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Magneto-optical studies of CdTe:Cd1−xMnxTe superlattices
Surface Science 267 ,. 1992) 354-359 North-Holland
surface science
Magneto-optical studies of CdTe- Cd _,Mn. Te superlattices M.J. Lawless, R.J. Nicholas, M.J. McNamee, W. Hayes Clarendon Laboratoly, Oxford Unirersity, Oxford OX1 3PU, UK
D.E. A s h e n f o r d and B. L u n n Dept. Engineering Design and Manufacture, University of Hull, Cottingham Road, North Humberside HU6 7RX, UK Received 7 June 1991; accepted for publication 11 July 1991
Magneto-reflectivity studies have been conducted on a wide range of CdTe : Cd t - , Mn.,Te quantum wells and superlattices with L,~ = 19 A to 200 A, and x = 0.065 to 0.25. The observed excitonic transitions demonstrate large Zeeman splittings due to carrier exchange interactions in the dilute magnetic barriers, with the magnitude of the splitting providing a measure of carrier confinement, For short period superlattices (L~, _< 40 ,A) we observe a transition from type I to type II confinement for the mj = . ~, heavy-hole states. The Zeeman splitting is seen to be highly anisotropic, with the light-hole anisotropy reversed with respect to the heavy-hole, indicating 2D spin behaviour. We show that for the short period superlattices (L,,, < 75 /~), the perpendicular field splitting of the light-hole transitions is considerably higher than expected. From the observation of 2s exciton states we are a>~e to calculate exciton binding energies for various sample parameters.
1. Introduction Compared to III-V semiconductor structures, semi-magnetic II-VI heterostructures are a comparatively new innovation, and have not been studied to the same extent. Previous studies of these structures reveal many interesting and novel phenomena that are yet to be explored. The electronic states of dilute magnetic semiconductors (DMS) are heavily influenced by large exchange interactions with the magnetic ions [1,2]. Incorporation of DMS layers in semiconductor heterostructures leads to confinement potentials that are strongly spin-dependent in applied fields, producing large Zeeman splitting of the excitonic transitions [3]. The confinement of carriers in nonmagnetic (CdTe)wells by DMS (Cd~_xMn . Te) barriers results in an effective carrier exchange energy that is proportional to wave function penetration into the barriers. The small valence band offset, strain, and tke large Zeeman splitting result in many interesting phenomena including the field induced transition from type I
to type II band alignment for the m j = - ~ 3 valence band states [4,5] and the evolution of 2D spin behaviour in applied fields.
2. Experimental results Low temperature (4.2 K) magneto-reflectivity studies have been conducted on a series of CdTe:Cdt_xMnxTe superlattices grown by MBE on InSb[001] substrates [6] with Cd~_xMnxTe buffer and capping layers (typical thicknesses 0.1 p.m and 0.2/zm, respectively). The nominal sample parameters are given in table 1. Reflectivity measurements were made with both unpolarised and circularly po!arised light in magnetic fields of up to 15 T applied perpendicular and parallel to the superlattice layers. The reflectivity spectra for all the samples clearly shew the large Zeeman splitting of the main heavy-hole and light-hole exciton transitions for both the bulk (buffer and cap l a y e r ) C d l _ , M n , T e states and the confined superlattice and quantum well states (see, for
0(139-6028/92/$05.(1{1 ~. 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation. All rights rese~'ed
M.J. Lawless et aL / Magneto-optical studies of CdTe : C d t _ ~ Mn~Te
example, fig. 1 for the spectra of a short period superlattice). Circularly polarised reflectivity allows the individual cr+(Amj = + 1) and o--(Amj = - 1) transitions to be identified. In the parallel field orientation, the .rr(Amj = 0) transitions can also be seen. As the well widths increase, the carrier penetration into the DMS barriers falls, and the magnitude of the Zeeman splitting of the confined exciton transitions decreases (see table 1 for a summary of the exciton splittings). Whilst there is as yet no well accepted value for the valence band offset, it is generally agreed that it is small [3,5,7]. As a result of this, and the larger p - d exchange interaction, the Zeeman splitting of the hole states provides the dominant contribution to the observed excitonic splittings. The lighter (LH) mass of the mj = + ~ states leads to increased barrier penetration for the light-holes, which is further enhanced by the slight lattice mismatch
