13 March 2013 Model for thickness dependence of mobility and concentration in highly conductive zinc oxide
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The dependences of the 294 and 10 K mobility μ and volume carrier concentration n on thickness (d=25 to 147 nm) are examined in aluminum-doped zinc oxide (AZO). Two AZO layers are grown at each thickness, one with and one without a 20-nm-thick ZnON buffer layer. Plots of the 10 K sheet concentration ns versus d for buffered (B) and unbuffered (UB) samples give straight lines of similar slope, n=8.36×1020 and 8.32×1020  cm−3, but different x-axis intercepts, δd=−4 and +13  nm, respectively. Plots of ns versus d at 294 K produce substantially the same results. Plots of μ versus d can be well fitted with the equation μ(d)=μ()/[1+d*/(dδd)], where d* is the thickness for which μ() is reduced by a factor 2. For the B and UB samples, d*=7 and 23 nm, respectively, showing the efficacy of the ZnON buffer. Finally, from n and μ() we can use degenerate electron scattering theory to calculate bulk donor and acceptor concentrations of 1.23×1021  cm−3 and 1.95×1020 cm−3, respectively, and Drude theory to predict a plasmonic resonance at 1.34 μm. The latter is confirmed by reflectance measurements



Transparent conductive electrodes, typically formed from transparent conductive oxides (TCOs), are an important component of liquid crystal displays, solar cells, and light-emitting diodes.12.3.4 The current leading TCO material is indium tin oxide (ITO), but its high cost has prompted a search for replacements, and a strong candidate is zinc oxide (ZnO) highly doped with Al, Ga, or In. ZnO has also recently been proposed as a plasmonic material in the near-infrared (IR) region, a range not accessible to noble-metal-based plasmonics. The attractiveness of ZnO in these applications is partially due to the demonstrations of high-quality growth on many different substrates using many different growth techniques. However, a troubling problem is that films on lattice-mismatched substrates nearly always exhibit a thickness dependence of the electrical parameters, resistivity ρ, mobility μ, and carrier concentration n.1112. The origin of this problem seems to be connected with poor crystallinity near the substrate/layer interface. Recently, however, Itagaki et al.16,18,19 have demonstrated significant improvement in the crystallinity of radio frequency (RF)-sputtered ZnO by inserting a thin ZnON buffer layer between the substrate and ZnO layer. For example, in undoped ZnO grown on c-plane aluminum oxide (Al2O3), the rocking-curve full width half maximum of the (002) diffraction drops from 0.490 to 0.061 deg, and in Al-doped ZnO (AZO) grown on quartz-glass substrates, the thickness dependences of ρ, μ, and n greatly decrease. In the present work, we attempt to quantify these effects and understand their causes by carrying out detailed Hall effect and reflectance measurements and analysis. Among other things, we show that the measured thickness dependence of n is artificial and results from the electrical thickness del being different than the metallurgical thickness d (i.e., del=dδd). As it turns out, the true value of n is independent of both thickness and the presence or absence of the buffer, as confirmed by reflectance measurements in the plasmonic region. On the other hand, the measured thickness dependence of mobility (and thus resistivity) is not artificial and results from the presence of interface scattering, which has a stronger effect on electrons in thinner samples. Finally, as a general result of this study, we introduce a new figure of merit d* to describe interface quality. This quantity is defined by μ(d*δd)=μ()/2, where d* and μ() are fitting parameters in the formula μ(d)=μ()/[1+d*/(dδd)]. Essentially, for d<d*+δd, interface scattering dominates all other scattering mechanisms; thus, a good interface has a low value of d*. We find that d*=23nm for the unbuffered (UB) samples, and only 7 nm for the buffered (B) samples. Also, from the values of n and μ(), we can use degenerate electron scattering theory to determine donor and acceptor concentrations.



