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Electric-field effects in optically generated spin transport
Physics Letters A 373 (2009) 2097–2100
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Electric-field effects in optically generated spin transport M. Idrish Miah a,b,∗ a b
Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111, Australia Department of Physics, University of Chittagong, Chittagong 4331, Bangladesh
a r t i c l e
i n f o
Article history: Received 13 January 2009 Received in revised form 17 March 2009 Accepted 10 April 2009 Available online 17 April 2009 Communicated by R. Wu PACS: 78.66.Fd 42.70.-a 74.25.Gz 78.20.-e
a b s t r a c t Transport of spin-polarized electrons in semiconductors is studied experimentally. Spins are generated by optical excitation because of the selection rules governing optical transitions from heavy-hole and lighthole states to conduction-band states. Experiments designed for the control of spins in semiconductors investigate the bias-dependent spin transport process and detect the spin-polarized electrons during transport. A strong bias dependence is observed. The electric-field effects on the spin-polarized electron transport are also found to be depended on the excitation photon energy and temperature. Based on a field-dependent spin relaxation mechanism, the electric-field effects in the transport process are discussed. © 2009 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Optical properties Electronic transport
1. Introduction
is effectively zero and need not be considered. Hence the initial value p (0, 0) of electron spin polarization, defined as
Recently, there has been an increasing interest in the emerging field of spin electronics [1,2] or spintronics [3,4], or spin physics in broader sense [5], where the electron spin degree of freedom is exploited and new semiconductor devices are proposed. One of the important requirements necessary in developing semiconductor spintronic devices is the transporting spin-polarized carriers over reasonable distances without spin-flipping or spin relaxation in a semiconductor. However, the generation (or injection) of spins is a prerequisite for the study of spin transport. The generation of electron spins in a semiconductor has successfully been obtained by optical excitations [3]. For optical excitation of bulk zinc-blende semiconductors with photon energy just above the band gap (E g ), because of the selection rules governing optical transitions from heavy-hole, or light-hole, states to conduction band states, right circular polarized light (RPL) generates a density of spin-down electrons (N ↓ ) which is three times the density of spin-up electrons (N ↑ ), and vice versa for left circularly polarized light (LPL) [6,7]. Since optically excited hole spin relaxation is extremely fast ( 100 fs), their polarization
p (r , t ) = N ↓ (r , t ) − N ↑ (r , t ) / N ↓ (r , t ) + N ↑ (r , t ) ,
*
Correspondence address: Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111, Australia. Tel.: +61 7 3735 3625; fax: +61 7 3735 7656. E-mail address: m.miah@griffith.edu.au. 0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.04.021
(1)
generated by a RPL (LPL) beam in a zinc-blende semiconductor is +0.5 (−0.5), i.e. 50%. Optical excitation with RPL (LPL) generates spins along the direction parallel (antiparallel) to the direction of the light propagation. By obeying the same selection rules the reverse is also possible that the recombination of spin polarized charge carriers results in the emission of circularly polarized light. In the present investigation, we studied experimentally the transport of spin-polarized electrons in semiconductors. Spins are generated by optical excitation as discussed above. Experiments aimed for the optical manipulation of spins in semiconductors investigate the bias-dependent transport process and detect the spin-polarized electrons during transport. A strong bias dependence is observed. The electric-field effects on the spin-polarized electron transport are also studied in dependences of excitation power as well as of excitation photon energy. The field effects in the transport process are discussed in details. 2. Experimental details 2.1. Device fabrication and characterization Investigated samples were fabricated on moderately doped GaAs with different Si-doping densities. Prior to contact deposi-
2098
M.I. Miah / Physics Letters A 373 (2009) 2097–2100
tion, the substrates (A: 1.4 × 1016 cm−3 , B: 1 × 1017 cm−3 and C: 5 × 1017 cm−3 ) were cleaned using conventional organic solvents. The native surface oxide was then removed using HCl : H2 O (1 : 1 vol.) followed by a de-ionized water rinse and blown dry with nitrogen before loading the substrates in the evaporation chamber. Au(100 nm)/Ge(40 nm)/Pd(10 nm) contacts were deposited on the substrates, with Pd layers adjacent to the GaAs substrates, using an e-beam evaporator with a base pressure of ∼ 5 × 10−8 Torr. The contact metallization was annealed in a tube furnace in flowing nitrogen at 180 ◦ C for 1 h to achieve reliable or ohmic contacts with low contact resistance. Gold wires were bonded from the sample-holder to the contact pads. The specific contact resistivity was assessed using transmission line model [8]. The doping density-dependent contact resistivity is shown in Fig. 1. As can be seen, the resistivity increases with decreasing doping density and values are within a range between 1.9 × 10−6 and 8 × 10−6 cm2 . The results confirm that the devices contain transparent contacts. 2.2. Experimental setup and measurements For optical excitation, a mode-locked Ti:sapphire laser (which generates ps pulses at 76 MHz repetition rate) was used. A neutral density wheel (NDW) was used to vary the optical power. The polarization of the optical beam was modulated using a photo-elastic
Fig. 1. Contact resistivity as a function of doping density. The insert shows a photograph of the sample device (expanded view).
