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DMS based quantum wells with magnetically tuned heavy hole confinement
JOURNAL OF
LUMINESCENCE
Journal of Luminescence 52 (1992) 175-181 North-Holland
DMS based quantum wells with magnetically tuned heavy hole confinement A. Petrou a, W.C. Chou a, X.C. Liu a,1, J. Warnock b and B.T. Jonker ’ a Department of Physics and Astronomy and Center for Electronic and Electra-Optic Materials, State University of Buffalo, Buffalo, NY 14260, USA b IBM, Yorktown Heights, NY 10598, USA ’ jNaua1 Research Laboratory, Washington, DC 20375-5000,
New York at
USA
We discuss the results of a magneto-optical study of ZnFeSe/ZnSe/ZnFeSe and ZnMnSe/ZnSe/ZnMnSe quantum well structures grown by molecular beam epitaxy on GaAs. In both systems the zero field heavy hole offset is near zero and the heavy hole confinement is controlled by an externally applied magnetic field which produces large spin splittings in the diluted magnetic semiconductor (DMS) layers. The changes in the band structure induced by the magnetic field result in a pronounced asymmetry of the heavy hole exciton spin components as the barrier and well hole populations become spin-polarized. Both the iron- and the manganese-based structures show similar behavior even though ZnFeSe is a Van Vleck paramagnet while ZnMnSe is a Brillouin paramagnet.
1. Introduction
Diluted magnetic semiconductors (DMS) exhibit a number of extraordinary properties, the most striking of which is the very large band spin splitting in the presence of a magnetic field 111. These large splittings are due to the spin-exchange interaction between the band electrons (holes) and the magnetic ions. In non-magnetic semiconductor quantum wells, e.g. GaAs/AlGaAs, the electrons and holes are confined in potential wells formed by the band edge discontinuities at the interfaces. External perturbations (e.g. electric field) can modify the depth or shape of the confining potential to a limited extent. If one, or both constituent layers of a semiconductor structure are made of DMS material, these discontinuities can be altered to a much larger degree by applying a magnetic field that causes
large band splittings of the magnetic layers. This was recognized by several authors [2-41 who proposed a variety of DMS based quantum wells in which aspects of the band structure were modified by the application of an external field. In some of these proposed systems the changes in the band structure affected physical properties such as conductivity in a very dramatic way [3]. In this paper, we shall discuss two such systems in which important modifications of the band structure, and thus the optical properties, are induced by the application of a magnetic field in a direction perpendicular to the structures’ layers. In both systems the magnetic field controlls the confinement of the heavy holes, separating them according to their spin to the DMS or non-DMS layers.
2. Experimental Correspondence to: Dr. A. Petrou, Department of Physics and Astronomy and Center for Electronic and Electra-Optic Materials, State University of New York at Buffalo, Buffalo, NY 14260, USA. ’ Present address: University of Illinois, 127 Microelectronics Laboratory, Urbana, IL 61801, USA. 0022-2313/92/$05.00
The samples were grown by molecular beam epitaxy (MBE) from elemental Knudsen cell style sources of Zn, Se, Mn and Fe. The substrates were GaAs(OO1) semi-insulating device grade
Q 1992 - Elsevier Science Publishers B.V. All rights reserved
A. Petrou et al. / DMS based quantum wells
176
wafers prepared in a conventional manner using a 5:l:l H,SO,:H,O,:H,O 3 min room temperature etch and deionized water rinse. Square pieces of 1 cm2 were In-mounted on molybdenum holders, and final cleaning was achieved by thermally desorbing the surface oxide at - 585°C in ultrahigh vacuum just prior to growth. The substrate surface exhibited a well-ordered 4 x 3 reconstruction as observed with reflection high energy electron diffraction (RHEED) with the shuttered Se source at operating temperature. The samples grew in (001) orientation at a substrate ttmperature of 300°C and growth rates of 20-40 A/min, with a Se: Zn beam equivalent pressure ratio > 2 : 1. RHEED was used to monitor the growth, and showed a well-ordered Sestabilized 2 x 1 surface reconstruction. The thickness and composition of the samples were confirmed with X-ray fluorescence measurements following growth. The samples used in this study belong in two groups: (a) iron-based ZnFeSe/ ZnSe/ZnFeSe, and (b) manganese-based ZnMnSe/ ZnSe/ ZnMnSe quantum wells. The dimensions of the samples reported on here are summarized in table 1. Both types of structures are ZnSe based with barriers consisting of DMS material; Zn 1_,Fe,Se x = 0.1 for samples 1, 2 and 3; and Zn 1_,Mn,Se x = 0.088 for sample 4. The ironbased structures (samples 1, 2 and 3) do not show any photoluminescence. They have been studied using magnetoreflectance spectroscopy, in the Faraday geometry. A monochromatic light beam was produced by the combination of a broad-band
Table 1 Sample dimensions Sample
DMS layer
ZnSe layer
DMS layer
thickness
thickness
thickness
[AI
[A]
[A]
1
100
100
100
2
Zno.Pea.+e 100
150
Zno.Pco.ISe 100
3
Zno.Pco.?e 100
200
Zno.Peo.,Sc 100
4
Zno.Pe& 116 Zn 0.912Mn0.0ssSe
116
Zno.Peo.,Se 348 Zn 0.9l~Mno.ossSe
tungsten-halogen source and a grating monochromator. The incident beam was circularly polarized as cr+ or u_ using a linear polarizer in conjunction with a quater-wave plate. The intensity of the light reflected from the sample surface was synchronously detected by a photomultiplier tube. In the case of sample 4, both reflectance and photoluminescence spectroscopies were used to study its band edge magneto-optical properties. The luminescence spectra were excited using the 3250 A line of a helium-cadmium laser. The emitted light was analyzed by a double monochromator equipped with a cooled photomultiplier tube and the associated photon counting electronics. For both types of experiments the samples were placed in a variable temperature optical cryostat equipped with an 8 T superconducting magnet coil.
