IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 6, JUNE 2009 2383

Determination of Spin-Orbit Interaction in InAs HeterostructureTae Young Lee, Hyun Cheol Koo, Kyung Ho Kim, Hyung-Jun Kim, Joonyeon Chang, and Suk-Hee Han

Center for Spintronics Research, Korea Institute of Science and Technology, Seoul 136-791, Korea

Spin-orbit interaction (SOI) gives a useful tool to control spin precession in the semiconductor without external magnetic field. TheRashba effect induced by spin-orbit interaction enables to imagine the spin field effect transistor in which the resistance modulationis achieved by precession of spins moving in a channel. The oscillatory magnetoresistance was measured to determine SOI parameterof inverted type high electron mobility transistor structure where InAs quantum well is inserted to InAlAs/InGaAs barrier layer. Theband structure and electron charge distribution of the structure was calculated using WinGreen simulator. Observed SOI parametersare large enough to produce high Rashba field of about a few Tesla. The magnitude of the SOI parameter is subject to change with theInAs quantum-well thickness.

Index Terms—Quantum well, Rashba effect, Shubnikov-de Hass oscillation, spin-orbit interaction.

I. INTRODUCTION

G ENERATION, manipulation, and detection of spin-po-larized electrons in nanostructures define the main chal-

lenges of spin-based electronics [1]–[3]. Spin-orbit interaction(SOI), which couples the spin of an electron to its momentum,has attracted remarkable interest because it is a key mechanismfor spin field effect transistors (spin FETs) [4]. The fundamentalfunctions of spin FETs is that an electric field applied by a gatepotential modulates precession of spins injected from a ferro-magnetic source. It turns out that the amount of spin preces-sion traveling through semiconductor quantum well (QW) canbe controlled by applying gate electric field owing to the SOI.Therefore, SOI is an essential parameter of QW semiconductorfor spin FET applications.

In channel, traveling electrons with a perpendicularelectric field induce an effective magnetic field (Rashbafield, ) in the -direction which is called the Rashba effect.The induced magnetic field interacts with the spin-polar-ized electrons and hence controls the spin direction as shownin Fig. 1. Rashba Hamiltonian can be expressed as

(1)

where is the Rashba constant (SOI parameter) and is thePauli matrices [5]. The structural inversion asymmetry of QWheterostructure produces effective interfacial electric field alongthe -direction. Because the effective magnetic field acts per-pendicular to both the electron momentum and the potentialgradient, the SOI rotates spin precession inside the - planes.Even without any external magnetic field, a -direction electricfield perpendicular to the QW layer yields an effective magneticfield for moving electrons which lifts the spin degeneracy. TheShubnikov-de Hass oscillation (S-dH) effect is widely used tocharacterize two-dimensional electron gas (2DEG) systems insemiconductor hetero-junctions [6]. The oscillatory magnetore-sistance reflecting on spin splitting can be found in the S-dH

Manuscript received October 16, 2008. Current version published May 20,2009. Corresponding author: J. Chang (e-mail: presto@kist.re.kr).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2009.2018581

Fig. 1. Schematic explanation of the Rashba effect.

observations. SOI results in the appearance of specific beatsin oscillatory phenomena with which Rashba constant can beevaluated.

In the work, SOI parameters are evaluated for inverted typeInAs high electron mobility transistor (HEMT) structure withdifferent InAs QW thickness ranging from 0 to 7 nm by ana-lyzing the S-dH oscillations. We also calculated the energy bandstructure and electron charge distribution of the heterostructureto understand QW thickness effect on the SOI.

II. EXPERIMENT DETAILS

Inverted type InAs HEMT structure is used to evaluate on SOIparameter. It is believed to suitable for spin FET study becauseit has a high breakdown voltage and a low gate-leakage current[7].

Fig. 2 shows the layer structure of the inverted type InAsHEMT structure we prepared for the work. The InAs QWis placed between the In Al As/In Ga As doublecladding layers and the carrier supply layer is located below theInAs/In Ga As double QW.

The samples with different InAs QW thickness of 0–7 nmwere grown on a InP(001) substrate in the molecular beam epi-taxy (MBE). The samples were processed into 64 80 mHall bars to obtain S-dH curve.

While perpendicular magnetic field was applied to the QWsplane, we observed the period of the beat patterns in the mea-surement of the S-dH. From the results, we decided the SOI pa-rameter and sheet carrier concentration without an ex-ternal electric field.

The total carrier concentration and mobility of the 2DEGbefore the channel patterning were

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2384 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 6, JUNE 2009

Fig. 2. Substrate layer structure of an InAs-inserted InGaAs/InAlAs het-erostructure.

cm and – (20 000–50000) cm V s at 300 K (77 K). After channel patterningwith Ar ion-milling, carrier concentration is decreased

at 1.8 K. The decrease is due to low measure-ment temperature of 1.8 K and size reduction from millimeterto micron scale after channel patterning.