355
between CdTe and Cd~_xMn,Te which results in a small tetragonal strain. The uniaxial strain component decreases the light-hole well depth whiI.,,t increasing that of the heavy-holes. In the short period structures, there is a strong inter-well coupling for the light-hole states compared to the more strongly confined heavy-holes and electrons as can be seen from the calculated miniband widths shown in table 1. The increased penetration of the light-hole wave function should therefore lead to a relatively large exchange shift of the light-hole states. This can be seen for the wider well structures (figs. 2 and 3), where our results show that for both field orientations, the light-hole exciton splitting is in most cases larger than that seen for the heavy-hole exckon. Modelling this behaviour for the longer period structures, using k.p theory with separaLe envelope functions for each spin state, we calculate the changes in confine-
Table 1 The main bulk and superlattice exciton transition and binding e o e r g i e s . T h e e x c i t o n s p i n splitting e n e r g i e s a r e s h o w n , with t h e individual spin state shifts for the superlattices. All c n e r g i e s a r e ,qven in n : e V Nominal s a m p l e parameters
Well. barrier widths
Bulk exciton transitions
E-HII (B = i)T) E-Ltt (B = (iT)
30 A ' 3 0 , ~ x = 20¢~
37A'37A x = 4.5c>
75 A ' 7 5 A x -= 6.8">
1705.5 --- 170(1
1902.2 ~ 1889
1668.7 --- 1667
1720.0 ~ 1712
101.1
143.5
77.3
1660.3 1666.3
1718.3 1730.2
1633.5 1642.8
1672.7
1739.2
-
15
25
-
15
17
E1 conduction band H H 1 valence band I.HI valence band
222
48
58
3
0
56
9
13
1
0
197
66
79
9
1
S L H H exciton spin splitting at B ~ = 1 5 T
.~,( E 1- H t l I ) ,~,r ~
46,0 -34.0
32.5 -21.9
33.5 -21.7
5.6 4.51
3.1 -
Act--
12.0
1tl.6
11.8
SL LH exciton spin splitting
A~'EI-I,HI )
Mn fraction
E - H H exciton spin splitting ( B = 15 T) Superlattices ( S L ) exciton transitions (B = 0T)
E1-HH1 E1-LH1 EI-HHI
2s
Is binding energy
Calculated superlattice bandv.idths
at B ~ = 1 5 T SL exciton spin
19A'I9A x = 73%
~ 100 1620.3 1629.1 (,,- 16331
(
~1.11
150A:I50A x = 6.6% 1693.3 16~6.5 95.1 1600.0 1604.2 1614.0
--
"-- 33
6.1
2.2
- 31.1 14.1
- 25.~) 14.4
- 2(I.3
-
13.0
-
-
A(E1-HHI)
-
"-- 0
-
-%(EI-LH1 )
-
A~r"
A(r--
45.2
( ~ 40)
~ (1
~ 0
splitting at B 'i = 15 T
17.9
-
16.9
~ 0
356
M.J. Lawless et aL / Magneto-optical studies of CdTe "Cd /_ .,. M n , T e
BCZ)
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eeoeeoeeeoo®oeoooeeeo®o °
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ing as if significant mixing occurs with the mj = +_ ~3 heavy-hole states [8,9]. Warburton et al. [9] have recently shown that in high magnetic fields 3 strong mixing occurs between the rnj = + ~ and mj = - ~2 states in strongly coupled superlattices. Indeed, the splittings seen for the short period superlattices [figs, 1 and 4] demonstrate almost identical behaviour for the heavy- and light-hole transitions. It is interesting to note that the short period exciton splitting can be fitted quite, well by reversing signs of the electron and valence band exchange energies (see table 2). In this case the total heavy-hole exeiton splitting is given by A HH A E and the light-hole exciton splitting is A LH +AE. Although the bulk (barrier) exchange energies evolve with the field as symmetric Brillouin functions, the observed splitting of the exciton states can be very asymmetric with respect to the spin direction. A larger Zeeman shift is observed for the o-+ transition than for the or- transitions (see
I
!
4 8 Mognetic ~ield
12 (Teslo)
Fig. 1. The perpendicular field fan diagram ~ r the (37 A ' 3 7 A, x = 4.5%) sample, showing the main bulk ([]) and superlattice E 1 - H H I (©) and E1-LHI ( ~ ) exciton transitions. The asymmetff of E1-HH1 transition can be clearly seen in reference to the dashed line, representing the average diamagnetic shift. Solid shapes indicate strong reflectivity features.