3. Band structure The ability to tune band alignments, and thereby carrier confinement, in semiconductor heterostructures has been an elusive goal in semiconductor physics. Application of external perturbations such as strain, electric field etc. gives only a limited range of tunability. Heterostructures based on diluted magnetic semiconductors on the other hand inherently offer a substantial tunability due to the giant spin-splitting they exhibit. In addition they offer the potential for spin resolved band engineering i.e. the creation of a spinpolarized two-dimensional electron or hole gas. The effect of the application of a magnetic field on the band structure of a DMS-based quantum well is shown in fig. 1. Figure l(a) is a schematic of the band alignment at zero field showing the relative position of the conduction and heavy hole (hh, m = f i) band edges. The light hole band edge is shifted to lower energy by strain and lies = 15 meV below the heavy hole band. The heavy hole bands in fig. l(a) are shown to have zero offset, and this is very nearly true for these samples. In reality, the heavy hole offset in all samples is very small relative to the field-induced spin-splitting. The fitting of the magneto-optical data, which will be discussed below, yields the
A. Petrou et al. / DMS based quantum wells
I 2
-l-J +1/2
2
J-k2
ICI
El#O m-
Fig. 1. Schematic diagram of the conduction and heavy hole band alignment in ZnSe based DMS structures. (a) B = 0, (b) B # 0, band alignment for the M = - f electrons and m = - 2 heavy holes. (c) B # 0, band alignment for the m = + $ electrons and m = + t heavy holes.
following values for the heavy hole offset at zero field. In samples 1, 2 and 3 the heavy hole band edge in the ZnFeSe layers lies 1.1 meV above the corresponding band edge in the ZnSe wells resulting in a type-II alignment. In sample 4 on the other hand, the heavy hole band edge of the ZnMnSe layers lies 1 meV below that of the ZnSe layer resulting in a nominal type-1 structure. In both cases, the heavy hole offset is very nearly zero as shown in fig. l(a), and the total band offset A E is accomodated in the conduction band. AE is 33 meV for the Fe-based samples [5] and 20 meV for the Mn-based structure [6]. The zero field conduction band offset in all samples is always larger than the field induced splitting. When a magnetic field is applied, the conduction band offset decreases for the m = - i electrons (fig. l(b)), while it increases for the m = f i electrons (fig. l(c)). However, the confinement of electrons is only slightly perturbed by the applied field for the samples of this study. The heavy hole confinement on the other hand, is completely controlled by the external magnetic field. The reason is that the spin splitting of the heavy holes is larger than that of the conduction band by a factor equal to p/a, where p and cy are the exchange integrals for the valence and conduction band, respectively. These P/a ratios
177
are: 7.1 for ZnFeSe [7] and 4.8 for ZnMnSe [61. The initially small valence band offsets ( - 1 meV) are overwhelmed by the much larger spin splittings produced by the applied magnetic field. These are - 25 meV for samples 1, 2 and 3 and - 50 meV for sample 4 at 8 T. The m = - + heavy hole level shifts to higher energy (fig. l(b)), while the m = + g hole state shifts to lower energy (fig. l(c)) with respect to their zero field position. As a result, the m = - + spin down holes are localized in the DMS layers, while the m = + 1 spin up holes are confined in the nonmagnetic ZnSe wells. The corresponding (- +, - i> u+ and (+ 5, + i> u_ excitonic transitions are shown in figs. l(b) and (c), respectively. The CT+ transition is spatially indirect (type-II), and as such, has a smaller oscillator strength compared to similar direct transitions. In addition, since the m = - 5 holes are localized inside the DMS layers, the energy of the u+ (- +, - i) exciton component exhibits a large red shift as function of magnetic field due to the spin-exchange interaction between the holes and the magnetic ions in the DMS layers. The u_ (+ 5, + i) transition shown in fig. l(c) is spatially direct (type-11 with a large oscillator strength. The constituent m = + : hole and m = + i electron are both localized in the nonmagnetic ZnSe layer. The energy of the u_ component thus depends very little on magnetic field. The band alignment changes produced by the external magnetic field, summarized in fig. 1, are possible because of the large band spin-splitting of the magnetic layers. These splittings are proportional to the magnetization of the DMS material. We note here, that even though ZnFeSe is a Van Vleck paramagnet [7] and ZnMnSe is a Brillouin paramagnet [6], the band structure changes produced by the magnetic field are quite similar because the important underlying factor is the large size of the band spin-splitting relative to the natural zero-field band offset which exists in both materials. The magnetization of ZnMnSe, and thus the band spin-splitting, is larger than that of ZnFeSe. This difference manifests itself in the increased m = + t electron confinement in sample 4, as will be discussed below.
