Quantitative analysis of surface donors in ZnO

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Surface Science 601 (2007) 5315–5319 www.elsevier.com/locate/susc

Quantitative analysis of surface donors in ZnO D.C. Look Semiconductor Research Center, Wright State University, Dayton, OH 45435, United States Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, United States Received 25 July 2007; accepted for publication 18 September 2007 Available online 26 September 2007

Abstract At low temperatures, typically up to 30 K or even higher, the electrical properties of bulk ZnO samples are nearly always dominated by a conductive near-surface region. Here we show that a single, low-temperature Hall-effect measurement, say at 20 K, and a reasonable assumption regarding the upper limit of the surface compensation ratio, yields a value of surface donor concentration ND,surf accurate to within about a factor two. Examples are given for bulk materials grown by the vapor-phase, melt, and hydrothermal processes.  2007 Elsevier B.V. All rights reserved. Keywords: Zinc oxide; Hall-effect; Temperature dependence; Surface conductivity; Donors; Acceptors

1. Introduction In recent years, ZnO has gained significant attention because of several important photonic and electronic applications [1–3], such as UV light-emitting diodes [4], UV laser diodes [5], and transparent transistors [6]. One strong advantage of ZnO over that of some of its rivals is the availability of bulk crystals, with 3 in. wafers now in commercial production [7]. However, such wafers nearly always contain a strongly conductive region near the surface [8,9], not fully understood but often thought to be associated with H accumulation since annealing in ambients containing H can greatly increase the surface conduction [10]. Not only bulk materials, but even thin films experience this phenomenon. It is important to thoroughly characterize the surface layer because it can affect the formation of Ohmic and Schottky contacts, and can even contribute to the room-temperature electrical properties, especially in thin films. Recently we have shown that the sheet surface carrier concentration nsurf,sheet and mobility lsurf can be measured by the Hall-effect at temperatures low enough that the bulk electrons are frozen out onto their parent donors [9]. Unfortunately, it is E-mail address: [email protected] 0039-6028/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2007.09.030

much more difficult to determine the volume carrier concentration nsurf because the effective surface-layer thickness dsurf is not known. In this work, we present a method for obtaining information on dsurf, and more importantly on the surface donor concentration, ND,surf. Specifically, we find that a Hall measurement at a single temperature will yield the minimum value of dsurf, and a reasonable value of ND,surf, accurate to within about a factor two. The process is illustrated on commercially available bulk ZnO samples grown by three different methods. 2. Hall-effect measurements The samples were 5-mm · 5-mm · 0.05-mm squares cut from 10-mm · 10-mm c-plane plates supplied by the respective manufacturers. Ohmic contacts were formed by soldering small indium dots on the four corners, and temperature-dependent Hall-effect measurements were performed in a LakeShore 7507 Hall-effect apparatus, using the van der Pauw technique. The measured carrier concentration nmeas and Hall mobility lH,meas of four different samples are presented in Figs. 1 and 2, respectively. The sample designated ‘‘VP’’ was grown by the vapor-phase method at ZN Technology [11]; ‘‘MLT’’, melt method, at

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16

10

nmeas (cm-3)

nmeas  nbulk at high temperatures. (Note that the relationship dsurf  dbulk is not necessarily true for thin films.) However, for the near-surface electrons, which dominate at low temperatures, we would have to calculate the true volume concentration nsurf from the relationship nsurf = nmeas Æ dbulk/dsurf, and we do not know a priori the value of dsurf.

MLT

17

10

VP

15

HYD#2

10

14

3. Theoretical analysis

13

The solid lines in Figs. 1 and 2 are theoretical fits obtained from a two-layer model [9,15]

10

10

HYD#1 0

10

20 30 103/T (K-1)

40

50

lH;meas ¼

Fig. 1. Experimental (symbols) and theoretical (lines) plots of the measured carrier concentrations in as-grown, bulk ZnO samples. ‘‘MLT’’ denotes melt-grown sample Cermet C7d; ‘‘VP’’, vapor-phasegrown sample ZN Technology 02B#5; ‘‘HYD#1’’, hydrothermally-grown sample Tokyo Denpa 3212-8d; and ‘‘HYD#2’’, hydrothermally-grown sample MTI 11a.