-
1
1.64eV
E1-LH1 ment energy (AE, ,AHH, ALH) produced by the magnetic field induced change in the barrier heights, as shown in table 2. This predicts both the HH (AHH + AE) and LH ( A L H - AE) exciton splittings quite well; however, unlike earlier reports the measured splittings are smaller than calculated for a conventional band offset of k E~b = 0.8 A Eg. We attribute this to the high quality of the interfaces and additional excitonic localisation of the wave function within the wells which reduces the barrier penetration. In contrast, the experimental values for the light-hole exciton sp!ittings of t h e ~ h o r t period < t r , , r t , , r o < r a n l c t h , diverge from the theoretical calculations, which predict almost no increase in splitting due to the compensation of the electron and light-hole spin exchange. This compensation leads to the very small light-hc~e exciton spin splitting seen for the bulk. The results suggest that tJ;c superlattice has substantially altered the spin character of the confined states, with the lig!',t-hole states behav-
B(Z) 1.605eV
o--
E1-HH1
1.64eV
Fig. 2. The families of reflectivily spectra for the (75 ,~" 74/k. x = 6.8¢~) sample for magnetic fields to () to 15 T applied in both the (a) perpendicular and (b) parallel orl~,~tations. The spectra demonstrates the anisotr,apy of the supcrla:ticc heavyand light-hole transilions in applied Pe'.ds.
357
M.J. Lawless et aL / Magneto-optical studies o f C d T e ' C d z _ x MnxTe
B(Z)
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4 8 12 Magnet i c ~ i mi d (Tes I a) Fig. 3. oThe perpendicular field can diagram for the [150 A: 150 A, x = 6.6%] sample showing the observed superlattice transitions. The dashed lines represent the diamagnetic shift of each feature. Solid shapes indicate strong reflectivity fea0
tures,
fig. 1). This asymmetry is particularly apparent when account is taken of the positive diamagnetic shifts of the excitons, which have been estimated from the values observed for the mean of the bulk transitions (see table 1). For a given change in barrier height, the reduction in the confinement of the m j - 32, ~l states is greater than the corresponding increase in the confinement of 1 the mj = + 3, + ~ states. The small valence band offset and large negative exchange energies can lead to a field-induced change from type I to type II band alignment for the mj = - s3 hole state [5]. This change is characterised by a Zeeman shift approaching and exceeding half the corresponding bulk shift (for equal well and barrier thicknesses), as +he hole becomes Iocalised in the DMS barriers. Whilst this is seen for the shorter period superlattices (Lw < 40/k). this is not the case for the longer period superlattices as the (type I) Coulomb potential of the more localised electrons dominates the band alignment. Comparison between the perpendicular and parallel field data demonstrates a considerable anisotr6py in the splitting of the heavy- and
Table 2 The observed spin splitting of the bulk and superlattice excitons at B c = 5 T. The superlattice results are compared with the theoretical spin splittings, using individual spin state well depths calculated from the bulk spli'.ting. All energies are given in meV
Nominal sample parameters
Well: barrier widths Mn fraction
19 ,~," 19 A x = 7.3%
30 ,~. • 30 ,~ x = 20%
37 .~, : 37 ,~, x = 4.5%
75 ,~ : 75/~. x = 6.8c~
150 ~,: 150/~ x = 6.6c~
Bulk exciton spin splitting
A(E-HH)
77.9
89.0
61.0
74.6
73.,I
Calculated difference in spin state confinement
A(E confinement) ,&(HH confinement) 2x(LH confinement)
9.0 35.4 12.4
6.1 211.9 11.6
5.0 19.3 7.3
2.0 6.2 8.7
0.6 2.1 3.6
Calculated superlattice exciton ,,,pin splitting; (conventional assignment)
A: ~ H H I + ~E1 B: ,.kLHI - ,.~EI Ratio A : B
44.4 3.4 13.1
27.(I 5.5 4.9
24.3 2.3 11).6
8.2 6.7 1.2
2.7 3.0 0. t)
Calculated superlattice cxciton spin splitting (reverse assignment)
A: A H H I - ..XEI B: ALII1 + AE1 Ratio A : B
26.4 21.4 1.2
14.5 17,7 0.8
14.3 12.3 1.2
4.2 10.7 0.4
1.5 4.8 0.3
Experimental superlattice cxciton spin ,~;plitting
A: ~ ( E 1 - H H 1 ) B: A ( E I - L H I ) Ratio A : B
32.3 33.8 1.0
23.8 27.9 0.9
26.8 24.3 1.1
4.0 4,6 0,9
2.2 2.2 1.0
358
M.J. Lawless et aL / Magneto-optical studies of CdTe "Cd t _ x MnxTe
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Fig. 4. The fan diagrams for the (30 ,~'30 ,~, x = 20%) in both the (a) perpendicular and (b) parallel field orientations, showing the main E l - H I ( I s ) , E I - L H I ( I s ) and E1-HHI(2s) superlattice transitions in a~cending order of energy al zero field. The dotted line indicates that one of the lower two transitions at high fields (Mginates from the light-hole transition. Solid shapes in(icate strong reflectivity features.
