Polymer Light-Emitting Diode Interlayers' Formation Studied by

Dec 9, 2009 - This work describes the use of current-sensing atomic force microscopy and dynamic scaling laws to characterize the surface morphologies...
0 downloads 0 Views 3MB Size
572

J. Phys. Chem. C 2010, 114, 572–579

Polymer Light-Emitting Diode Interlayers’ Formation Studied by Current-Sensing Atomic Force Microscopy and Scaling Laws Quirina Ferreira,*,† Gabriel Bernardo,† Ana Charas,† Luı´s Alca´cer,†,‡ and Jorge Morgado†,‡ Instituto de Telecomunicac¸o˜es, Instituto Superior Te´cnico, AV. RoVisco Pais, P-1049-001 Lisboa, Portugal, and Departamento de Engenharia Quı´mica e Biolo´gica, Instituto Superior Te´cnico, AV. RoVisco Pais, P-1049-001 Lisboa, Portugal ReceiVed: September 7, 2009; ReVised Manuscript ReceiVed: NoVember 13, 2009

This work describes the use of current-sensing atomic force microscopy and dynamic scaling laws to characterize the surface morphologies of polymer light-emitting diode interlayers formed by poly(9,9dioctylfluorene), PFO, on top of poly(3,4-ethylene dioxythiophene) doped with poly(styrene sulfonic acid), PEDOT:PSS. Two types of PFO differing in molecular weight are compared. Surface current maps and calculated energy gaps of PEDOT:PSS evidence surface segregation of the two components of the blend, being PEDOT preferentially located in the surface valleys. Upon formation of PFO interlayers, an overall current decrease occurs, with this decrease being more pronounced for the interlayer based on PFO with higher molecular weight. It is observed that, under the preparation conditions used, neither of the two PFO samples leads to full coverage of the surface. The submonolayer nature of these interlayers has allowed us to establish that PFO chains are preferentially deposited in the valleys of the PEDOT:PSS surface; that is, they are anchored at doped PEDOT domains. The mechanism involved in the PFO deposition was studied using power spectral density analysis with scaling laws. This study provided quantitative information on the surface growth for each interlayer. 1. Introduction Innovation in materials and new device architectures is at the origin of the very impressive development of polymer-based light-emitting diodes (LEDs) and displays. In particular, the use of multilayer structures to assist charge injection or impose charge blocking has led to significant improvements of efficiency, maximum luminance, and lifetime. One of the latest approaches is the use of very thin insoluble interlayers,1-6 formed upon annealing of conjugated luminescent polymers on the surface of poly(3,4-ethylene dioxythiophene) doped with poly(styrene sulfonic acid), PEDOT:PSS. This was shown to improve lifetime and efficiency, if the right choice of the interlayer material is made. The beneficial effects have been attributed to improved hole injection, introduction of an electron barrier preventing the electrons to escape through the PEDOT: PSS layer and separation of the recombination zone from PEDOT:PSS which quenches luminescence. Such an interlayer also influences the adhesion of the subsequent active layer, while probably preventing its degradation due to the direct contact with the highly acidic PEDOT:PSS.1,7 The thickness of such an interlayer may vary from less than 1 nm up to about 10 nm. The nature of the interactions between the PEDOT:PSS surface and the conjugated polymer which forms the interlayer is not yet a resolved issue, remaining a matter of debate. In particular it has not yet been established where, at the surface of the PEDOT:PSS blend, the conjugated polymer chains are anchored and how they distribute on the surface, in particular when the * To whom correspondence should be addressed. E-mail: [email protected]; Phone: +351 21 841 84 54. Fax: +351 21 841 84 72. † Instituto de Telecomunicac¸o˜es. ‡ Departamento de Engenharia Quı´mica e Biolo´gica.

