Solid-State Electronics 82 (2013) 34–37

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Solid-State Electronics

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Gate voltage control of the Rashba effect in a p-type GaSb quantum welland application in a complementary device

Youn Ho Park a,b, Sang-Hoon Shin a, Jin Dong Song a, Joonyeon Chang a, Suk Hee Han a, Heon-Jin Choi b,Hyun Cheol Koo a,c,⇑a Spin Convergence Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Koreab Department of Materials Science and Engineering, Yonsei University, Seoul 120-749, Republic of Koreac KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 136-701, Republic of Korea

a r t i c l e i n f o

Article history:Received 6 September 2012Received in revised form 7 January 2013Accepted 28 January 2013Available online 28 February 2013

The review of this paper was arranged byProf. A. Zaslavsky

Keywords:Rashba effectGaSb p-type quantum wellComplementary deviceSpin transistor

0038-1101/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.sse.2013.01.016

⇑ Corresponding author at: Spin Convergence ReseaScience and Technology, Seoul 136-791, Republic ofSchool of Converging Science and Technology, KoreRepublic of Korea. Tel.: +82 2 958 5423; fax: +82 2 9

E-mail address: hckoo@kist.re.kr (H.C. Koo).

a b s t r a c t

The gate voltage dependence of the Rashba effect in a p-type quantum well was investigated by usingShubnikov–de Haas measurements. The GaSb-based p-type quantum well has a large Rashba spin–orbitinteraction parameter of 1.71 � 10�11 eVm for a zero gate voltage and exhibits gate controllability. Wealso propose a complementary logic device using n- and p-type spin transistors that simultaneously uti-lize charge and spin currents to improve the signal margin.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction ing because of its strong Rashba effect. Habib et al. [5] also pre-

Rashba spin splitting is a fascinating phenomenon that can beused to control spin information via an electrical method. Thecontrol of the Rashba spin–orbit interaction parameter (a) isthe most important factor in device applications. The spin pre-cession angle is used to modulate transistor operation and isdetermined by the gate-controlled Rashba effect [1–3]. In anasymmetric quantum well system, moving electrons feel aneffective magnetic field that interacts with the spin-polarizedelectrons and finally modulates the spin orientation. The inducedRashba field can be expressed as [2,3] BR = 2akF/(glB), where g isthe g-factor of the carriers in the channel, lB = 9.27 � 10�24 J/T isthe Bohr magneton, and kF is the Fermi wavevector. In order toobtain a large a, a small band gap material with an asymmetricquantum well is required.

Usually n-type channels are selected for spin transport devicesbecause of their high speed, but p-type channels are also requiredfor compatibility with complementary logic devices. The previousarticle [4] reported that the p-type spin transistor is more promis-

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rch Center, Korea Institute ofKorea and KU-KIST Graduatea University, Seoul 136-701,58 6851.

sented a spin interference device, which is possibly utilized for aspin-based transistor, in a strong spin–orbit interaction system.Thus, understanding the Rashba spin–orbit interaction in p-typechannels is also useful in the development of spin transistor de-vices. Matsuyama et al. [6] observed the Rashba effect in a triangu-lar surface potential by using a p-type InAs layer. The carrierdensity dependence of the Rashba parameter was investigatedbut the actual carriers inside the interfacial potential were elec-trons rather than holes. Grbic et al. [7] studied the spin splitting in-duced by the spin–orbit interaction in a p-type GaAs/AlGaAsheterostructure. Habib et al. [8,9], Lu et al. [10], Papadakis et al.[11], and Winkler et al. [12] also investigated Rashba effect in ap-type semiconductor. They reported spin splitting energy andtwo spin-subband densities in the GaAs/AlGaAs structures but theyrequired very large voltages (�100 V) to control the Rashba spinsplitting. In our work, we present the feasible gate modulation ofRashba constant (a) in a p-type GaSb quantum well which needsonly a few volts to control the Rashba effect.

2. Device structure

In this study of a two-dimensional hole gas (2DHG) structure,Shubnikov–de Haas (SdH) oscillation measurements [2,3,13–17]were performed to determine the spin–orbit interaction parameter

Fig. 1. Schematic diagram of a p-type quantum well. (a) Vertical view and (b) energy band and carrier distribution.

Fig. 2. Shubnikov–de Haas (SdH) oscillation at T = 1.8 K in the absence of a gatevoltage. The inset shows the measurement geometry and the fast Fourier transformof the SdH curve.