2D spin behaviour for the heavy-hole [10] and an enhanced light-hole splitting when the field lies in the superlattice plane. In several of the samples, additional excitonic transitions and Landau levels are observed at higher energies than the ground state heavy- and light-hole transitions. The observation of the 2s exciton provides an estimate of the binding energy, using R * = 1.2(Ez.~-Ens). In most cases this lies between 15 meV and 20 meV (see table 1), in good agreement with previous measurements [5,7,11]; although the short period, strongly confined structure with 20% Mn barriers, shows some evidence of an enhancement of the binding energy to approximately 25 meV. In some sampies, additional features are observed which are thought to be higher order transitions, although further modelling is required to provide positive identifications. It is possible that the transition above the 2s exciton in the (150 ,~" 150 A, x = 6.6%) sample (see fig. 3) is an excitonic polaron replica of the E1-HH1 transition, as the energy separation ( ~ 21.3 meV) is close to previously recorded values for the CdTe LO phono'a energy [12]. It is interesting to note the strong interactions between the Landau levels originating from the 2s state and the two upper transitions.
3. Conclusions
light-hole transitioas (see figs. 2 and 4), and gives some insight into the changing spin configuration. In the case of the heavy-hole transitions, the exciton splitting is considerably reduced in the parallel field orieatation whiE: the reverse occurs for the light-hole transitions. This behaviour is particularly obvious in the 75 A" 75 A sample for which families ot! reflectivity spectra are shown in fig. 2 for the two orientations, and for the 30 A" 30 A sample for which energy plots are shown in fig. 4. The presence of strain and the superlat rice potential reduces the crystal symmetry from a cubic to a tctragonal structure. This projects the magnetic spin vector onto the growth (c) axis, being equivalent to a paramagnetic S = ~3 ion in an axially symmetric environment. The result is a
We have conducted a comprehensive study of the magneto-optical properties of a wide range of CdTe:Cd~_xMnxTe heterostructures. Our resuits demonstrate the large spin- and field-dependent exchange interactions with the DMS barriers, leading to an effective carrier exchange energy that is dependent on carrier confinement, magnetic spin vector and field orientation. The observation of 2s exciton states confirms previous estimates of exciton binding energy, although further modelling is required to identify the additional observed transiti~ns. The behaviour of the light-hole transitions in perpendicular fields indicates the.: the superlattice band structure is more complex than that usually assumed, and that more detailed theoretical study is required.
M.J. Lawless et al. / Magneto-optical studies of CdTe : Cd~_ , Mn, Te
References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] J.L. Aggarwai, S.N. Japerson, J. Stankiewicz, Y. Shapira, S. Foner, B. Khazi and A. Wold, Phys. Rev. B 28 (1983) 6907. [3] S.-K. Chang, A.V. Nurmiko, J.-W. Wu, L.A. Kolodziejski and R.L. Gunshor, Phys. Rev. B 37 (1988) 1191. [4] X. Liu, A, Petrou, J. Warnock, B.T. Jonker, G.A. Prinz and J.J. Krebs, Phys. Rev. Lett. 63 (1989) 2280. [5] E. Deleporte, J.M. Berroir, G. Bastard, C. Delalande, J.M. Hong and L.L. Chang, Phys. Rev. B 42 (1990) 5891. [6] G.M. Williams, A.G, Cullis, C.R. Whitehouse, D,E. Ashenford and B. Lunn, Appl. Phys. Lett. 55 (1989) 1303.