A. Petrou et al. / DMS based quantum wells
178
4. Results and discussion In this section we present and discuss the results of a magneto-optical study of samples l-4. In fig. 2(a) the derivative dR/A E of the reflectance spectrum at zero magnetic field is shown for sample 1. It contains two features marked (i) and (ii) at 2810.7 and 2824.4 meV, respectively. They are attributed to the heavy hole Cm = f t> and light hole Cm = f t> excitons. The observed heavy-light hole exciton splitting is due to the biaxial compressive strain present in the structure. The strain can be calculated from low temperature lattice parameters of ZnSe [81, GaAs [9] and the elastic constants of bulk ZnSe [lo], assuming pseudomorphic growth. Once the strain is determined, the heavy and light hole band energy shifts follow from deformation potentials [ll] measured for ZnSe [ 121. Theoretical calculations [13] allow the separation of the hydrostatic deformation potential into valence and conduction band components. The calculated value, without taking into account the hole confinement, is equal to 13.3 meV. It is very close to the experimental heavy-light hole exciton splitting (13.7 meV1, which is an indication that in structures 1, 2 and 3 the ZnSe and ZnFeSe layers are commensurate with the GaAs substrate, as exptcted for total sample thickness of less than 400 A.
I
I
alSample
I
I
T=4.2
1
In fig. 2(b) the PL spectrum from sample 4 is shown. The feature marked (i) at 2802.8 meV is identified as the heavy hole exciton of this structure. In the reflectance spectrum this feature occurs at 2805.0 meV, while the light hole exciton feature comes at 2816.9 meV. The calculated zero field, strain-induced heavy-light hole exciton splitting is equal to 19.5 meV, which is significantly higher than the experimental value of 11.9 meV. This difference indicates a partial relaxation of strain at the GaAs/ZnMnSe interface, for sample 4, attributed to the greater total thickness (580 A> of the sample. In figs. 3(a) and (b) the energies of the heavy hole exciton spin components are plotted as function of magnetic field for samples 1 and 4, respectively. In both samples a pronounced asymmetry between the two spin components is observed. The weaker (- +, - i> u+ component shows a large red shift as function of magnetic field. The observed red shift confirms the picture shown in fig. l(b), i.e. that the - + hole is confined in the DMS layers. The low intensity of this component is consistent with its indirect character. The stronger (+ ;, + $1 u_ exciton component shows an initial blue shift for field values between 0 and 1 T. For B > 2 T the U_ exciton energy does not vary appreciably with magnetic field, i.e. it shows a nonmagnetic behavior. This is consistent with
I
1
,
I
~)Sample
K
T=4.2
I
I
I
1
4 K *
B=O
(i)
2705
2805
PHOTON
ENERGY
2825
(meV)
2045
2780
2790
PHOTON
2800
ENERGY
2810
2820
(meV)
Fig. 2. (a) Reflectance derivative spectrum from sample 1. (b) Photoluminescence spectrum from sample 4 excited by the 3250 w line of a He-Cd laser. The asterisk indicates a laser plasma line. Both spectra were recorded at B = 0; T = 4.2 K.
A. Petrou et al. / DMS based
(al
Sample
179
quantum wells 2850
I
1
(b)
1
I
,
I
Sample ___,_,-.-.--‘--’
•o~n ___-----
> g
I
I
4
I3
I
I
_.-._ 0
L7
---
_
OK_
2800
w 5 z
2790
F 0 :
2790
I
2770 0
1
I
2
MAGNETIC Fig. 3. Energy
I
1
4
I
6
FIELD
I
I
0
I
2750
I
10
I
#
I
2
0
(TESLA)
6
I
1
6
MAGNETIC
FIELD
of the (- $, - $) o+ and (+ t, + $1 (T_ heavy hole exciton spin components plotted represent theoretical fits to the data. (a) Sample 1; (b) sample 4.
the schematic of fig. l(c) which indicates a type-1 (+ ;, + ;> (T_ exciton in the nonmagnetic ZnSe layer. For samples 1, 2 and 3, the u_ exciton component undergoes a type-II to type-1 transition as the magnetic field is increased from 0 to 2 T. In fig. 3(b) a second excitonic feature appears for B > 2 T in the u_ polarization, approximately 24 meV above the (+ 3, + i> transition. It is attributed to an exciton associated with the second (n = 2) conduction confinement subband as shown in the inset of fig. 3(b). The height of the conduction band potential well increases with field for the m = + 4 electrons and for B > 2 T it becomes large enough to confine the n = 2 subband. This is possible in the Mn-based structure because the magnetization, and thus the conduction band spin splitting is larger than that in the Fe-based layers by approximately a factor of two. No such magnetically confined n = 2 conduction subband was observed in samples 1, 2 and 3. In fig. 4 the ratio I( + )/I( - 1 of the intensities of the u, and u_ heavy hole excitons is plotted as function of magnetic field for samples 1 and 2. For both structures the ratio drops sharply with increasing field and remains almost constant for
I
4
1
10
8
(TESLA)
versus magnetic
field. The lines
B > 2 T. The saturation value of the I( + )/I( - ) ratio is equal to 0.18, 0.06 and 0.015 for samples 1, 2 and 3, respectively. The u, component is clearly weaker than the u_ and the intensity ratio 1
I
I
I
I
,
,
,
I
Samp 1
Samp 1
0.01 0
”
” 2
MAGNETIC
‘1 4
” 6
FIELD
’ 9
I 10
(TESLA)
Fig. 4. Intensity ratio I(+ )/I(-) of the o+ and U_ heavy hole exciton components plotted versus magnetic field. Triangles: sample 1; squares: sample 2.