interlayers are very thin. In addition, the effect of the thermal annealing promoting the interlayer formation is not clear. We have previously used5,6 cross-linkable polymers to form interlayers with thickness values of approximately 5-7 nm and the performance of the corresponding LEDs could be well explained by consideration of their frontier energy levels. The interlayers formed, under similar conditions, with regular polymers (namely low molecular weight poly(9,9-dioctylfluorene), lmwPFO, and high molecular weight PFO, hmwPFO, and poly[(9,9-dioctylfluorene)-alt-bithiophene)], F8T2, had thickness values below 1 nm, as estimated from optical absorption studies, and the performance of the corresponding LEDs could not be directly correlated with the energy of the frontier levels of the polymers used in the interlayers. Thin film growth results from atomistic processes such as surface nucleation and diffusion,8 grain boundary motion, and deposition flux shadowing.9 During the formation of interfaces, a competition between nucleation and diffusion processes may occur, with the polymeric chains adopting conformations that minimize their free energy on the surface. In this work, a combination of current-sensing atomic force microscopy (CS-AFM) and dynamic scaling analysis10 was applied to characterize interlayers formed with lmwPFO (Mn ) 9850, Mw ) 17 450) and hmwPFO (Mn ) 187 000; Mw ) 331 000)6 on PEDOT:PSS. With CS-AFM it is possible to obtain surface current maps and correlate them with topographic images that are obtained at the same time. This technique enables the measurements with nanoresolution of electric properties of interlayers using current-voltage characteristics obtained at selected points of the scan. Within this study we aim at correlating the electrical properties with the mechanisms involved in PFO interlayers formation on PEDOT:PSS, char-

10.1021/jp908632a  2010 American Chemical Society Published on Web 12/09/2009

Diodes Interlayers’ Formation acterizing polymers structure development and establishing correlations between film surface structure and microstructure evolution. A dynamic scaling analysis is used to characterize the various surfaces at the submicrometer level. The surface features can be described using a power spectral density (PSD) function which encompasses fractal geometry and scaling concepts. Such analysis permits the intrinsic mechanisms determining the surface morphology to be understood and can also help to achieve a better control of the film properties. Dynamical scaling analysis was previously used with success in the characterization of layer-by-layer films,11,12 polymeric blends,13 field-effect transistors,14 and biological samples.15 Heeger et al.16 have used power spectral density (PSD) analysis to study the phase separation in poly(3-hexylthiophene)(P3HT):fullerene blends at nanoscale. They correlated device performance with the quasiperiodic structure detected in the PSD function of this bulk heterojunction. In this work the surface morphologies of PLEDs interlayers were evaluated by power spectrum density analysis. PSD functions were fitted using empirical models that describe the superstructures and the fractal contributions for the evolution of surface morphology. We have previously obtained an estimate6 of these PFO interlayers thicknesses as being below 1 nm, based on optical absorption. Being this thin, AFM studies can provide information on the anchoring sites of the conjugated polymer (PFO) at the PEDOT:PSS surface. In fact, AFM shows that none of the two PFO samples leads to full coverage of the PEDOT:PSS surface. The preparation of such a submonolayer is proven to be very important to identify the anchoring points of the PFO chains. To summarize, the main goal of the present study is to obtain a deeper understanding of the interlayers formation and elucidate the interactions between the conjugated polymers and PEDOT: PSS. We aim at identifying different regions of polymers structure development and establish correlations between film surface structure and microstructure evolution. The study based on scaling laws and PSD functions showed the preferential PEDOT segregation in surface valleys, promoting the PFO deposition at these places. These results are supported by surface features models, for which intrinsic roughness, fractal properties and superstructures were obtained. 2. Experimental Section 2.1. Interlayers Preparation. Indium-tin oxide (ITO)coated glass substrates were cleaned with acetone and 2-propanol and treated with oxygen plasma. PEDOT:PSS (or PEDOT) (Baytron P from Bayer) was spun coated on top and annealed on a hot plate at 150 °C for 2 min, in air. Its final thickness was 45-50 nm, as measured with a Dektak profilometer. Thin films (ca. 50 nm thick, as measured with a Dektak profilometer) of low molecular weight PFO, lmwPFO, or high molecular weight PFO, hmwPFO, were then spun coated on top of PEDOT:PSS. These were annealed under vacuum at 100 °C for 10 min and then rinsed several times with the polymer solvent (chloroform for lmwPFO and toluene for hmwPFO) until no changes in the UV-vis absorbance of the films could be detected and no traces of polymer could be detected on the solvent after the rinse by UV/vis absorbance. Finally, the samples were dried under a flow of nitrogen and placed in vacuum for, at least, 12 h. As shown in our previous work5,6 this procedure yields very thin layers (thicknesses 0.1 nm-1). The correlation lengths ξ1 and ξ2 are marked by arrows in the graph.