2000 VP

μmeas (cm2/V s)

1500

1000

MLT

HYD#1

500

HYD#2 0 0

100

200

300

T (K) Fig. 2. Experimental (symbols) and theoretical (lines) plots of the measured mobilities in as-grown, bulk ZnO samples.

Cermet [12]; ‘‘HYD#1’’, hydrothermal method, at Tokyo Denpa [13]; and ‘‘HYD#2’’, hydrothermal method, at MTI [14]. We must point out that the measured carrier concentration nmeas for each curve in Fig. 1 is not necessarily the actual carrier concentration, since the Hall-effect experiment yields only a sheet concentration (cm2), not a volume concentration (cm3). To go from a sheet to a volume concentration, an electrical thickness must be assigned, dbulk for the bulk electrons, and dsurf for the surface electrons, where dbulk + dsurf = d, the total sample thickness. However, for the sake of convenience, we have used the total thickness d for each curve in Fig. 1; i.e., we are not distinguishing between bulk and surface electrons in Fig. 1. For the bulk electrons, which are dominant at high temperatures, the relevant thickness is approximately the whole sample thickness; i.e., dbulk  d, since dsurf  dbulk for our samples; thus,

nbulk d bulk l2H;bulk þ nsurf d surf l2H;surf nbulk d bulk lH;bulk þ nsurf d surf lH;surf

ð1Þ 2

nmeas ¼

1 ðnbulk d bulk lH;bulk þ nsurf d surf lH;surf Þ d nbulk d bulk l2H;bulk þ nsurf d surf l2H;surf

ð2Þ

where lH,bulk and lH,surf are the Hall mobilities in the bulk and surface regions, respectively. In glancing at Fig. 1, we see that nmeas for all four samples, and indeed for nearly all ZnO samples that we have examined, can be split into three regions: (I) a strongly temperature-dependent region above, say, 100 K; (II) a ‘‘mixed’’ region, often resulting in an apparent minimum in n; and (III) a degenerate (temperature-independent) region below about 30 K for MLT and VP, and 50 K for HYD#1 and HYD#2. Region I represents bulk electrons, i.e., nmeas = nbulk; region III, surface electrons, i.e., nmeas = nsurf Æ dsurf/dbulk; and region II, a mixture of bulk and surface electrons described by Eq. (1). Note that minima in nmeas are commonly observed when dealing with two electron populations with different mobilities. In our calculation, the expression for nbulk(T) in Eqs. (1) and (2) is derived from the classical, nondegenerate solution of the charge-balance equation, which is discussed in many different sources. For a single, dominant donor ND,bulk, nbulk(T) can be written in a closed-form solution; for two or more donors, a transcendental equation in nbulk(T) must be solved [15]. Similarly, the expression for lH,bulk(T) can be determined with sufficient accuracy by solving the Boltzmann transport equation in the relaxation-time approximation [15]. For the present samples we have included not only the usual phonon and ionized-impurity scattering terms, but also an ‘‘impenetrable-barrier’’ term that improves the fit near room temperature. However, the bulk properties, represented by nbulk and lH,bulk, are not the main focus of the present paper; instead, we will concentrate on nsurf and lH,surf. To determine an expression for nsurf(T), we note that, below about 30 K, nmeas(T) is constant for all of the samples. Thus, nsurf(T) is also constant, and can be found from nsurf(T) = nmeas(T) Æ dbulk/dsurf. The constancy of nsurf also implies that all surface-region donors and acceptors are ionized so that nsurf(T) = ND,surf  NA,surf, for T < 30 K. Unfortunately, the situation for lH,meas(T) is more complicated, since it is not independent of temperature, even at low temperatures. One simplification, however, is that the