180
A. Petrou et al. / DMS based quantum wells
I( + )/I( - > gets progressively smaller as the ZnSe layer thickness increases. This is because the ZnSe thickness defines the spatial separation of the wavefunctions for the m = - f electrons and the m = - G holes. The intensity ratio I( +)/I( - > for sample 4 shows similar behavior as that of samples 1, 2 and 3, i.e. it decreases rapidly as function of B. The saturation value of Z( + )/I( -1 for sample 4 is 0.50, i.e. significantly larger than that for sample 1, even though the two structures have comparable dimensions. This difference is attributed to the presence of potential fluctuations at the ZnSe/ZnMnSe interfaces which decouple, to some extent, the magnetic from the nonmagnetic layers. These fluctuations could be connected with the hole pinning defects responsible for the partial strain relaxation in this sample. In the remaining portion of this section we discuss the theoretical fitting to the data shown in figs. 3(a) and (b). A more detailed model is required to describe quantitatively the phenomena as observed in the quantum wells applied here. Such a model should incorporate the following effects: 1) strain-related band and excitonic energy shifts; 2) magnetic field induced spin-splitting in the barrier layer; 3) quantum confinement energies associated with the changing potential in the barriers; and 4) the effect of the Coulomb potential, including how the exciton binding energy and wave function change as the barrier potentials vary. In the treatment to be described here, only the first three of the above are included. The fourth is important for shallow wells [14] but makes calculations considerably more difficult. A more complete description of these shallow magnetic quantum well systems including all four items will be reported later. To estimate the exciton energies as a function of applied magnetic field, we first calculate the combined valence and conduction band offset at zero field. This offset is just the sum of the bulk band gap difference (33 meV for samples 1, 2, 3 and 20 meV for sample 41, and the difference in the strain-induced splitting between the DMS layers and the ZnSe layer. Then, the net valence band offset is extracted from the field dependent data. In this way, the value obtained for the valence band offset is relatively insensitive to the
values used for the deformation potentials in the strain calculation, since the overall band offset for the heavy hole exciton is primarily determined by the bulk band offset. However by neglecting exciton effects, all the energies obtained for the valence band offsets will be shifted by some fraction of the excitonic binding energy. The changes in the barrier potential as a function of magnetic field for the hole and electron spin states according to spin-exchange induced splitting are shown in fig. 1. At high fields, one heavy hole spin state (- 3) is confined primarily to the barrier while the other (+ :) is confined in the well. In the conduction band, the spin splitting is less and acts more as a perturbation on the original quantum well potential. The ratios P/a of the DMS layers in these structures are known [6,71 so that the conduction and valence band quantum well potentials can be calculated as a function of magnetic field. To extract the net valence band offset from the field dependent data, single particle wave functions and energies for heavy holes and electrons are calculated numerically as a function of magnetic field, assuming infinite potential barriers at both boundaries of the structure. For samples 1, 2 and 3 the field dependent data are fitted using two parameters; the zero field valence band offset and an effective g factor describing the spin splitting in the barrier layer. The fit shown in fig. 3(a) is continued only up to 4 T, since at higher fields the saturation of the magnetization must be taken into account. For sample 4, the spin splitting was measured from a thick epilayer of the same magnetic concentration as the barrier layers. In this way the fit is extended over the whole range of magnetic fields investigated, and only one parameter (the zero field valence band offset) is required to describe the data. The net zero field valence band offsets (well to barrier) obtained from the data in this way are 1.1 meV for samples l-3 and - 1 meV for sample 4. It should be noted that these numbers are strictly for purposes of comparison between the two types of samples. To calculate the true value of the valence band offset requires a detailed accounting of excitonic effects, which would tend to increase the values obtained by some fraction of the bulk exciton
A. Petrou et al. / DMS based quantum
binding energy. Since the electrons are primarily localized in the ZnSe wells, the Coulomb interaction will tend to confine the holes in the same layers, even for small positive offsets (i.e. for weak type-11 potentials). Thus ignoring the Coulomb interaction leads to an underestimation of the band offset. However, the general description is still correct since in these samples the spin splitting and consequently the high-field valence band offset is much larger than the exciton binding energy. In sample 4, another feature thought to be a higher-order transition appears in the spectrum at intermediate fields. As the conduction band well depth increases with field, it becomes large enough so that there is more than one state confined in the well. The energy of this state CB(2) was calculated, along with the energy of the first excited hole state VB(2). In fig. 3(b) the calculated energy of the transition CB(2) --) VB(2) and CB(2) + VB(1) are drawn using dash-dotted and dashed lines respectively. Although the transition CB(2) -+ VB(1) is a forbidden transition, the symmetry of the quantum potential in the conduction and the valence band may not be perfectly the same, leading to a non-zero transition probability. In any case the calculated energies bracket the observed peak energy in the reflectivity spectrum.
5. Summary We have presented a magneto-optical study of ZnSe/ZnFeSe and ZnSe/ZnMnSe quantum wells. In these two systems the hole confinement is controlled by an external magnetic field, which induces large changes in the band structure. To our knowledge, this is the first time in which such
wells
181
wide control1 of the electronic states in semiconductor quantum well structures has been achieved, by the application of an external perturbation.
Acknowledgements
The work at SUNY was supported by ONR/SDIO under the MMFEL program and NSF, Grant No. DMR8922177; at NRL work was supported by the Office of Naval Research. The authors thank T. Schmiedel and L.P. Fu for technical assistance, and B.D. McCombe for helpful discussions.