359
[7] A. Wasiela, Y. Merle d'Aubign6, J.E. Nicholls, D.E. Ashenford and B. Lunn, Solid Stale Commun. 76 (19o0~ 263. [8] V.A. Chitta and G.E. Marques, Scmicond. Sci. ~lechnol. 3 (1988) 564. [9] R.J. Warburton, M.J. Lawless and R,J. Nicholas, Surf. Sci. 267 (1992) 365. [10] R.W. Martin, R.J. Nicholas, G,J. Rees, S.K. Haywood, N.J, Mason and P.J. Walker, Phys. Rev. B 42 (1990) 9237. [11] J.-W. Wu, A.V. Nurmikko and J.J. Quinn, Phys. Rev. B 34 (1986) 1080. [12] Z.C. Feng, S. Perkowitz, J.M. Wrobel and J.J. Dubowski, Phys. Rev. B 39 (1989) 12997.
surface science
Magneto-optical studies of CdTe- Cd _,Mn. Te superlattices M.J. Lawless, R.J. Nicholas, M.J. McNamee, W. Hayes Clarendon Laboratoly, Oxford Unirersity, Oxford OX1 3PU, UK
D.E. A s h e n f o r d and B. L u n n Dept. Engineering Design and Manufacture, University of Hull, Cottingham Road, North Humberside HU6 7RX, UK Received 7 June 1991; accepted for publication 11 July 1991
Magneto-reflectivity studies have been conducted on a wide range of CdTe : Cd t - , Mn.,Te quantum wells and superlattices with L,~ = 19 A to 200 A, and x = 0.065 to 0.25. The observed excitonic transitions demonstrate large Zeeman splittings due to carrier exchange interactions in the dilute magnetic barriers, with the magnitude of the splitting providing a measure of carrier confinement, For short period superlattices (L~, _< 40 ,A) we observe a transition from type I to type II confinement for the mj = . ~, heavy-hole states. The Zeeman splitting is seen to be highly anisotropic, with the light-hole anisotropy reversed with respect to the heavy-hole, indicating 2D spin behaviour. We show that for the short period superlattices (L,,, < 75 /~), the perpendicular field splitting of the light-hole transitions is considerably higher than expected. From the observation of 2s exciton states we are a>~e to calculate exciton binding energies for various sample parameters.
1. Introduction Compared to III-V semiconductor structures, semi-magnetic II-VI heterostructures are a comparatively new innovation, and have not been studied to the same extent. Previous studies of these structures reveal many interesting and novel phenomena that are yet to be explored. The electronic states of dilute magnetic semiconductors (DMS) are heavily influenced by large exchange interactions with the magnetic ions [1,2]. Incorporation of DMS layers in semiconductor heterostructures leads to confinement potentials that are strongly spin-dependent in applied fields, producing large Zeeman splitting of the excitonic transitions [3]. The confinement of carriers in nonmagnetic (CdTe)wells by DMS (Cd~_xMn . Te) barriers results in an effective carrier exchange energy that is proportional to wave function penetration into the barriers. The small valence band offset, strain, and tke large Zeeman splitting result in many interesting phenomena including the field induced transition from type I
to type II band alignment for the m j = - ~ 3 valence band states [4,5] and the evolution of 2D spin behaviour in applied fields.