(2D-PSD) function (eq 1, see the Supporting Information) for each of the three surfaces. N

PSD2D(fx, fy) )

N

∑ ∑ Zmne-2πi∆L(f m+f n)(∆L)2]2

1 [ L2 m)1

x

x

n)1

(1) Figure 9 shows the 2D-PSD spectra for PEDOT:PSS and the two PFO interlayers on PEDOT:PSS obtained from topographic AFM images over 1 × 1 µm2 scanned area. Three distinct regions, marked as regions A, B, and C, are observed for all spectra. For low spatial frequency values (f < 4.5 × 10-3 nm-1) there is a nearly constant value for the roughness, meaning that it does not change with the scale and indicating the absence of any characteristic length beyond ca. 220 nm. For intermediate frequencies, region B, PSD is strongly frequency dependent. This region is further subdivided into two subregions with constant slope (regions BI and BII), indicating a combination of two processes that are involved in the surface growth. The mechanism of surface formation characterized in region BI corresponds to an anomalous dynamic scaling, i.e., roughening and smoothing mechanisms cannot reach an equilibrium and the local surface changes with time. The second subregion (region BII) is attributed to the balance between random fluctuations and diffusion processes, so that the local structure remains unchanged. This region characterizes the surface selfaffine behavior.27 In region C, f > 0.1 nm-1, PSD is strongly influenced by tip artifacts and was not considered for surface analysis. In fact, convolution of the tip and particle may occur due to the 10-20 nm radius of curvature of the AFM tip.

Figure 10. 2D-PSD spectra for PEDOT:PSS and the two PFO interlayers, specifying the characteristic dimensions ξ1 and ξ2. Also shown are the slopes of the two regions, FI and FII.

The transition frequencies, marked by arrows in Figure 9, correspond to correlation lengths that define transitions between physical processes responsible for the surface evolution. The first correlation length, ξ1, is defined by the inverse frequency of transition between the high-frequency and self-affine intermediate-frequency regions (transition between region BI and BII). The second correlation length, ξ2, is defined by the inverse frequency of transition between the low-frequency random roughness plateau and the intermediate-frequency self-affine region (transition between region A and BII).28 In region A, the magnitude of the 2D-PSD is higher for PEDOT:PSS than for both PFO interlayers, having these two similar values. This result is in agreement with the decrease of Rrms upon interlayer formation (see Table 2). Figure 10 shows, in detail, the 2D-PSD spectra for PEDOT:PSS and for the interlayers based on hmwPFO and lmwPFO, evidencing that region B has, indeed, two subregions with constant slope. Table 3 summarizes the correlation lengths (ξ1 and ξ2) identified in Figure 10 for the various surfaces.

578

J. Phys. Chem. C, Vol. 114, No. 1, 2010

Ferreira et al.

TABLE 3: Plateau Height Value (R0), Spatial Frequency (f) at the Change of Slope, and Correlation Lengths (ξ) Obtained from the PSD Curves (Figure 10) R0 (nm4)

fBII (nm -1)

ξ2 (nm)

fBI (nm -1)

TABLE 4: Scaling Exponents for Regions BII and BI Estimated from the Slopes of the PSD Curves PEDOT:PSS lmwPFO hmwPFO

RBI

0.53 0.64 0.64

1.25 0.84 1.99

Superstructure Contribution (PSDsh Model)

ξ1 (nm)

PEDOT:PSS 1.2 × 105 [0.005; 0.006] 184 ( 23 [0.016; 0.029] 60 ( 4 lmwPFO 8.8 × 104 [0.007; 0.0075] 138 ( 7 [0.016; 0.017] 60 ( 4 hmwPFO 8.8 × 104 [0.008; 0.0085] 121 ( 5 [0.014; 0.015] 69 ( 4

RBII

TABLE 5: Parameters of the PSD Curves Resulting from the Fitting of the Experimental Data Represented in Figure 9 a

PEDOT:PSS lmwPFO hmwPFO

σsh (nm)

τsh (nm)

fsh (nm-1)

1.26 ( 0.17 1.15 ( 0.11 1.32 ( 0.12

187 ( 30 141 ( 16 122 ( 13

2.3 × 10-3 ( 2.0 × 10-4 2.2 × 10-3 ( 1.8 × 10-4

b

Intrinsic Contributions (PSDABC or k-Correlation Model)