modulator (PEM) at a lock-in reference frequency of 42 kHz. The laser beam (LB) was focused on to a ∼ 90 μm (FWHM) spot of the sample with a lens (L). Care was taken not to illuminate any of the electrical contacts to avoid the generation of any artefacts. To check that the beam hits the sample on the desired location, a microscope was used. The lens was designed for minimum spherical aberrations. The spot size was measured by knife-edge scans and the spatial (or the sequence focus) profile of the pulse was found to be Gaussian. A regulated electric power supply was used as a bias source. The signal was measured by a lock-in amplifier coupled to a computer. The sign of the signal was found to be reversed with reversing the bias field. A schema of the experimental setup along with an illustration of the sample geometry and the excitation scheme is shown in Fig. 2. To show the temperature dependence, we measured the signal at liquid helium, liquid nitrogen and room temperatures. All other experiments were performed at room temperature. The room temperature mobility and excited carrier density were estimated for the three samples. They are (5300 cm2 /V s; 6 × 1017 cm−3 ), (4100 cm2 /V s; 2 × 1018 cm−3 ) and (3200 cm2 /V s; 5 × 1018 cm−3 ) for A, B and C respectively. 3. Results and discussion We study the spin transport process and investigate the effects of a longitudinal electric field (field effects) on the spin-polarized electrons generated by a circularly polarized light in semiconductors [9]. Our experiment observes the effects resulting from nonequilibrium magnetization induced by the spin-carrier electrons [10] accumulating at the transverse edges of the sample. In a semiconductor, if two spin populations are unequal, for example, current carriers contain more spin-up electrons than spin-down electrons, there would be more electrons scattered to the right than to the left (asymmetries in scattering) via skewscattering [11] and side jump [12] in the presence of spin–orbit interaction. This leads to both spin [13] and charge [14] accumulations in the transverse direction of the sample. When the photoinduced spin-polarized carriers are dragged by an external bias in a sample, an optically spin-induced transverse voltage is observed. The voltage is a measure of the net charge accumulation on the transverse edges of the sample for the generated spin-polarized electrons. Fig. 3 shows the bias-field dependence of the voltage for samples A, B and C excited with the power P ex = 5 mW and photon energy (E ex ) having an excess E ex = 100 meV, where
E ex = E ex − E g = h¯ ω − E g .
Fig. 2. A schema of the experimental setup along with an illustration of the sample geometry and the excitation scheme.
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M.I. Miah / Physics Letters A 373 (2009) 2097–2100
Fig. 3. Field dependence of the transverse voltage for sample A, B and C (excited with P ex = 5 mW and E ex = 100 meV).