2. Experimental results Low temperature (4.2 K) magneto-reflectivity studies have been conducted on a series of CdTe:Cdt_xMnxTe superlattices grown by MBE on InSb[001] substrates [6] with Cd~_xMnxTe buffer and capping layers (typical thicknesses 0.1 p.m and 0.2/zm, respectively). The nominal sample parameters are given in table 1. Reflectivity measurements were made with both unpolarised and circularly po!arised light in magnetic fields of up to 15 T applied perpendicular and parallel to the superlattice layers. The reflectivity spectra for all the samples clearly shew the large Zeeman splitting of the main heavy-hole and light-hole exciton transitions for both the bulk (buffer and cap l a y e r ) C d l _ , M n , T e states and the confined superlattice and quantum well states (see, for
0(139-6028/92/$05.(1{1 ~. 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation. All rights rese~'ed
M.J. Lawless et aL / Magneto-optical studies of CdTe : C d t _ ~ Mn~Te
example, fig. 1 for the spectra of a short period superlattice). Circularly polarised reflectivity allows the individual cr+(Amj = + 1) and o--(Amj = - 1) transitions to be identified. In the parallel field orientation, the .rr(Amj = 0) transitions can also be seen. As the well widths increase, the carrier penetration into the DMS barriers falls, and the magnitude of the Zeeman splitting of the confined exciton transitions decreases (see table 1 for a summary of the exciton splittings). Whilst there is as yet no well accepted value for the valence band offset, it is generally agreed that it is small [3,5,7]. As a result of this, and the larger p - d exchange interaction, the Zeeman splitting of the hole states provides the dominant contribution to the observed excitonic splittings. The lighter (LH) mass of the mj = + ~ states leads to increased barrier penetration for the light-holes, which is further enhanced by the slight lattice mismatch
355
between CdTe and Cd~_xMn,Te which results in a small tetragonal strain. The uniaxial strain component decreases the light-hole well depth whiI.,,t increasing that of the heavy-holes. In the short period structures, there is a strong inter-well coupling for the light-hole states compared to the more strongly confined heavy-holes and electrons as can be seen from the calculated miniband widths shown in table 1. The increased penetration of the light-hole wave function should therefore lead to a relatively large exchange shift of the light-hole states. This can be seen for the wider well structures (figs. 2 and 3), where our results show that for both field orientations, the light-hole exciton splitting is in most cases larger than that seen for the heavy-hole exckon. Modelling this behaviour for the longer period structures, using k.p theory with separaLe envelope functions for each spin state, we calculate the changes in confine-
Table 1 The main bulk and superlattice exciton transition and binding e o e r g i e s . T h e e x c i t o n s p i n splitting e n e r g i e s a r e s h o w n , with t h e individual spin state shifts for the superlattices. All c n e r g i e s a r e ,qven in n : e V Nominal s a m p l e parameters
Well. barrier widths
Bulk exciton transitions
E-HII (B = i)T) E-Ltt (B = (iT)
30 A ' 3 0 , ~ x = 20¢~
37A'37A x = 4.5c>
75 A ' 7 5 A x -= 6.8">
1705.5 --- 170(1
1902.2 ~ 1889
1668.7 --- 1667
1720.0 ~ 1712
101.1
143.5
77.3
1660.3 1666.3
1718.3 1730.2
1633.5 1642.8
1672.7
1739.2
-
15
25
-
15
17
E1 conduction band H H 1 valence band I.HI valence band
222
48
58
3
0
56
9
13
1
0
197
66
79
9
1
S L H H exciton spin splitting at B ~ = 1 5 T
.~,( E 1- H t l I ) ,~,r ~
46,0 -34.0
32.5 -21.9
33.5 -21.7
5.6 4.51
3.1 -
Act--
12.0
1tl.6
11.8
SL LH exciton spin splitting
A~'EI-I,HI )
Mn fraction
E - H H exciton spin splitting ( B = 15 T) Superlattices ( S L ) exciton transitions (B = 0T)
E1-HH1 E1-LH1 EI-HHI
2s
Is binding energy
Calculated superlattice bandv.idths
at B ~ = 1 5 T SL exciton spin
19A'I9A x = 73%
~ 100 1620.3 1629.1 (,,- 16331
(
~1.11
150A:I50A x = 6.6% 1693.3 16~6.5 95.1 1600.0 1604.2 1614.0
--
"-- 33
6.1
2.2
- 31.1 14.1
- 25.~) 14.4
- 2(I.3
-
13.0
-
-
A(E1-HHI)
-
"-- 0
-
-%(EI-LH1 )
-
A~r"
A(r--
45.2
( ~ 40)
~ (1
~ 0
splitting at B 'i = 15 T
17.9
-
16.9
~ 0
356
M.J. Lawless et aL / Magneto-optical studies of CdTe "Cd /_ .,. M n , T e
BCZ)
=uoooo
NSR i
1700
BRgUma mWm
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!
