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Localized and bound excitons in type-II ZnMnSe/ZnSSe quantum wells
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 425301 (http://iopscience.iop.org/0953-8984/26/42/425301) View the table of contents for this issue, or go to the journal homepage for more
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 425301 (8pp)
doi:10.1088/0953-8984/26/42/425301
Localized and bound excitons in type-II ZnMnSe/ZnSSe quantum wells A V Chernenko and A S Brichkin Institute of Solid State Physics, RAS, 142432, Chernogolovka, Russia E-mail: [email protected] Received 1 July 2014, revised 18 August 2014 Accepted for publication 2 September 2014 Published 2 October 2014 Abstract
Photoluminescence of ZnMnSe/ZnSSe multiple quantum wells under a bandgap continuous wave and fs-pulsed excitations is measured in magnetic fields up to 10 T in Faraday geometry at temperatures within the range of 1.6–20 K. The measurements reveal two dominant lines in the spectra and LO-phonon replicas of the lower-energy line. The photoluminescence and time-resolved studies show dramatically different behaviour of the lines. Analysis of their properties reveals that they correspond to recombination of indirect localized excitons and indirect acceptor-bound excitons (A0 X). Crossing of exciton and A0 X lines because of the difference in magnitudes of their Zeeman shifts is observed. Analysis of LO-phonon replicas of photoluminescence lines provides additional evidence for strong carrier localization bound to A0 X. A model of phonon-assisted recombination of indirect acceptor-bound excitons is proposed. The fitting of photoluminescence lines with this model gives the Huang–Rhys factor S 0.25 for A0 X and the hole localization size ah 30 Å. Contrary to expectations the exciton magnetic polaron effect is hardly observed in these structures. Keywords: diluted magnetic semiconductors, quantum wells, excitonic magnetic polaron, time-resolved spectroscopy, acceptor-bound exciton (Some figures may appear in colour only in the online journal)
in [2, 3] revealed the presence of two broad lines in PL spectra. The lower- and upper- energy lines were attributed to recombination of strong magnetically and non-magnetically localized EMPs, respectively. To explain the presence of the lines two types of localizing potential with characteristic sizes 4 nm and 20 nm were proposed in [3]. However, later studies of these structures [4] revealed that the EMP effect is much smaller than reported in [5] The authors of [4] focused on PL studies of the structures and did not pay attention to this experimental fact, whereas it clearly contradicts the results of [3]. The EMP energy EEMP 7 meV found by Maksimov et al [4] is much smaller than EEMP 20 meV reported in [3]. According to the EMP theory [1] it also means a much larger EMP lateral dimension than d 4 as reported in [3] for the magnetically localized EMP. The observed discrepancy demands additional study of the structures. In order to address this issue magnetoluminescence measurements were carried out on type-II ZnMnSe/ZnSSe multiple QW structures under various excitation power densities, temperatures and magnetic fields using CW and fspulsed non-resonant excitations.
1. Introduction
In diluted magnetic semiconductors (DMS) the exchange interaction between the spins of charge carriers and magnetic ions results in the giant Zeeman splitting and exciton magnetic polaron (EMP) formation. Intensive optical studies of EMPs in type-I DMS quantum wells (QWs), mainly localized EMPs, revealed that the EMP formation can be limited by the long spin relaxation time which often exceeds the exciton lifetime [1] so that the polaron system cannot reach complete thermal equilibrium. Type-II quantum wells (QWs) are attractive objects for studying exciton magnetic polarons (EMPs) because of the supposedly long lifetimes of excitons in such structures of the order of nanoseconds. The formation of EMP in type-II DMS structures could be realized if the influence of bound exciton complexes was negligible. The experimental results presented below show that this is not the case and the bound exciton complexes, mainly acceptor-bound excitons, could dramatically change exciton dynamics and prevent the formation of EMPs. Photoluminescence studies of type-II DMS QW structures 0953-8984/14/425301+08$33.00
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© 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 425301
A V Chernenko and A S Brichkin
Our PL studies under CW excitation and time-integrated measurements using pulsed excitation showed the presence of LO and 2LO replicas only of the lower-energy line and their absence for the upper-energy line. Besides this, time-resolved PL measurements revealed that temporal evolutions of upperand lower-energy lines are dramatically different. Namely, the initially stronger upper-energy line almost disappears during the 50–150 ps period after the laser pulse, whereas the intensity of the lower-energy line substantially increases. The lifetime of the lower-energy line exceeds 10 ns. It is also found that the energy shift of the EMP line in time-resolved spectra is much smaller than that predicted by the theory for EMPs localized by means of 4 nm traps as was proposed by Toropov et al [3]. The obtained results can be explained by attributing the upper- and lower-energy lines to recombination of indirect localized excitons and acceptor-bound excitons (A0 X), respectively. Analysis of LO-phonon replicas of A0 X allows for the estimation of A0 X size ah 30 Å at B = 0 T. The experimental data shows that the EMP effect is negligible for excitons because of their short lifespan and for bound excitons because of their singlet structure. This paper is organized as follows: in section 2 we describe the samples and the experimental setup, section 3 presents the results of PL measurements under CW excitation while the results of time-resolved measurements are presented in section 4. The model of LO-phonon assisted recombination of type-II A0 X is presented in section 5. The fitting procedure for PL curves is presented and the values of the Huang–Rhys factor extracted from PL data are discussed in this section. The relation of the experimental data with the magnetic polaron effect and impurity bound excitons is discussed in sections 6 and 7 summarizes the results.
(a)
(b)
Iup
I 0 A X
I 0 A X
1000J0
Intensity, a.u.
1000J0 200J0
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50J0
50J0
10J0 I I 2LO LO
2.70
Iup
J0
2.76 2.82 Energy, eV
I 2LO
2.70
I LO
10J0 J0
2.76 2.82 Energy, eV
Figure 1. Normalized PL spectra of (a) sample #1 (x = 10% Mn) and (b) sample #2 (x = 16% Mn) recorded at B = 0 T, T = 1.6 K and various levels of excitation power density. Here J0 = 0.2 W cm−2 . LO- and 2LO-phonon replicas of the A0 X line are marked.
each of full width at a half-maximum of approximately 12–15 meV. The peaks are separated from each other by 18–20 meV. LO-phonon replicas of the lower-energy line are well resolved, whereas those of the upper-energy line are invisible in the spectra. The large width of the lines indicates strong inhomogeneous broadening due to the interface roughness and alloy content fluctuations in ZnSSe and ZnMnSe layers. The intensity of the lower-energy line quickly decreases with an increase in the temperature T for both samples, whereas the intensity of the upper-energy line Iup increases with T as is clear in figure 2. The spectra demonstrate that the peak position of the lower-energy line does not change with the increase in T . The intensities of the lines demonstrate different dependencies on excitation power. Particularly, the lowerenergy line dominates in the PL spectra at low excitation power density (J = J0 = 0.2 W cm−2 ) in sample #1 (figure 1(a)). The intensity of the upper-energy line quickly increases with J whereas the increase in the lower-energy line is much smaller. The lower-energy line demonstrates saturation with the increase in excitation power, so that the upper-energy line dominates at high J . In contrast, in sample #2 the lower-energy line dominates for the whole range of J and the intensity of the upper-energy line becomes comparable to that of the lower-energy line only at the highest excitation power J = 1000J0 = 200 W cm−2 (See figure 1(b)). The spectra are recorded at the same power but various temperatures are shown in figure 2. They reveal a sharp decrease in the intensity of the lower-energy line IA0 X and an increase in the intensity of the upper-energy line Iup 1 .
2. Experimental details
Two MBE grown samples containing 10 periods of Zn0.9 Mn0.1 Se[8 nm]/ZnS0.16 Se0.84 [18 nm] (sample #1) and Zn0.84 Mn0.16 Se [8 nm]/ZnS0.16 Se0.84 [18 nm] (sample #2) QWs’ were used in the measurements. The sample #2 with x = 16% is similar to that used in [3], where details of the growth procedure can be found. Both samples were also used in the paper of Maksimov et al [4]. A CW Ar+ laser (λ = 351 nm) was used for the above bandgap excitation. The PL signal was dispersed by a monochromator with 600 gr mm−1 grating and was recorded by a liquid nitrogen cooled CCD camera. The frequency-doubled emission of a Ti:Sp fs-laser with λ 400 nm and a repetition rate 80 MHz was used for pulsed excitation of the sample. A streak camera with a time-scale resolution of 10 ps was used in time-resolved measurements. The samples were immersed in liquid He in a cryostat equipped with a superconducting magnet.
1 The decrease in the intensity of A0 X line with T allows estimation of its binding energy under the assumption that intensities of the exiton and D0 X lines similarly vary with T. Approximating the dependence IA0 X (T ) by the expression IA0 X (T ) = A/(1 + B exp (−/kB T )) the values of 1 = 17 ± 3 meV and 2 = 20 ± 6 meV are obtained for spectra of sample #1 and sample #2, respectively (figure 2). Here A and B are additional fitting parameters. More complicated temperature dependence of IA0 X is proposed by [6].
