Controlled GMR enhancement from conducting inhomogeneities in non-magnetic semiconductors

Physica B 279 (2000) 37}40

Controlled GMR enhancement from conducting inhomogeneities in non-magnetic semiconductors S.A. Solin*, Tineke Thio, D.R. Hines NEC Research Institute, 4 Independence Way, Princeton NJ 08540, USA

Abstract We report results of magneto-transport studies of homogeneous, high-mobility, Te-doped InSb in a thin "lm van der Pauw disk geometry (radius r ) containing a lithographically patterned, concentric, cylindrical metallic inhomogeneity " (radius r ). The room temperature giant magnetoresistance (GMR) increases dramatically with increasing r . We show ! ! that the GMR enhancement could in principle be made far larger by optimizing the material selection and lithographic patterning. We also discuss the potential impact of our results on read-head devices in high-density recording and on other magnetic sensors. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Inhomogeneous semiconductors; Giant magnetoresistance enhancement

1. Introduction There is intense current interest in materials that exhibit large (e.g. giant) magnetoresistance (GMR) [1,2]. This interest is stimulated by both the need to understand the novel physical origin of the GMR and by the application of such materials as magnetic sensors, most notably as read-heads in high-density magnetic recording. We show that macroscopic conducting inhomogeneities produced by lithographic patterning of a homogeneous narrow gap semiconductor can result in a very large and controllable enhancement of the GMR. We also provide both qualitative and quantitative explanations for our results. The magnetoresistance of a semiconductor, *o(H)/o 0 where o(H) is the "eld-dependent resistivity, o "o(0) 0 and H is the magnetic "eld, depends on both the physical properties intrinsic to the material and on the geometry of the measurement con"guration [3]. The physical MR is determined by parameters such as the carrier mobility

* Corresponding author. Tel.: 609-951-2610; fax: 609-9512615. E-mail address: [email protected] (S.A. Solin)

and carrier density and by their variation, if any, with applied magnetic "eld. In the case of high-mobility nonmagnetic semiconductors, the MR is due to the orbital motion of the carriers rather than to "eld-induced changes in the spin-dependent scattering cross section [4,5] which gives rise to GMR in spin valves. The geometric MR depends on the measurement con"guration that is usually chosen to be a Hall bar, van der Pauw (vdP) disk or Corbino disk structure [6]. In a semiconductor, the Lorentz force from an external magnetic "eld causes a de#ection of the charge carriers. However, in a long-Hall bar the MR from this e!ect is diminished because the Hall "eld, due to space charge built up at the edges, cancels the Lorentz force. (This cancellation is complete if one makes the assumption that the system consists of a single carrier with a deltafunction velocity distribution and that both the carrier density and mobility are independent of the applied magnetic "eld.) In contrast, the Corbino structure does not support a space charge. At H"0 the current #ows radially between the concentric electrodes. At "nite H, the Lorentz force causes the current trajectories to become spirals, resulting in an increase of the e!ective length of the current path and a pronounced MR of *o(H)/o "k2H2 (for a one-carrier system with an en0 ergy-independent carrier relaxation time) where k is the

0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 6 6 1 - 4

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S.A. Solin et al. / Physica B 279 (2000) 37}40

carrier mobility [7]. Since k&1/mH where mH is the e!ective mass of the carrier, and since mH is proportional to the semiconductor band gap [8], it is narrow (zero)gap materials which exhibit the highest mobilities and thus the highest MR. We have previously shown that natural inhomogeneities with conductance higher than that of the semiconductor enhance its already large GMR [9]. Here we show how such inhomogeneities, intentionally introduced in van der Pauw samples, give a signi"cant boost to the GMR of InSb which has a small 0.168 eV gap at 300 K [10].

k and conductivity p as shown in Fig. 1A, with the x-, yand z- axes as indicated. Assume that current #ows along the x direction and that a uniform magnetic "eld is applied along the z direction. Suppose that there is a cylindrical inhomogeneity with corresponding parameters k and p embedded in the semiconductor matrix as 0 0 shown. Assume further that neither p nor p depend on 0 H and that p;p . The magnetoconductivity tensor p(H) 0 for the semiconductor in the geometry of Fig. 1A is p !pb 0 1#b2 1#b2

C

p(H)" 2. Experimental details The InSb samples studied here were MBE grown epilayers of homogeneous Te-doped InSb. A bu!er layer consisting of 50 nm undoped GaAs, 50 nm undoped GaSb and 200 nm undoped InSb was grown on a semi-insulating GaAs substrate (resistivity '1]1017 ) cm). A 1.3 lm thick layer of Te-doped InSb was deposited on the bu!er layer and capped by a 50 nm insulating layer of Si N . Room temperature measurements of the resulting 3 4 doped InSb "lm using the vdP geometry yielded values for the electron mobility k "29,100 cm2/V s and carrier % concentration n"5.54]1016 cm~3. The samples were subsequently patterned into chips containing various con"gurations of vdP disk geometries. Standard lithographic techniques [11] and ion-beam milling [12] were employed to create both surface electrical current and voltage contacts and embedded cylindrical conducting inhomogeneities whose interface with the surrounding InSb matrix was ohmic. The vdP disk structure used in the InSb measurements reported here is shown schematically in Fig. 1B. Additional details of the sample preparation and characterization will be given elsewhere [13].