I []
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ing as if significant mixing occurs with the mj = +_ ~3 heavy-hole states [8,9]. Warburton et al. [9] have recently shown that in high magnetic fields 3 strong mixing occurs between the rnj = + ~ and mj = - ~2 states in strongly coupled superlattices. Indeed, the splittings seen for the short period superlattices [figs, 1 and 4] demonstrate almost identical behaviour for the heavy- and light-hole transitions. It is interesting to note that the short period exciton splitting can be fitted quite, well by reversing signs of the electron and valence band exchange energies (see table 2). In this case the total heavy-hole exeiton splitting is given by A HH A E and the light-hole exciton splitting is A LH +AE. Although the bulk (barrier) exchange energies evolve with the field as symmetric Brillouin functions, the observed splitting of the exciton states can be very asymmetric with respect to the spin direction. A larger Zeeman shift is observed for the o-+ transition than for the or- transitions (see
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Fig. 1. The perpendicular field fan diagram ~ r the (37 A ' 3 7 A, x = 4.5%) sample, showing the main bulk ([]) and superlattice E 1 - H H I (©) and E1-LHI ( ~ ) exciton transitions. The asymmetff of E1-HH1 transition can be clearly seen in reference to the dashed line, representing the average diamagnetic shift. Solid shapes indicate strong reflectivity features.
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B(Z) 1.605eV
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Fig. 2. The families of reflectivily spectra for the (75 ,~" 74/k. x = 6.8¢~) sample for magnetic fields to () to 15 T applied in both the (a) perpendicular and (b) parallel orl~,~tations. The spectra demonstrates the anisotr,apy of the supcrla:ticc heavyand light-hole transilions in applied Pe'.ds.
357
M.J. Lawless et aL / Magneto-optical studies o f C d T e ' C d z _ x MnxTe
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fig. 1). This asymmetry is particularly apparent when account is taken of the positive diamagnetic shifts of the excitons, which have been estimated from the values observed for the mean of the bulk transitions (see table 1). For a given change in barrier height, the reduction in the confinement of the m j - 32, ~l states is greater than the corresponding increase in the confinement of 1 the mj = + 3, + ~ states. The small valence band offset and large negative exchange energies can lead to a field-induced change from type I to type II band alignment for the mj = - s3 hole state [5]. This change is characterised by a Zeeman shift approaching and exceeding half the corresponding bulk shift (for equal well and barrier thicknesses), as +he hole becomes Iocalised in the DMS barriers. Whilst this is seen for the shorter period superlattices (Lw < 40/k). this is not the case for the longer period superlattices as the (type I) Coulomb potential of the more localised electrons dominates the band alignment. Comparison between the perpendicular and parallel field data demonstrates a considerable anisotr6py in the splitting of the heavy- and
Table 2 The observed spin splitting of the bulk and superlattice excitons at B c = 5 T. The superlattice results are compared with the theoretical spin splittings, using individual spin state well depths calculated from the bulk spli'.ting. All energies are given in meV
Nominal sample parameters
Well: barrier widths Mn fraction
19 ,~," 19 A x = 7.3%
30 ,~. • 30 ,~ x = 20%
37 .~, : 37 ,~, x = 4.5%
75 ,~ : 75/~. x = 6.8c~
150 ~,: 150/~ x = 6.6c~
Bulk exciton spin splitting
A(E-HH)
77.9
89.0
61.0
74.6
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A(E confinement) ,&(HH confinement) 2x(LH confinement)
9.0 35.4 12.4
6.1 211.9 11.6
5.0 19.3 7.3
2.0 6.2 8.7
0.6 2.1 3.6
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A: ~ H H I + ~E1 B: ,.kLHI - ,.~EI Ratio A : B
44.4 3.4 13.1
27.(I 5.5 4.9
24.3 2.3 11).6
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A: A H H I - ..XEI B: ALII1 + AE1 Ratio A : B
26.4 21.4 1.2
14.5 17,7 0.8
14.3 12.3 1.2
4.2 10.7 0.4
1.5 4.8 0.3
Experimental superlattice cxciton spin ,~;plitting
A: ~ ( E 1 - H H 1 ) B: A ( E I - L H I ) Ratio A : B
32.3 33.8 1.0
23.8 27.9 0.9
26.8 24.3 1.1
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2.2 2.2 1.0
358
M.J. Lawless et aL / Magneto-optical studies of CdTe "Cd t _ x MnxTe
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Fig. 4. The fan diagrams for the (30 ,~'30 ,~, x = 20%) in both the (a) perpendicular and (b) parallel field orientations, showing the main E l - H I ( I s ) , E I - L H I ( I s ) and E1-HHI(2s) superlattice transitions in a~cending order of energy al zero field. The dotted line indicates that one of the lower two transitions at high fields (Mginates from the light-hole transition. Solid shapes in(icate strong reflectivity features.