3. PL spectra under CW excitation and line identification
Two broad lines dominate in the photoluminescence spectra of the samples under CW laser excitation as shown in figure 1, 2
J. Phys.: Condens. Matter 26 (2014) 425301 Iup 10 K IA0X
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A V Chernenko and A S Brichkin
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Iup10 K IA0X
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12 K I2LO
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2.75
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Energy, eV
Figure 2. PL spectra of (a) sample #1 (x = 10% 0) at constant
excitation power density J = 0.2 W cm−2 and (b) sample #2 (x = 16%) at J = 10 W cm−2 . The spectra are recorded at B = 0 T and various temperatures.
Figure 3. PL spectra of (a) sample #1 recorded at excitation power density J = 2 W cm−2 and (b) sample #2 recorded at J = 40 W cm−2 at various magnetic fields B = 0 − 10 T . The results of fitting the data with (3) are shown as a dotted lines for all B values. The detailed structure of the fitting line is shown for both samples of data at B = 0 T and B = 10 T. The red dotted curve corresponds to the aggregated fitting curve, which includes contributions from the dashed magenta line Iup corresponding to exciton+D0 X recombination, the dashed green curve IA0 X corresponding to A0 X and its LO-phonon replicas, the solid blue curve which is related to the additional line Iadd and its LO-phonon replica. The circular polarization of the additional line rapidly reaches 100% with B > 0.5T . The additional line can be attributed the exciton bound on an acceptor with larger binding energy. The detailed evolution of the PL spectra of sample #1 recorded at J = 2 W cm−2 in magnetic fields up to 2 T is shown in (c). The complex structure of the upper-energy line Iup from the PL of sample #1 is clearly visible on the spectrum. It is related to the recombination of donor-bound excitons D 0 X.
The lines demonstrate different behaviour in a magnetic field. Both lines exhibit substantial redshift and become σ + polarized in magnetic field B 0z . The upper-energy line shifts faster than the lower-energy line and at high magnetic fields B 6 T the lines become poorly resolved so that only one combined line remains in the spectrum (see figure 3). The upper-energy line Iup in the PL spectra presented in figure 1 was attributed by Toropov et al to the recombination of weakly non-magnetically localized excitons, whereas the lower-energy line was attributed to the EMP of strong magnetically localized excitons [3]. The existence of two types of localizing potentials with different characteristic sizes ∼20–30 nm and ∼4 nm and two mechanisms of localization were proposed. However, our studies of PL spectra recorded at low excitation powers and with the PL line fitting as discussed in section 5 unambiguously indicate that both lines have a complex structure and each consists of at least two lines. The fitting of PL curves presented in figures 3(a) and (b) shows that an additional line Iadd exists in the vicinity of the lower-energy line. The line Iadd increases in intensity with B and forms a well-resolved shoulder at the magnetic fields B > 6 T. The complex structure of the upper-energy line is clearly visible in figures 1 and 3. The presence of additional lines contradicts the model of [3]. The experimental results are well explained if one accepts the dominant role of non-magnetic localization for both lines. The lines related to recombinations of acceptor (A0 X) and donor (D 0 X) bound excitons usually dominate in PL spectra of bulk DMS materials at low excitation densities [7, 8]. A similar picture is observed in the PL spectra of CdTe/CdMnTe [1] and CdMnTe/CdMgTe QWs [9]. A magnetic field dependence similar to that of figure 3 was reported for bulk DMS [10, 11], where two lines and their crossing in a magnetic field was observed. The lowerenergy and upper-energy lines were attributed, respectively, to recombinations of acceptor-bound and free excitons. It is straightforward for us to ascribe the lower-energy line to
the recombination of the indirect acceptor bound excitons and upper-energy line to the indirect localized excitons together with donor bound excitons. With such an interpretation the whole set of experimental results presented here can be easily explained. For instance, the decrease in intensity of the lowerenergy line and the increase in intensity of the upper-energy line with the increase in temperature shown in figure 2 is caused by the thermal dissociation of acceptor bound excitons [7]2 . The Zeeman shift of both lines in Faraday geometry is well described by the modified Brillouin function [1]: 1 EZ = (e (B) + h (B)) 2 1 5µb g(B + Bex ) = − (αN0 − βN0 )xγ S0 × Br5/2 , 2 2kB (T + T0 ) (1) where g = 2 is the g-factor of Mn2+ electrons, T is the bath temperature, S0 is the effective Mn2+ spin, x is the Mn2+ fraction; e (B) and h (B) are splittings of electron and hole states in a magnetic field, αN0 260 meV and βN0 −1310 meV are the parameters of exchange interaction 2
3
See footnote 1.
J. Phys.: Condens. Matter 26 (2014) 425301
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0 2 4 6 8 10 0 2 4 6 8 10 Magnetic field, T
2.80
+
Iup (Iex ID0X) IA0X
2.78 2.76 2.74
Figure 4. Zeeman shift of Iup (exciton +D 0 X) and A0 X line peak positions in σ + -polarized spectra for a) sample #1 and b) sample #2 in Faraday geometry. The results of fitting the lines with the Brilluene function (1) are shown by solid black lines.
0
100
200
300
400
500
600
Time. ps Figure 5. Streak-camera images of sample #1 photoluminescence spectra recorded at B = 0 T and excitation power densities (a) 40 W cm−2 and (b) 120 W cm−2 . The PL intensity increases from a blue color to red. The time scale is shifted backwards by 60 ps.
of electrons and holes, respectively. Parameter T0 is introduced to describe antiferromagnetic coupling of Mn2+ pairs and parameter γ reflects the fact that only part of the exciton function can penetrate inside the DMS area. The polaron magnetic field Bex is introduced to account for the possible polaron effect [1, 12]. The equation (1) was used in [4] to fit the Zeeman shift of the lower-energy line under the assumption that the polaron effect takes place. With the same assumption the best fit of the Zeeman shift of the A0 X line displayed in figure 4 gives Bex 0.5 − 0.9 T and T0 5, which corresponds to Emp 6−8 meV for both samples. However, the Zeeman shift is equally well fitted with Bex = 0 T and with Teff = 10 ± 1 K and Teff = 12 ± 1 K for samples #1 and #2, respectively. It means that the fitting procedure by means of (1) cannot serve as evidence for the presence or absence of the polaron effect, mainly because of the broad PL lines. The upper-energy line (exciton + D 0 X) demonstrates a larger Zeeman shift than that of the A0 X line and crosses the latter at relatively low magnetic fields. This effect was attributed by Toropov et al to destabilization of EMP [3]. Note, however, that the presence of LO-phonon replicas of the EMP line even at B = 10 T would imply the existence of EMP even at such a high field, while the disappearance of the EMP line from PL spectra was observed at B > 6 T in type-I DMS QWs [1], where EMP binding energy is Eex 20 meV. The Eex does not exceed 7 meV in our case therefore complete destabilization of EMP is expected at lower magnetic fields [1]. Thus, the lower-energy line in our structures must disappear from spectra at B < 10 T.
decays exponentially with a characteristic time 110 ps. The upper-energy line dominates in the spectra until 250 ps after the excitation pulse. At longer times, Iup demonstrates a 5 meV and 6 meV redshift and disappears from the spectra at τ > 600 ps. The A0 X line dominates in the spectra at τ > 400 ps. A comparison of the spectra at τ = 13 ns and 650 ps reveals an additional redshift of the A0 X line by E 2 − 3 meV. Similar time-resolved spectra are observed for sample #2 at two levels of laser excitation, J = 20 W cm−2 and J = 200 W cm−2 as presented in figure 6. Both lower- and upperenergy lines are well resolved in the spectra. The characteristic rise times of the intensity are about 20 ps for both lines. The decay time of the upper-energy line strongly depends on the excitation power density. The spectrum recorded at J = 20 W cm−2 reveals domination of the upper-energy line during the first 120 ps after the laser pulse. Under higher laser excitations the upper-energy line becomes more robust and dominates in the spectra up to τ = 250 ps. A weak and longliving tail related to exciton + D 0 X luminescence is visible in the spectra even at τ > 650 ps after the laser pulse. It demonstrates no redshift. The dependence of the upper-energy line on the excitation power leads to the 3 meV and 4 meV blueshift of the exciton line peak with an increase in power clearly visible in the PL spectra under CW excitation. The intensity of IA0 X quickly increases at τ < 30 ps. It continues to increase up to 400 ps and slowly decreases afterwards. The lower-energy line lives even longer than the distance between the subsequent laser pulses (13 ns). The behaviour of the decay of the IA0 X line does not depend on the excitation intensity. The lower-energy line demonstrates a 5–7 meV redshift during a 120–650 ps period after the laser pulse. The LO-phonon replica located approximately 32 meV below the lower-energy line is well resolved in the spectra. The A0 X line demonstrates a total redshift of 6–8 meV at 13 ns after the laser pulse as shown in figures 5 and 6 which is much smaller than that predicted by the EMP theory [1]. The
4. Analysis of time-resolved spectra
Time-resolved PL measurements produce important information about temporal evolution of the lines and clearly demonstrate their different nature. The spectra of sample #1 are presented in figure 5. The characteristic rise times of the intensity are about 20 ps for both IA0 X and Iup lines. The upper-energy line Iup reaches maximum intensity at τ = 20 ps, and after that the line 4
J. Phys.: Condens. Matter 26 (2014) 425301
Energy, eV
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A V Chernenko and A S Brichkin
2.80 IA0X
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Energy, eV
The model of phonon-assisted donor-acceptor pair recombination is appropriate in our case because of the spacial separation between electrons and holes. The model allows an estimation of the HR factor and provides an understanding of its evolution with a magnetic field. Within the effective mass approximation the wavefunction of thee-h pair localized on a donor-acceptor pair is merely a product of the electron fe (r) and hole fh (r) envelopes F (re , rh , R) = fe (re )fh (rh − R). Here re and rh are electron and hole coordinates with respect to the acceptor and donor centres, respectively, and R is the distance between the centres. It is assumed that the acceptor bound hole wave-function has a hydrogen-like form. The anisotropy of the hole mass is also omitted for the purpose of simplicity because it substantially complicates the analytical expression [18]. Even in this case the final expression, which relates S with the electron and hole characteristic sizes and the separation between their centres of localization R, has a complicated form [19]. In the limit ae ah and ah /R → 0, a well-known expression can be obtained:
+
Iup (Iex ID0X)
+
Iup (Iex ID0X)
2.80 IA0X
2.78 2.76
ILO
2.74 0
100
200
300
400
500
600
Time. ps Figure 6. Streak-camera images of sample #2 photoluminescence spectra recorded at B = 0 T and excitation power densities (a) 20 W cm−2 and (b) 200 W cm−2 . The PL intensity increases from a blue color to red. The time scale is shifted backwards by 60 ps. A luminescence reminiscent of the previous pulse is clearly visible.