References
ill J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. l21M. Von Ortenberg, Phys. Rev. Lett. 49 (1982)
1041. J.K. Furdyna and R.L. Gunshor, Superlattices and Microstructures 1 (1985) 327. I41 J.A. Brum, G. Bastard and M. Voos, Solid State Commun. 59 (1986) 561. PI B.T. Jonker, J.J. Krebs, S.B. Qadri and G.A. Prinz, Appl. Phys. Lett. 50 (1987) 848. (61 A. Twardowski, T. Diet1 and M. Demianiuk, Solid State Commun. 48 (1983) 845. I71 A. Twardowski, P. Glad, W.J.M. de Jonge and M. Demianiuk, Solid State Commun. 64 (1987) 63. ls1 H.P. Singh and B. Dayal, Phys. Stat. Sol. 23 (1967) K93. Properties of [91 Y.S. Touloukian et al., in: Thermophysical Matter, Vol. 13, ed. Y.S. Touloukian (Plenum, New York, 1977) p. 747. [lOI B.H. Lee, J. Appl. Phys. 41 (1970) 2984. 1111 See for example: H. Asai and Oe, J. Appl. Phys. 54 (1983) 2052. [121 D.W. Langer et al., Phys. Rev. B 2 (1970) 4005. G.A. Nevile Connell and William H31 Don L. Camphausen, Paul, Phys. Rev. Lett. 26 (1971) 184. (141 S.K. Chang, A.V. Nurmikko, J.W. Wu, L.A. Kolodziejski and R.L. Gunshor, Phys. Rev. B 37 (1988) 1191.
[31 S. Datta,
LUMINESCENCE
Journal of Luminescence 52 (1992) 175-181 North-Holland
DMS based quantum wells with magnetically tuned heavy hole confinement A. Petrou a, W.C. Chou a, X.C. Liu a,1, J. Warnock b and B.T. Jonker ’ a Department of Physics and Astronomy and Center for Electronic and Electra-Optic Materials, State University of Buffalo, Buffalo, NY 14260, USA b IBM, Yorktown Heights, NY 10598, USA ’ jNaua1 Research Laboratory, Washington, DC 20375-5000,
New York at
USA
We discuss the results of a magneto-optical study of ZnFeSe/ZnSe/ZnFeSe and ZnMnSe/ZnSe/ZnMnSe quantum well structures grown by molecular beam epitaxy on GaAs. In both systems the zero field heavy hole offset is near zero and the heavy hole confinement is controlled by an externally applied magnetic field which produces large spin splittings in the diluted magnetic semiconductor (DMS) layers. The changes in the band structure induced by the magnetic field result in a pronounced asymmetry of the heavy hole exciton spin components as the barrier and well hole populations become spin-polarized. Both the iron- and the manganese-based structures show similar behavior even though ZnFeSe is a Van Vleck paramagnet while ZnMnSe is a Brillouin paramagnet.
1. Introduction
Diluted magnetic semiconductors (DMS) exhibit a number of extraordinary properties, the most striking of which is the very large band spin splitting in the presence of a magnetic field 111. These large splittings are due to the spin-exchange interaction between the band electrons (holes) and the magnetic ions. In non-magnetic semiconductor quantum wells, e.g. GaAs/AlGaAs, the electrons and holes are confined in potential wells formed by the band edge discontinuities at the interfaces. External perturbations (e.g. electric field) can modify the depth or shape of the confining potential to a limited extent. If one, or both constituent layers of a semiconductor structure are made of DMS material, these discontinuities can be altered to a much larger degree by applying a magnetic field that causes
large band splittings of the magnetic layers. This was recognized by several authors [2-41 who proposed a variety of DMS based quantum wells in which aspects of the band structure were modified by the application of an external field. In some of these proposed systems the changes in the band structure affected physical properties such as conductivity in a very dramatic way [3]. In this paper, we shall discuss two such systems in which important modifications of the band structure, and thus the optical properties, are induced by the application of a magnetic field in a direction perpendicular to the structures’ layers. In both systems the magnetic field controlls the confinement of the heavy holes, separating them according to their spin to the DMS or non-DMS layers.
2. Experimental Correspondence to: Dr. A. Petrou, Department of Physics and Astronomy and Center for Electronic and Electra-Optic Materials, State University of New York at Buffalo, Buffalo, NY 14260, USA. ’ Present address: University of Illinois, 127 Microelectronics Laboratory, Urbana, IL 61801, USA. 0022-2313/92/$05.00
The samples were grown by molecular beam epitaxy (MBE) from elemental Knudsen cell style sources of Zn, Se, Mn and Fe. The substrates were GaAs(OO1) semi-insulating device grade
Q 1992 - Elsevier Science Publishers B.V. All rights reserved
A. Petrou et al. / DMS based quantum wells
176
wafers prepared in a conventional manner using a 5:l:l H,SO,:H,O,:H,O 3 min room temperature etch and deionized water rinse. Square pieces of 1 cm2 were In-mounted on molybdenum holders, and final cleaning was achieved by thermally desorbing the surface oxide at - 585°C in ultrahigh vacuum just prior to growth. The substrate surface exhibited a well-ordered 4 x 3 reconstruction as observed with reflection high energy electron diffraction (RHEED) with the shuttered Se source at operating temperature. The samples grew in (001) orientation at a substrate ttmperature of 300°C and growth rates of 20-40 A/min, with a Se: Zn beam equivalent pressure ratio > 2 : 1. RHEED was used to monitor the growth, and showed a well-ordered Sestabilized 2 x 1 surface reconstruction. The thickness and composition of the samples were confirmed with X-ray fluorescence measurements following growth. The samples used in this study belong in two groups: (a) iron-based ZnFeSe/ ZnSe/ZnFeSe, and (b) manganese-based ZnMnSe/ ZnSe/ ZnMnSe quantum wells. The dimensions of the samples reported on here are summarized in table 1. Both types of structures are ZnSe based with barriers consisting of DMS material; Zn 1_,Fe,Se x = 0.1 for samples 1, 2 and 3; and Zn 1_,Mn,Se x = 0.088 for sample 4. The ironbased structures (samples 1, 2 and 3) do not show any photoluminescence. They have been studied using magnetoreflectance spectroscopy, in the Faraday geometry. A monochromatic light beam was produced by the combination of a broad-band
Table 1 Sample dimensions Sample
DMS layer
ZnSe layer
DMS layer
thickness
thickness
thickness
[AI
[A]
[A]
1
100
100
100
2
Zno.Pea.+e 100
150
Zno.Pco.ISe 100
3
Zno.Pco.?e 100
200
Zno.Peo.,Sc 100
4
Zno.Pe& 116 Zn 0.912Mn0.0ssSe
116
Zno.Peo.,Se 348 Zn 0.9l~Mno.ossSe
tungsten-halogen source and a grating monochromator. The incident beam was circularly polarized as cr+ or u_ using a linear polarizer in conjunction with a quater-wave plate. The intensity of the light reflected from the sample surface was synchronously detected by a photomultiplier tube. In the case of sample 4, both reflectance and photoluminescence spectroscopies were used to study its band edge magneto-optical properties. The luminescence spectra were excited using the 3250 A line of a helium-cadmium laser. The emitted light was analyzed by a double monochromator equipped with a cooled photomultiplier tube and the associated photon counting electronics. For both types of experiments the samples were placed in a variable temperature optical cryostat equipped with an 8 T superconducting magnet coil.
