- Email: [email protected]
Energy transfer by exciton tunneling in GaP : N
Journal of Luminescence 12/13 (1976) 265—270 © North-1-Iolland Publishing Company
ENERGY TRANSFER BY EXCITON TUNNELING IN GaP : N P.J. WIESNER, R.A. STREET Max-Planck Inst itut für Festkorperforschung, Stuttgart, Germany
and H.D. WOLF
*
Siemens AG, Forschungslaboratorien, Munchen, Germany
Energy transfer by tunneling of bound excitons in GaP : N is investigated by timeresolved resonant excitation spectroscopy. Evidence for this process is observed in below band gap excitation spectra and the transfer rate is deduced from time-resolved measurenients using a simplified model.
The emission spectrum of excitons bound to the isoelectronic impurity nitrogen and to pairs of impurity atoms of differing separation has been investigated by Thomas and Hopfield [1]. The excitons bound to these pairs are labeled NN~,the subscript i indicating different pair separations. The series of the NN lines converge at high energy (i. 00) to the A and B lines, the isolated nitrogen bound excitons. Thomas and Hopfield [lj noticed that with increasing nitrogen concentration the relative emission strength shifts to the low energy NN lines. This behaviour is called “concentration quenching” and affects the performance of green light emitting GaP N diodes. In the present work this effect is investigated by excitation spectroscopy below the band gap and by time-resolved studies. Excitation spectra were obtained with a cw-dye laser operating with sodium fluorescein being continuously tunable from 5330 to 5670 A with 0.3 A resolution. The 2excitation power was of the order of 10mW focused to an area of about 0.1 mm on crystals immersed in liquid helium at 1.5 K. A rnonochromator with a resolution of typically 0.1 A was set to a fixed observation energy. Luminescence was detected by an RCA 31034 A02 photomultiplier and a photon counting system. Three typical excitation spectra of samples with different concentrations are shown in fig. 1. The observing monochromator was set to the NN 1 line in each case. The three epitaxial samples were selected out of a large number of crystals for high -~
*
Work performed while on leave of absence at the Max-Planck Institut für Festkorperforschung, Stuttgart. W. Germany. 265
266
P.1 Wiesner
[
Ct a!.
/ Energy
GaP:N
transfer by exciton tunneling in GaP: N
1.6 K
NN~~i~
2.5i0’~ N/cm~
NN~
X64
2
L 58 3 2.2 .1018 N /cm
I~I
/NN3
lOx Resolution
/
/
1A
/ NN I
I
7
I
I
2.20
2.24 2.28 2.32 EXCITATION ENERGY I cv) Fig. 1. NN1 excitation spectra of three GaP N samples with differing concentrations.
purity and homogeneous nitrogen distribution through the epitaxial layer. The nitrogen concentrations were determined by optical absorption measurements using 3 the V57, calculation Lightowlers al. [2] were 5.6InX sample 1017 N/cm for 2.2 X of 1018 N/cm3 foretL58 and. The 2.5 Xconcentrations 1019N/cm3 for V59. V59 approximately 14% of nitrogen atoms form near neighbour pairs. In the NN 1 excitation spectra, the presence of peaks corresponding to absorption h~tohigher energy exciton lines establishes that energy transfer to an NN state from exciton states of higher energy occurs when the N-concentration is sufficiently large
[31. In the low N concentration sample V57 the spectrum is dominated by transfer from the excitons bound to isolated N atoms (A, B —~ NN1) since NN pairing is weak. At higher concentrations (samples L58 and V59) transfer from excitons bound to MN pairs also becomes important (NN1 —~ NN1). The peaks in the spectra due to this process are labeled NN3--NN7. The other strong peaks are due to direct phonon assisted absorption into the NN1 level and to excited states of the NN1 state [41, and here no energy transfer is involved. Details of the transfer process are investigated by time resolved resonant luminescence measurements using a cavity pumped dye laser with a pulse width of 15 ns and a spectral resolution of 0.3 A. Time resolved photon counting allowed us to observe the luminescence build up and decay over more than three decades of intensity. Time resolved measurements were made corresponding to excitation into NN1 and emission from NN1. When i = / we refer to this as resonant decay and if / >/ as transfer decay. The reverse process (j> 1) cannot be observed because of the low phonon
P.J. Wiesner et al.