AZO layers of thickness 25 to 147 nm were deposited by RF magnetron sputtering on quartz-glass substrates. For each thickness, one AZO layer was grown on a bare substrate, and another on a substrate with a 20-nm-thick ZnON buffer layer, deposited by RF magnetron sputtering at 300°C in 4/20.5[sccm]N2/Ar ambient, producing a total pressure of 0.35 Pa. The targets for the buffers were 99.99%-pure ZnO, and the applied RF power was 100 W. The AZO films themselves were grown at 200°C in pure Ar ambient using ZnO targets with 2wt%Al2O3. Although the buffer layers in this case were 20-nm thick, results have been shown to be substantially the same with thicknesses from 5 to 100 nm. Electrically, they are semi-insulating and have minimal direct effect on the conductivity of the AZO layer on top. The purpose of the N in the buffer layer is to inhibit the strong nucleation tendency of ZnO, which leads to small grain sizes. Indeed, x-ray diffraction ω2θ scans indicate an increase in grain size from 38 to 68 nm due to the buffer. Further details on growth and structural analysis can be found in Refs. 16, 18, and 19.

Hall-effect measurements were carried out in a LakeShore 7507 apparatus. The magnetic field strength was 1 T and the temperature range, 6 to 320 K. The samples were of size 1×1cm, and ohmic indium dots were placed at the four corners. Spectroscopic reflectance measurements were performed in a Perkin-Elmer Lambda 900UV/Vis spectrometer at 294 K and over a wavelength range 190 to 3200 nm (6.52 to 0.39 eV).


Mobility Model

We have previously developed a general mobility model for degenerate electrons in semiconductor materials.20 For purposes of the present paper, that model can be summarized as:


where μbulk includes contributions from all bulk scattering mechanisms, such as lattice vibrations and ionized impurities, and


where C is a constant of order unity. Here del is the electrical thickness, i.e., del=dδd, where d is the metallurgical thickness and δd is the thickness of a depletion layer, if any. As an example, C=2.5 and δd17nm in some Ga-doped ZnO samples grown by pulsed laser deposition in another laboratory.14,20 One hypothesis in this simple mobility model is that the donor ND and acceptor NA concentrations (and thus n=NDNA) do not vary with depth. Indeed, it should be pointed out that there are many instances in which this hypothesis may be violated. For example, in an ion-implanted sample, the concentration of ions, and thus the resulting μ and n, will usually vary with depth. However, for our samples we will explicitly show that n is not a function of depth so that all of the depth dependence of μ is contained in the del term in Eq. (2). Then Eq. (1) can be written as:


Noting that μbulk=μ(), we can finally write Eq. (3) as


Here the formal definition of d* as a function of n, μ(), and C can be found from Eqs. (2) and (3), but for our purposes it simply replaces C as a fitting parameter in a μ(d) versus d plot. The only other fitting parameter is μ(), since δd is found from the intercept of a sheet concentration ns versus d plot (Fig. 1). The motivation in fitting μ(d) to Eq. (4), rather than Eq. (1), is that d* has practical significance as the thickness at which the maximum possible mobility, μ(), has dropped by half; i.e., μ(d*δd)=μ()/2. In this regard, the value of d* can be used as a figure of merit for the effects of interfaces on mobility.

Fig. 1

The sheet carrier concentration ns at 10 K versus thickness d for unbuffered and buffered samples. In each case, the slope is the volume carrier concentration n and the y-axis intercept is the excess electronic charge. The buffered sample has an additional electronic charge of 3.14×1014cm2, while the unbuffered sample has a deficit of 1.07×1015cm2.