pb 1#b2

p 1#b2

0

0

D

0 ,

(3)

p

where b"lH. Let the electric "eld at some point on the surface of the inhomogeneity be E"E x( #E y( . The x y current density, J, is obtained from J"p(H)E. Note that the electric "eld is normal to the equipotential surface of a highly conducting inhomogeneity. At zero magnetic "eld, the magnetoconductivity tensor is diagonal and J"pE. Thus JEE and the current #ows into the conducting inhomogeneity which acts as a short circuit. In this case the resistance of the semiconductor

3. Results and discussion Let us "rst de"ne the enhancement of the GMR from inhomogeneities as *o(H, MSN)/o (MSN) 0 G(H, MSN)" , *o(H, M0N)/o (M0N) 0

(2)

where M0N represents the homogeneous material and MSN represents a set of parameters which characterize the inhomogeneous material. These could include the conductivity and mobility of the carriers in the inhomogeneities and their size and shape distribution etc. The physical principles [9,14], underlying the geometric GMR enhancement in inhomogeneous materials can be understood as follows. Consider a rectangular parallelepiped of homogeneous, extrinsic semiconductor with mobility

Fig. 1. (A) A schematic diagram of a cylindrical conducting inhomogeneity of conductivity p and mobility k embedded in 0 0 a homogeneous semiconductor with conductivity p and mobility k. Current #ow is assumed to be along the x direction. The electric "eld E is normal to the interface between the semiconductor and inhomogeneity. The vector H represents a uniform magnetic "eld perpendicular to the sample, HEz( . (B) A schematic diagram of a van der Pauw disk of radius r with an " embedded concentric cylindrical inhomogeneity (gray) of radius r showing the voltage and current probe con"guration used for ! the magnetoresistance measurements reported here.

S.A. Solin et al. / Physica B 279 (2000) 37}40

slab measured along the x direction would be less than that of a homogeneous sample of the same dimensions. At high magnetic "eld (b'1), the o!-diagonal components of p(H) dominate and J"(p/b)[E x( !E y( ]. Then y x JoE or equivalently, the Hall angle between the electric "eld and the current density [15] approaches 903, and the current tends to be tangent to, i.e. de#ected around, the inhomogeneity. This de#ection is total at su$ciently high "eld so that the current #ows only through the matrix in which case the conducting inhomogeneity acts as an open circuit. The transition of the inhomogeneity from short circuit at low-magnetic "eld to open circuit at highmagnetic "eld results in an enhancement of the measured MR of the semiconductor in which it is embedded even if the resistivity (conductivity) of the semiconductor itself is "eld-independent [9]. The crossover "eld between the high- and low-"eld regions is determined by the condition b"1 or H "1/k (in SI units). Thus, narrow #3044 gap semiconductors that exhibit very high mobilities [16] are the most attractive materials for exploiting the e!ects of inhomogeneities on MR. Indeed, materials such as Hg Cd Te and InSb have such high mobilities, 1~x x k n30,000 cm2/V s, that even without inhomogeneities % they exhibit giant magnetoresistance (GMR) at room temperature [16]. This already large GMR is enhanced further by the presence of the conducting inhomogeneities. In the absence of inhomogeneities, the GMR in both the Corbino and vdP geometry is maximal when the magnetic "eld is normal to the plane of the "lm. When an inhomogeneity is present, the boundary conditions for maximal enhancement of the GMR require [9] the applied magnetic "eld to be parallel to the interface between the inhomogeneity and the surrounding matrix while the current density must lie in the plane of the "lm. For the cylindrical inhomogeneity shown in Fig. 1A these boundary conditions are HEz( and JoH. Note that the GMR enhancement described here is a di!erent e!ect from that reported by Weiss and Wilhelm [17] who found a smaller enhancement from semiconductors containing an oriented distribution of &1% volume fraction of rodlike conducting inhomogeneities (with their long axes Ez in Fig. 1A). In that case, the enhancement was maximal with HEy and minimal with HEz. This is because the primary e!ect of the rod-like inhomogeneities was to short out the Hall voltage when HEy. In our previous work [9] on Hg Cd Te, we have 1~x x shown that a vdP disk with a concentric embedded conducting inhomogeneity such as that depicted in Fig. 1B is mathematically convenient for testing GMR enhancement e!ects. In that work the distribution of arbitrarily shaped microscopic inclusions was modeled as a collection of randomly oriented cylindrical inhomogeneities, each concentrically embedded in a vdP disk of the con"guration shown in Fig. 1B. For practical purposes, it is obviously more desirable to control the shape, size and distribution of the in-