D.C. Look / Surface Science 601 (2007) 5315–5319

phonon scattering terms for T < 30 K are negligible, and only the ionized-impurity/defect scattering term needs to be included. For the present investigation, we employ the nondegenerate Brooks–Herring version of this term, which can be written as [15]

lH;meas ðT Þ ¼

1

e3 m2 ½2N A;surf 106 þ

3 3 1 1 312p 128p2 22 e20 k 2 T 2 512 nmeas 106 ddbulk fln½1 þ surf

yðd surf Þ ¼

 13 1 8 33 4p3 e0  h2 6 d bulk n 10 meas e2 m d surf

left-hand side of Eq. (5) equal to zero and solve the right-hand side for dsurf,min. Also, if NA,surf = 0, then from Eqs. (5) and (7), ND,surf = nmeas(T) Æ dbulk/dsurf. [A convenient iterative method of solving for dsurf,min and ND,surf(dsurf,min) is as follows: (1) choose any value for dsurf,min,

yðd surf Þ yðd surf Þ  1þyðd g surf Þ

where ð4Þ

Here e0 is the dielectric constant, (8.12)(8.8542 · 1012) F/ m for ZnO; k is Boltzmann’s constant, 1.3805 · 1023 J/K; e is the electronic charge, 1.6022 · 1019 C; m* is the effective mass, (0.3)(9.9091 · 1031) kg for ZnO; and h = 1.0544 · 1034 J s. The factor (312p/512) in the numerator of Eq. (3) converts conductivity mobility to Hall mobility; the factors of 106 in Eqs. (3) and (4) convert concentrations in cm3 to those in m3; and the factor of 104 in Eq. (3) converts m2/V s to cm2/V s. Thus, the physical constants are all entered in MKS units, but the concentrations, in cgs units (cm3). Also, note that we have evaluated y(dsurf) in the degenerate limit, consistent with the temperatureindependence of nsurf. To create some convenient working equations, we evaluate the physical constants for ZnO, and then solve Eq. (3) for NA,surf N A;surf

( ) 3 1 7:647  1017 T 2 d bulk  nmeas ¼ 2 lH;meas ðT Þfln½1 þ yðd surf Þ  yðd surf Þ g d surf 1þyðd surf Þ

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 104

ð3Þ

say dsurf,1; (2) then, calculate ND,surf(dsurf,1) from Eq. (7); (3) next, calculate dtest,2 = nmeas(T)dbulk/ND,surf(dsurf,1), since that condition must hold if NA,surf = 0; (4) finally, plug dsurf,2 back into Eq. (7) and start over. The iteration dsurf,1, . . .. , n quickly converges, giving dsurf,n = dsurf.min and ND,surf(dsurf,n) = ND,surf(dsurf,min).] We will illustrate this procedure by considering the lowest-temperature point for the melt-grown sample MLT in Figs. 1 and 2: T = 20.5 K, lH,meas = 173 cm2/V s, and nmeas = 7.31 · 13 3 10 cm . (Remember that nmeas is normalized to the bulk thickness, dbulk  d = 0.05 cm.) From Eq. (5) we find that NA,surf = 0 when dsurf = dsurf,min = 28.5 nm, and then, from Eq. (7), ND,surf(dsurf,min) = nmeas(T) Æ dbulk/dsurf,min = 1.28 · 1018 cm3. Next, we plot ND,surf and NA,surf for all possible values of dsurf, as shown in Fig. 3. Of course, no values of dsurf < 28.5 nm (in this case) are allowed, because NA,surf < 0 for dsurf < dsurf,min. Here it is seen that ND,surf varies rather slowly beyond dsurf,min, going through a minimum value of 1.16 · 1018 cm3 at dsurf = 54 nm, and then increasing almost linearly beyond this point. A reasonable maximum value of ND,surf might be the point at which the surface compensation ratio K = NA,surf/ND,surf reaches a value of, say, 0.9, because we would not expect a surface compensation

ð5Þ

20

 1 d bulk 3 yðd surf Þ ¼ 1:392  10 nmeas d surf 6

ð6Þ

Here NA,surf and nmeas are in units of cm3 and lH,meas is in units of cm2/V s. Note that the only two unknowns in Eq. (5) are NA,surf and dsurf. We can obtain ND,surf from the relationship discussed above, namely, nmeas(T) Æ dbulk/ dsurf = nsurf(T) = ND,surf  NA,surf, giving N D;surf 8 1< ¼ 2 :l