3. Band structure The ability to tune band alignments, and thereby carrier confinement, in semiconductor heterostructures has been an elusive goal in semiconductor physics. Application of external perturbations such as strain, electric field etc. gives only a limited range of tunability. Heterostructures based on diluted magnetic semiconductors on the other hand inherently offer a substantial tunability due to the giant spin-splitting they exhibit. In addition they offer the potential for spin resolved band engineering i.e. the creation of a spinpolarized two-dimensional electron or hole gas. The effect of the application of a magnetic field on the band structure of a DMS-based quantum well is shown in fig. 1. Figure l(a) is a schematic of the band alignment at zero field showing the relative position of the conduction and heavy hole (hh, m = f i) band edges. The light hole band edge is shifted to lower energy by strain and lies = 15 meV below the heavy hole band. The heavy hole bands in fig. l(a) are shown to have zero offset, and this is very nearly true for these samples. In reality, the heavy hole offset in all samples is very small relative to the field-induced spin-splitting. The fitting of the magneto-optical data, which will be discussed below, yields the
A. Petrou et al. / DMS based quantum wells
I 2
-l-J +1/2
2
J-k2
ICI
El#O m-
Fig. 1. Schematic diagram of the conduction and heavy hole band alignment in ZnSe based DMS structures. (a) B = 0, (b) B # 0, band alignment for the M = - f electrons and m = - 2 heavy holes. (c) B # 0, band alignment for the m = + $ electrons and m = + t heavy holes.
following values for the heavy hole offset at zero field. In samples 1, 2 and 3 the heavy hole band edge in the ZnFeSe layers lies 1.1 meV above the corresponding band edge in the ZnSe wells resulting in a type-II alignment. In sample 4 on the other hand, the heavy hole band edge of the ZnMnSe layers lies 1 meV below that of the ZnSe layer resulting in a nominal type-1 structure. In both cases, the heavy hole offset is very nearly zero as shown in fig. l(a), and the total band offset A E is accomodated in the conduction band. AE is 33 meV for the Fe-based samples [5] and 20 meV for the Mn-based structure [6]. The zero field conduction band offset in all samples is always larger than the field induced splitting. When a magnetic field is applied, the conduction band offset decreases for the m = - i electrons (fig. l(b)), while it increases for the m = f i electrons (fig. l(c)). However, the confinement of electrons is only slightly perturbed by the applied field for the samples of this study. The heavy hole confinement on the other hand, is completely controlled by the external magnetic field. The reason is that the spin splitting of the heavy holes is larger than that of the conduction band by a factor equal to p/a, where p and cy are the exchange integrals for the valence and conduction band, respectively. These P/a ratios
177
are: 7.1 for ZnFeSe [7] and 4.8 for ZnMnSe [61. The initially small valence band offsets ( - 1 meV) are overwhelmed by the much larger spin splittings produced by the applied magnetic field. These are - 25 meV for samples 1, 2 and 3 and - 50 meV for sample 4 at 8 T. The m = - + heavy hole level shifts to higher energy (fig. l(b)), while the m = + g hole state shifts to lower energy (fig. l(c)) with respect to their zero field position. As a result, the m = - + spin down holes are localized in the DMS layers, while the m = + 1 spin up holes are confined in the nonmagnetic ZnSe wells. The corresponding (- +, - i> u+ and (+ 5, + i> u_ excitonic transitions are shown in figs. l(b) and (c), respectively. The CT+ transition is spatially indirect (type-II), and as such, has a smaller oscillator strength compared to similar direct transitions. In addition, since the m = - 5 holes are localized inside the DMS layers, the energy of the u+ (- +, - i) exciton component exhibits a large red shift as function of magnetic field due to the spin-exchange interaction between the holes and the magnetic ions in the DMS layers. The u_ (+ 5, + i) transition shown in fig. l(c) is spatially direct (type-11 with a large oscillator strength. The constituent m = + : hole and m = + i electron are both localized in the nonmagnetic ZnSe layer. The energy of the u_ component thus depends very little on magnetic field. The band alignment changes produced by the external magnetic field, summarized in fig. 1, are possible because of the large band spin-splitting of the magnetic layers. These splittings are proportional to the magnetization of the DMS material. We note here, that even though ZnFeSe is a Van Vleck paramagnet [7] and ZnMnSe is a Brillouin paramagnet [6], the band structure changes produced by the magnetic field are quite similar because the important underlying factor is the large size of the band spin-splitting relative to the natural zero-field band offset which exists in both materials. The magnetization of ZnMnSe, and thus the band spin-splitting, is larger than that of ZnFeSe. This difference manifests itself in the increased m = + t electron confinement in sample 4, as will be discussed below.