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homogeneity by lithographic patterning of a homogeneous semiconductor rather than to rely on nature to provide a distribution of inhomogeneities. Accordingly, here, we have prepared a series of four InSb : Te vdP disks of radius r "1 mm with concentric cylindrical " macroscopic conducting inhomogeneities of radius r " ! 0, r /8, r /4, and r /2, respectively, thereby eliminating " " " the size and shape approximations associated with the modeling of GMR enhancement in Hg Cd Te. The 1~x x geometry of the inhomogeneity is characterized by the parameter a"r /r . ! " In the vdP disk con"guration with a concentric inhomogeneity, the e!ective magnetoresistance depends on the parameter a and is given by *o(H, a)/o (a)" 0 *R(H, a)/R (a) where R(H, a)"<(H, a)/I (see Fig. 1B), 0 0 R (a)"R(0, a) and I is a constant applied current. The 0 0 use of the 4-probe vdP con"guration eliminates any complications associated with contact resistances [6]. In support of this assertion, we note that R(0, a) decreases monotonically with increasing a as expected. The dependence of the GMR of InSb on the magnetic "eld and on the size of the inhomogeneity is shown in Fig. 2 for "elds up to 1 T. Below the crossover "eld H " # 0.34 ¹, the GMR is quadratic with "eld as expected [6] (see also below). Above H , the GMR has a weaker # "eld dependence due to the saturation of the enhancement and the contribution of holes to the conduction process [9]. For the vdP geometry with a concentric highly conducting inhomogeneity (p
(4)

Fig. 2. Magnetoresistance of an InSb : Te van der Pauw disk patterned with an inhomogeneity (see Fig. 1B) as a function of the diameter of the concentric conducting inhomogeneity characterized by the radius ratio a"r /r . The legend shows a and ! ! the corresponding enhancement, G(a).

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S.A. Solin et al. / Physica B 279 (2000) 37}40

Then in the low-"eld quadratic MR region with curvature c(a), o(H, a)"o (a)[1#c(a)H2] (5) 0 and G(a)"[c(a)]/[c(0)]. Note the dramatic increase in the GMR enhancement with the increase in a as evidenced in the legend of Fig. 2. One can envision applying the concepts developed above to improve the sensitivity of a variety of magnetic sensors. For example, semiconductor Corbino structures have been suggested as read-head sensors in high-density recording applications because of their high GMR and a number of other desirable properties [18]. Even for the proof of principle vdP studies discussed here, patterned InSb exhibits an enhanced GMR of &7% at ¹"300 K with k "29,100 cm2/V s and the relevant "eld of 500 G. % Signi"cantly higher GMR values should be achievable in narrow-gap semiconductor structures using improved side-wall design and higher mobility materials. Acknowledgements We thank J.A. Giordmaine for stimulating our interest in this work and N.S. Wingreen for useful discussions. We also thank the Sarno! Corporation for the contract MBE growth and device fabrication of the InSb samples. References [1] J.A. Brug, T.C. Anthony, J.H. Nickel, MRS Bull. 21 (1996) 23.

[2] G.A. Prinz, Phys. Today 48 (1995) 58. [3] H.H. Wieder, Hall Generators and Magnetoresistors, Pion Ltd., London, 1971. [4] P.M. Levy, Science 256 (1992) 972. [5] P.M. Levy, Solid State Phys. 47 (1994) 367. [6] R.S. Popovi, Hall E!ect Devices, Adam Hilger, Bristol 1991. [7] H. Weider, Laboratory Notes on Electrical and Galvanomagnetic Measurements, Elsevier, New York, 1979. [8] E.O. Kane, in: R.K. Willardson, A.C. Beer (Eds.), Semimetals and semiconductors, Vol. 1, Academic Press, New York, 1966, p. 75. [9] Tineke Thio, S.A. Solin, Appl. Phys. Lett. 72 (1998) 3497. [10] O. Madelung (Ed.), Semiconductors * Group IV Elements and III}V Compounds, Springer, New York, 1991, p. 143. [11] George E. Anner, Planar Processing Primer, Van Nostrand, New York, 1990. [12] C.J. Mogab, in: S.M. Sze, VLSI Technology, (Ed.), McGraw-Hill, New York, 1983. [13] S.A. Solin, T. Thio, D.R. Hines, Jean Heremans, to be published. [14] C.M. Wolfe, G.E. Stillman, J.A. Rossi, J. Electrochem. Soc.: Solid-State Sci. Technol. 119 (1972) 250. [15] R.S. Allgaier, Semicond. Sci. Technol. 3 (1988) 306. [16] W. Zawadzki, Adv. Phys. 23 (1974) 435. [17] H. Weiss, M. Wilhelm, Z. Phy. 176 (1963) 399. [18] S.A. Solin, Tineke Thio, J.W. Bennett, D.R. Hines, M. Kawano, N. Oda, M. Sano, Appl. Phys. Lett. 69 (1996) 4105.