PEDOT:PSS lmwPFO hmwPFO

σABC (nm)

τABC (nm)

1.77 1.21 1.32

29.18 30.85 29.31

Fractal Contribution (PSDfractal)

The second correlation length (ξ2) decreases upon PFO interlayer formation on PEDOT:PSS. The decrease of ξ2 with PFO deposition could be explained by the presence of PFO agglomerates on the PEDOT:PSS surface, especially in the valleys. Doped PEDOT appears to act as an active site for the anchoring of PFO chains as deduced from the CS-AFM measurements. The hmwPFO interlayer has the lower ξ2, which points to a higher surface PEDOT coverage due to the longer PFO chains. The respective current image, Figure 6a, has fewer current domains due to the hmwPFO presence not only in the valleys but also in some top regions. The first correlation length (ξ1) is similar for all surfaces, suggesting that the main surface modifications are attributed to the interactions between PEDOT and PFO. The slopes (F) of regions BI and BII are related to the scaling exponents (R) according to the relation F ) 2(R + 1).10 These exponents can describe two combinations of processes controlling the surface morphologies during the growth and describe the mechanism responsible for the particles deposition (see the Supporting Information). The obtained R values are shown in Table 4. The values of RBII scaling exponents, RBII ) 0.53 for PEDOT: PSS and RBII ) 0.64 for both PFO interlayers, are consistent with the Villain model.29,30 In this model, deposition of the particles is preferentially driven by the interactions with neighboring particles. Note that Rrms decreases upon formation of the PFO interlayer on PEDOT:PSS (Table 2), again suggesting that the valleys could be associated with reactive sites. The deposition of PFO in these valleys contributes to the decrease of conductivity. The electrical current images (Figure 5) showed that the valleys are more conductive, a fact which we associate to doped PEDOT domains. In region BI, at variance with the observation in region BII, RBI of PFO interlayers depends on the PFO molecular weight. The growth mechanism in region BI is similar for PEDOT: PSS and hmwPFO interlayers, having anomalous dynamic scaling behavior as RBI > 1. In this situation, the roughening fluctuations and the smoothing effects cannot reach a balance, and the local surface slope increases and changes with time. For the lmwPFO interlayer, RBI < 1 in both regions BI and BII suggesting that the molecular weight has a significant influence on the equilibrium of roughening and diffusion mechanisms. Compared with the hmwPFO, the polymeric chains of lmwPFO have higher probability to reach and fill the PEDOT valleys, as they are expected to be more mobile, being their deposition at the surface driven by a minimization of the conformational energy. The lmwPFO could be better accommodated in the valleys, but with less PEDOT coverage because their polymeric

k (nm) PEDOT:PSS lmwPFO hmwPFO

-4

-5

6.55 × 10 ( 9.08 × 10 2.06 × 10-3 ( 2.72 × 10-4 3.33 × 10-4 ( 2.62 × 10-5

ν

Df

1.88 ( 0.06 1.57 ( 0.05 1.97 ( 0.03

2.06 2.21 2.02

a Equations 2-4 were used for the fractal, the intrinsic and the superstructure contributions, respectively. The intrinsic roughness (σABC) and the correlation length (τABC) were obtained from eqs 5 and 6 respectively. The fractal dimension (Df) was obtained using eq 7. The errors of parameters result from the fitting of the equations. b For the PEDOT:PSS, the fsh increases up to 1.4 × 10-3 nm -1, without a well-defined plateau.

chains are shorter. To unravel the mechanism responsible for the interlayers’ morphology and their relation with fractals and superstructure contribution, the experimental PSD functions were fitted to three analytical models: fractal analytical model (PSDfractal), superstructures (PSDsh) and the k-correlation model (PSDABC) given by eqs 2-4 respectively (see the Supporting Information).

PSDfractal(f, K, ν) ) PSDABC )

K ν+1

f

A (1 + B f )

2 2 (C+1)/2

(2) (3)

PSDsh(f;σsh ;τsh ;fsh) ) πσsh2τsh2 exp[-π2τsh2(f - fsh)2]

(4) The fitting parameters for each model are given in Table 5. The PSDsh model was used for low frequencies, in the transition between regions A and BII, to characterize the superstructures on the surface. In view of the limited number of points in region A the fit to the Gaussian function of the PSDsh model is essentially based on one-half of the Gaussian distribution. We conclude that there are superstructures or aggregates and that their dimensions are comparable to ξ2 (see Table 3). Superstructures height (σsh) is similar for all interlayers because the growth mechanism of the surfaces is controlled by diffusion. The PSDABC model was applied to the transition between Regions BI and BII to obtain the intrinsic roughness parameters, σABC and τABC, using eqs 5 and 6, respectively (see the Supporting Information).