17

3 2

9 =

7:647  10 T d n o þ nmeas bulk yðd surf Þ d surf ; H;meas ðT Þ ln½1 þ yðd surf Þ  1þyðd surf Þ ð7Þ

Even though we do not, in general, know the value of dsurf, we can quickly establish a lower limit dsurf,min from the obvious requirement NA,surf P 0. Thus, we set the

Concentration (cm-3)

where ND,surf

10

NA,surf

0 0

100

200

300

dsurf (nm) Fig. 3. Theoretical surface donor concentration ND,surf and acceptor concentration NA,surf of the melt-grown sample as a function of dsurf, the (unknown) electrical thickness of the surface layer. At the minimum possible value of dsurf, 28.5 nm, ND,surf = 1.28 · 1018 cm3. At a maximum likely value of dsurf, 225 nm, the point at which the compensation ratio NA,surf/ND,surf = 0.9, ND,surf = 1.62 · 1018 cm3.

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Table 1 Measured parameters nmeas and lmeas, and calculated parameters dsurf,min and ND,surf Sample MLT VP HYD#1 HYD#2

T (K) 20.5 20.2 20.0 19.4

nmeas (norm. to dbulk) (cm3) 13

7.31 · 10 6.52 · 1013 3.97 · 1013 3.09 · 1013

nmeas,sheet (cm2) 12

3.65 · 10 3.26 · 1012 2.10 · 1012 1.48 · 1012

ratio higher than 0.9. This value of K occurs at dsurf = 225 nm, and here ND,surf = 1.62 · 1018 and NA,surf = 1.46 · 1018 cm3. Thus, without any additional measurements, and only the reasonable assumption that K 6 0.9, we have determined a range of 1.16–1.62 · 1018 cm3 for ND,surf, with concomitant values for NA,surf, 0–1.46 · 1018 cm3. The precision of ND,surf, (1.4 ± 0.3) · 1018 cm3, is rather impressive, considering the simplicity of the measurement. Unfortunately, such precision cannot be obtained for NA,surf without a knowledge of dsurf. 4. Discussion A summary of the results for all of the samples is presented in Table 1. Here, in each case, we have evaluated dsurf,min and ND,surf(dsurf,min) at the lowest measurement temperature, about 20 K. However, if our model is correct, the same analysis should be applicable at somewhat higher temperatures, i.e., as long as nmeas remains constant. The relevant temperature range is about 20–30 K for MLT and VP, and 20–50 K for HYD#1 and HYD#2. By evaluating all of the experimental points in these respective temperature ranges, we find that ND,surf has an uncertainty of about 13% for MLT and VP, 10% for HYD#1, and 22% for HYD#2. Thus, it is reasonable to claim that the model itself is valid to about 20%. It is interesting that the total sheet carrier concentration at 20 K, nmeas,sheet, differs by less than a factor of three among the samples, but the values of dsurf,min and ND,surf differ by much larger factors. This fact may suggest that the ZnO surface tends to incorporate a relatively fixed number of donors, but that various other factors control their diffusion below the surface and thus determine dsurf and ND,surf. A possible component of the surface donors is H, because the donor concentration is increased by an anneal in forming gas (5% H2 in N2), but not in N2 alone (unless the sample already contains bulk H which can diffuse to the surface) [10]. Corroboration of these results by independent measurements is not easy because there are few other surface-sensitive techniques that can accurately determine concentrations at the 1017–1018-cm3 level. For example, secondary-ion mass spectroscopy (SIMS) is sensitive enough to measure H at these levels, but the H background in most SIMS instruments is too high to get sufficient accuracy. However, one promising technique for carrier-concentration determination is electrochemical C–V (ECV), which involves a liquid Schottky barrier and thus is easy

lmeas (cm2/V s)

dsurf,min (nm)

ND,surf (cm3)