As can be seen, the signal in a sample first increases quickly to a maximum and remains almost constant up to ∼ 1.2 kV/cm, and then decreases exponentially to a background level at ∼ 3 kV/cm. This background signal is not due to the optically spin-induced transverse voltage, since a net charge accumulation does not occur at zero applied bias. We also observed the same background signal with illumination with linearly polarized light. Because our devices had transparent contacts, they measured the actual field accelerating the carriers. The background signal might be the threshold of the modulating system used in the experiment. The decay of the signal with bias might be due to the enhanced electron spin relaxation at higher electric fields. In strong fields, initial cloud of electron spin polarization is immediately displaced from the contacts by the field so that spin polarized electrons simply do not have enough time to reach the contacts, and consequently, the transverse spin diffusion length decreases. However, the signal remained conserved within moderate fields, demonstrating that the spin polarization of electrons was preserved during the transport in a moderate electric field. Although the spin for the moderate electric field is preserved, the spin relaxation rate becomes considerably larger for fields higher than ∼ 2 kV/cm. When the electrons were drifted with a high-electric field, a significant reduction in the spin lifetimes (τs ) (due to abrupt decay of electron spin polarization) was observed. Increasing field leads to larger charge and spin accumulations near the sample edges, but the polarization saturates because of shorter τs for larger E. The suppression of τs with increasing field from the saturation implies that spin decay increases with the field is consistent with other observations [3]. The photo-generated spins in GaAs can traverse without losing their initial orientation as long as their field is below a threshold value of ∼ 1.2 kV/cm. Above the threshold, however, the spin depolarization is considerably enhanced most probably due to the enhanced spin relaxation as a result of increasing of the electron temperature. Above ∼ 3 kV/cm, the electron spin is completely lost. The results are in good agreement with those obtained from bias-dependent spin relaxation studies by others [15]. They studied spin relaxation of photo-generated electrons during drift transport in GaAs at low temperatures by time-resolved photoluminescence measurements. They showed that the photo-generated spins could travel without losing their initial spin orientation as long as the electric field was below a threshold value of 1 kV/cm and the spin relaxation rate increased rapidly with the field, and the polarization disappeared at ∼ 3.5 kV/cm.
2099
Fig. 4. Temperature dependence of the transverse voltage for the sample C ( E ex = 100 meV).
The spin relaxation in GaAs is discussed based on the Dyakonov–Perel (DP) spin relaxation mechanism [13]. The DP spin relaxation occurs due to the spin precession about an intrinsic magnetic field induced by the presence of a spin–orbit interaction in a zincblende structure. During transport in the electric field, electrons are accelerated to higher velocities at higher fields, where the electron temperature increases sharply due to the energy-independent nature of the dominant energy relaxation process via longitudinal polar optical phonon scattering [16]. The resulting high electron temperature leads to enhanced DP spin relaxation (electrons experience rapid spin relaxation) because they have large kinetic energy between successive collisions and the DP spin relaxation rate is proportional to approximately the cube of the electron temperature or kinetic energy [17]: 1/τs ∼ E 3 τ p ( E k ), k
(3)
where τ p ( E k ) is the momentum relaxation time. As expected, the spin relaxation rate increases rapidly with the applied bias, which agrees well with the results of the theoretical study as well as of other investigations [18,19]. As also seen from Fig. 3, an enhancement of the signal with increasing doping density is observed. The introduction of n-type dopants in semiconductors increases τs , because the electronic spin polarization in these systems survives for longer times. Studies of spin precession in n-type GaAs reveal that moderately ndoping yields significantly extended τs [3]. The similar trend was observed in a different experiment [20], where the author studied the doing density dependence of the spin-polarization of conduction band electrons and found that the polarization increased with increasing doping. The results for the sample C at different temperatures are shown in Fig. 4. As seen, an enhancement of the signal with decreasing temperature is observed. This is expected because with decreasing temperature the process enters the degenerate regime [21]. Fig. 5 shows the excitation power dependence of the signal for the sample C with E ex = 100 meV. As can be seen, the signal does not depend significantly on the excitation power. This is expected because our devices contained ohmic contacts. However, a slight decrease in the signal was observed at P ex > 12 mW, which might be due to the mixing of the spin states as a result of the heating of the sample. Because we used P ex = 5 mW in our measurements, there was no chance that the measured voltage contained any contribution from this effect.
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M.I. Miah / Physics Letters A 373 (2009) 2097–2100
tion dipole-matrix elements for the heavy-hole (hh), light-hole (lh) and SO bands and are 3, 1, 2, respectively. Excitation with energies E ex E g + , i.e. with energies equal to or larger than the SO band transition, yields no electron spin polarization since lh and SO band transitions create the same electron spin orientation and the sum of their inter-band dipole transition-matrix elements is equal to the hh transition matrix element [22]. 4. Conclusions
Fig. 5. Excitation power dependence of the transverse voltage for the sample C ( E ex = 100 meV).
We studied the transport of spin-polarized electrons in semiconductors. Spins were generated by optical excitation of the hh and lh states. Experiments designed for the control of spins in semiconductors investigated the bias-dependent transport process and detected the spin-polarized electrons during transport. A strong bias dependence was observed. The electric-field effects on the spin-polarized electron transport were also found to depend on the excitation photon energy. The field effects in the transport process were discussed based on the dominant spin relaxation mechanism in n-type semiconductors with wide-band gaps. References
Fig. 6. Excitation photon-energy dependence of the transverse voltage for the sample C ( P ex = 5 mW).