Diodes Interlayers’ Formation

J. Phys. Chem. C, Vol. 114, No. 1, 2010 579

σABC2 )

2πA B (C - 1)

(5)

τABC )

(C - 1)2B2 2π2C

(6)

2

The correlation lengths determined by this model (τABC) are similar for the three surfaces but smaller than the values obtained by the frequency inverse mode (ξ1), see Table 3. This difference can be attributed to the difficulty in applying the PSDABC model in this frequency region. Another parameter obtained with this model is the intrinsic roughness (σABC, Table 5). σABC is higher for PEDOT:PSS (1.77) than for both PFO interlayers. This result is in agreement with the Rrms values shown in Table 2. In order to understand all phenomena involved in the formation of these interlayers, it is necessary to analyze also the fractal components and to compare the results with the intrinsic roughness parameters. To determine the fractal components, region BII was fitted with the PSD fractal model given by eq 5. The spectral strength (K) and spectral index (υ) parameters are shown in Table 5. The spectral strength (K) of the interlayers is strongly dependent on the PFO molecular weight, being higher for lmwPFO. This result suggests that lmwPFO has stronger fractal components. The fractal dimensions (Df), obtained by eq 7 (see the Supporting Information), are in agreement with this result, being 2.21 for lmwFO compared with 2.06 for PEDOT and 2.02 for hmwPFO.

Df ) (6 - ν)/2

with

0eνe2

(7)

The fractal dimension takes into account the substrate influence. In this case, the fractal dimension of the PFO interlayers is influenced by the PEDOT surface. The higher value of Df for the lmwPFO indicates that its surface has stronger fractal components than the hmwPFO. This is due to its higher probability of going into the PEDOT valleys, in view of the shorter chain length, as discussed above. 4. Conclusions The PEDOT:PSS surface consists of PSS (or PSS rich) heights and doped PEDOT (or PEDOT rich) valleys, as deduced from the CS-AFM results. The formation of PFO interlayers with submonolayer nature on the surface of PEDOT:PSS has allowed us to establish that the chains of the conjugated polymer are mainly anchored at the doped PEDOT regions (valleys). Charge transfer between PFO and doped PEDOT may be at the origin of the attractive interaction resulting in the formation of the insoluble interlayer. The current measured for the surfaces is strongly dependent on topographic features like fractals and superstructures. We showed that scaling concepts can describe the complexity of the surface morphology and, in this case, can explain the interlayer interactions responsible for the changes on the electrical properties. Acknowledgment. This work was partially supported by FCT-Portugal under the Contract PTDC/FIS/72831/2006. G.B. thanks FCT for a post doctoral grant.