A. Petrou et al. / DMS based quantum wells
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4. Results and discussion In this section we present and discuss the results of a magneto-optical study of samples l-4. In fig. 2(a) the derivative dR/A E of the reflectance spectrum at zero magnetic field is shown for sample 1. It contains two features marked (i) and (ii) at 2810.7 and 2824.4 meV, respectively. They are attributed to the heavy hole Cm = f t> and light hole Cm = f t> excitons. The observed heavy-light hole exciton splitting is due to the biaxial compressive strain present in the structure. The strain can be calculated from low temperature lattice parameters of ZnSe [81, GaAs [9] and the elastic constants of bulk ZnSe [lo], assuming pseudomorphic growth. Once the strain is determined, the heavy and light hole band energy shifts follow from deformation potentials [ll] measured for ZnSe [ 121. Theoretical calculations [13] allow the separation of the hydrostatic deformation potential into valence and conduction band components. The calculated value, without taking into account the hole confinement, is equal to 13.3 meV. It is very close to the experimental heavy-light hole exciton splitting (13.7 meV1, which is an indication that in structures 1, 2 and 3 the ZnSe and ZnFeSe layers are commensurate with the GaAs substrate, as exptcted for total sample thickness of less than 400 A.
I
I
alSample
I
I
T=4.2
1
In fig. 2(b) the PL spectrum from sample 4 is shown. The feature marked (i) at 2802.8 meV is identified as the heavy hole exciton of this structure. In the reflectance spectrum this feature occurs at 2805.0 meV, while the light hole exciton feature comes at 2816.9 meV. The calculated zero field, strain-induced heavy-light hole exciton splitting is equal to 19.5 meV, which is significantly higher than the experimental value of 11.9 meV. This difference indicates a partial relaxation of strain at the GaAs/ZnMnSe interface, for sample 4, attributed to the greater total thickness (580 A> of the sample. In figs. 3(a) and (b) the energies of the heavy hole exciton spin components are plotted as function of magnetic field for samples 1 and 4, respectively. In both samples a pronounced asymmetry between the two spin components is observed. The weaker (- +, - i> u+ component shows a large red shift as function of magnetic field. The observed red shift confirms the picture shown in fig. l(b), i.e. that the - + hole is confined in the DMS layers. The low intensity of this component is consistent with its indirect character. The stronger (+ ;, + $1 u_ exciton component shows an initial blue shift for field values between 0 and 1 T. For B > 2 T the U_ exciton energy does not vary appreciably with magnetic field, i.e. it shows a nonmagnetic behavior. This is consistent with
I
1
,
I
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K
T=4.2
I
I
I
1
4 K *
B=O
(i)
2705
2805
PHOTON
ENERGY
2825
(meV)
2045
2780
2790
PHOTON
2800
ENERGY
2810
2820
(meV)
Fig. 2. (a) Reflectance derivative spectrum from sample 1. (b) Photoluminescence spectrum from sample 4 excited by the 3250 w line of a He-Cd laser. The asterisk indicates a laser plasma line. Both spectra were recorded at B = 0; T = 4.2 K.
A. Petrou et al. / DMS based
(al
Sample
179
quantum wells 2850
I
1
(b)
1
I
,
I
Sample ___,_,-.-.--‘--’
•o~n ___-----
> g
I
I
4
I3
I
I
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---
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OK_
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2790
F 0 :
2790
I
2770 0
1
I
2
MAGNETIC Fig. 3. Energy
I
1
4
I
6
FIELD
I
I
0
I
2750
I
10
I
#
I
2
0
(TESLA)
6
I
1
6
MAGNETIC
FIELD
of the (- $, - $) o+ and (+ t, + $1 (T_ heavy hole exciton spin components plotted represent theoretical fits to the data. (a) Sample 1; (b) sample 4.
the schematic of fig. l(c) which indicates a type-1 (+ ;, + ;> (T_ exciton in the nonmagnetic ZnSe layer. For samples 1, 2 and 3, the u_ exciton component undergoes a type-II to type-1 transition as the magnetic field is increased from 0 to 2 T. In fig. 3(b) a second excitonic feature appears for B > 2 T in the u_ polarization, approximately 24 meV above the (+ 3, + i> transition. It is attributed to an exciton associated with the second (n = 2) conduction confinement subband as shown in the inset of fig. 3(b). The height of the conduction band potential well increases with field for the m = + 4 electrons and for B > 2 T it becomes large enough to confine the n = 2 subband. This is possible in the Mn-based structure because the magnetization, and thus the conduction band spin splitting is larger than that in the Fe-based layers by approximately a factor of two. No such magnetically confined n = 2 conduction subband was observed in samples 1, 2 and 3. In fig. 4 the ratio I( + )/I( - 1 of the intensities of the u, and u_ heavy hole excitons is plotted as function of magnetic field for samples 1 and 2. For both structures the ratio drops sharply with increasing field and remains almost constant for
I
4
1
10
8
(TESLA)
versus magnetic
field. The lines
B > 2 T. The saturation value of the I( + )/I( - ) ratio is equal to 0.18, 0.06 and 0.015 for samples 1, 2 and 3, respectively. The u, component is clearly weaker than the u_ and the intensity ratio 1
I
I
I
I
,
,
,
I
Samp 1
Samp 1
0.01 0
”
” 2
MAGNETIC
‘1 4
” 6
FIELD
’ 9
I 10
(TESLA)
Fig. 4. Intensity ratio I(+ )/I(-) of the o+ and U_ heavy hole exciton components plotted versus magnetic field. Triangles: sample 1; squares: sample 2.
