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AlGaAs strained layer superlattices
SurfaceScience22X(1990) 15&15X North-Holland
156
CYCLOTRON RESONANCE SUPERLAITICES R. RANGANATHAN,
IN (ill)-ORIENTED
B.S. YOO, Y.J. WANG,
InGaAs/AlGaAs
STRAINED
LAYER
B.D. McCOMBE
LIepcrrm~~enr of Physics A? Astronomy, SUNY at Buflalo, Buffalo, NY 14260, USA K.Y. LIM. F. KUCHAR Ludwrg Boltzmann
lnstitut
ftir FestkBrperph_vsik, Wwn. Austrra
K. ELCESS and C. FONSTAD Depurtment Received
of Electrical Engmeering,
1 June 1989; accepted
MIT,
Cambudge,
for publication
MA 02139, USA
9 August
1989
Strain-induced electric fields are known to occur in (11 I)-oriented InGaAs/AlGaAs strained layer superlattices (SLS). These fields lead to interesting electro-optic behavior and changes in the confined subband structure. Cyclotron resonance (CR) in nominally undoped InGaAs/AlGaAs SLS reveals some complex features of the subbands that include absence of circular polarization selection rule, and an effective mass that depends on magnetic field and also on barrier composition. This behavior is attributed to the nature of the valence band states, and it is concluded that the CR is due to holes. These results support an earlier tnterpretation of interband and CR measurements in the same samples.
Strong electric fields due to a strain-induced piezoelectric effect have been predicted for (ill)oriented InGaAs/AlGaAs strained layer superlattices (SLS) [l]. The built-in electric field leads to useful non-linear optical and electro-optic behavior and also to a rich variety of electronic structure, particularly in the valence band. These properties can be varied, in principle. in a controlled manner, motivating an interest to verify the presence of built-in fields and to determine the details of the electronic states. The present work concerns the study of cyclotron resonance in two (111) structures grown by MBE on an InGaAs buffer graded from GaAs to a composition nominally having the average lattice constant of the superlattice. The samples consisted of 20 wells each, with a 70 A well width and a barrier width of 140 A. Sample 1 consisted wells and sample 2 was of Jn,,.,Ga,,.9 As/GaAs III,,,G~,,.,A~/AI,,G~,,,A~. Fig. 1 is a sketch of the band profile, including the effect of the built-in 0039-602X/90/$03.50 (North-Holland)
‘y, Elsevier Science Publishers
B.V.
electric field which has opposite senses depending on whether the strain is compressive or tensile [I]. Evidence for the existence of the built-in electric field has been inferred from a combination of reflectivity and CR measurements [2], as well as from luminescence and absorption measurements and comparison with detailed theoretical calculations [3]. The detailed interpretation of the spectra in these two studies differs but the qualitative
Fig. 1. The band profile in (Ill)-lnGaAs/AIGaAa SLS. The bands are tilted by the built-in electric field.
R. Rangnnathan
et al. / (I II )-oriented InGaAs/AICaAs
conclusions are the same. Reflectivity data [2] show the presence of two doublets in sample 1. CR measurements were also performed on this sample in which energy level anticrossing between the first excited Landau level (LL) and the second subband was observed in fields tilted away from the normal to the superlattice planes. A value of 11 meV for the subband separation was inferred, which agreed with the doublet separation observed in reflectivity. A consistent but tentative interpretation [2] assigned the CR to holes and the reflectivity doublets to the pairs of transitions Hl-Cl, H2-Cl and Hl-C2, H2-C2, where Cl, C2 are the lowest conduction subbands and Hl, H2 are the highest heavy hole (J = 3/2, m, = 3/2) valence subbands. This interpretation yields 11 meV for the heavy hole (HH) subband separation. With sample parameters not being precisely known, it is not possible to conclude unambiguously if the subbands involved in the anti-level-crossing are those of the heavy holes in the valence band or of excess free electrons trapped in a weak confining potential at the graded InGaAs/GaAs interface. Moreover, an effective mass of 0.066 m0 (at 9 T) determined from the CR is suspiciously close to that of electrons in GaAs. It is believed though that an unintentional p-type modulation doping due to excess carbon impurities exists in the material. To probe intraband transitions in detail more CR measurements were performed with a Fourier transform spectrometer as well as a far infrared (FIR) laser and a backward wave oscillator. In particular, the circular polarization selection rule for the CR was studied. Magnetotransmission of the 118.8 pm line of a FIR laser was used with a circular polarizer in the incident beam immediately before the sample. From measurements on a known circularly polarized transition, the radiation was determined to be comprised of - 80% of one sense of polarization. The CR in sample 1 was characterized by a strong absorption (20%) at 5.9 T. More importantly, the CR was not selective of the sense of circular polarization, as illustrated in fig. 2. However a stronger circular polarization selection rule for holes was observed for radiation of 150 GHz (resonant field - 0.4 T) obtained with the backward wave oscillator, as
LUI
superlattices
_.ul-
-8-7-6-5-4-3-2-I
12345678
B CT) Fig. 2. The CR in sample 1 observed in magnetotransmission with circufarly polarized radiation. There is no change on reversing the orientation of the magnetic field applied normal to the superlattice planes.