Experimental Results and Analysis

In our study, the measured values of ρ, μ, and n vary as a function of metallurgical thickness d, consistent with the results of many other studies.1112. However, it must be remembered that ρ and n (but not μ) require knowledge of the electrical thickness del, which may not be the same as d. That is, the Hall effect does not directly measure a volume concentration n(cm3), but a sheet concentration ns(cm2). If n is uniform, then these two quantities are simply related by n=ns/del, where del=dδd is the electrical thickness, the region that contains free electrons. (If n is not uniform, then ns is an averaged quantity,21 not of importance here.) If δdd, then deld, as is usually assumed; however, in very thin samples there may be depleted regions that cover a significant fraction of the total thickness, so that deld. To test this possibility, we plot ns versus d, shown in Fig. 1. Both B and UB samples display straight lines of slope n=8.36×1020cm3, showing immediately that the bulk n is not a function of depth or of the quality of the interface, at least for d>25nm. (In our calculations, we will ignore the slight difference in the slopes of the two lines.) But the intercepts of the B and UB lines differ significantly. The UB samples have a y-axis intercept of δns=1.07×1015cm2, and an x-axis intercept of δd=+13nm. Thus, the electrical thickness is del=d13nm, so that n(d)=ns(d)/(d13), not ns(d)/d. Similarly, the resistivity is now given by ρ(d)=ρs(d)·(d13), not ρs(d)·d. These renormalized ρ, μ, and n points for the UB samples are plotted in Fig. 2, and it is seen that indeed, most of the n points fall very close to the straight dashed line n=8.36×1020cm3; thus, when properly normalized, n is independent of thickness. Note also that n(10K)n(294K), showing that the electrons are truly degenerate.

Fig. 2

The resistivity ρ, mobility μ, and carrier concentration n as a function of metallurgical thickness d for the unbuffered sample. Here n and ρ are normalized to the electrical thickness del=d13nm; i.e., n=ns/(d13), and ρ=ρs×(d13).


We now examine ns versus d for the B samples, also plotted in Fig. 1, and see that this line has the same slope as that of the UB samples, but not the same intercepts. Indeed, the B samples have δns=+3.14×1014cm2, and δd=4nm. Thus del=d-δd=d+4. This result can perhaps be understood as a slight diffusion of Al into the ZnON buffer that thereby increases the effective electrical thickness of the AZO layer. However, we should be cautious about any final explanations in this case because δd is small enough that a slight change in slope would make a large percentage change in δd. The renormalized ρ, μ, and n versus d results for the B samples are plotted in Fig. 3, and it is again seen that n=ns/(d+4) is constant with thickness and moreover has the same magnitude as that of the UB samples. We also see that μ has a much smaller thickness dependence, showing that the buffer is very effective in this regard.

Fig. 3

The resistivity ρ, mobility μ, and carrier concentration n as a function of metallurgical thickness d for the buffered sample. Here n and ρ are normalized to the electrical thickness del=d+4nm; i.e., n=ns/(d+4), and ρ=ρs×(d+4).


From the data and analysis so far, we can draw three conclusions: (1) the volume concentration n does not depend on metallurgical thickness d for either B or UB samples; (2) moreover, n does not depend on the presence or absence of the buffer; and (3) the mobility μ does depend on d, and it does depend on the buffer. If we had no other knowledge, the simplest explanation for (3) would be that ND and NA are varying with d because it is well known that μ is a strong function of these quantities in heavily doped materials. But this possibility is unlikely because ND and NA would then have to track each other exactly in order to maintain a constant n=ND-NA. A more likely explanation is that interface scattering is occurring and that electrons in thinner samples will scatter more from the interface because they are closer to it on the average. This latter explanation is strongly supported by the fact that Eq. (4) gives a good fit to the data.

The μ versus d data for the B and UB samples at 10 and 294 K are plotted in Figs. 4 and 5, respectively, and fitted to Eq. (4), μ(d)=μ()/[1+d*/(d-δd)], where δd=4 and +13nm for the B and UB samples, respectively. For both B and UB samples, μ()=27.6±0.3cm2/V-s at 10 K, and 25.5±0.2cm2/V-s at 294 K; and for both 10 and 294 K, d*=6.9±0.2nm for the B samples, and 23±1nm for the UB samples. By applying the mobility theory in Ref. 20 to n and μ(), we get ND=1.23×1021cm3 and NA=1.97×1020cm3 from the data at 10 K, and ND=1.23×1021cm3 and NA=1.95×1020cm3 from the data at 294 K, values very consistent with each other. In these calculations, we have assumed that the dominant acceptor has a charge of 2, because it is likely the Zn vacancy.20 The donors, of course, are assumed to consist mainly of AlZn impurities (charge 1), although no analytical measurements have been performed as yet.