180
A. Petrou et al. / DMS based quantum wells
I( + )/I( - > gets progressively smaller as the ZnSe layer thickness increases. This is because the ZnSe thickness defines the spatial separation of the wavefunctions for the m = - f electrons and the m = - G holes. The intensity ratio I( +)/I( - > for sample 4 shows similar behavior as that of samples 1, 2 and 3, i.e. it decreases rapidly as function of B. The saturation value of Z( + )/I( -1 for sample 4 is 0.50, i.e. significantly larger than that for sample 1, even though the two structures have comparable dimensions. This difference is attributed to the presence of potential fluctuations at the ZnSe/ZnMnSe interfaces which decouple, to some extent, the magnetic from the nonmagnetic layers. These fluctuations could be connected with the hole pinning defects responsible for the partial strain relaxation in this sample. In the remaining portion of this section we discuss the theoretical fitting to the data shown in figs. 3(a) and (b). A more detailed model is required to describe quantitatively the phenomena as observed in the quantum wells applied here. Such a model should incorporate the following effects: 1) strain-related band and excitonic energy shifts; 2) magnetic field induced spin-splitting in the barrier layer; 3) quantum confinement energies associated with the changing potential in the barriers; and 4) the effect of the Coulomb potential, including how the exciton binding energy and wave function change as the barrier potentials vary. In the treatment to be described here, only the first three of the above are included. The fourth is important for shallow wells [14] but makes calculations considerably more difficult. A more complete description of these shallow magnetic quantum well systems including all four items will be reported later. To estimate the exciton energies as a function of applied magnetic field, we first calculate the combined valence and conduction band offset at zero field. This offset is just the sum of the bulk band gap difference (33 meV for samples 1, 2, 3 and 20 meV for sample 41, and the difference in the strain-induced splitting between the DMS layers and the ZnSe layer. Then, the net valence band offset is extracted from the field dependent data. In this way, the value obtained for the valence band offset is relatively insensitive to the
values used for the deformation potentials in the strain calculation, since the overall band offset for the heavy hole exciton is primarily determined by the bulk band offset. However by neglecting exciton effects, all the energies obtained for the valence band offsets will be shifted by some fraction of the excitonic binding energy. The changes in the barrier potential as a function of magnetic field for the hole and electron spin states according to spin-exchange induced splitting are shown in fig. 1. At high fields, one heavy hole spin state (- 3) is confined primarily to the barrier while the other (+ :) is confined in the well. In the conduction band, the spin splitting is less and acts more as a perturbation on the original quantum well potential. The ratios P/a of the DMS layers in these structures are known [6,71 so that the conduction and valence band quantum well potentials can be calculated as a function of magnetic field. To extract the net valence band offset from the field dependent data, single particle wave functions and energies for heavy holes and electrons are calculated numerically as a function of magnetic field, assuming infinite potential barriers at both boundaries of the structure. For samples 1, 2 and 3 the field dependent data are fitted using two parameters; the zero field valence band offset and an effective g factor describing the spin splitting in the barrier layer. The fit shown in fig. 3(a) is continued only up to 4 T, since at higher fields the saturation of the magnetization must be taken into account. For sample 4, the spin splitting was measured from a thick epilayer of the same magnetic concentration as the barrier layers. In this way the fit is extended over the whole range of magnetic fields investigated, and only one parameter (the zero field valence band offset) is required to describe the data. The net zero field valence band offsets (well to barrier) obtained from the data in this way are 1.1 meV for samples l-3 and - 1 meV for sample 4. It should be noted that these numbers are strictly for purposes of comparison between the two types of samples. To calculate the true value of the valence band offset requires a detailed accounting of excitonic effects, which would tend to increase the values obtained by some fraction of the bulk exciton
A. Petrou et al. / DMS based quantum
binding energy. Since the electrons are primarily localized in the ZnSe wells, the Coulomb interaction will tend to confine the holes in the same layers, even for small positive offsets (i.e. for weak type-11 potentials). Thus ignoring the Coulomb interaction leads to an underestimation of the band offset. However, the general description is still correct since in these samples the spin splitting and consequently the high-field valence band offset is much larger than the exciton binding energy. In sample 4, another feature thought to be a higher-order transition appears in the spectrum at intermediate fields. As the conduction band well depth increases with field, it becomes large enough so that there is more than one state confined in the well. The energy of this state CB(2) was calculated, along with the energy of the first excited hole state VB(2). In fig. 3(b) the calculated energy of the transition CB(2) --) VB(2) and CB(2) + VB(1) are drawn using dash-dotted and dashed lines respectively. Although the transition CB(2) -+ VB(1) is a forbidden transition, the symmetry of the quantum potential in the conduction and the valence band may not be perfectly the same, leading to a non-zero transition probability. In any case the calculated energies bracket the observed peak energy in the reflectivity spectrum.
5. Summary We have presented a magneto-optical study of ZnSe/ZnFeSe and ZnSe/ZnMnSe quantum wells. In these two systems the hole confinement is controlled by an external magnetic field, which induces large changes in the band structure. To our knowledge, this is the first time in which such
wells
181
wide control1 of the electronic states in semiconductor quantum well structures has been achieved, by the application of an external perturbation.
Acknowledgements
The work at SUNY was supported by ONR/SDIO under the MMFEL program and NSF, Grant No. DMR8922177; at NRL work was supported by the Office of Naval Research. The authors thank T. Schmiedel and L.P. Fu for technical assistance, and B.D. McCombe for helpful discussions.
References
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[31 S. Datta,