/ Energy
3
transfer by exciton tunneling in GaP: N
K/N
267
5 resonant decay
TIME
(~.tsec)
Fig. 2. Resonant decay of NN
5 and transfer decay of NN5
-+
NN1.
occupation numbers at 1 .5 K. Examples of resonant and transfer decay are shown in fig. 2 for the highly doped sample V59. The first part of the resonant decay in fig. 2 deviates markedly from an exponential, in contrast to the resonant decay of weaker doped samples. The shape of the transfer decay further differs from the resonant one; a distinct, finite risetime in the signal is observed. Both effects are due to the time required for energy transfer. Decay curves for transfer between NN pairs have been analysed elsewhere [3]. Taking into account the spatial distribution of NN pairs, the details of the transfer process can be explained by tunneling of the exciton between neighbouring pairs. We could show that other possible mechanisms for the energy transfer such as phonon assisted reabsorption or dipole—dipole interaction are of minor importa.nce in the present situation. The numerical analysis in terms of the tunneling model yields a characteristic tunneling length of about 40 A, consistent with the estimated extent of the bound exciton wave function. A very strong transfer process also occurs from isolated nitrogen atoms to NN pairs: examples for the B —~ NN1 transfer are shown in fig. 3, again for three different N concentrations. The exciting light is absorbed into the A-exciton (J = 1, allowed transition). From this state there is a very fast relaxation into the B-state of the same center. Before capture by an NN pair, the exciton will hop between B exciton levels many times since the concentration of isolated nitrogen is higher than that of all the NN pairs. This migration of the exciton can be described by a random walk with a capture probability by NN pairs which is constant in time. Thus the spatial distribution of N atoms need not be taken into account, and the B —~ NN1 TB transand fer decay can then be analysed simply as a three level system with lifetimes TNN 1. ~ is the lifetime of the B exciton and is determined by a combination of the true radiative lifetime and the rate of energy transfers to a//lower energy exciton levels. In all our samples transfer is very strong and dominates TB. TNN1 is the decay time of the NN1 exciton which is expected to be the radiative lifetime as there is no
268
P.1 Wiesner eta!.
/ Energy
transfer by exciton tunneling in GaP: N
;/Btransfrd
TIME
(~i
sec)
Fig. 3. Transfer decay of B — NN
1 for three different N concentrations. Measured data appear as dots. Solid lines are theoretical fits to the data as described in text.
significant transfer process from this level. The shorter lifetime appears as the risetime of the signal and the longer one as the decay time. The data in fig. 3 could therefore be analysed to obtain the two lifetimes both of which are found to depend on concentration. The fitting curves are shown in fig. 3 as solid lines, the resulting lifetimes are listed in table 1. The risetime of sample V59 is too short to be detected. The observed risetinies vary strongly with N-concentration and therefore clearly correspond to the B-exciton lifetime since this is dominated by transfer processes. The deduced NN1 lifetimes depend much less on concentration, and agree with values obtained from NN1 resonant decay experiments. From the above model the contribution TT, to the B exciton lifetime TB, from the transfer mechanism can be estimated as (1) where n is the average number of times the exciton hops between B exciton sites before a transfer event takes place, and p0 is the hopping rate. n can be calculated from the total nitrogen concentration N0 when we assume that pairing up to9the 51,tenth p nearest neighbours is significant. For sample V57, we find 3 X i0 0 is expected to be given by a tunneling formula Po
=
~o exp(—2R/a0),
(2)
where w0 is 1012__ 1013 s~, a0 the effective exciton radius, and R the average ni3. Setting a trogen separation, which varies as N~5~’ 0 = 40 A, this formula gives p0 = l010__lOhl s~ for sample V57, in reasonable agreement with experiment. Finally from table 1 it is seen that 1/TB increases with N0, and this is predicted by eq.(1) from the N0 dependence of 1/n and p0. In conclusion, we find that energy transfer between bound ecxitons in GaP: N can be identified from below band gap excitation spectra. The transfer rate was investigated by time resolved measurements and an analysis of the B —* NN 1 transfer
P.J. Wiesner et al. Table 1 Lifetimes
TB
/ Energy transfer by exciton
tunneling in GaP: N
and ~~NN
1deduced from the theoretical fit to the B
—~
269
NN1 transfer decay data
shown in fig. 3. Sample
Risetiine 120 ns
V.57 V58
N concentration 17 cm3 5.6 X i0 2.2 X 1018 cm3
45 ns
1.5 ~zs
V.59
2.5
<10 ns
1.05 gs
X
1019 cm3
(TB)
Falltinie (TNN) 1.9 ~s
is given. The resulting parameters are found to be consistent with the model of exciton tunneling [3].