The excitation photon energy dependence of the signal for the sample C is shown in Fig. 6. As can be seen, for optical excitation of the sample with excess photon energies between 50 and 150 meV, the sample gives the maximum signal. With a further increase in the energy, the signal decreases and finally reduces to the background for larger excess energy (comparable to the spin– orbit splitting energy ) because of the exciting carriers from the spit-off (SO) band. This is a consequence of the optical selection rules (m j = ±1). The strengths of the optical inter-band valence to conduction band transitions are given by the inter-band transi-
[1] S.D. Sarma, Am. Sci. 89 (2001) 516. [2] M. Ziese, M.J. Thornton (Eds.), Spin Electronics, vol. 569, Springer-Verlag, Heidelberg, 2001. [3] D.D. Awschalom, D. Loss, N. Samarth (Eds.), Semiconductor Spintronics and Quantum Computation, Springer, Berlin, 2002. ´ J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76 (2004) 323. [4] I. Žutic, [5] M.I. Dyakonov, A.V. Khaetskii, in: M.I. Dyakonov (Ed.), Spin Hall Effect, Spin Physics in Semiconductors, Springer-Verlag, Berlin, 2008. [6] G. Lampel, C. Weisbuch, Solid State Commun. 16 (1975) 877. [7] D.T. Pierce, F. Meier, Phys. Rev. B 13 (1976) 5484. [8] L. Howe, W.W. Hooper, B.R. Cairns, R.D. Fairman, D.A. Tremere, in: R.K. Willardson, A.C. Beer (Eds.), Semiconductors and Semimetals, vol. 7A, Academic Press, New York, 1971, p. 178. [9] M.I. Miah, J. Optoelectron. Adv. Mater. 10 (2008) 2487. [10] M.I. Miah, Mater. Lett. 60 (2006) 2863. [11] N.F. Mott, H.S.W. Massey, The Theory of Atomic Collisions, 3rd ed., Clarendon Press, Oxford, 1965. [12] I. Berger, Phys. Rev. B 2 (1970) 4559. [13] M.I. Dyakonov, V.I. Perel, Zh. Eksp. Teor. Fiz. 60 (1971) 1954, Sov. Phys. JETP 33 (1971) 1053. [14] J. Smit, Physica 17 (1951) 612. [15] H. Sanada, I. Arata, Y. Ohno, Z. Chen, K. Kayanuma, Y. Oka, F. Matsukura, H. Ohno, in: The Second International Conference on Physics and Application of Spin Related Phenomena in Semiconductors, Würzburg, Germany, 2002. [16] E.M. Conwell, High Field Transport in Semiconductor, Academic Press, New York, 1967. [17] G.E. Pikus, A.N. Titkov, in: F. Meier, B.P. Zakharchenya (Eds.), Optical Orientation, Modern Problems in Condensed Matter Science, vol. 8, North-Holland, Amsterdam, 1984. [18] R.S. Britton, T. Grevatt, A. Malinowski, R.T. Harley, P. Perozzo, A.R. Cameron, A. Miller, Appl. Phys. Lett. 73 (1998) 2140. [19] M.I. Miah, J. Phys. D: Appl. Phys. 40 (2007) 1659. [20] M.I. Miah, J. Phys. D: Appl. Phys. 42 (2009) 045503. [21] M.I. Miah, Phys. Scr. 78 (2008) 045302. [22] M. Chaichian, R. Hagedorn, Symmetries in Quantum Mechanics, Institute of Physics Publishing, 1998.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Electric-field effects in optically generated spin transport M. Idrish Miah a,b,∗ a b
Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111, Australia Department of Physics, University of Chittagong, Chittagong 4331, Bangladesh
a r t i c l e
i n f o
Article history: Received 13 January 2009 Received in revised form 17 March 2009 Accepted 10 April 2009 Available online 17 April 2009 Communicated by R. Wu PACS: 78.66.Fd 42.70.-a 74.25.Gz 78.20.-e
a b s t r a c t Transport of spin-polarized electrons in semiconductors is studied experimentally. Spins are generated by optical excitation because of the selection rules governing optical transitions from heavy-hole and lighthole states to conduction-band states. Experiments designed for the control of spins in semiconductors investigate the bias-dependent spin transport process and detect the spin-polarized electrons during transport. A strong bias dependence is observed. The electric-field effects on the spin-polarized electron transport are also found to be depended on the excitation photon energy and temperature. Based on a field-dependent spin relaxation mechanism, the electric-field effects in the transport process are discussed. © 2009 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Optical properties Electronic transport
1. Introduction
is effectively zero and need not be considered. Hence the initial value p (0, 0) of electron spin polarization, defined as
