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Two-Photon Spin-Polarization Spectroscopy in Silicon-Doped GaAs M. Idrish Miah* Nanoscale Science and Technology Centre, Griffith UniVersity, Nathan, Brisbane, QLD 4111, Australia, School of Biomolecular and Physical Sciences, Griffith UniVersity, Nathan, Brisbane, QLD 4111, Australia, and Department of Physics, UniVersity of Chittagong, Chittagong 4331, Bangladesh ReceiVed: January 16, 2009; ReVised Manuscript ReceiVed: March 16, 2009
We generate spin-polarized electrons in bulk GaAs using circularly polarized two-photon pumping with excess photon energy (∆E) and detect them by probing the spin-dependent transmission of the sample. The spin polarization of conduction band electrons is measured and is found to be strongly dependent on ∆E. The initial polarization, pumped with ∆E ) 100 meV, at liquid helium temperature is estimated to be ∼49.5%, which is very close to the theoretical value (50%) permitted by the optical selection rules governing transitions from heavy-hole and light-hole states to conduction band states in a bulk sample. However, the polarization pumped with larger ∆E decreases rapidly because of the exciting carriers from the split-off band. 1. Introduction Electronics has relied on the charge degree of freedom of electrons in semiconductors. Another freedom of electrons, namely the spin degree of freedom, already used in magnetic mass storage,1 has long been ignored in semiconductors because of the almost degenerate energies of the two spin states (up, v, and down, V) of electrons in semiconductors. However, because of advances in semiconductor science and technology,1-5 the control and manipulation of the spin degree of freedom in semiconductors is becoming increasingly possible. The idea of utilizing the electron spin in semiconductor devices leads to the growth of the field “semiconductor spintronics”, where both charge and spin degrees of freedom play a crucial rule in realizing operations and functionalities.2,6,7 However, one of the major obstacles in the development of semiconductor spintronic devices has been the problem of transporting spins in semiconductors reliably (without spinflipping or spin relaxation) over reasonable distances. For this, for example, efficient (e.g., fully or highly polarized) generation, or injection, of spin-polarized electrons in a semiconductor is required. The generation (or injection) of spin-polarized electrons has been obtained by either optical or electrical methods.2,6 However, the actual advantages of these processes in practical devices have not yet been clearly established.6,7 To fully understand the transport of spins in semiconductors and to successfully implement spintronic device concepts, substantial research effort in this area is required. It has recently been suggested8 that high spin-polarization could be achieved in unstrained bulk GaAs from two-photon (TP) excitation absorption. For this class of semiconductors, similar predictions have also been observed in the earlier theoretical calculations using TP excitation.9-11 Here, in the present work, we perform time- and polarization-resolved TP pump-probe spectroscopy in GaAs. We generate spin-polarized electrons in the sample at various temperatures using circularly polarized TP pumping with excess photon energies and detect them by probing the spin-dependent transmission of the sample. The spin polarization of conduction band electrons, as measured * To whom correspondence should be addressed. E-mail: m.miah@ griffith.edu.au.
Figure 1. Experimental setup along with an illustration of the TP excitation scheme showing the pump pulse (ω) coupling the initial and final states in the valence (VB) and conduction (CB) bands and the probe pulse (ω0) tuned to the band gap (Eg) excitation resonance (pω0 ≈ Eg).
using probe pulses with the same and opposite circular polarization, is found to be dependent on temperature as well as on excess pumping photon energy. 2. Experimental Section Samples used in the experiments are silicon-doped (n ) 1 × 1016 cm-3) bulk GaAs (∼1 µm thick). To measure the degree of spin polarization, we performed a polarization-resolved TP pump-probe experiment, as schematically shown in Figure 1, where the differential transmission ∆L/L ) (L - L0)/L [where L(L0) is the transmission with (without) the pump] of the probe pulses was measured as a function of the delay (τ) between circularly polarized pump and probe pulses. Broadband quarter wave plates were used to transform pump and probe beams from linear to circularly polarized light. The measurements were performed at various temperatures starting from the liquid helium temperature (LHeT) using fs pulses from an optical parametric amplifier pumped by a regeneratively amplified Ti: sapphire laser operating at 250 kHz. The laser system was tuned to produce ∼150 fs pulses (signal and idler). A BBO crystal was used to generate pulses from the signal and idler. The second harmonic and fundamental pulses were then separated using a dichroic beamsplitter. We used ∼150 fs pulses to excite the sample by TP absorption12 and 825 nm pulses to probe the transmission of the sample.13 The probe beam (ω0) was resonant
10.1021/jp900456d CCC: $40.75 2009 American Chemical Society Published on Web 04/17/2009
Two-Photon Spectroscopy in Silicon-Doped GaAs
Figure 2. Differential transmission, excited by TP σ+-pump pulses with ∆E ) 100 meV, as measured at LHeT using probe pulses with the same (σ+σ+) and opposite circular polarization (σ+σ-). Insert: spin polarization of electrons, as calculated from the transmission data, as a function of time delay.