5 e S(B) = 16 h ¯ ωLO
timescale is shifted backwards by 60 ps in order to demonstrate the reminiscent luminescence from the previous pulse which does not disappear even after 13 ns from the laser pulse. The increase in total intensity of the PL spectra with the magnetic field clearly visible in figure 3 is related mainly to the destabilization of A0 X in the magnetic field since excitons start to develop a much shorter lifespan. The suppression of nonradiative recombination of e-h complexes by the magnetic field observed in bulk and low-dimensional DMS structures [13] can also contribute to the observed effect.
1 1 − ∞ 0
1 ah (B)
(2)
The assumptions are reasonable because the electron mass is much smaller than that of the hole and the distance R between the electron and hole centres of gravity is much larger than ah . Within the framework of the model PL curves in figure 3 are fitted with the expression [20]: E 3 S p −S e E03 p=0 p! E0 − p¯hωLO − E 2 + Iex (E) × exp −4 ln 2
I (E) = A
5. LO-phonon replicas of A0 X line and their relation to hole localization
+Iadd (E),
The results of magnetic field dependencies under steady state excitation presented in figure 3 display an evolution of no-phonon (NP), 1LO- and 2LO- phonon replicas of A0 X line in a magnetic field in Faraday geometry. The LO-phonon replicas can be used for an estimation of the exciton localization dimension in the structures under study here because the ration ILO /INO is related to the strength of the exciton-complex-LO-phonon interaction, which, in turn, depends on e-h pair localization. Within the Frank–Condon approximation [14] the intensity of j -th phonon-assisted replica is Ij = S j e−S /j !, where j = 0, 1..n. The Huang–Rhys (HR) factor S determines the strength of polar exciton-LO-phonon coupling [15–17]. It is given by the expression S = q |Vq |2 /(¯hωLO )|ρq |2 , where ρq is the Fourier transform of the charge distribution and |Vq |2 = (2π e2 )/(|q|2 V )(1/ ∞ − 1/ 0 ) is the square of the amplitude Vq of exciton-LO-phonon polar interaction. The charge distribution for the free exciton ground state is given by ρq = F (re = r, rh = r)|eiqre − eiqrh |F (re = r, rh = r), where F (re , rh ) is the exciton envelope function and re and rh are electron and hole coordinates, respectively. The LOphonon energy is h ¯ ωLO
(3)
where , E0 , S are the width of PL lines (p = 0, 1, 2, 3..), the position of the no-phonon (NP) line, the HR factor, respectively. The constant A = I (E0 )/( p=0 S p /p!e−S × exp(−4 ln 2(E0 − p¯hωLO − E/ )2 )) is related with spectrum intensity I (E0 ) at the energy position E0 . The term Iex (E) = Aex exp((Eex − E)/ ex )2 is added in order to account for the exciton recombination. Here Eex is the exciton peak position and ex is its line-width. In order to take into account the additional line clearly visible in the spectra at B > 5T a term Iadd (E) similar to I (E) is also added. The Iadd line is essential to obtain an acceptable fitting of the PL lines at small magnetic fields B < 5 T which is demonstrated in figure 3 on the example of line fitting at B = 0 T. The origin of Iadd is not clear. Its peak is located 17 ± 1 meV below the IA0 X and 35 ± 1 meV below Iex . It can hardly be related to the LO-phonon replica of exciton PL, because it is clearly visible in the spectra at B = 10 T, whereas Iex is not observed at an energy 35 meV above Iadd . It is also not related to the TO-phonon replica of IA0 X , since TO-phonon energy in ZnSe is about h ¯ ωTO 25 meV. It could be related 5
J. Phys.: Condens. Matter 26 (2014) 425301
A V Chernenko and A S Brichkin
by the magnetic field. However, the crossing of A0 X and the upper-energy lines in the magnetic field was previously observed in bulk materials [10, 23, 24]. The crossing of X+ trions and exciton X lines in a magnetic field in a p-doped CdMnTe/CdTe QWs was also reported [25]. A comprehensive theoretical model for this effect has not been created up to now [26] although the effect was observed in earlier DMS studies [27]. In the paper of Mycielski [28] the smaller Zeeman shift of the A0 X line was attributed to the strong hh and lh mixture of hole states, which leads to the smaller Zeeman splitting of these states with B. This could be the reason for the reduction in the Zeeman splitting in weak magnetic fields. However, the hh-lh splitting Ehh−lh in the structures under study is estimated to be larger than 60 meV. Indeed, the size quantization and strain caused by the lattice mismatch between ZnMnSe and ZnSSe layers contribute to Ehh−lh . The hh-lh splitting at k = 0 produced by the strain is Ehh−lh = b( xx + yy − 2 zz ) [29], where xx = yy = (aZnMnSe − aZnSSe )/aZnMnSe and b is a material constant. The material parameters for ZnMnSe are not known; for the estimation of Ehh−lh we assume them to be equal to those for ZnSe [5]. With the lattice parameters from [5] the strain is xx = 1% for x = 10% and xx = 1.5% for x = 16%. ZnSe ZnSe For instance, bZnSe = −1.2 eV, C11 = 0.826 Mbar, C12 = 0.498 Mbar. Using these parameters the hh-lh splitting turns out to be Ehh−lh = Ehh − Elh = −2bZnSe ( xx − zz ) −50 meV, where zz = −2C12 /C11 . With the lh and hh masses in ZnSe mhh (ZnSe) = 0.6, mlh (ZnSe) = 0.145 [5] the contribution to Ehh−lh splitting due to the size quantization is estimated to be less than 10 meV in both samples. Thus, the total value of Ehh−lh is within the range −50 to 60 meV. The gap in Zeeman splitting between hh and lh levels does not exceed 50 meV at B = 10 T and, therefore, the hh-lh mixing is negligible at B < 6 T. The substantial penetration of the electron wave-function into the DMS layer could also lead to the smaller Zeeman splitting of the exciton line. The high intensity of Iup line observed in time-resolved spectra in figures 5 and 6 implies a strong overlap of the electron and hole wave-functions. Timeresolved spectra in figures 5 and 6 also demonstrate only a weak redshift, which contradicts the exciton-polaron model5 . All of this data indicates the absence of the polaron effect in this case. It is important to note that both the Iup and A0 X lines possess the same σ + polarization, which can be understood as a consequence of the singlet structure of A0 X as shown in figure 7. A similar conclusion was made in [25], where X+ trions in CdMnTe QWs were observed. The smaller than exciton Zeeman shift of A0 X is also evidence of the singlet structure of the A0 X state. The polaron effect is not expected in such a case. It can be shown in a similar manner so that the D 0 X luminescence also possesses σ + polarization. It is worth noting that the critical role played by the A0 X centres in the structures under study here is directly related to
to excitons bound to acceptors with a higher binding energy or vacancies3 . The LO-phonon energies in the ZnSx Se1−x and ZnMnx Se1−x layers depend on Mn or S content x and the strain caused by the lattice mismatch between the ZnMnSe and ZnSSe layers. The energy shift of h ¯ ωLO can be as high as several meV. For example, in bulk ZnS0.16 Se0.84 h ¯ ωLO 34.3 meV [21]. The shift of LO-phonon energy h ¯ ωLO due to the in-plane strain is small and does not exceed 1 meV [22]. The spectra in figures 1–3 indicate that the peak of the LOphonon replica of the low-energy line is located about 32 ± 1 meV below the low-energy line. This is very close to the LOphonon energy in bulk wurtzite ZnSe h ¯ ωLO = 31.8 meV. This energy was chosen for the line fitting presented in figure 3. The expression of (2) leads to ah 37 ± 7 Å for S(B = 0 T) = 0.25 ± 0.5. The binding energy of the EMP magnetic polaron with the localization size ah 30 Å is about 25 meV, which contradicts the results of the Zeeman shift measurements and the value of the redshift of the lines in time-resolved spectra. The HR factor extracted from PL spectra at various magnetic fields by means of (3) demonstrates a substantial decrease with B. However, it is not necessarily related to the increase in A0 X dimensions because of binding energy reduction. It can also be caused by the increase in intensity of Iex , which is also related to the destabilization of A0 X. These two contributions to the reduction of S can hardly be separated due to the strong lines overlapping. 6. Discussion
As has been mentioned above, the attribution of the upperenergy line to the exciton + D 0 X recombination and lowerenergy line to the A0 X recombination explains all of the facts observed in the experiment. In particular, our model explains the behaviour of the lower-energy line shown in figures 1 and 2, for instance its saturation under intensive excitation and its dissipation with temperature which is typical for impurity bound excitons4 . The rapid reduction of the intensity of the upper-energy line and simultaneous rise of the lower-energy line is typical for bound excitons. The redshift of the lower-energy line in time-resolved spectra, which is much smaller than the theoretical prediction, is related to spectral diffusion rather than to EMP formation. Our model explains a smaller than expected Zeeman shift of PL lines for EMPs. Finally, it explains why the lower-energy line is quite stable even at B = 10 T, whereas the disappearance of EMP in magnetic fields B > 6 T was observed in type-I DMS QWs [1]. The crossing of the upper- and lower-energy lines shown in figure 3 is interpreted in [3, 4] as evidence of EMP suppression 3 Donors and acceptors are not the only charge carrier traps in DMS structures. Studies of the self-compensation effect in II–VI materials revealed that the excitons can become bound by Zn and Se vacancies [7]. For instance, Zn vacancies in ZnSe (VZn ) effectively capture holes whereas Se vacancies (VSe ) act as donors and attract electrons. Binding energy of the exciton bound to VZn in bulk ZnSe is about 20 meV, which is very close to the energy gap between lower- and upper-energy lines (see figure 1). 4 See footnote 1.