References [11 D.G. Thomas and J.J. Hopfield, Phys. Rev. 150 (1966) 680. [21 E.C. Lightowlers, J.C. North and O.G. Lorinior, J. AppI. Phys. 45 (1974) 2191. [31 P.J. Wiesner, R.A. Street and H.D. Wolf, Phys. Rev. Letters 35 (1975) 1366. [41 R.A. Faulkner and P.J. Dean, J. Luminescence 1,2 (1970) 522; E. Cohen, M.D. Sturge, N.O. Lipari, M. Altarelli and A. Baldareschi, to be published.
Discussion R. Bhargava: Have you observed any tunneling process in which the transfer from nitrogen pairs to other radiative or nonradiative centers takes place? P. Wiesner: Yes, in samples of GaP: N codoped with Zn as an acceptor we could observe a transfer from excitons bound to isolated nitrogen to nitrogen—acceptor pairs with higher binding energy for excitons. A similar transfer process may be possible for other impurity states. P.J. Dean: Isn’t it true that there are analogies in the mathematics describing energy transfer between the system you discuss here and donor—acceptor pairs, much studied in GaP? Of course, in the latter case one is dealing with the diffuse tails of single particle wave—functions rather than exciton wave functions. P. Wiesner: Of course there are similarities in the analysis apart from the facts that the transfer ends at a pair of impurities and that the interaction is different.
ENERGY TRANSFER BY EXCITON TUNNELING IN GaP : N P.J. WIESNER, R.A. STREET Max-Planck Inst itut für Festkorperforschung, Stuttgart, Germany
and H.D. WOLF
*
Siemens AG, Forschungslaboratorien, Munchen, Germany
Energy transfer by tunneling of bound excitons in GaP : N is investigated by timeresolved resonant excitation spectroscopy. Evidence for this process is observed in below band gap excitation spectra and the transfer rate is deduced from time-resolved measurenients using a simplified model.
The emission spectrum of excitons bound to the isoelectronic impurity nitrogen and to pairs of impurity atoms of differing separation has been investigated by Thomas and Hopfield [1]. The excitons bound to these pairs are labeled NN~,the subscript i indicating different pair separations. The series of the NN lines converge at high energy (i. 00) to the A and B lines, the isolated nitrogen bound excitons. Thomas and Hopfield [lj noticed that with increasing nitrogen concentration the relative emission strength shifts to the low energy NN lines. This behaviour is called “concentration quenching” and affects the performance of green light emitting GaP N diodes. In the present work this effect is investigated by excitation spectroscopy below the band gap and by time-resolved studies. Excitation spectra were obtained with a cw-dye laser operating with sodium fluorescein being continuously tunable from 5330 to 5670 A with 0.3 A resolution. The 2excitation power was of the order of 10mW focused to an area of about 0.1 mm on crystals immersed in liquid helium at 1.5 K. A rnonochromator with a resolution of typically 0.1 A was set to a fixed observation energy. Luminescence was detected by an RCA 31034 A02 photomultiplier and a photon counting system. Three typical excitation spectra of samples with different concentrations are shown in fig. 1. The observing monochromator was set to the NN 1 line in each case. The three epitaxial samples were selected out of a large number of crystals for high -~
*
Work performed while on leave of absence at the Max-Planck Institut für Festkorperforschung, Stuttgart. W. Germany. 265
266
P.1 Wiesner
[
Ct a!.