173 656 7.0 16.2

28 53 1.5 2.1

1.3 · 1018 4.9 · 1017 1.4 · 1019 7.0 · 1018

to apply [16]. We have carried out preliminary ECV experiments on a melt-grown sample, similar to the one presented here, and find a flat nECV profile at depths greater than 50 nm from the surface, and increasing nECV at shallower depths. In comparison with our Hall-effect measurements, the flat-nECV profile could correspond to the bulk region, and the increasing-nECV profile, the surface region. However, quantitative agreement is difficult to establish, for at least two reasons: (1) in the flat region we find that nECV  2 Æ nbulk, which could be due to an additional, deeper donor (not generating free carriers at room temperature and thus not seen by the Hall-effect), or to an inaccurate determination of the effective Schottky-diode area in the ECV experiment; and (2) in the increasing-nECV (forward-bias) region, the Schottky diode experiences high current leakage, which distorts the nECV values. Further work is continuing on these issues. 5. Summary In summary, we have developed a quantitative method of determining the near-surface donor concentration in ZnO. A single Hall-effect measurement at a temperature of 20 K, or up to 50 K for some samples, allows this concentration to be determined to within about a factor two. Much better accuracy would be available if the effective electrical thickness of the surface region could be measured, perhaps by the capacitance–voltage technique. Although the identity of the surface donors is unknown, the results of forming-gas annealing experiments suggest that H might be involved. Acknowledgements We wish to thank T.A. Cooper for the Hall-effect measurements, and M. Morales for the ECV measurements. We also wish to thank M. Morales, G.C. Farlow, B. Claflin, and Z.-Q. Fang for helpful discussions. Support was provided by NSF Grant DMR0513968 (L. Hess), ARO Grant DAAD19-02-D-0001 (M. Gerhold), SVTA Subcontract W911NF-06-C-0015 (A. Osinsky), AFOSR Grant FA9550-07-1-0013 (K. Reinhardt), and AFRL Contract FA8650-06-D-5401 (D. Silversmith). References [1] D.C. Look, Mater. Sci. Eng. B 80 (2001) 383. [2] S.J. Pearton, D.P. Norton, K. Ip, Y.W. Heo, T. Steiner, Prog. Mater. Sci. 50 (2005) 293.

D.C. Look / Surface Science 601 (2007) 5315–5319 [3] U. Ozgur, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, V. Avrutin, S.J. Cho, H. Morkoc, J. Appl. Phys. 98 (2005) 041301. [4] Y.R. Ryu, T.S. Lee, J.A. Lubguban, H.W. White, B.J. Kim, Y.S. Park, C.J. Youn, Appl. Phys. Lett. 88 (2006) 241108. [5] E.S.P. Leong, S.F. Yu, S.P. Lau, Appl. Phys. Lett. 89 (2006) 221109. [6] P. Barquinha, E. Fortunato, A. Goncalves, A. Pimentel, A. Marques, L. Pereira, R. Martins, Adv. Mater. Forum 514–516 (Pts 1 and 2) (2006) 68 (Trans. Tech. Publications Ltd., Zurich-Uetikon). [7] K. Maeda, M. Sato, I. Niikura, T. Fukuda, Semicond. Sci. Technol. 20 (2005) S49. [8] O. Schmidt, P. Kiesel, C.G. Van de Walle, N.M. Johnson, J. Nause, G.H. Do¨hler, Jpn. J. Appl. Phys. Part 1 44 (2005) 7271.

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[9] D.C. Look, H.L. Mosbacker, Y.M. Strzhemechny, L.J. Brillson, Superlattice Microstruct. 38 (2005) 406. [10] D.C. Look, Superlattice Microstruct. 42 (2007) 284. [11] ZN Technology, Inc., 910 Columbia Street, Brea, CA 92821. [12] Cermet, Inc., 1019 Collier RD, Suite C-1, Atlanta, GA 30318. [13] Tokyo Denpa Co., Ltd., 5–6–11 Chuo, Ohta-ku, Tokyo 143-0024, Japan. [14] MTI Corp., 5327 Jacuzzi St., Bldg. 3H, Richmond, CA 94804. [15] D.C. Look, Electrical Characterization of GaAs Materials and Devices, Wiley, New York, 1989 (Chapter 1). [16] C.E. Stutz, J. Electron. Mater. 30 (2001) L40.