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Figure 3. Differential transmission excited by TP σ+-pump pulses (∆E ) 100 meV) at 300 K. Insert: spin polarization of electrons as a function of time delay.
with the band gap energy (Eg), and the pump beam (ω) had an excess energy ∆E ) 2pω - pω0 = 2pω - Eg. The ∆E was varied for the measurements of its dependence. 3. Results and Discussion For optical pumping of bulk zinc-blende semiconductors, such as GaAs, with photon energies just above the band gap, because of the selection rules governing optical transitions from heavyhole, or light-hole, states to conduction band states, right circularly polarization (σ+) generates a density of spin-down CB electrons (nV) which is three times the density of spin-up CB electrons (nv), and vice versa for left circularly polarized light (σ-).14 Hence, according to the selection rules, the initial value (p0) of the electron spin polarization (p), defined as p ) (nV - nv)/ (nV + nv), generated by a σ+(σ-) beam in a zinc-blende semiconductor, is +0.5(-0.5) or 50%, provided that the photon energy is low enough to avoid exciting carriers from the splitoff band. Since, for probe pulses near the band edge, (∆L/L)σ+ σ+ ∝ 3nV + nv and (∆L/L)σ+ σ- ∝ 3nv + nV, as a result of the selection rules, one can determine p from the relation p ) 2[(∆L/L)σ+ σ+ - (∆L/L)σ+ σ-]/[(∆L/L)σ+ σ+ + (∆L/L)σ+ σ-] by measuring the differential transmission for pump and probe pulses having the same [(∆L/L)σ+ σ+] and opposite [(∆L/L)σ+ σ-] circular polarizations. We first measure the differential transmission ∆L/L excited by TP σ+-pump pulses with ∆E ) 100 meV at various temperatures. Figure 2 shows the results for the LHeT. The upper curve corresponds to probing with a σ+ pulse, whereas the lower curve was measured with a σ- pulse. As can be seen, there is a difference between the different polarization conditions (σ+ σ+ and σ+ σ-), which is caused by spin-dependent phasespace filling.15,16 The resulting p, as measured using probe pulses with the same and opposite circular polarization, as a function of τ is shown in Figure 2 insert. The p decays with τ with a time constant (t0) of ∼205 ps, giving a value for the spin relaxation time of τs ) 410 ps since t0 is considered as a half of τs. The decay of p might be due to the randomization of the initial spin polarization, p0, by the Dyakonov-Perel (DP) spin relaxation mechanism.17 The DP spin relaxation occurs in semiconductors lacking inversion symmetry due to the spin precession about an intrinsic magnetic field induced by the presence of spin-orbit (SO) interaction in a zinc-blende structure.
Figure 4. Temperature dependence of the initial spin polarization (∆E ) 100 meV).
