1.

Introduction

Transparent conductive electrodes, typically formed from transparent conductive oxides (TCOs), are an important component of liquid crystal displays, solar cells, and light-emitting diodes.^1–4 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.^5–10 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 $\rho$, mobility $\mu$, and carrier concentration $n$.^11–17 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 (${\mathrm{Al}}_2{\mathrm{O}}_3$), 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 $\rho$, $\mu$, 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 $d_{\mathrm{el}}$ being different than the metallurgical thickness $d$ (i.e., $d_{\mathrm{el}}=d-\delta d$). 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 $\mu (d^{*}-\delta d)=\mu (\infty )/2$, where $d^{*}$ and $\mu (\infty )$ are fitting parameters in the formula $\mu (d)=\mu (\infty )/[1+d^{*}/(d-\delta d)]$. Essentially, for $d<d^{*}+\delta d$, interface scattering dominates all other scattering mechanisms; thus, a good interface has a low value of $d^{*}$. We find that $d^{*}=23\mathrm{nm}$ for the unbuffered (UB) samples, and only 7 nm for the buffered (B) samples. Also, from the values of $n$ and $\mu (\infty )$, we can use degenerate electron scattering theory to determine donor and acceptor concentrations.

2.

Experiment

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 $4/20.5[\mathrm{sccm}]{\mathrm{N}}_2/\mathrm{Ar}$ 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 $2\mathrm{wt}\%{\mathrm{Al}}_2{\mathrm{O}}_3$. 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 $\omega -2\theta$ 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 $1\times 1\mathrm{cm}$, and ohmic indium dots were placed at the four corners. Spectroscopic reflectance measurements were performed in a Perkin-Elmer Lambda $900\mathrm{UV}/\mathrm{Vis}$ spectrometer at 294 K and over a wavelength range 190 to 3200 nm (6.52 to 0.39 eV).

3.

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:

Fig. 1

The sheet carrier concentration $n_s$ 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 $3.14\times {10}^{14}{\mathrm{cm}}^{-2}$, while the unbuffered sample has a deficit of $1.07\times {10}^{15}{\mathrm{cm}}^{-2}$.

4.

Experimental Results and Analysis

In our study, the measured values of $\rho$, $\mu$, and $n$ vary as a function of metallurgical thickness $d$, consistent with the results of many other studies.^11–17 However, it must be remembered that $\rho$ and $n$ (but not $\mu$) require knowledge of the electrical thickness $d_{\mathrm{el}}$, which may not be the same as $d$. That is, the Hall effect does not directly measure a volume concentration $n({\mathrm{cm}}^{-3})$, but a sheet concentration $n_s({\mathrm{cm}}^{-2})$. If $n$ is uniform, then these two quantities are simply related by $n=n_s/d_{\mathrm{el}}$, where $d_{\mathrm{el}}=d-\delta d$ is the electrical thickness, the region that contains free electrons. (If $n$ is not uniform, then $n_s$ is an averaged quantity,²¹ not of importance here.) If $\delta d\ll d$, then $d_{\mathrm{el}}\approx d$, 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 $d_{\mathrm{el}}\ne d$. To test this possibility, we plot $n_s$ versus $d$, shown in Fig. 1. Both B and UB samples display straight lines of slope $n=8.36\times {10}^{20}{\mathrm{cm}}^{-3}$, showing immediately that the bulk $n$ is not a function of depth or of the quality of the interface, at least for $d>25\mathrm{nm}$. (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 $\delta n_s=-1.07\times {10}^{15}{\mathrm{cm}}^{-2}$, and an $x$-axis intercept of $\delta d=+13\mathrm{nm}$. Thus, the electrical thickness is $d_{\mathrm{el}}=d-13\mathrm{nm}$, so that $n(d)=n_s(d)/(d-13)$, not $n_s(d)/d$. Similarly, the resistivity is now given by $\rho (d)={\rho }_s(d)·(d-13)$, not ${\rho }_s(d)·d$. These renormalized $\rho$, $\mu$, 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 $n=8.36\times {10}^{20}{\mathrm{cm}}^{-3}$; thus, when properly normalized, $n$ is independent of thickness. Note also that $n(10\mathrm{K})\approx n(294\mathrm{K})$, showing that the electrons are truly degenerate.

Fig. 2

The resistivity $\rho$, mobility $\mu$, and carrier concentration $n$ as a function of metallurgical thickness $d$ for the unbuffered sample. Here $n$ and $\rho$ are normalized to the electrical thickness $d_{\mathrm{el}}=d-13\mathrm{nm}$; i.e., $n=n_s/(d-13)$, and $\rho ={\rho }_s\times (d-13)$.