5
Magnetic polaron formation related to A0 X was reported for bulk CdMnTe on the basis of the temperature shift of A0 X line [11, 24]. See also [30]. It would mean, however, that the A0 X state is not a singlet. The discussion of possible structure of A0 X centers can be found in [24].
6
J. Phys.: Condens. Matter 26 (2014) 425301
hh +3/2
A V Chernenko and A S Brichkin
These lines demonstrate significantly different behaviour with changes in excitation power, temperature, and magnetic field. The time-resolved measurements reveal dramatically different temporal evolution of the lines and indicate their different nature. The lifespan of the upper-energy line does not exceed 650 ps, whereas the lifespan of the lower-energy line exceeds 10 ns. The presence of LO-phonon replicas of the lower-energy line and their absence for the upper-energy line prove a much stronger hole localization in the former case. These LO-phonon replicas allow us to estimate the size of A0 X ah 30 Å. All of our experimental data are clearly explained if one attributes the upper-energy line to the recombination of indirect localized and donor bound excitons and the lowerenergy line to the recombination of indirect acceptor bound excitons. Contrary to expectations, the magnetic polaron effect in the studied structures is negligible for localized excitons because of their short lifespan and for acceptor bound excitons because of their singlet spin state.
e +1/2
Energy
X +hh 0 AX
σ+
σ+
hh
Magnetic field Figure 7. Three-carrier diagram of optical transitions between the initial (A0 X and exciton X) level and the final hh-hole level in a magnetic field. The thin arrows show the electron spin and the thick arrows show the hole spin. The luminescence of the lower energy lines of exciton and A0 X centres is σ + polarized.
Acknowledgments
The authors are grateful to S V Ivanov and S V Sorokin for providing samples, and to S I Gubarev and V D Kulakovskii for fruitful discussions. This work was supported by RFBR grants.
the spatial separation of electrons and holes. Intentionally undoped ZnSe/ZnSSe type-I QWs are usually negatively charged with a sheet electron density n 1010 cm2 because of ionization of donors in the barriers and substrate. The emission of D 0 X dominates in the spectra at He temperatures and low excitation powers similar to other DMS QWs [31, 32]. Spatial separation of the electron and hole layers in type-II QWs boosts the importance of acceptors and leads to the intensive luminescence of A0 X centres6 . These arguments allow us to suggest that A0 X centres could be important for the correct interpretation of previously reported results concerning type-II DMS QWs. In particular, an additional line observed in ZnMnSe/ZnSe QWs in [33] at energies 10 meV below the exciton emission might be related to A0 X rather than to the so called ‘interface EMP’. The line appearing in PL spectra at certain B > 0 was attributed to the formation of EMP because of the magnetic field induced typeI-type-II transition for heavy holes. Similarly, the dynamical behaviour of PL lines in type-II ZnMnSe/ZnSe multiple QWs in [34] could be explained by the capture of the indirect excitons by acceptors. The presence of bound excitons in type-I and type-II structures affects the lifespan of free and localized excitons and leads to the overestimation of EMP binding energy and its lifespan. Our arguments may be also important for the interpretation of PL spectra of type-II QDs which were recently reported [35].
References [1] Yakovlev D R and Ossau W 2010 Introduction to the Physics of Diluted Magnetic Semiconductors (Springer Series in Material Science vol 144) ed J Kossut and J A Gaj (Berlin: Springer) pp 221–62 [2] Toropov A A, Terent’ev Y V, Lebedev A V, Sorokin S V, Kaygorodov V A, Ivanov S V, Kop’ev P, Buyanova I A, Bergman J and Monemar B 2004 Phys. Status Solidi 1 847 [3] Toropov A A et al 2006 Phys. Rev. B 73 245335 [4] Maksimov A A, Pashkov A V, Brichkin A S, Kulakovskii V, Toropov A and Ivanov S V 2008 J. Exp. Theor. Phys. 106 1130 [5] Toropov A, Lebedev A, Sorokin S, Solnyshkov D, Ivanov S, Kop’ev P, Buyanova I, Chen W and Monemar B 2002 Semiconductors 36 1288 [6] Bimberg D et al 1971 Phys. Rev. B 4 3451 [7] Gutowski J, Grifoni M and Morolli L 1990 Phys. Status Solidi 120 11 [8] Bogani F, Grifoni M and Morolli L 1995 Phys. Rev. B 52 2543 [9] Kulakovskii V D, Tyazhlov M G, Dite A F, Filin A I, Forchel A, Yakovlev D R, Waag A and Landwehr G 1996 Phys. Rev. B 49 4981 [10] Planel R, Gaj J and Benoit a la Guillame C 1980 J. Phys. Colloques 41 39–41 [11] Golnik A, Ginter J and Gaj J A 1983 J. Phys. C 16 6073 [12] Dorozhkin P S, Chernenko A V, Kulakovskii V D, Brichkin A S, Maksimov A A, Schoemig H, Bacher G, Forchel S A Lee, Dobrowolska M and Furdyna J K 2003 Phys. Rev. B 68 195313 [13] Chernenko A V, Brichkin A S, Sobolev N A and Carmo M C 2010 J. Phys.: Condens. Matter 22 355306 [14] Condon E U 1991 The Franck–Condon Principle and Related Topics, Selected Papers of Condon (Berlin: Springer) p 515 [15] Huang K and Rhys A 1950 Proc. R. Soc. A 204 406
7. Conclusions
In summary, time-resolved and CW magneto- photoluminescence studies of Znx Mn1−x Se/ ZnSSe MQWs with Mn content x = 10% and x = 16% in a magnetic field up to 10 T revealed two dominant emission lines in the spectra. 6
See footnote 3. 7
J. Phys.: Condens. Matter 26 (2014) 425301
A V Chernenko and A S Brichkin
[26] Kossut J and Gaj J A 2010 Introduction to the Physics of Diluted Magnetic Semiconductors (Springer Series in Material Science vol 144) ed J Kossut and J A Gaj (Berlin: Springer) pp 1–36 [27] Gaj J A 1988 Diluted Magnetic Semiconductors (Semiconductors and Semimetals vol 25) ed J Kossut and J A Gaj (Boston: Academic) pp 275–309 [28] Mycielski J 1988 Diluted Magnetic Semiconductors (Semiconductors and Semimetals vol 25) ed J Kossut and J A Gaj (Boston: Academic) pp 263–303 [29] Harrison P 2005 Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures 2nd edn (Hoboken, NJ: Wiley) [30] Takeyama S et al 1995 Phys. Rev. B 51 4858 [31] Yakovlev D R, Ossau W, Landwher G, Bicknell-Tasius R N, Waag A and Schmeusser S 1992 Surf. Sci. 263 485 [32] Kulakovskii V D, Tyazhlov M G, Gubarev S I, Yakovslev D R, Waag A and Landwehr G 1995 Nuovo Cimento D 17 1549 [33] Rossin V V, Puls J and Henneberger F 1995 Phys. Rev. B 51 11209 [34] Poweleit C D, Smith L M and Jonker B T 1994 Phys. Rev. B 50 18662 [35] Sellers I R et al 2010 Phys. Rev. B 82 195320
[16] Hopfield J 1959 J. Phys. Chem. Solids 10 110 [17] Abakumov V N, Perel V I and Yassievich I N 1991 Nonradiative Recombination in Semiconductors (Modern Problems in Condensed Matter Sciences vol 33) ed V M Agranovich and A A Maradudin (Amsterdam: Elsevier) [18] Kartheuser E, Evrard R and Williams F 2010 Phys. Rev. B 21 648 [19] Soltani M, Certier M and Kartheuse E 1995 J. Appl. Phys. 78 5626 [20] Gurskii A L 2000 J. Appl. Spectrosc. 67 111 [21] Ram R K, Kushwaha S S and Shukla A 1989 Phys. Status Solidi 154 553 [22] Steller U, Hoffman N, Sch¨ulzgen, Griesche J, Babucke H, Henneberger F and Jacobs K 1995 Semicond. Sci. Technol. 10 201 [23] Rybchenko S M, Terletskii O V, Mizetskaya I B and Oleinik G S 1981 Sov. Phys. Semicond. 15 1345 [24] Heiman D, Becla P, Kershaw R, Ridgley D, Dwight K, Wold A and Galazka R R 1986 Phys. Rev. B 34 3961 [25] Kossacki P, Boukari H, Bertolini M, Ferrand D, Cibert J, Tatarenko S, Gaj J A, Deveaud B, Ciulin V and Potemski M 2004 Phys. Rev. B 70 195337
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Localized and bound excitons in type-II ZnMnSe/ZnSSe quantum wells
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 425301 (8pp)
doi:10.1088/0953-8984/26/42/425301
Localized and bound excitons in type-II ZnMnSe/ZnSSe quantum wells A V Chernenko and A S Brichkin Institute of Solid State Physics, RAS, 142432, Chernogolovka, Russia E-mail: [email protected] Received 1 July 2014, revised 18 August 2014 Accepted for publication 2 September 2014 Published 2 October 2014 Abstract