/ Energy
GaP:N
transfer by exciton tunneling in GaP: N
1.6 K
NN~~i~
2.5i0’~ N/cm~
NN~
X64
2
L 58 3 2.2 .1018 N /cm
I~I
/NN3
lOx Resolution
/
/
1A
/ NN I
I
7
I
I
2.20
2.24 2.28 2.32 EXCITATION ENERGY I cv) Fig. 1. NN1 excitation spectra of three GaP N samples with differing concentrations.
purity and homogeneous nitrogen distribution through the epitaxial layer. The nitrogen concentrations were determined by optical absorption measurements using 3 the V57, calculation Lightowlers al. [2] were 5.6InX sample 1017 N/cm for 2.2 X of 1018 N/cm3 foretL58 and. The 2.5 Xconcentrations 1019N/cm3 for V59. V59 approximately 14% of nitrogen atoms form near neighbour pairs. In the NN 1 excitation spectra, the presence of peaks corresponding to absorption h~tohigher energy exciton lines establishes that energy transfer to an NN state from exciton states of higher energy occurs when the N-concentration is sufficiently large
[31. In the low N concentration sample V57 the spectrum is dominated by transfer from the excitons bound to isolated N atoms (A, B —~ NN1) since NN pairing is weak. At higher concentrations (samples L58 and V59) transfer from excitons bound to MN pairs also becomes important (NN1 —~ NN1). The peaks in the spectra due to this process are labeled NN3--NN7. The other strong peaks are due to direct phonon assisted absorption into the NN1 level and to excited states of the NN1 state [41, and here no energy transfer is involved. Details of the transfer process are investigated by time resolved resonant luminescence measurements using a cavity pumped dye laser with a pulse width of 15 ns and a spectral resolution of 0.3 A. Time resolved photon counting allowed us to observe the luminescence build up and decay over more than three decades of intensity. Time resolved measurements were made corresponding to excitation into NN1 and emission from NN1. When i = / we refer to this as resonant decay and if / >/ as transfer decay. The reverse process (j> 1) cannot be observed because of the low phonon
P.J. Wiesner et al.
/ Energy
3
transfer by exciton tunneling in GaP: N
K/N
267
5 resonant decay
TIME
(~.tsec)
Fig. 2. Resonant decay of NN
5 and transfer decay of NN5
-+
NN1.
occupation numbers at 1 .5 K. Examples of resonant and transfer decay are shown in fig. 2 for the highly doped sample V59. The first part of the resonant decay in fig. 2 deviates markedly from an exponential, in contrast to the resonant decay of weaker doped samples. The shape of the transfer decay further differs from the resonant one; a distinct, finite risetime in the signal is observed. Both effects are due to the time required for energy transfer. Decay curves for transfer between NN pairs have been analysed elsewhere [3]. Taking into account the spatial distribution of NN pairs, the details of the transfer process can be explained by tunneling of the exciton between neighbouring pairs. We could show that other possible mechanisms for the energy transfer such as phonon assisted reabsorption or dipole—dipole interaction are of minor importa.nce in the present situation. The numerical analysis in terms of the tunneling model yields a characteristic tunneling length of about 40 A, consistent with the estimated extent of the bound exciton wave function. A very strong transfer process also occurs from isolated nitrogen atoms to NN pairs: examples for the B —~ NN1 transfer are shown in fig. 3, again for three different N concentrations. The exciting light is absorbed into the A-exciton (J = 1, allowed transition). From this state there is a very fast relaxation into the B-state of the same center. Before capture by an NN pair, the exciton will hop between B exciton levels many times since the concentration of isolated nitrogen is higher than that of all the NN pairs. This migration of the exciton can be described by a random walk with a capture probability by NN pairs which is constant in time. Thus the spatial distribution of N atoms need not be taken into account, and the B —~ NN1 TB transand fer decay can then be analysed simply as a three level system with lifetimes TNN 1. ~ is the lifetime of the B exciton and is determined by a combination of the true radiative lifetime and the rate of energy transfers to a//lower energy exciton levels. In all our samples transfer is very strong and dominates TB. TNN1 is the decay time of the NN1 exciton which is expected to be the radiative lifetime as there is no
268
P.1 Wiesner eta!.