We now examine $n_s$ 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 $\delta n_s=+3.14\times {10}^{14}{\mathrm{cm}}^{-2}$, and $\delta d=-4\mathrm{nm}$. Thus $d_{\mathrm{el}}=d\text{-}\delta d=d+4$. 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 $\delta d$ is small enough that a slight change in slope would make a large percentage change in $\delta d$. The renormalized $\rho$, $\mu$, and $n$ versus $d$ results for the B samples are plotted in Fig. 3, and it is again seen that $n=n_s/(d+4)$ is constant with thickness and moreover has the same magnitude as that of the UB samples. We also see that $\mu$ has a much smaller thickness dependence, showing that the buffer is very effective in this regard.

Fig. 3

The resistivity $\rho$, mobility $\mu$, and carrier concentration $n$ as a function of metallurgical thickness $d$ for the buffered sample. Here $n$ and $\rho$ are normalized to the electrical thickness $d_{\mathrm{el}}=d+4\mathrm{nm}$; i.e., $n=n_s/(d+4)$, and $\rho ={\rho }_s\times (d+4)$.

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 $\mu$ 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 $N_D$ and $N_A$ are varying with $d$ because it is well known that $\mu$ is a strong function of these quantities in heavily doped materials. But this possibility is unlikely because $N_D$ and $N_A$ would then have to track each other exactly in order to maintain a constant $n=N_D\text{-}{N}_A$. 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 $\mu$ 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), $\mu (d)=\mu (\infty )/[1+d^{*}/(d\text{-}\delta d)]$, where $\delta d=-4$ and $+13\mathrm{nm}$ for the B and UB samples, respectively. For both B and UB samples, $\mu (\infty )=27.6\pm 0.3{\mathrm{cm}}^2/\mathrm{V}\text{-}\mathrm{s}$ at 10 K, and $25.5\pm 0.2{\mathrm{cm}}^2/\mathrm{V}\text{-}\mathrm{s}$ at 294 K; and for both 10 and 294 K, $d^{*}=6.9\pm 0.2\mathrm{nm}$ for the B samples, and $23\pm 1\mathrm{nm}$ for the UB samples. By applying the mobility theory in Ref. 20 to n and $\mu (\infty )$, we get $N_D=1.23\times {10}^{21}{\mathrm{cm}}^{-3}$ and $N_A=1.97\times {10}^{20}{\mathrm{cm}}^{-3}$ from the data at 10 K, and $N_D=1.23\times {10}^{21}{\mathrm{cm}}^{-3}$ and $N_A=1.95\times {10}^{20}{\mathrm{cm}}^{-3}$ 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 ${\mathrm{Al}}_{\mathrm{Zn}}$ impurities (charge 1), although no analytical measurements have been performed as yet.

Fig. 4

The mobility $\mu$ as a function of metallurgical thickness $d$ at 10 K. The parameters $\mu (\infty )$ and $d^{*}$ result from a fit of Eq. (4): $\mu (d)=\mu (\infty )/[1+d^{*}/(d-\delta d)]$, where $\delta d=-4$ and $+13\mathrm{nm}$ for the buffered and unbuffered layers, respectively.

Fig. 5

The mobility $\mu$ as a function of metallurgical thickness $d$ at 294 K. The parameters $\mu (\infty )$ and $d^{*}$ result from a fit of Eq. (4): $\mu (d)=\mu (\infty )/[1+d^{*}/(d-\delta d)]$, where $\delta d=-4$ and $+13\mathrm{nm}$ for the buffered and unbuffered layers, respectively.

The efficacy of the ZnON buffer layer is clear from a comparison of $\mu$ versus $d$ in Figs. 2 and 3. In more quantitative terms, we have values $d^{*}=7\mathrm{nm}$ for the B samples and 23 nm for the UB samples. From the definition $\mu (d^{*}-\delta d)=\mu (\infty )/2$, this means that a 294 K mobility of $25.5/2=12.8{\mathrm{cm}}^2/\mathrm{V}\text{-}\mathrm{s}$ could be reasonably expected in a buffered sample of metallurgical thickness $d=7-4=3\mathrm{nm}$ and in an UB sample of $d=23+13=36\mathrm{nm}$. Even though the B value of 3 nm is not very accurate because of the inaccuracy in $\delta d$, 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 $\mu (\infty )$, 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.

5.

Summary

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 $\mu$ 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 $\mu (\infty )$, donor and acceptor concentrations are calculated as $1.23\times {10}^{21}$ and $1.97\times {10}^{20}{\mathrm{cm}}^{-3}$, respectively. From these same values, a plasmonic resonance wavelength of 1.34 μm is predicted and is confirmed by reflectance measurements.