Photoluminescence of ZnMnSe/ZnSSe multiple quantum wells under a bandgap continuous wave and fs-pulsed excitations is measured in magnetic fields up to 10 T in Faraday geometry at temperatures within the range of 1.6–20 K. The measurements reveal two dominant lines in the spectra and LO-phonon replicas of the lower-energy line. The photoluminescence and time-resolved studies show dramatically different behaviour of the lines. Analysis of their properties reveals that they correspond to recombination of indirect localized excitons and indirect acceptor-bound excitons (A0 X). Crossing of exciton and A0 X lines because of the difference in magnitudes of their Zeeman shifts is observed. Analysis of LO-phonon replicas of photoluminescence lines provides additional evidence for strong carrier localization bound to A0 X. A model of phonon-assisted recombination of indirect acceptor-bound excitons is proposed. The fitting of photoluminescence lines with this model gives the Huang–Rhys factor S 0.25 for A0 X and the hole localization size ah 30 Å. Contrary to expectations the exciton magnetic polaron effect is hardly observed in these structures. Keywords: diluted magnetic semiconductors, quantum wells, excitonic magnetic polaron, time-resolved spectroscopy, acceptor-bound exciton (Some figures may appear in colour only in the online journal)
in [2, 3] revealed the presence of two broad lines in PL spectra. The lower- and upper- energy lines were attributed to recombination of strong magnetically and non-magnetically localized EMPs, respectively. To explain the presence of the lines two types of localizing potential with characteristic sizes 4 nm and 20 nm were proposed in [3]. However, later studies of these structures [4] revealed that the EMP effect is much smaller than reported in [5] The authors of [4] focused on PL studies of the structures and did not pay attention to this experimental fact, whereas it clearly contradicts the results of [3]. The EMP energy EEMP 7 meV found by Maksimov et al [4] is much smaller than EEMP 20 meV reported in [3]. According to the EMP theory [1] it also means a much larger EMP lateral dimension than d 4 as reported in [3] for the magnetically localized EMP. The observed discrepancy demands additional study of the structures. In order to address this issue magnetoluminescence measurements were carried out on type-II ZnMnSe/ZnSSe multiple QW structures under various excitation power densities, temperatures and magnetic fields using CW and fspulsed non-resonant excitations.
1. Introduction
In diluted magnetic semiconductors (DMS) the exchange interaction between the spins of charge carriers and magnetic ions results in the giant Zeeman splitting and exciton magnetic polaron (EMP) formation. Intensive optical studies of EMPs in type-I DMS quantum wells (QWs), mainly localized EMPs, revealed that the EMP formation can be limited by the long spin relaxation time which often exceeds the exciton lifetime [1] so that the polaron system cannot reach complete thermal equilibrium. Type-II quantum wells (QWs) are attractive objects for studying exciton magnetic polarons (EMPs) because of the supposedly long lifetimes of excitons in such structures of the order of nanoseconds. The formation of EMP in type-II DMS structures could be realized if the influence of bound exciton complexes was negligible. The experimental results presented below show that this is not the case and the bound exciton complexes, mainly acceptor-bound excitons, could dramatically change exciton dynamics and prevent the formation of EMPs. Photoluminescence studies of type-II DMS QW structures 0953-8984/14/425301+08$33.00
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© 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 425301
A V Chernenko and A S Brichkin
Our PL studies under CW excitation and time-integrated measurements using pulsed excitation showed the presence of LO and 2LO replicas only of the lower-energy line and their absence for the upper-energy line. Besides this, time-resolved PL measurements revealed that temporal evolutions of upperand lower-energy lines are dramatically different. Namely, the initially stronger upper-energy line almost disappears during the 50–150 ps period after the laser pulse, whereas the intensity of the lower-energy line substantially increases. The lifetime of the lower-energy line exceeds 10 ns. It is also found that the energy shift of the EMP line in time-resolved spectra is much smaller than that predicted by the theory for EMPs localized by means of 4 nm traps as was proposed by Toropov et al [3]. The obtained results can be explained by attributing the upper- and lower-energy lines to recombination of indirect localized excitons and acceptor-bound excitons (A0 X), respectively. Analysis of LO-phonon replicas of A0 X allows for the estimation of A0 X size ah 30 Å at B = 0 T. The experimental data shows that the EMP effect is negligible for excitons because of their short lifespan and for bound excitons because of their singlet structure. This paper is organized as follows: in section 2 we describe the samples and the experimental setup, section 3 presents the results of PL measurements under CW excitation while the results of time-resolved measurements are presented in section 4. The model of LO-phonon assisted recombination of type-II A0 X is presented in section 5. The fitting procedure for PL curves is presented and the values of the Huang–Rhys factor extracted from PL data are discussed in this section. The relation of the experimental data with the magnetic polaron effect and impurity bound excitons is discussed in sections 6 and 7 summarizes the results.
(a)
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Figure 1. Normalized PL spectra of (a) sample #1 (x = 10% Mn) and (b) sample #2 (x = 16% Mn) recorded at B = 0 T, T = 1.6 K and various levels of excitation power density. Here J0 = 0.2 W cm−2 . LO- and 2LO-phonon replicas of the A0 X line are marked.
each of full width at a half-maximum of approximately 12–15 meV. The peaks are separated from each other by 18–20 meV. LO-phonon replicas of the lower-energy line are well resolved, whereas those of the upper-energy line are invisible in the spectra. The large width of the lines indicates strong inhomogeneous broadening due to the interface roughness and alloy content fluctuations in ZnSSe and ZnMnSe layers. The intensity of the lower-energy line quickly decreases with an increase in the temperature T for both samples, whereas the intensity of the upper-energy line Iup increases with T as is clear in figure 2. The spectra demonstrate that the peak position of the lower-energy line does not change with the increase in T . The intensities of the lines demonstrate different dependencies on excitation power. Particularly, the lowerenergy line dominates in the PL spectra at low excitation power density (J = J0 = 0.2 W cm−2 ) in sample #1 (figure 1(a)). The intensity of the upper-energy line quickly increases with J whereas the increase in the lower-energy line is much smaller. The lower-energy line demonstrates saturation with the increase in excitation power, so that the upper-energy line dominates at high J . In contrast, in sample #2 the lower-energy line dominates for the whole range of J and the intensity of the upper-energy line becomes comparable to that of the lower-energy line only at the highest excitation power J = 1000J0 = 200 W cm−2 (See figure 1(b)). The spectra are recorded at the same power but various temperatures are shown in figure 2. They reveal a sharp decrease in the intensity of the lower-energy line IA0 X and an increase in the intensity of the upper-energy line Iup 1 .
2. Experimental details
Two MBE grown samples containing 10 periods of Zn0.9 Mn0.1 Se[8 nm]/ZnS0.16 Se0.84 [18 nm] (sample #1) and Zn0.84 Mn0.16 Se [8 nm]/ZnS0.16 Se0.84 [18 nm] (sample #2) QWs’ were used in the measurements. The sample #2 with x = 16% is similar to that used in [3], where details of the growth procedure can be found. Both samples were also used in the paper of Maksimov et al [4]. A CW Ar+ laser (λ = 351 nm) was used for the above bandgap excitation. The PL signal was dispersed by a monochromator with 600 gr mm−1 grating and was recorded by a liquid nitrogen cooled CCD camera. The frequency-doubled emission of a Ti:Sp fs-laser with λ 400 nm and a repetition rate 80 MHz was used for pulsed excitation of the sample. A streak camera with a time-scale resolution of 10 ps was used in time-resolved measurements. The samples were immersed in liquid He in a cryostat equipped with a superconducting magnet.