The results of the TP pump-probe experiment for T ) 300 K is shown in Figure 3. Here, the difference between the different polarization conditions is decreased. Figure 4 shows the temperature dependence of p0. As can be seen, a slight temperature dependence of p0 is observed, with a maximum value of 49.5% at LHeT. This might be due to the temperaturedependent band gap shift of GaAs. As mentioned above, although the maximum optical spinpolarization for an unstrained bulk sample is expected to be 50% in theory, the maximum has been experimentally observed to be ∼40%.14 In the earlier polarization measurements, they used one-photon (OP) excitation. In a bulk sample, there are usually some background unpolarized (not photoexcited) electrons. If there is a background density of unpolarized electrons nu in the sample, then the polarization would be p0 ) 0.5/(1 + nu/n0) for an optically generated electron density n0 ) nV(0) + nv(0).18 The TP excitation enhances the spin polarization because it takes the advantage over OP spin generation due to a much longer absorption depth, which allows spin excitation in the deep level, i.e., throughout the volume of a thin bulk sample. The p0 as a function of the excess energy ∆E ) 2pω - Eg is shown in Figure 5. As can be seen, p0 increases quickly to a maximum and remains almost constant, and then decreases. The maximum is obtained for ∆E ) 50 - 120 meV, which is
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Miah was found to depend strongly on the excess energy. The initial spin polarization, pumped with ∆E ) 100 meV, at LHeT was estimated to be ∼49.5%. However, the polarization pumped with larger ∆E decreases rapidly because of the exciting carriers from the split-off band. The results experimentally demonstrate that, due to a much longer absorption depth, highly spin-polarized conduction band electrons can be generated optically by the TP heavy-hole and light-hole states excitation of the bulk semiconductors. References and Notes
Figure 5. Initial spin polarization as a function of the excess photon energy of the σ+-pump beam at LHeT.
considerably less than the SO splitting energy of ∆E SO)340 meV. However, the polarization pumped with higher excess energy decreases rapidly because of exciting carriers from the split-off band which has the energy ESO ) Eg + ∆ESO (where ESO is the split-off band to conduction band energy gap). 4. Conclusions A two-photon spin polarization spectroscopy was performed in bulk GaAs. We generated spin-polarized electrons in the sample at various temperatures using circularly polarized TP pumping with excess photon energy and detected them by probing the spin-dependent transmission of the sample. The spin polarization of conduction band electrons was measured and
(1) Prinz, G. A. Science 1998, 282, 1660. (2) Semiconductor Spintronics and Quantum Computation; Awschalom, D., Loss, D., Samarth, N., Eds.; Springer: Berlin, 2002). (3) Kityk, I. V. Phys. Solid State 1991, 33, 1026. (4) Kitykz, I. V.; Ebothe´, J.; Liu, Q.; Sun, Zh.; Jiye, F. Nanotechnology 2006, 17, 1871. (5) Miah, M. I.; Optoelectron, J. AdV. Mater. 2008, 10, 2487. (6) eˇutic´, I.; Fabian, J.; Sarma, S. D. ReV. Mod. Phys. 2004, 76, 323. (7) Dyakonov M. I.; Khaetskii, A. V. Spin Hall Effect (Spin Physics in Semiconductors; Dyakonov, M. I. Ed.; Springer-Verlag: Berlin, 2008). (8) Matsuyama, T.; Horinaka, H.; Wada, W.; Kondo, T.; Hangyo, M.; Nakanishi, T.; Okumi, S.; Togawa, K. Jpn. J. Appl. Phys. 2001, 40, L555 (part 2). (9) Danishevskii, A. M.; Ivchenko, E. L.; Kochegarov, S. F.; Stepanova, M. I. SoV. Phys. JETP 1972, 16, 440. (10) Ivchenko, E. L. SoV. Phys. Solid State 1973, 14, 2942. (11) Arifzhanov, S. B.; Ivchenko, E. L. SoV. Phys. Solid State 1975, 17, 46. (12) Fahmi, A. I.; Kityk, V., M.; Sahraoui, B.; Sylla, M.; Rivoire, G. J. Opt. A: Pure Appl. Opt. 1999, 1, 192. (13) Miah, M. I. Opt. Mater. 2001, 18, 231. (14) Pierce, D. T.; Meier, F. Phys. ReV. B 1976, 13, 5484. (15) Avrutsky, I. A.; Vosmishev, A. V. Phys. Low-Dim. Struct. 1995, 10/11, 257. (16) Wang, T.; Li, A.; Tan, Z. Proc. SPIE 2007, 6838, 683814. (17) Dyakonov, M. I.; Perel, V. I. SoV. Phys. JETP 1971, 33, 1053. (18) Miah, M. I. J. Appl. Phys. 2008, 103, 123711.
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