shown in fig. 3. The effective mass for the resonance was found to decrease with increasing magnetic fields. At 0.4 T the mass was - 0.077 m. decreasing to 0.066 m, at 9 T. A very different effective mass of 0.11 m, was found for sample 2. Also, no energy level anticrossing behavior in tilted fields was observed up to 9 T in this sample. This is consistent with the mass being heavier and the subband separation being larger in this deeper well sample, requiring larger fields to achieve the crossing of the unperturbed levels. In tilted fields, the CR linewidth increases with the field approximately a7 fi which is characteristic of 2D behavior with short range scattering. The CR shifts to lower energies in tilted fields as shown in fig. 4. The resonance position is determined by the normal component of the field as expected for confined carriers in a quasi 2D system. The lack of a polarization selection rule, a field dependent effective mass in sample 1, differences
B (T) Fig. 3. Magnetotransmission of circularly polarized 150 GHz radiation in sample 1. CR occurs for that direction of the magnetic field for which holes are active (left portion) and not for the opposite, electron active, direction (right portion).
R. Ranganuthan
158
et (11. / (I I I ) -orirnied
1nCuA.s / A1CuA.s superluttices
b)
0
1 20
I 40
I 60
I 60
I 100
FREQUENCY
Fig. 4. CR in sample
I 120
I 140
I 160
I 180
0
12
(i/Cm1
a
Normal
x
Tilted
3
A
by
4 B
x
25
5
6
7
2. (a) Increase m linewidth illustrated by CR at three representative fields (tilted dependence of the resonance frequency for normal and tilted fields.
in CR characteristics, including a heavier mass in sample 2, all point out that an explanation may be sought in terms of the complexity of the valence band structure. The conduction band LL’s are simple, have a simple circular polarization selection rule; and the separation in a given magnetic field is little affected by the conduction band offset. In the valence band, the subbands no longer have a purely heavy- or light-hole character and are mixed in order to satisfy the boundary conditions at the interfaces. Further complexity can arise from inversion asymmetry of the crystal and internal electric fields. The most remarkable effects of the hole subband mixing are the strong non-parabolicity of the subband structure and a positive curvature (electron-like) at some k-values [4]. Ancilotto et al. [5] have calculated the magneto-optical effects of mixing. Although the calculation is for a GaAs/AlGaAs simple square well, some general conclusions may be drawn. The LL’s originating from the HH (J = 3/2, m, = k 3/2) subband and the light hole (J = 3/2, m, = k l/2) interact with each other. The angular momentum and the harmonic oscillator index are no longer good quantum numbers. The interaction between the LL’s leads to an anticrossing behavior for certain LL’s that produces a strong non-linear dependence of the energy on the magnetic field. This could account for the field dependent spec-
6
9
(TESLA)
at 25O ). (h) The field
troscopic effective mass. The mixing effects are quite sensitive to sample parameters (e.g.. band offset, strain, etc.) which is likely the reason for the heavier mass in sample 2. The lack of polarization selection rule at the higher field may be an illustration of field dependent mixing of the hole subbands. A detailed calculation of hole subbands for the present sample parameters including strain and electric field is necessary for a quantitative understanding of the data. The present data provides a qualitative agreement with the interpretation in ref. [2]. This work was supported by ONR/SDIO, NSF Grant # Int 86-19783, and Fonds fur Forderung der Wissenschaftlichen Forschung.
References Ill D.L. Smith and C. Mailhiot, Phys. Rev. B 35 (1987) 1242. PI B.S. Yoo, X.C. Liu, A. Petrou. J.P. Cheng. A.A. Reeder. B.D. McCombe, K. Elcess and C. Fonstad, Superlatticea Microstruct. 5 (1989) 363. PI B.K. Laurich, K. Elcess, C. Fonstad. J.G. Berry, C. Mailhiot and D.L. Smith, Phys. Rev. Lett. 62 (1989) 649. 141 M. Altarelli, U. Ekenberg and A. Fasolino. Phya. Rev. B 32 (1985) 5138. [Xl F. Ancilotto, A. Fasolino and J.C. Maan, Phys. Rev. B 3X (1988) 1788.