1 The decrease in the intensity of A0 X line with T allows estimation of its binding energy under the assumption that intensities of the exiton and D0 X lines similarly vary with T. Approximating the dependence IA0 X (T ) by the expression IA0 X (T ) = A/(1 + B exp (−/kB T )) the values of 1 = 17 ± 3 meV and 2 = 20 ± 6 meV are obtained for spectra of sample #1 and sample #2, respectively (figure 2). Here A and B are additional fitting parameters. More complicated temperature dependence of IA0 X is proposed by [6].
3. PL spectra under CW excitation and line identification
Two broad lines dominate in the photoluminescence spectra of the samples under CW laser excitation as shown in figure 1, 2
J. Phys.: Condens. Matter 26 (2014) 425301 Iup 10 K IA0X
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A V Chernenko and A S Brichkin
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Figure 2. PL spectra of (a) sample #1 (x = 10% 0) at constant
excitation power density J = 0.2 W cm−2 and (b) sample #2 (x = 16%) at J = 10 W cm−2 . The spectra are recorded at B = 0 T and various temperatures.
Figure 3. PL spectra of (a) sample #1 recorded at excitation power density J = 2 W cm−2 and (b) sample #2 recorded at J = 40 W cm−2 at various magnetic fields B = 0 − 10 T . The results of fitting the data with (3) are shown as a dotted lines for all B values. The detailed structure of the fitting line is shown for both samples of data at B = 0 T and B = 10 T. The red dotted curve corresponds to the aggregated fitting curve, which includes contributions from the dashed magenta line Iup corresponding to exciton+D0 X recombination, the dashed green curve IA0 X corresponding to A0 X and its LO-phonon replicas, the solid blue curve which is related to the additional line Iadd and its LO-phonon replica. The circular polarization of the additional line rapidly reaches 100% with B > 0.5T . The additional line can be attributed the exciton bound on an acceptor with larger binding energy. The detailed evolution of the PL spectra of sample #1 recorded at J = 2 W cm−2 in magnetic fields up to 2 T is shown in (c). The complex structure of the upper-energy line Iup from the PL of sample #1 is clearly visible on the spectrum. It is related to the recombination of donor-bound excitons D 0 X.
The lines demonstrate different behaviour in a magnetic field. Both lines exhibit substantial redshift and become σ + polarized in magnetic field B 0z . The upper-energy line shifts faster than the lower-energy line and at high magnetic fields B 6 T the lines become poorly resolved so that only one combined line remains in the spectrum (see figure 3). The upper-energy line Iup in the PL spectra presented in figure 1 was attributed by Toropov et al to the recombination of weakly non-magnetically localized excitons, whereas the lower-energy line was attributed to the EMP of strong magnetically localized excitons [3]. The existence of two types of localizing potentials with different characteristic sizes ∼20–30 nm and ∼4 nm and two mechanisms of localization were proposed. However, our studies of PL spectra recorded at low excitation powers and with the PL line fitting as discussed in section 5 unambiguously indicate that both lines have a complex structure and each consists of at least two lines. The fitting of PL curves presented in figures 3(a) and (b) shows that an additional line Iadd exists in the vicinity of the lower-energy line. The line Iadd increases in intensity with B and forms a well-resolved shoulder at the magnetic fields B > 6 T. The complex structure of the upper-energy line is clearly visible in figures 1 and 3. The presence of additional lines contradicts the model of [3]. The experimental results are well explained if one accepts the dominant role of non-magnetic localization for both lines. The lines related to recombinations of acceptor (A0 X) and donor (D 0 X) bound excitons usually dominate in PL spectra of bulk DMS materials at low excitation densities [7, 8]. A similar picture is observed in the PL spectra of CdTe/CdMnTe [1] and CdMnTe/CdMgTe QWs [9]. A magnetic field dependence similar to that of figure 3 was reported for bulk DMS [10, 11], where two lines and their crossing in a magnetic field was observed. The lowerenergy and upper-energy lines were attributed, respectively, to recombinations of acceptor-bound and free excitons. It is straightforward for us to ascribe the lower-energy line to
the recombination of the indirect acceptor bound excitons and upper-energy line to the indirect localized excitons together with donor bound excitons. With such an interpretation the whole set of experimental results presented here can be easily explained. For instance, the decrease in intensity of the lowerenergy line and the increase in intensity of the upper-energy line with the increase in temperature shown in figure 2 is caused by the thermal dissociation of acceptor bound excitons [7]2 . The Zeeman shift of both lines in Faraday geometry is well described by the modified Brillouin function [1]: 1 EZ = (e (B) + h (B)) 2 1 5µb g(B + Bex ) = − (αN0 − βN0 )xγ S0 × Br5/2 , 2 2kB (T + T0 ) (1) where g = 2 is the g-factor of Mn2+ electrons, T is the bath temperature, S0 is the effective Mn2+ spin, x is the Mn2+ fraction; e (B) and h (B) are splittings of electron and hole states in a magnetic field, αN0 260 meV and βN0 −1310 meV are the parameters of exchange interaction 2
3
See footnote 1.
J. Phys.: Condens. Matter 26 (2014) 425301
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Figure 4. Zeeman shift of Iup (exciton +D 0 X) and A0 X line peak positions in σ + -polarized spectra for a) sample #1 and b) sample #2 in Faraday geometry. The results of fitting the lines with the Brilluene function (1) are shown by solid black lines.
0
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600
Time. ps Figure 5. Streak-camera images of sample #1 photoluminescence spectra recorded at B = 0 T and excitation power densities (a) 40 W cm−2 and (b) 120 W cm−2 . The PL intensity increases from a blue color to red. The time scale is shifted backwards by 60 ps.
of electrons and holes, respectively. Parameter T0 is introduced to describe antiferromagnetic coupling of Mn2+ pairs and parameter γ reflects the fact that only part of the exciton function can penetrate inside the DMS area. The polaron magnetic field Bex is introduced to account for the possible polaron effect [1, 12]. The equation (1) was used in [4] to fit the Zeeman shift of the lower-energy line under the assumption that the polaron effect takes place. With the same assumption the best fit of the Zeeman shift of the A0 X line displayed in figure 4 gives Bex 0.5 − 0.9 T and T0 5, which corresponds to Emp 6−8 meV for both samples. However, the Zeeman shift is equally well fitted with Bex = 0 T and with Teff = 10 ± 1 K and Teff = 12 ± 1 K for samples #1 and #2, respectively. It means that the fitting procedure by means of (1) cannot serve as evidence for the presence or absence of the polaron effect, mainly because of the broad PL lines. The upper-energy line (exciton + D 0 X) demonstrates a larger Zeeman shift than that of the A0 X line and crosses the latter at relatively low magnetic fields. This effect was attributed by Toropov et al to destabilization of EMP [3]. Note, however, that the presence of LO-phonon replicas of the EMP line even at B = 10 T would imply the existence of EMP even at such a high field, while the disappearance of the EMP line from PL spectra was observed at B > 6 T in type-I DMS QWs [1], where EMP binding energy is Eex 20 meV. The Eex does not exceed 7 meV in our case therefore complete destabilization of EMP is expected at lower magnetic fields [1]. Thus, the lower-energy line in our structures must disappear from spectra at B < 10 T.
decays exponentially with a characteristic time 110 ps. The upper-energy line dominates in the spectra until 250 ps after the excitation pulse. At longer times, Iup demonstrates a 5 meV and 6 meV redshift and disappears from the spectra at τ > 600 ps. The A0 X line dominates in the spectra at τ > 400 ps. A comparison of the spectra at τ = 13 ns and 650 ps reveals an additional redshift of the A0 X line by E 2 − 3 meV. Similar time-resolved spectra are observed for sample #2 at two levels of laser excitation, J = 20 W cm−2 and J = 200 W cm−2 as presented in figure 6. Both lower- and upperenergy lines are well resolved in the spectra. The characteristic rise times of the intensity are about 20 ps for both lines. The decay time of the upper-energy line strongly depends on the excitation power density. The spectrum recorded at J = 20 W cm−2 reveals domination of the upper-energy line during the first 120 ps after the laser pulse. Under higher laser excitations the upper-energy line becomes more robust and dominates in the spectra up to τ = 250 ps. A weak and longliving tail related to exciton + D 0 X luminescence is visible in the spectra even at τ > 650 ps after the laser pulse. It demonstrates no redshift. The dependence of the upper-energy line on the excitation power leads to the 3 meV and 4 meV blueshift of the exciton line peak with an increase in power clearly visible in the PL spectra under CW excitation. The intensity of IA0 X quickly increases at τ < 30 ps. It continues to increase up to 400 ps and slowly decreases afterwards. The lower-energy line lives even longer than the distance between the subsequent laser pulses (13 ns). The behaviour of the decay of the IA0 X line does not depend on the excitation intensity. The lower-energy line demonstrates a 5–7 meV redshift during a 120–650 ps period after the laser pulse. The LO-phonon replica located approximately 32 meV below the lower-energy line is well resolved in the spectra. The A0 X line demonstrates a total redshift of 6–8 meV at 13 ns after the laser pulse as shown in figures 5 and 6 which is much smaller than that predicted by the EMP theory [1]. The
4. Analysis of time-resolved spectra
Time-resolved PL measurements produce important information about temporal evolution of the lines and clearly demonstrate their different nature. The spectra of sample #1 are presented in figure 5. The characteristic rise times of the intensity are about 20 ps for both IA0 X and Iup lines. The upper-energy line Iup reaches maximum intensity at τ = 20 ps, and after that the line 4
J. Phys.: Condens. Matter 26 (2014) 425301
Energy, eV
2.82 (a)
A V Chernenko and A S Brichkin
2.80 IA0X
2.78 2.76 ILO
2.74 2.82 (b)
Energy, eV
The model of phonon-assisted donor-acceptor pair recombination is appropriate in our case because of the spacial separation between electrons and holes. The model allows an estimation of the HR factor and provides an understanding of its evolution with a magnetic field. Within the effective mass approximation the wavefunction of thee-h pair localized on a donor-acceptor pair is merely a product of the electron fe (r) and hole fh (r) envelopes F (re , rh , R) = fe (re )fh (rh − R). Here re and rh are electron and hole coordinates with respect to the acceptor and donor centres, respectively, and R is the distance between the centres. It is assumed that the acceptor bound hole wave-function has a hydrogen-like form. The anisotropy of the hole mass is also omitted for the purpose of simplicity because it substantially complicates the analytical expression [18]. Even in this case the final expression, which relates S with the electron and hole characteristic sizes and the separation between their centres of localization R, has a complicated form [19]. In the limit ae ah and ah /R → 0, a well-known expression can be obtained:
+
Iup (Iex ID0X)
+
Iup (Iex ID0X)
2.80 IA0X
2.78 2.76
ILO
2.74 0
100
200
300
400
500
600
Time. ps Figure 6. Streak-camera images of sample #2 photoluminescence spectra recorded at B = 0 T and excitation power densities (a) 20 W cm−2 and (b) 200 W cm−2 . The PL intensity increases from a blue color to red. The time scale is shifted backwards by 60 ps. A luminescence reminiscent of the previous pulse is clearly visible.