Y.H. Park et al. / Solid-State Electronics 82 (2013) 34–37 35

of the p-type channel. A GaSb quantum well layer was inserted as ap-type channel and sandwiched between double cladding layers ofIn0.53Ga0.47As and In0.52Al0.48As, as shown in Fig. 1a. A Be-doped InPlayer was used as the carrier supplier in the 2DHG structure andthe doping concentration is 4 � 1018 cm�3. The results of the bandcalculation are shown with charge distribution in Fig. 1b; z is thedistance from the top of the heterostructure. For the band calcula-tion, we utilized WinGreen simulator [18] and its material data. Inthis calculation, the band offset of the valence band is around0.6 eV, which is sufficiently large for the Fermi level to cross thequantum well of the valence band. This result means that the car-riers in this system are holes instead of electrons. Further, a Hall ef-fect experiment confirmed that this structure is a p-type quantumwell. The hole mobility and carrier concentration arel = 2600 cm2 V�1 s�1 and pS = 2.28 � 1012 cm�2 at 1.8 K, respec-tively. The charge distribution in Fig. 1b shows that the carrier islocated at the top of the potential well. This quantum well asym-metry produces an internal electric field and thus the Rashba effectarises even in the absence of a gate electric field. The intrinsic elec-tric field is proportional to the slope of the potential well and themagnitude of the Rashba spin splitting. The other source of thespin–orbit interaction is the Dresselhaus effect, which is inducedby bulk inversion asymmetry. The strength of the Dresselhaus fieldis determined by the crystal direction of the channel, whereas theRashba effect is always perpendicular to the wavevector in thetwo-dimensional plane. The Dresselhaus effect is usually negligiblein highly asymmetric heterostructure systems such as the quan-tum well investigated in this research.

3. Results and discussion

Fig. 2 shows the SdH oscillation results for the GaSb channel.The inset illustrates the device geometry; a 64 lm wide Hall barwas utilized. With a perpendicular magnetic field, the resistanceof the channel was measured. The Hall bar pattern was definedby using photo-lithography with dry etching.

The oscillation from the SdH measurement at T = 1.8 K is shownin Fig. 2. The spin-up and spin-down hole densities are propor-tional to the oscillation frequencies. The beat patterns in the oscil-lation curve originate from the asymmetric population of spin-upand spin-down holes and the frequency difference determinesthe node position indicated by the arrow in Fig. 2. The carrier den-sity of spin-up (p") and spin-down (p;) holes can be described by[13] p",; = f",;/eh, where f is the frequency of the Shubnikov–deHaas oscillation, e is the electron charge, and h is Planck’s constant.

The difference between the populations of spin-up and spin-downholes can be expressed as [9,14] p" � p; = (2pm�/h2)(E" � E;), wherem� is the effective mass of holes and E" (E;) is the chemical poten-tial of spin-up (spin-down) holes. A large spin splitting energy (E" -� E;) corresponds to a large frequency difference and a short beatperiod. Consequently, if the lowest subband is occupied, the spin–orbit interaction parameter is [15,16]

a ¼ ðp" � p#Þh2

4pm�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p½pS � ðp" � p#Þ�

q ð1Þ

where the total hole concentration is pS = p" + p;. The effective masswas extracted from the temperature dependence of the amplitudeof the SdH oscillation [19,20]. In our case an effective hole massof 0.094m0 was obtained.

After applying the fast Fourier transform to the SdH signal, twopeaks are present, as shown in the inset in Fig. 2. The two fre-quency terms represent the spin-up (major) and spin-down (min-or) holes. From the two peaks, we determined that without a gatefield p" and p; are 1.26 � 1012 cm�2 and 1.02 � 1012 cm�2, respec-tively. The Rashba spin–orbit interaction parameter is1.71 � 10�11 eVm for a zero gate voltage. This is a relatively largervalue than that of a typical n-type quantum well, which is usuallyless than 10�11 eVm at zero gate voltage [2,3,14,17]. The stronglynonparabolic subband dispersion is one possible reason of the

36 Y.H. Park et al. / Solid-State Electronics 82 (2013) 34–37

large Rashba effect in p-type quantum well [4]. However, the re-sults of Fourier transform show clear two peaks. It means the effectof nonparabolic subband dispersion is not very strong to nullify Eq.(1). If the carrier density increases, the subband dispersion effectwill be very strong and other frequency terms may arise.

