europhys. Lett. 13 (1990) 555; Y. Burki, P. Schwendimann, W. Czaja and V. Capozzi, Europhys. Lett. 16 (1991) 163. [2] A. Testa, W. Czaja, A. Quattropani and P. Schwendimann, J. Phys. C 20 (1987) 1253. [3] V. Slusarenko, V. Burki, W. Czaja and H. Berger, Phys. Stat. Sol. B 161 (1990) 897. [4] RE. Dietz, D.G. Thomas and J.J. Hopfield, Phys. Rev. Lett. 8 (1962) 391 [5] Y. Burki, W. Czaja, V. Capozzi and P. Schwendimann, J. Phys.: Condens. Matter, to be published.