156
CYCLOTRON RESONANCE SUPERLAITICES R. RANGANATHAN,
IN (ill)-ORIENTED
B.S. YOO, Y.J. WANG,
InGaAs/AlGaAs
STRAINED
LAYER
B.D. McCOMBE
LIepcrrm~~enr of Physics A? Astronomy, SUNY at Buflalo, Buffalo, NY 14260, USA K.Y. LIM. F. KUCHAR Ludwrg Boltzmann
lnstitut
ftir FestkBrperph_vsik, Wwn. Austrra
K. ELCESS and C. FONSTAD Depurtment Received
of Electrical Engmeering,
1 June 1989; accepted
MIT,
Cambudge,
for publication
MA 02139, USA
9 August
1989
Strain-induced electric fields are known to occur in (11 I)-oriented InGaAs/AlGaAs strained layer superlattices (SLS). These fields lead to interesting electro-optic behavior and changes in the confined subband structure. Cyclotron resonance (CR) in nominally undoped InGaAs/AlGaAs SLS reveals some complex features of the subbands that include absence of circular polarization selection rule, and an effective mass that depends on magnetic field and also on barrier composition. This behavior is attributed to the nature of the valence band states, and it is concluded that the CR is due to holes. These results support an earlier tnterpretation of interband and CR measurements in the same samples.
Strong electric fields due to a strain-induced piezoelectric effect have been predicted for (ill)oriented InGaAs/AlGaAs strained layer superlattices (SLS) [l]. The built-in electric field leads to useful non-linear optical and electro-optic behavior and also to a rich variety of electronic structure, particularly in the valence band. These properties can be varied, in principle. in a controlled manner, motivating an interest to verify the presence of built-in fields and to determine the details of the electronic states. The present work concerns the study of cyclotron resonance in two (111) structures grown by MBE on an InGaAs buffer graded from GaAs to a composition nominally having the average lattice constant of the superlattice. The samples consisted of 20 wells each, with a 70 A well width and a barrier width of 140 A. Sample 1 consisted wells and sample 2 was of Jn,,.,Ga,,.9 As/GaAs III,,,G~,,.,A~/AI,,G~,,,A~. Fig. 1 is a sketch of the band profile, including the effect of the built-in 0039-602X/90/$03.50 (North-Holland)
‘y, Elsevier Science Publishers
B.V.
electric field which has opposite senses depending on whether the strain is compressive or tensile [I]. Evidence for the existence of the built-in electric field has been inferred from a combination of reflectivity and CR measurements [2], as well as from luminescence and absorption measurements and comparison with detailed theoretical calculations [3]. The detailed interpretation of the spectra in these two studies differs but the qualitative
Fig. 1. The band profile in (Ill)-lnGaAs/AIGaAa SLS. The bands are tilted by the built-in electric field.
R. Rangnnathan
et al. / (I II )-oriented InGaAs/AICaAs
conclusions are the same. Reflectivity data [2] show the presence of two doublets in sample 1. CR measurements were also performed on this sample in which energy level anticrossing between the first excited Landau level (LL) and the second subband was observed in fields tilted away from the normal to the superlattice planes. A value of 11 meV for the subband separation was inferred, which agreed with the doublet separation observed in reflectivity. A consistent but tentative interpretation [2] assigned the CR to holes and the reflectivity doublets to the pairs of transitions Hl-Cl, H2-Cl and Hl-C2, H2-C2, where Cl, C2 are the lowest conduction subbands and Hl, H2 are the highest heavy hole (J = 3/2, m, = 3/2) valence subbands. This interpretation yields 11 meV for the heavy hole (HH) subband separation. With sample parameters not being precisely known, it is not possible to conclude unambiguously if the subbands involved in the anti-level-crossing are those of the heavy holes in the valence band or of excess free electrons trapped in a weak confining potential at the graded InGaAs/GaAs interface. Moreover, an effective mass of 0.066 m0 (at 9 T) determined from the CR is suspiciously close to that of electrons in GaAs. It is believed though that an unintentional p-type modulation doping due to excess carbon impurities exists in the material. To probe intraband transitions in detail more CR measurements were performed with a Fourier transform spectrometer as well as a far infrared (FIR) laser and a backward wave oscillator. In particular, the circular polarization selection rule for the CR was studied. Magnetotransmission of the 118.8 pm line of a FIR laser was used with a circular polarizer in the incident beam immediately before the sample. From measurements on a known circularly polarized transition, the radiation was determined to be comprised of - 80% of one sense of polarization. The CR in sample 1 was characterized by a strong absorption (20%) at 5.9 T. More importantly, the CR was not selective of the sense of circular polarization, as illustrated in fig. 2. However a stronger circular polarization selection rule for holes was observed for radiation of 150 GHz (resonant field - 0.4 T) obtained with the backward wave oscillator, as
LUI
superlattices
_.ul-
-8-7-6-5-4-3-2-I
12345678
B CT) Fig. 2. The CR in sample 1 observed in magnetotransmission with circufarly polarized radiation. There is no change on reversing the orientation of the magnetic field applied normal to the superlattice planes.