Next, we measured the SdH oscillation as a function of the gatevoltage, VG, at 1.8 K. An insulator consisting of a 100 nm thick SiO2

layer and a gate electrode were deposited for the gate dependenceof the SdH measurements. Fig. 3a shows the Fourier amplitudes forVG = �3 V, �1 V, 0 V, and +1 V. When the two peaks are located faraway from each other, the difference between the populations ofmajor and minor spins is large, which means that the Rashba spinsplitting is strong. As the gate voltage increases, the density differ-ence decreases as indicated by arrows. From these results, we canextract the gate dependences of the spin–orbit interaction param-eter and the total hole concentration, as shown in Fig. 3b. As thegate voltage increases, both the spin–orbit interaction parameterand the total hole concentration decrease. For the larger negativegate voltages, the positive charge moves further toward the top

Fig. 3. Gate voltage dependences of (a) fast Fourier transform (FFT) of Shubnikov–de Haas oscillation and (b) the Rashba spin–orbit interaction parameter and carrierdensity. The peaks in FFT are indicated by arrows.

of the quantum well and the slope of the quantum well becomessteeper. Thus, the spin–orbit interaction parameter increases withlarger negative voltages. The difference between the spin–orbitinteraction parameters (Da) for VG = �4 V and +1 V is1.37 � 10�11 eVm, which is sufficiently large for spin transistoroperation. In general, the spin precession angle is h = 8p2m�La/h2,where L is the traveling distance of the spin-polarized hole. Dueto the relatively large effective mass, the spin precession angle isvery large even in a short channel. For example, if L is 680 nm,the spin precession angle would be �1620� (180�) for VG = 0 Vand �1800� (360�) for VG = �1 V. The channel conductance isdetermined by the spin precession angle. When the spin precessionangle is 360� (180�), the arriving spins at drain will be parallel(antiparallel) to the magnetization direction of the drain and thechannel conductance will be the highest (lowest) state. The spinprecession angle can be modulated by the gate-controlled Rashbaspin–orbit interaction parameter. Thus, spin transistor operationis possible with a small variation of gate voltage. In order to eval-uate spin precession angle, we compare the values of ðp" � p#Þ=p0:5

#which is proportional to h ( =8p2m�La/h2). At VG = 0 V, the valuesare 2.4 � 105 cm�1 for our structure and 5.1 � 104 cm�1 for GaAs/AlGaAs structure [11], which means our GaSb quantum well struc-ture has larger spin precession angle than GaAs/AlGaAs structure.

In conventional complementary metal oxide semiconductor(CMOS) devices, either the n-MOS or the p-MOS transistor is ONwhen VG is high or low respectively. This complementary behaviorenables the implementation of logic devices. Fig. 4 shows a con-ventional CMOS inverter for which the charge current drives thelogic operation. Spin current can also performs the same function.Fig. 4 shows the spin dependent channel conductance, rSPIN, as afunction of the gate voltage which controls the Rashba spin–orbitinteraction parameter (a) and finally determines the spin preces-sion angle. These curves are based on the experimental values ofthe gate dependence on a. For the n-type channel, we extractedthe Rashba parameters, a, from the InAs quantum well layer,where a decreases with the gate voltage [2,3]. We assumed chan-nel lengths of 680 nm and 550 nm for the p- and n- type spin tran-sistors, respectively. The conductance is highest (lowest) forparallel (antiparallel) alignment between the arriving spins atdrain and the magnetization of drain. As shown in Fig. 4, for a spinrelative term, complementary operation can be implemented. Forexample, when VG = �3 V, the p-type transistor is ON but the n-type transistor is OFF. If, however, we let VG = 0 V, the n-type tran-sistor is ON but the p-type transistor is OFF. The spin dependentsignal basically oscillates so the multiple sets of operational gatevoltages are possible. Further, the oscillatory period can be modu-lated by varying the thickness of the gate oxide as well as the chan-nel length. In our experiments, we utilized a 100 nm thick gateoxide to exclude any side effects from the leakage current. If we

Fig. 4. Gate voltage dependences of the channel conductances for n- and p-typespin transistors. The image on the left shows a schematic diagram of thecomplementary inverter.

Y.H. Park et al. / Solid-State Electronics 82 (2013) 34–37 37

reduce the oxide thickness down to 10 nm, the operation voltagecan be lessened by a factor of ten. It could be argued that both n-and p-type transistors are not necessary if two spin transistorshave two different gate dependences of Rashba parameters. Thisargument is correct but the generation of pure spin current to drivea transistor is not simple. Furthermore, in order to enhance the ON/OFF ratio, it is better to adopt both n- and p- type spin transistorsthat utilize conventional charge behavior in addition to the spincontribution.

4. Conclusion

In summary, we have investigated the dependence of the Rash-ba spin–orbit interaction parameter on gate voltage using a p-typeheterostructure with a GaSb active layer. The spin–orbit interac-tion parameter decreases with increasing the gate voltage. It wasfound that spin–orbit interaction strength increases with the car-rier concentration in the p-type channel whereas the oppositetrend was found for the n-type channel [2,3,17]. If we employ bothcharge and spin properties at the same time, a device combining p-and n-type spin transistors could be used as a complementary logicdevice.

Acknowledgements

This work was supported by the National Research Foundationof Korea (NRF) grant funded by the Korea government (MEST) (No.2012-0005631) and the KIST Institutional Programs includingDream Project.

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