5 e S(B) = 16 h ¯ ωLO
timescale is shifted backwards by 60 ps in order to demonstrate the reminiscent luminescence from the previous pulse which does not disappear even after 13 ns from the laser pulse. The increase in total intensity of the PL spectra with the magnetic field clearly visible in figure 3 is related mainly to the destabilization of A0 X in the magnetic field since excitons start to develop a much shorter lifespan. The suppression of nonradiative recombination of e-h complexes by the magnetic field observed in bulk and low-dimensional DMS structures [13] can also contribute to the observed effect.
1 1 − ∞ 0
1 ah (B)
(2)
The assumptions are reasonable because the electron mass is much smaller than that of the hole and the distance R between the electron and hole centres of gravity is much larger than ah . Within the framework of the model PL curves in figure 3 are fitted with the expression [20]: E 3 S p −S e E03 p=0 p! E0 − p¯hωLO − E 2 + Iex (E) × exp −4 ln 2
I (E) = A
5. LO-phonon replicas of A0 X line and their relation to hole localization
+Iadd (E),
The results of magnetic field dependencies under steady state excitation presented in figure 3 display an evolution of no-phonon (NP), 1LO- and 2LO- phonon replicas of A0 X line in a magnetic field in Faraday geometry. The LO-phonon replicas can be used for an estimation of the exciton localization dimension in the structures under study here because the ration ILO /INO is related to the strength of the exciton-complex-LO-phonon interaction, which, in turn, depends on e-h pair localization. Within the Frank–Condon approximation [14] the intensity of j -th phonon-assisted replica is Ij = S j e−S /j !, where j = 0, 1..n. The Huang–Rhys (HR) factor S determines the strength of polar exciton-LO-phonon coupling [15–17]. It is given by the expression S = q |Vq |2 /(¯hωLO )|ρq |2 , where ρq is the Fourier transform of the charge distribution and |Vq |2 = (2π e2 )/(|q|2 V )(1/ ∞ − 1/ 0 ) is the square of the amplitude Vq of exciton-LO-phonon polar interaction. The charge distribution for the free exciton ground state is given by ρq = F (re = r, rh = r)|eiqre − eiqrh |F (re = r, rh = r), where F (re , rh ) is the exciton envelope function and re and rh are electron and hole coordinates, respectively. The LOphonon energy is h ¯ ωLO
(3)
where , E0 , S are the width of PL lines (p = 0, 1, 2, 3..), the position of the no-phonon (NP) line, the HR factor, respectively. The constant A = I (E0 )/( p=0 S p /p!e−S × exp(−4 ln 2(E0 − p¯hωLO − E/ )2 )) is related with spectrum intensity I (E0 ) at the energy position E0 . The term Iex (E) = Aex exp((Eex − E)/ ex )2 is added in order to account for the exciton recombination. Here Eex is the exciton peak position and ex is its line-width. In order to take into account the additional line clearly visible in the spectra at B > 5T a term Iadd (E) similar to I (E) is also added. The Iadd line is essential to obtain an acceptable fitting of the PL lines at small magnetic fields B < 5 T which is demonstrated in figure 3 on the example of line fitting at B = 0 T. The origin of Iadd is not clear. Its peak is located 17 ± 1 meV below the IA0 X and 35 ± 1 meV below Iex . It can hardly be related to the LO-phonon replica of exciton PL, because it is clearly visible in the spectra at B = 10 T, whereas Iex is not observed at an energy 35 meV above Iadd . It is also not related to the TO-phonon replica of IA0 X , since TO-phonon energy in ZnSe is about h ¯ ωTO 25 meV. It could be related 5
J. Phys.: Condens. Matter 26 (2014) 425301
A V Chernenko and A S Brichkin
by the magnetic field. However, the crossing of A0 X and the upper-energy lines in the magnetic field was previously observed in bulk materials [10, 23, 24]. The crossing of X+ trions and exciton X lines in a magnetic field in a p-doped CdMnTe/CdTe QWs was also reported [25]. A comprehensive theoretical model for this effect has not been created up to now [26] although the effect was observed in earlier DMS studies [27]. In the paper of Mycielski [28] the smaller Zeeman shift of the A0 X line was attributed to the strong hh and lh mixture of hole states, which leads to the smaller Zeeman splitting of these states with B. This could be the reason for the reduction in the Zeeman splitting in weak magnetic fields. However, the hh-lh splitting Ehh−lh in the structures under study is estimated to be larger than 60 meV. Indeed, the size quantization and strain caused by the lattice mismatch between ZnMnSe and ZnSSe layers contribute to Ehh−lh . The hh-lh splitting at k = 0 produced by the strain is Ehh−lh = b( xx + yy − 2 zz ) [29], where xx = yy = (aZnMnSe − aZnSSe )/aZnMnSe and b is a material constant. The material parameters for ZnMnSe are not known; for the estimation of Ehh−lh we assume them to be equal to those for ZnSe [5]. With the lattice parameters from [5] the strain is xx = 1% for x = 10% and xx = 1.5% for x = 16%. ZnSe ZnSe For instance, bZnSe = −1.2 eV, C11 = 0.826 Mbar, C12 = 0.498 Mbar. Using these parameters the hh-lh splitting turns out to be Ehh−lh = Ehh − Elh = −2bZnSe ( xx − zz ) −50 meV, where zz = −2C12 /C11 . With the lh and hh masses in ZnSe mhh (ZnSe) = 0.6, mlh (ZnSe) = 0.145 [5] the contribution to Ehh−lh splitting due to the size quantization is estimated to be less than 10 meV in both samples. Thus, the total value of Ehh−lh is within the range −50 to 60 meV. The gap in Zeeman splitting between hh and lh levels does not exceed 50 meV at B = 10 T and, therefore, the hh-lh mixing is negligible at B < 6 T. The substantial penetration of the electron wave-function into the DMS layer could also lead to the smaller Zeeman splitting of the exciton line. The high intensity of Iup line observed in time-resolved spectra in figures 5 and 6 implies a strong overlap of the electron and hole wave-functions. Timeresolved spectra in figures 5 and 6 also demonstrate only a weak redshift, which contradicts the exciton-polaron model5 . All of this data indicates the absence of the polaron effect in this case. It is important to note that both the Iup and A0 X lines possess the same σ + polarization, which can be understood as a consequence of the singlet structure of A0 X as shown in figure 7. A similar conclusion was made in [25], where X+ trions in CdMnTe QWs were observed. The smaller than exciton Zeeman shift of A0 X is also evidence of the singlet structure of the A0 X state. The polaron effect is not expected in such a case. It can be shown in a similar manner so that the D 0 X luminescence also possesses σ + polarization. It is worth noting that the critical role played by the A0 X centres in the structures under study here is directly related to
to excitons bound to acceptors with a higher binding energy or vacancies3 . The LO-phonon energies in the ZnSx Se1−x and ZnMnx Se1−x layers depend on Mn or S content x and the strain caused by the lattice mismatch between the ZnMnSe and ZnSSe layers. The energy shift of h ¯ ωLO can be as high as several meV. For example, in bulk ZnS0.16 Se0.84 h ¯ ωLO 34.3 meV [21]. The shift of LO-phonon energy h ¯ ωLO due to the in-plane strain is small and does not exceed 1 meV [22]. The spectra in figures 1–3 indicate that the peak of the LOphonon replica of the low-energy line is located about 32 ± 1 meV below the low-energy line. This is very close to the LOphonon energy in bulk wurtzite ZnSe h ¯ ωLO = 31.8 meV. This energy was chosen for the line fitting presented in figure 3. The expression of (2) leads to ah 37 ± 7 Å for S(B = 0 T) = 0.25 ± 0.5. The binding energy of the EMP magnetic polaron with the localization size ah 30 Å is about 25 meV, which contradicts the results of the Zeeman shift measurements and the value of the redshift of the lines in time-resolved spectra. The HR factor extracted from PL spectra at various magnetic fields by means of (3) demonstrates a substantial decrease with B. However, it is not necessarily related to the increase in A0 X dimensions because of binding energy reduction. It can also be caused by the increase in intensity of Iex , which is also related to the destabilization of A0 X. These two contributions to the reduction of S can hardly be separated due to the strong lines overlapping. 6. Discussion
As has been mentioned above, the attribution of the upperenergy line to the exciton + D 0 X recombination and lowerenergy line to the A0 X recombination explains all of the facts observed in the experiment. In particular, our model explains the behaviour of the lower-energy line shown in figures 1 and 2, for instance its saturation under intensive excitation and its dissipation with temperature which is typical for impurity bound excitons4 . The rapid reduction of the intensity of the upper-energy line and simultaneous rise of the lower-energy line is typical for bound excitons. The redshift of the lower-energy line in time-resolved spectra, which is much smaller than the theoretical prediction, is related to spectral diffusion rather than to EMP formation. Our model explains a smaller than expected Zeeman shift of PL lines for EMPs. Finally, it explains why the lower-energy line is quite stable even at B = 10 T, whereas the disappearance of EMP in magnetic fields B > 6 T was observed in type-I DMS QWs [1]. The crossing of the upper- and lower-energy lines shown in figure 3 is interpreted in [3, 4] as evidence of EMP suppression 3 Donors and acceptors are not the only charge carrier traps in DMS structures. Studies of the self-compensation effect in II–VI materials revealed that the excitons can become bound by Zn and Se vacancies [7]. For instance, Zn vacancies in ZnSe (VZn ) effectively capture holes whereas Se vacancies (VSe ) act as donors and attract electrons. Binding energy of the exciton bound to VZn in bulk ZnSe is about 20 meV, which is very close to the energy gap between lower- and upper-energy lines (see figure 1). 4 See footnote 1.