III. RESULTS AND DISCUSSION

Fig. 3 shows the calculated energy band diagrams (a) and theelectron charge distributions (b). We employed the WinGreen[9] simulator with its data files for the band calculation.From the files of WinGreen the energy band gaps of InAsand In Ga As are 0.355 eV and 0.917 eV, respectively.Therefore the energy band gap difference between InAs andIn Ga As layer is 0.562 eV. This potential difference(0.562 eV) is divided into conduction band and valence bandoffset. From this simulation we found that the band offset ofthe conduction band is about 0.5 eV. As shown in Fig. 3(a),the QWs are not symmetric and the charge distributions areconcentrated on the side of the carrier supply layer, which is

doped In Al As ( cm ) layer. Thisasymmetric potential gradient induces a strong internal electricfield which produces effective magnetic field of .

Fig. 4 shows signals of the S-dH oscillations measured at tem-perature of 1.8 K. Because of the thermal agitation disturbingthe Rashba-effect-induced Zeeman splitting [8], the beat patternwas observed at low temperature. The inset shows the measure-ment geometry. When the current is applied in the channel, thevoltage is measured at the channel with perpendicular magneticfield. We systematically observed the QW thickness dependenceof the beat patterns of S-dH oscillation. Spin up and down elec-trons generate oscillation with different frequency, respectively.Therefore, beat patterns arise when these two different signalscombine. A large spin splitting energy means a large frequencydifference and hence a short beat pattern period. Therefore, thefrequency of the beat pattern is proportional to the spin splittingenergy.

Another possible source of the oscillatory magnetoresistancein a 2DEG is magneto-intersubband scattering (MIS), which

Fig. 3. Results of simulation with a various QW thickness. (a) Energy banddiagrams and (b) Electron charge distribution of QW. � is the distance from thetop surface.

Fig. 4. Shubnikov-de Hass (S-dH) oscillations at � � ��� K. InAs QW thick-ness ranging from 0–7 nm. Arrows indicate the first and second node positionsin the beat patterns. The inset shows the measurement geometry.

does not include a thermal damping term [6], [10]. The prob-ability of taking the second subband is very low at the temper-ature ( K) in this measurement because of the thin QWthickness. Furthermore, in a finite rectangular potential well

LEE et al.: DETERMINATION OF SPIN-ORBIT INTERACTION IN INAS HETEROSTRUCTURE 2385

model [11], we found that only a single bound state can existfor a few nanometer thick QW of our structure. Therefore, weconclude that the observed beat pattern of the S-dH oscillationin our experiment entirely due to the Rashba effect.

In Fig. 4, the beat pattern period indicated by arrows de-creases with increasing QW thickness. Especially, the beat pat-tern period for 0 nm thickness InAs QW is larger than the others.This result indicates that the QW thickness, which determinesthe confinement of the wave function in the heterostructure, af-fects the overall strength of the Rashba SOI. It is noted that theRashba SOI can be subject to change with InAs QW thickness.

Fig. 5 shows the SOI parameter and the total carrier con-centration including spin-up and spin-down electrons as afunction of InAs QW thickness. From the peak point frequencyof the S-dH oscillation, we obtained the total carrier concen-tration. These results are well matched with the values calcu-lated by the conventional Hall measurement. As shown in Fig. 5,the total carrier concentration almost remains constant with QWthickness and it seems to be less dependent on it. While the SOIparameter drastically increases from eV m to

eV m when 3 nm thick InAs QW is introduced andthen decayed with increasing the thickness. Usually, the SOI pa-rameter, , is expressed as

(2)

where is the spin precession length, and are the spinrelaxation time and the momentum scattering time, respectively[12]. From the equation, the SOI parameter would be ex-pected to remain constant regardless of the InAs QW thickness.However, our experimental results show that the SOI param-eter is sensitive to InAs QW thickness. The result indicatesthat the QW thickness influences SOI parameter and should beconcerned for the accurate control of the Rashba field. The QWthickness effect on SOI has not been understood yet but the spinprecession length is restrained by the narrow channel [12]. Itmeans that the narrow channel acts like a qusi-one-dimensionalwire, thus the two-dimensional spin dynamics which determinethe spin diffusion length is limited due to the side wall effect ofthe channel [12], [13]. Therefore, SOI parameter of the thinQW thickness is larger than that of thicker one. On the otherhand, this work reveals that insert of InAs QW layer increasesSOI parameter which is useful to increase Rashba field.

IV. CONCLUSION

SOI parameters of inverted type InAs HEMT structure withdifferent InAs QW thickness have been determined by ana-lyzing the S-dH oscillations. We found that the SOI parameter

of no InAs QW is eV m and increases toeV m at 3 nm InAs QW. SOI parameter decayed

with increasing the thickness over 3 nm. The total carrierdensity is less dependent on the InAs QW thickness. The InAsQW thickness yielding a substantial change of SOI parameter

Fig. 5. InAs QW thickness dependence of the spin-orbit interaction parameter��� and the total carrier concentration �� � including spin up and down.

indicates that it should be optimized in order to have easymanipulation of spin precession inside 2DEG.

ACKNOWLEDGMENT

This work was supported by the KIST Institutional Program.

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