Recently, there has been an increasing interest in the emerging field of spin electronics [1,2] or spintronics [3,4], or spin physics in broader sense [5], where the electron spin degree of freedom is exploited and new semiconductor devices are proposed. One of the important requirements necessary in developing semiconductor spintronic devices is the transporting spin-polarized carriers over reasonable distances without spin-flipping or spin relaxation in a semiconductor. However, the generation (or injection) of spins is a prerequisite for the study of spin transport. The generation of electron spins in a semiconductor has successfully been obtained by optical excitations [3]. For optical excitation of bulk zinc-blende semiconductors with photon energy just above the band gap (E g ), because of the selection rules governing optical transitions from heavy-hole, or light-hole, states to conduction band states, right circular polarized light (RPL) generates a density of spin-down electrons (N ↓ ) which is three times the density of spin-up electrons (N ↑ ), and vice versa for left circularly polarized light (LPL) [6,7]. Since optically excited hole spin relaxation is extremely fast ( 100 fs), their polarization
p (r , t ) = N ↓ (r , t ) − N ↑ (r , t ) / N ↓ (r , t ) + N ↑ (r , t ) ,
*
Correspondence address: Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111, Australia. Tel.: +61 7 3735 3625; fax: +61 7 3735 7656. E-mail address: m.miah@griffith.edu.au. 0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.04.021
(1)
generated by a RPL (LPL) beam in a zinc-blende semiconductor is +0.5 (−0.5), i.e. 50%. Optical excitation with RPL (LPL) generates spins along the direction parallel (antiparallel) to the direction of the light propagation. By obeying the same selection rules the reverse is also possible that the recombination of spin polarized charge carriers results in the emission of circularly polarized light. In the present investigation, we studied experimentally the transport of spin-polarized electrons in semiconductors. Spins are generated by optical excitation as discussed above. Experiments aimed for the optical manipulation of spins in semiconductors investigate the bias-dependent transport process and detect the spin-polarized electrons during transport. A strong bias dependence is observed. The electric-field effects on the spin-polarized electron transport are also studied in dependences of excitation power as well as of excitation photon energy. The field effects in the transport process are discussed in details. 2. Experimental details 2.1. Device fabrication and characterization Investigated samples were fabricated on moderately doped GaAs with different Si-doping densities. Prior to contact deposi-
2098
M.I. Miah / Physics Letters A 373 (2009) 2097–2100
tion, the substrates (A: 1.4 × 1016 cm−3 , B: 1 × 1017 cm−3 and C: 5 × 1017 cm−3 ) were cleaned using conventional organic solvents. The native surface oxide was then removed using HCl : H2 O (1 : 1 vol.) followed by a de-ionized water rinse and blown dry with nitrogen before loading the substrates in the evaporation chamber. Au(100 nm)/Ge(40 nm)/Pd(10 nm) contacts were deposited on the substrates, with Pd layers adjacent to the GaAs substrates, using an e-beam evaporator with a base pressure of ∼ 5 × 10−8 Torr. The contact metallization was annealed in a tube furnace in flowing nitrogen at 180 ◦ C for 1 h to achieve reliable or ohmic contacts with low contact resistance. Gold wires were bonded from the sample-holder to the contact pads. The specific contact resistivity was assessed using transmission line model [8]. The doping density-dependent contact resistivity is shown in Fig. 1. As can be seen, the resistivity increases with decreasing doping density and values are within a range between 1.9 × 10−6 and 8 × 10−6 cm2 . The results confirm that the devices contain transparent contacts. 2.2. Experimental setup and measurements For optical excitation, a mode-locked Ti:sapphire laser (which generates ps pulses at 76 MHz repetition rate) was used. A neutral density wheel (NDW) was used to vary the optical power. The polarization of the optical beam was modulated using a photo-elastic
Fig. 1. Contact resistivity as a function of doping density. The insert shows a photograph of the sample device (expanded view).