/ Energy
transfer by exciton tunneling in GaP: N
;/Btransfrd
TIME
(~i
sec)
Fig. 3. Transfer decay of B — NN
1 for three different N concentrations. Measured data appear as dots. Solid lines are theoretical fits to the data as described in text.
significant transfer process from this level. The shorter lifetime appears as the risetime of the signal and the longer one as the decay time. The data in fig. 3 could therefore be analysed to obtain the two lifetimes both of which are found to depend on concentration. The fitting curves are shown in fig. 3 as solid lines, the resulting lifetimes are listed in table 1. The risetime of sample V59 is too short to be detected. The observed risetinies vary strongly with N-concentration and therefore clearly correspond to the B-exciton lifetime since this is dominated by transfer processes. The deduced NN1 lifetimes depend much less on concentration, and agree with values obtained from NN1 resonant decay experiments. From the above model the contribution TT, to the B exciton lifetime TB, from the transfer mechanism can be estimated as (1) where n is the average number of times the exciton hops between B exciton sites before a transfer event takes place, and p0 is the hopping rate. n can be calculated from the total nitrogen concentration N0 when we assume that pairing up to9the 51,tenth p nearest neighbours is significant. For sample V57, we find 3 X i0 0 is expected to be given by a tunneling formula Po
=
~o exp(—2R/a0),
(2)
where w0 is 1012__ 1013 s~, a0 the effective exciton radius, and R the average ni3. Setting a trogen separation, which varies as N~5~’ 0 = 40 A, this formula gives p0 = l010__lOhl s~ for sample V57, in reasonable agreement with experiment. Finally from table 1 it is seen that 1/TB increases with N0, and this is predicted by eq.(1) from the N0 dependence of 1/n and p0. In conclusion, we find that energy transfer between bound ecxitons in GaP: N can be identified from below band gap excitation spectra. The transfer rate was investigated by time resolved measurements and an analysis of the B —* NN 1 transfer
P.J. Wiesner et al. Table 1 Lifetimes
TB
/ Energy transfer by exciton
tunneling in GaP: N
and ~~NN
1deduced from the theoretical fit to the B
—~
269
NN1 transfer decay data
shown in fig. 3. Sample
Risetiine 120 ns
V.57 V58
N concentration 17 cm3 5.6 X i0 2.2 X 1018 cm3
45 ns
1.5 ~zs
V.59
2.5
<10 ns
1.05 gs
X
1019 cm3
(TB)
Falltinie (TNN) 1.9 ~s
is given. The resulting parameters are found to be consistent with the model of exciton tunneling [3].
References [11 D.G. Thomas and J.J. Hopfield, Phys. Rev. 150 (1966) 680. [21 E.C. Lightowlers, J.C. North and O.G. Lorinior, J. AppI. Phys. 45 (1974) 2191. [31 P.J. Wiesner, R.A. Street and H.D. Wolf, Phys. Rev. Letters 35 (1975) 1366. [41 R.A. Faulkner and P.J. Dean, J. Luminescence 1,2 (1970) 522; E. Cohen, M.D. Sturge, N.O. Lipari, M. Altarelli and A. Baldareschi, to be published.
Discussion R. Bhargava: Have you observed any tunneling process in which the transfer from nitrogen pairs to other radiative or nonradiative centers takes place? P. Wiesner: Yes, in samples of GaP: N codoped with Zn as an acceptor we could observe a transfer from excitons bound to isolated nitrogen to nitrogen—acceptor pairs with higher binding energy for excitons. A similar transfer process may be possible for other impurity states. P.J. Dean: Isn’t it true that there are analogies in the mathematics describing energy transfer between the system you discuss here and donor—acceptor pairs, much studied in GaP? Of course, in the latter case one is dealing with the diffuse tails of single particle wave—functions rather than exciton wave functions. P. Wiesner: Of course there are similarities in the analysis apart from the facts that the transfer ends at a pair of impurities and that the interaction is different.