2D spin behaviour for the heavy-hole [10] and an enhanced light-hole splitting when the field lies in the superlattice plane. In several of the samples, additional excitonic transitions and Landau levels are observed at higher energies than the ground state heavy- and light-hole transitions. The observation of the 2s exciton provides an estimate of the binding energy, using R * = 1.2(Ez.~-Ens). In most cases this lies between 15 meV and 20 meV (see table 1), in good agreement with previous measurements [5,7,11]; although the short period, strongly confined structure with 20% Mn barriers, shows some evidence of an enhancement of the binding energy to approximately 25 meV. In some sampies, additional features are observed which are thought to be higher order transitions, although further modelling is required to provide positive identifications. It is possible that the transition above the 2s exciton in the (150 ,~" 150 A, x = 6.6%) sample (see fig. 3) is an excitonic polaron replica of the E1-HH1 transition, as the energy separation ( ~ 21.3 meV) is close to previously recorded values for the CdTe LO phono'a energy [12]. It is interesting to note the strong interactions between the Landau levels originating from the 2s state and the two upper transitions.
3. Conclusions
light-hole transitioas (see figs. 2 and 4), and gives some insight into the changing spin configuration. In the case of the heavy-hole transitions, the exciton splitting is considerably reduced in the parallel field orieatation whiE: the reverse occurs for the light-hole transitions. This behaviour is particularly obvious in the 75 A" 75 A sample for which families ot! reflectivity spectra are shown in fig. 2 for the two orientations, and for the 30 A" 30 A sample for which energy plots are shown in fig. 4. The presence of strain and the superlat rice potential reduces the crystal symmetry from a cubic to a tctragonal structure. This projects the magnetic spin vector onto the growth (c) axis, being equivalent to a paramagnetic S = ~3 ion in an axially symmetric environment. The result is a
We have conducted a comprehensive study of the magneto-optical properties of a wide range of CdTe:Cd~_xMnxTe heterostructures. Our resuits demonstrate the large spin- and field-dependent exchange interactions with the DMS barriers, leading to an effective carrier exchange energy that is dependent on carrier confinement, magnetic spin vector and field orientation. The observation of 2s exciton states confirms previous estimates of exciton binding energy, although further modelling is required to identify the additional observed transiti~ns. The behaviour of the light-hole transitions in perpendicular fields indicates the.: the superlattice band structure is more complex than that usually assumed, and that more detailed theoretical study is required.
M.J. Lawless et al. / Magneto-optical studies of CdTe : Cd~_ , Mn, Te
References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] J.L. Aggarwai, S.N. Japerson, J. Stankiewicz, Y. Shapira, S. Foner, B. Khazi and A. Wold, Phys. Rev. B 28 (1983) 6907. [3] S.-K. Chang, A.V. Nurmiko, J.-W. Wu, L.A. Kolodziejski and R.L. Gunshor, Phys. Rev. B 37 (1988) 1191. [4] X. Liu, A, Petrou, J. Warnock, B.T. Jonker, G.A. Prinz and J.J. Krebs, Phys. Rev. Lett. 63 (1989) 2280. [5] E. Deleporte, J.M. Berroir, G. Bastard, C. Delalande, J.M. Hong and L.L. Chang, Phys. Rev. B 42 (1990) 5891. [6] G.M. Williams, A.G, Cullis, C.R. Whitehouse, D,E. Ashenford and B. Lunn, Appl. Phys. Lett. 55 (1989) 1303.
359
[7] A. Wasiela, Y. Merle d'Aubign6, J.E. Nicholls, D.E. Ashenford and B. Lunn, Solid Stale Commun. 76 (19o0~ 263. [8] V.A. Chitta and G.E. Marques, Scmicond. Sci. ~lechnol. 3 (1988) 564. [9] R.J. Warburton, M.J. Lawless and R,J. Nicholas, Surf. Sci. 267 (1992) 365. [10] R.W. Martin, R.J. Nicholas, G,J. Rees, S.K. Haywood, N.J, Mason and P.J. Walker, Phys. Rev. B 42 (1990) 9237. [11] J.-W. Wu, A.V. Nurmikko and J.J. Quinn, Phys. Rev. B 34 (1986) 1080. [12] Z.C. Feng, S. Perkowitz, J.M. Wrobel and J.J. Dubowski, Phys. Rev. B 39 (1989) 12997.