modulator (PEM) at a lock-in reference frequency of 42 kHz. The laser beam (LB) was focused on to a ∼ 90 μm (FWHM) spot of the sample with a lens (L). Care was taken not to illuminate any of the electrical contacts to avoid the generation of any artefacts. To check that the beam hits the sample on the desired location, a microscope was used. The lens was designed for minimum spherical aberrations. The spot size was measured by knife-edge scans and the spatial (or the sequence focus) profile of the pulse was found to be Gaussian. A regulated electric power supply was used as a bias source. The signal was measured by a lock-in amplifier coupled to a computer. The sign of the signal was found to be reversed with reversing the bias field. A schema of the experimental setup along with an illustration of the sample geometry and the excitation scheme is shown in Fig. 2. To show the temperature dependence, we measured the signal at liquid helium, liquid nitrogen and room temperatures. All other experiments were performed at room temperature. The room temperature mobility and excited carrier density were estimated for the three samples. They are (5300 cm2 /V s; 6 × 1017 cm−3 ), (4100 cm2 /V s; 2 × 1018 cm−3 ) and (3200 cm2 /V s; 5 × 1018 cm−3 ) for A, B and C respectively. 3. Results and discussion We study the spin transport process and investigate the effects of a longitudinal electric field (field effects) on the spin-polarized electrons generated by a circularly polarized light in semiconductors [9]. Our experiment observes the effects resulting from nonequilibrium magnetization induced by the spin-carrier electrons [10] accumulating at the transverse edges of the sample. In a semiconductor, if two spin populations are unequal, for example, current carriers contain more spin-up electrons than spin-down electrons, there would be more electrons scattered to the right than to the left (asymmetries in scattering) via skewscattering [11] and side jump [12] in the presence of spin–orbit interaction. This leads to both spin [13] and charge [14] accumulations in the transverse direction of the sample. When the photoinduced spin-polarized carriers are dragged by an external bias in a sample, an optically spin-induced transverse voltage is observed. The voltage is a measure of the net charge accumulation on the transverse edges of the sample for the generated spin-polarized electrons. Fig. 3 shows the bias-field dependence of the voltage for samples A, B and C excited with the power P ex = 5 mW and photon energy (E ex ) having an excess E ex = 100 meV, where
E ex = E ex − E g = h¯ ω − E g .
Fig. 2. A schema of the experimental setup along with an illustration of the sample geometry and the excitation scheme.
(2)
M.I. Miah / Physics Letters A 373 (2009) 2097–2100
Fig. 3. Field dependence of the transverse voltage for sample A, B and C (excited with P ex = 5 mW and E ex = 100 meV).
As can be seen, the signal in a sample first increases quickly to a maximum and remains almost constant up to ∼ 1.2 kV/cm, and then decreases exponentially to a background level at ∼ 3 kV/cm. This background signal is not due to the optically spin-induced transverse voltage, since a net charge accumulation does not occur at zero applied bias. We also observed the same background signal with illumination with linearly polarized light. Because our devices had transparent contacts, they measured the actual field accelerating the carriers. The background signal might be the threshold of the modulating system used in the experiment. The decay of the signal with bias might be due to the enhanced electron spin relaxation at higher electric fields. In strong fields, initial cloud of electron spin polarization is immediately displaced from the contacts by the field so that spin polarized electrons simply do not have enough time to reach the contacts, and consequently, the transverse spin diffusion length decreases. However, the signal remained conserved within moderate fields, demonstrating that the spin polarization of electrons was preserved during the transport in a moderate electric field. Although the spin for the moderate electric field is preserved, the spin relaxation rate becomes considerably larger for fields higher than ∼ 2 kV/cm. When the electrons were drifted with a high-electric field, a significant reduction in the spin lifetimes (τs ) (due to abrupt decay of electron spin polarization) was observed. Increasing field leads to larger charge and spin accumulations near the sample edges, but the polarization saturates because of shorter τs for larger E. The suppression of τs with increasing field from the saturation implies that spin decay increases with the field is consistent with other observations [3]. The photo-generated spins in GaAs can traverse without losing their initial orientation as long as their field is below a threshold value of ∼ 1.2 kV/cm. Above the threshold, however, the spin depolarization is considerably enhanced most probably due to the enhanced spin relaxation as a result of increasing of the electron temperature. Above ∼ 3 kV/cm, the electron spin is completely lost. The results are in good agreement with those obtained from bias-dependent spin relaxation studies by others [15]. They studied spin relaxation of photo-generated electrons during drift transport in GaAs at low temperatures by time-resolved photoluminescence measurements. They showed that the photo-generated spins could travel without losing their initial spin orientation as long as the electric field was below a threshold value of 1 kV/cm and the spin relaxation rate increased rapidly with the field, and the polarization disappeared at ∼ 3.5 kV/cm.