shown in fig. 3. The effective mass for the resonance was found to decrease with increasing magnetic fields. At 0.4 T the mass was - 0.077 m. decreasing to 0.066 m, at 9 T. A very different effective mass of 0.11 m, was found for sample 2. Also, no energy level anticrossing behavior in tilted fields was observed up to 9 T in this sample. This is consistent with the mass being heavier and the subband separation being larger in this deeper well sample, requiring larger fields to achieve the crossing of the unperturbed levels. In tilted fields, the CR linewidth increases with the field approximately a7 fi which is characteristic of 2D behavior with short range scattering. The CR shifts to lower energies in tilted fields as shown in fig. 4. The resonance position is determined by the normal component of the field as expected for confined carriers in a quasi 2D system. The lack of a polarization selection rule, a field dependent effective mass in sample 1, differences
B (T) Fig. 3. Magnetotransmission of circularly polarized 150 GHz radiation in sample 1. CR occurs for that direction of the magnetic field for which holes are active (left portion) and not for the opposite, electron active, direction (right portion).
R. Ranganuthan
158
et (11. / (I I I ) -orirnied
1nCuA.s / A1CuA.s superluttices
b)
0
1 20
I 40
I 60
I 60
I 100
FREQUENCY
Fig. 4. CR in sample
I 120
I 140
I 160
I 180
0
12
(i/Cm1
a
Normal
x
Tilted
3
A
by
4 B
x
25
5
6
7
2. (a) Increase m linewidth illustrated by CR at three representative fields (tilted dependence of the resonance frequency for normal and tilted fields.
in CR characteristics, including a heavier mass in sample 2, all point out that an explanation may be sought in terms of the complexity of the valence band structure. The conduction band LL’s are simple, have a simple circular polarization selection rule; and the separation in a given magnetic field is little affected by the conduction band offset. In the valence band, the subbands no longer have a purely heavy- or light-hole character and are mixed in order to satisfy the boundary conditions at the interfaces. Further complexity can arise from inversion asymmetry of the crystal and internal electric fields. The most remarkable effects of the hole subband mixing are the strong non-parabolicity of the subband structure and a positive curvature (electron-like) at some k-values [4]. Ancilotto et al. [5] have calculated the magneto-optical effects of mixing. Although the calculation is for a GaAs/AlGaAs simple square well, some general conclusions may be drawn. The LL’s originating from the HH (J = 3/2, m, = k 3/2) subband and the light hole (J = 3/2, m, = k l/2) interact with each other. The angular momentum and the harmonic oscillator index are no longer good quantum numbers. The interaction between the LL’s leads to an anticrossing behavior for certain LL’s that produces a strong non-linear dependence of the energy on the magnetic field. This could account for the field dependent spec-
6
9
(TESLA)
at 25O ). (h) The field
troscopic effective mass. The mixing effects are quite sensitive to sample parameters (e.g.. band offset, strain, etc.) which is likely the reason for the heavier mass in sample 2. The lack of polarization selection rule at the higher field may be an illustration of field dependent mixing of the hole subbands. A detailed calculation of hole subbands for the present sample parameters including strain and electric field is necessary for a quantitative understanding of the data. The present data provides a qualitative agreement with the interpretation in ref. [2]. This work was supported by ONR/SDIO, NSF Grant # Int 86-19783, and Fonds fur Forderung der Wissenschaftlichen Forschung.
References Ill D.L. Smith and C. Mailhiot, Phys. Rev. B 35 (1987) 1242. PI B.S. Yoo, X.C. Liu, A. Petrou. J.P. Cheng. A.A. Reeder. B.D. McCombe, K. Elcess and C. Fonstad, Superlatticea Microstruct. 5 (1989) 363. PI B.K. Laurich, K. Elcess, C. Fonstad. J.G. Berry, C. Mailhiot and D.L. Smith, Phys. Rev. Lett. 62 (1989) 649. 141 M. Altarelli, U. Ekenberg and A. Fasolino. Phya. Rev. B 32 (1985) 5138. [Xl F. Ancilotto, A. Fasolino and J.C. Maan, Phys. Rev. B 3X (1988) 1788.