5
Magnetic polaron formation related to A0 X was reported for bulk CdMnTe on the basis of the temperature shift of A0 X line [11, 24]. See also [30]. It would mean, however, that the A0 X state is not a singlet. The discussion of possible structure of A0 X centers can be found in [24].
6
J. Phys.: Condens. Matter 26 (2014) 425301
hh +3/2
A V Chernenko and A S Brichkin
These lines demonstrate significantly different behaviour with changes in excitation power, temperature, and magnetic field. The time-resolved measurements reveal dramatically different temporal evolution of the lines and indicate their different nature. The lifespan of the upper-energy line does not exceed 650 ps, whereas the lifespan of the lower-energy line exceeds 10 ns. The presence of LO-phonon replicas of the lower-energy line and their absence for the upper-energy line prove a much stronger hole localization in the former case. These LO-phonon replicas allow us to estimate the size of A0 X ah 30 Å. All of our experimental data are clearly explained if one attributes the upper-energy line to the recombination of indirect localized and donor bound excitons and the lowerenergy line to the recombination of indirect acceptor bound excitons. Contrary to expectations, the magnetic polaron effect in the studied structures is negligible for localized excitons because of their short lifespan and for acceptor bound excitons because of their singlet spin state.
e +1/2
Energy
X +hh 0 AX
σ+
σ+
hh
Magnetic field Figure 7. Three-carrier diagram of optical transitions between the initial (A0 X and exciton X) level and the final hh-hole level in a magnetic field. The thin arrows show the electron spin and the thick arrows show the hole spin. The luminescence of the lower energy lines of exciton and A0 X centres is σ + polarized.
Acknowledgments
The authors are grateful to S V Ivanov and S V Sorokin for providing samples, and to S I Gubarev and V D Kulakovskii for fruitful discussions. This work was supported by RFBR grants.
the spatial separation of electrons and holes. Intentionally undoped ZnSe/ZnSSe type-I QWs are usually negatively charged with a sheet electron density n 1010 cm2 because of ionization of donors in the barriers and substrate. The emission of D 0 X dominates in the spectra at He temperatures and low excitation powers similar to other DMS QWs [31, 32]. Spatial separation of the electron and hole layers in type-II QWs boosts the importance of acceptors and leads to the intensive luminescence of A0 X centres6 . These arguments allow us to suggest that A0 X centres could be important for the correct interpretation of previously reported results concerning type-II DMS QWs. In particular, an additional line observed in ZnMnSe/ZnSe QWs in [33] at energies 10 meV below the exciton emission might be related to A0 X rather than to the so called ‘interface EMP’. The line appearing in PL spectra at certain B > 0 was attributed to the formation of EMP because of the magnetic field induced typeI-type-II transition for heavy holes. Similarly, the dynamical behaviour of PL lines in type-II ZnMnSe/ZnSe multiple QWs in [34] could be explained by the capture of the indirect excitons by acceptors. The presence of bound excitons in type-I and type-II structures affects the lifespan of free and localized excitons and leads to the overestimation of EMP binding energy and its lifespan. Our arguments may be also important for the interpretation of PL spectra of type-II QDs which were recently reported [35].
References [1] Yakovlev D R and Ossau W 2010 Introduction to the Physics of Diluted Magnetic Semiconductors (Springer Series in Material Science vol 144) ed J Kossut and J A Gaj (Berlin: Springer) pp 221–62 [2] Toropov A A, Terent’ev Y V, Lebedev A V, Sorokin S V, Kaygorodov V A, Ivanov S V, Kop’ev P, Buyanova I A, Bergman J and Monemar B 2004 Phys. Status Solidi 1 847 [3] Toropov A A et al 2006 Phys. Rev. B 73 245335 [4] Maksimov A A, Pashkov A V, Brichkin A S, Kulakovskii V, Toropov A and Ivanov S V 2008 J. Exp. Theor. Phys. 106 1130 [5] Toropov A, Lebedev A, Sorokin S, Solnyshkov D, Ivanov S, Kop’ev P, Buyanova I, Chen W and Monemar B 2002 Semiconductors 36 1288 [6] Bimberg D et al 1971 Phys. Rev. B 4 3451 [7] Gutowski J, Grifoni M and Morolli L 1990 Phys. Status Solidi 120 11 [8] Bogani F, Grifoni M and Morolli L 1995 Phys. Rev. B 52 2543 [9] Kulakovskii V D, Tyazhlov M G, Dite A F, Filin A I, Forchel A, Yakovlev D R, Waag A and Landwehr G 1996 Phys. Rev. B 49 4981 [10] Planel R, Gaj J and Benoit a la Guillame C 1980 J. Phys. Colloques 41 39–41 [11] Golnik A, Ginter J and Gaj J A 1983 J. Phys. C 16 6073 [12] Dorozhkin P S, Chernenko A V, Kulakovskii V D, Brichkin A S, Maksimov A A, Schoemig H, Bacher G, Forchel S A Lee, Dobrowolska M and Furdyna J K 2003 Phys. Rev. B 68 195313 [13] Chernenko A V, Brichkin A S, Sobolev N A and Carmo M C 2010 J. Phys.: Condens. Matter 22 355306 [14] Condon E U 1991 The Franck–Condon Principle and Related Topics, Selected Papers of Condon (Berlin: Springer) p 515 [15] Huang K and Rhys A 1950 Proc. R. Soc. A 204 406
7. Conclusions
In summary, time-resolved and CW magneto- photoluminescence studies of Znx Mn1−x Se/ ZnSSe MQWs with Mn content x = 10% and x = 16% in a magnetic field up to 10 T revealed two dominant emission lines in the spectra. 6
See footnote 3. 7
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[26] Kossut J and Gaj J A 2010 Introduction to the Physics of Diluted Magnetic Semiconductors (Springer Series in Material Science vol 144) ed J Kossut and J A Gaj (Berlin: Springer) pp 1–36 [27] Gaj J A 1988 Diluted Magnetic Semiconductors (Semiconductors and Semimetals vol 25) ed J Kossut and J A Gaj (Boston: Academic) pp 275–309 [28] Mycielski J 1988 Diluted Magnetic Semiconductors (Semiconductors and Semimetals vol 25) ed J Kossut and J A Gaj (Boston: Academic) pp 263–303 [29] Harrison P 2005 Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures 2nd edn (Hoboken, NJ: Wiley) [30] Takeyama S et al 1995 Phys. Rev. B 51 4858 [31] Yakovlev D R, Ossau W, Landwher G, Bicknell-Tasius R N, Waag A and Schmeusser S 1992 Surf. Sci. 263 485 [32] Kulakovskii V D, Tyazhlov M G, Gubarev S I, Yakovslev D R, Waag A and Landwehr G 1995 Nuovo Cimento D 17 1549 [33] Rossin V V, Puls J and Henneberger F 1995 Phys. Rev. B 51 11209 [34] Poweleit C D, Smith L M and Jonker B T 1994 Phys. Rev. B 50 18662 [35] Sellers I R et al 2010 Phys. Rev. B 82 195320
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