2099
Fig. 4. Temperature dependence of the transverse voltage for the sample C ( E ex = 100 meV).
The spin relaxation in GaAs is discussed based on the Dyakonov–Perel (DP) spin relaxation mechanism [13]. The DP spin relaxation occurs due to the spin precession about an intrinsic magnetic field induced by the presence of a spin–orbit interaction in a zincblende structure. During transport in the electric field, electrons are accelerated to higher velocities at higher fields, where the electron temperature increases sharply due to the energy-independent nature of the dominant energy relaxation process via longitudinal polar optical phonon scattering [16]. The resulting high electron temperature leads to enhanced DP spin relaxation (electrons experience rapid spin relaxation) because they have large kinetic energy between successive collisions and the DP spin relaxation rate is proportional to approximately the cube of the electron temperature or kinetic energy [17]: 1/τs ∼ E 3 τ p ( E k ), k
(3)
where τ p ( E k ) is the momentum relaxation time. As expected, the spin relaxation rate increases rapidly with the applied bias, which agrees well with the results of the theoretical study as well as of other investigations [18,19]. As also seen from Fig. 3, an enhancement of the signal with increasing doping density is observed. The introduction of n-type dopants in semiconductors increases τs , because the electronic spin polarization in these systems survives for longer times. Studies of spin precession in n-type GaAs reveal that moderately ndoping yields significantly extended τs [3]. The similar trend was observed in a different experiment [20], where the author studied the doing density dependence of the spin-polarization of conduction band electrons and found that the polarization increased with increasing doping. The results for the sample C at different temperatures are shown in Fig. 4. As seen, an enhancement of the signal with decreasing temperature is observed. This is expected because with decreasing temperature the process enters the degenerate regime [21]. Fig. 5 shows the excitation power dependence of the signal for the sample C with E ex = 100 meV. As can be seen, the signal does not depend significantly on the excitation power. This is expected because our devices contained ohmic contacts. However, a slight decrease in the signal was observed at P ex > 12 mW, which might be due to the mixing of the spin states as a result of the heating of the sample. Because we used P ex = 5 mW in our measurements, there was no chance that the measured voltage contained any contribution from this effect.
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M.I. Miah / Physics Letters A 373 (2009) 2097–2100
tion dipole-matrix elements for the heavy-hole (hh), light-hole (lh) and SO bands and are 3, 1, 2, respectively. Excitation with energies E ex E g + , i.e. with energies equal to or larger than the SO band transition, yields no electron spin polarization since lh and SO band transitions create the same electron spin orientation and the sum of their inter-band dipole transition-matrix elements is equal to the hh transition matrix element [22]. 4. Conclusions
Fig. 5. Excitation power dependence of the transverse voltage for the sample C ( E ex = 100 meV).
We studied the transport of spin-polarized electrons in semiconductors. Spins were generated by optical excitation of the hh and lh states. Experiments designed for the control of spins in semiconductors investigated the bias-dependent transport process and detected the spin-polarized electrons during transport. A strong bias dependence was observed. The electric-field effects on the spin-polarized electron transport were also found to depend on the excitation photon energy. The field effects in the transport process were discussed based on the dominant spin relaxation mechanism in n-type semiconductors with wide-band gaps. References
Fig. 6. Excitation photon-energy dependence of the transverse voltage for the sample C ( P ex = 5 mW).
The excitation photon energy dependence of the signal for the sample C is shown in Fig. 6. As can be seen, for optical excitation of the sample with excess photon energies between 50 and 150 meV, the sample gives the maximum signal. With a further increase in the energy, the signal decreases and finally reduces to the background for larger excess energy (comparable to the spin– orbit splitting energy ) because of the exciting carriers from the spit-off (SO) band. This is a consequence of the optical selection rules (m j = ±1). The strengths of the optical inter-band valence to conduction band transitions are given by the inter-band transi-
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