Fig. 4

The mobility μ as a function of metallurgical thickness d at 10 K. The parameters μ() and d* result from a fit of Eq. (4): μ(d)=μ()/[1+d*/(dδd)], where δd=4 and +13nm for the buffered and unbuffered layers, respectively.


Fig. 5

The mobility μ as a function of metallurgical thickness d at 294 K. The parameters μ() and d* result from a fit of Eq. (4): μ(d)=μ()/[1+d*/(dδd)], where δd=4 and +13nm for the buffered and unbuffered layers, respectively.


The efficacy of the ZnON buffer layer is clear from a comparison of μ versus d in Figs. 2 and 3. In more quantitative terms, we have values d*=7nm for the B samples and 23 nm for the UB samples. From the definition μ(d*δd)=μ()/2, this means that a 294 K mobility of 25.5/2=12.8cm2/V-s could be reasonably expected in a buffered sample of metallurgical thickness d=74=3nm and in an UB sample of d=23+13=36nm. Even though the B value of 3 nm is not very accurate because of the inaccuracy in δd, still it is clear that the buffer makes it possible to grow very thin AZO layers that are conductive.

An example of reflectance data, for the B and UB samples of thickness 127 nm, is given in Fig. 6. From the values of n and μ(), a plasmonic resonance energy of 0.925 eV (1.34 μm) can be predicted10 and is indicated in the figure. Indeed, this energy is close to the threshold of the strong reflectance due to the plasmons. Interestingly, the resonance wavelength of 1.34 μm is near one of the major low-absorption regions in optical fibers used in telecommunications. Note also in Fig. 6 that the reflectances of the buffered and UB samples are nearly identical in the plasmonic region, further affirming that the presence or absence of the buffer does not affect n.

Fig. 6

Reflectance versus energy for the buffered and unbuffered samples of thickness 127 nm. The plasmonic resonance energy predicted from the Hall-effect results is shown as a vertical dashed line.




We have analyzed the effects of a ZnON buffer layer on the electrical properties of thin Al-doped ZnO films grown by RF sputtering on quartz glass substrates. The volume carrier concentration n is independent of thickness d over the range 25 to 147 nm and is also not affected by the presence of the buffer. However, the mobility μ is strongly influenced by the buffer, exhibiting decreased thickness dependence and increased magnitude at a given thickness. Theoretical analysis shows that the observed lower mobility in thinner AZO layers, especially in those without a buffer, is due to increased scattering at the interface because the electrons are closer to it. The effect of the ZnON buffer is to reduce this scattering and also to reduce or eliminate the trapping at the interface of free electrons from the bulk. From the values of n and μ(), donor and acceptor concentrations are calculated as 1.23×1021 and 1.97×1020cm3, respectively. From these same values, a plasmonic resonance wavelength of 1.34 μm is predicted and is confirmed by reflectance measurements.


We wish to thank T. A. Cooper for the Hall-effect measurements and W. Rice for the reflectance measurements. Support for DCL was provided by AFOSR Grant FA9550-10-1-0079 (J. Hwang), NSF Grant DMR0803276 (C. Ying), DOE Grant DE-FG02-11ER46820 (R. Kortan), and AFRL Contract HC1047-05-D-4005 (D. Tomich).


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© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
David C. Look, David C. Look, Kevin D. Leedy, Kevin D. Leedy, Arnold Kiefer, Arnold Kiefer, Bruce Claflin, Bruce Claflin, Naho Itagaki, Naho Itagaki, Koichi Matsushima, Koichi Matsushima, Iping Surhariadi, Iping Surhariadi, } "Model for thickness dependence of mobility and concentration in highly conductive zinc oxide," Optical Engineering 52(3), 033801 (13 March 2013). https://doi.org/10.1117/1.OE.52.3.033801 . Submission:

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