Supporting Information Available: Short introduction about dynamic scaling analysis and models used to characterize surfaces and the power density functions used in this work. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Kim, J.-S.; Friend, R. H.; Grizzi, I.; Burroughes, J. H. Appl. Phys. Lett. 2005, 87, 023506. (2) Choulis, S. A.; Choong, V.-E.; Mathai, M. K.; So, F. Appl. Phys. Lett. 2005, 87, 113503. (3) Yang, X. H.; Jaiser, F.; Stiller, B.; Neher, D.; Galbrecht, F.; Scherf, U. AdV. Funct. Mater. 2006, 16, 2156–2162. (4) Harding, M. J.; Poplavskyy, D.; Choong, V.-E.; Campbell, A. J.; So, F. Org. Electron. 2008, 9, 183–190. (5) Bernardo, G.; Charas, A.; Alca´cer, L.; Morgado, J. Appl. Phys. Lett. 2007, 91, 063509–1. (6) Bernardo, G.; Charas, A.; Alca´cer, L.; Morgado, J. J. Appl. Phys. 2008, 103, 084510. (7) Poplavskyy, D.; Su, W.; So, F. J. Appl. Phys. 2005, 98, 014501–1. (8) Ferreira, Q.; Gomes, P. J.; Maneira, M. J. P.; Ribeiro, P. A.; Raposo, M. Sens. Actuators B 2007, 126, 311–317. (9) Pelliccione, M.; Lu, T.-M. In EVolution of Thin Film Morphology Modelling and Simulations, 1st ed.; Hull, R., Osgood, R. M., Jr., Parisi, J., Warlimont, H., Eds.; Springer Series in Materials Science: Berlin, 2008; p 108, Part I. (10) Baraba´si, A.-L.; Stanley, H. E. in Fractal Concepts in Surface Growth, 1st ed.; Cambridge University Press: Cambridge, U.K., 1995. (11) de Souza, N. C.; Silva, J. R.; Thommazo, R. Di; Raposo, M.; Balogh, D. T.; Giacometti, J. A.; Oliveira, O. N., Jr. J. Phys. Chem. B 2004, 108, 13599–13606. (12) de Souza, N. C.; Silva, J. R.; Pereira-da-Silva, M. A.; Raposo, M.; Faria, R. M.; Giacometti, J. A.; Oliveira, Jr., O. N. J. Nanosci. Nanotechnol. 2004, 4, 548–552. (13) Calo, A.; Stoliar, P.; Bystrenova, E.; Valle, F.; Biscarini, F. J. Phys. Chem. B 2009, 113, 4987–4990. (14) Viville, P.; Lazzaroni, R.; Bre´das, J. L.; Moretti, P.; Samorı`, P.; Biscarini, F. AdV. Mater. 1998, 10, 57–60. (15) Calo, A.; Stoliar, P.; Bystrenova, E.; Valle, F.; Biscarini, F. J. Phys. Chem. B 2009, 113, 4987–4990. (16) Ma, B. W.; Yang, C.; Heeger, A. J. AdV. Mater. 2007, 19, 1387– 1390. (17) Horcas, I.; Ferna´ndez, R.; Go´mez-Rodrigues, J. M.; Colchero, J.; Go´mez-Herrero, J.; Baro, A. M. ReV. Sci. Instrum. 2007, 78, 013705. (18) Han, D.-H.; Kim, J.-W.; Park, S.-M. J. Phys. Chem. B 2006, 110, 14874–14880. (19) Pingree, L. S. C.; MacLeod, B. A.; Ginger, D. S. J. Phys. Chem. C 2008, 112, 7922–7927. (20) Crispin, X.; Jakobsson, F. L. E.; Crispin, A.; Grim, P. C. M.; Andersson, P.; Volodin, A.; van Haesendonck, C.; van der Auweraer, M.; Salaneck, W. R.; Berggren, M. Chem. Mater. 2006, 18, 4354–4360. (21) Nardes, A. M.; Kemerink, M.; Janssen, R. A. J.; Bastiaansen, J. A. M.; Kiggen, N. M. M.; Langeveld, B. M. W.; van Breemen, A. J. J. M.; de Kok, M. M. AdV. Mater. 2007, 19, 1196–1200. (22) Crispin, X.; Marciniak, S.; Osikowicz, W.; Zotti, G.; der Gon, A. W. D. V.; Louwet, F.; Fahlman, M.; Groenendaal, L.; de Schryver, F.; Salaneck, W. R. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 2561– 2583. (23) Ionuscu-Zanetti, C.; Mechler, A.; Carter, S. A.; Lal, R. AdV. Mater. 2004, 16, 385–389. (24) Lang, U.; Muller, E.; Naujoks, N.; Dual, J. AdV. Funct. Mater. 2009, 19, 1215–1220. (25) Elscher, A.; Bruder, F.; Heuer, H.-W.; Jonas, F.; Karbach, A.; Kirchmeyer, S.; Thurm, S.; Wehrmann, R. Synth. Met. 2000, 111, 139– 143. (26) Kirchmeyer, S.; Reuter, K. J. Mater. Chem. 2005, 15, 2077–2088. (27) Lita, A. E.; Sanchez, J. E., Jr. Phys. ReV. B 2000, 61, 7692–7699. (28) Lita, A. E.; Sanchez, J. E., Jr. J. Appl. Phys. 1999, 85, 876–882. (29) Wolf, D. E.; Villain, J. Europhys. Lett. 1990, 13, 389–394. (30) Lai, Z.-W.; Sarma, S. D. Phys. ReV. Lett. 1991, 66, 2348–2351.

JP908632A