Effects of free carriers on the optical properties of high mobility transition metal doped ${\mathrm{In}}_2{\mathrm{O}}_3$ transparent conductors

Transition metal doped ${\mathrm{In}}_2{\mathrm{O}}_3$ with high mobility can be used as a transparent conductor with enhanced transparency spectral window. In this work, we carried out a comprehensive study on the electrical and optical properties of ${\mathrm{In}}_2{\mathrm{O}}_3$ doped with several transition metal (TM) species (${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{TM}$) including W, Zr, Mo, and Ti. Detailed optical properties obtained by spectroscopic ellipsometry (SE) are correlated with electrical properties obtained by Hall effect measurements. We find that the mobility of ${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{TM}$ thin films lies in the range of $50\text{–}75\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{\text{−}1}{\mathrm{s}}^{\text{−}1}$, much higher than the typical mobility of $30\text{–}40\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{\text{−}1}{\mathrm{s}}^{\text{−}1}$ for conventional ITO. The complex dielectric functions of the thin films reveal remarkable carrier density dependent changes in the optical properties. SE analyses show that the electron effective mass of ${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{TM}$ at the bottom of the conduction band $m_o^{*}$ ($0.11\text{–}0.14m_o$) is much smaller than the reported $m_o^{*}\sim 0.18-0.30m_o$ for ITO, which directly results in their higher mobility. This low $m_o^{*}$ is consistent with recent theoretical studies which proposed that $4d$ donor states of the TMs are resonance in the CB. For films with comparably low resistivity of $1\text{–}2\times {10}^{\text{−}4}\mathrm{\Omega }\mathrm{cm}$, we find that ${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{TM}$ films have ∼4–10 times lower absorption coefficient at $\lambda =1300\mathrm{nm}$ due to free carrier absorption and have their plasma reflection edge extended to ∼1.7 μm compared to ∼1.2–1.4 μm for ITO. Hence, using TM doping we have achieved transparent conductors with conductivity comparable to ITO but with transmission extended to >1600 nm. These materials will be potentially important as transparent conductors for optoelectronic devices utilizing NIR photons.

Figure 1

The measured and fitted (red dashed lines) SE spectra [Ψ and Δ in (a) and (b), respectively] of ${\mathrm{In}}_2{\mathrm{O}}_3$:Mo thin film with $N_{\mathrm{Hall}}=7.1\times {10}^{20}\mathrm{c}{\mathrm{m}}^{\text{−}3}$ for angle of incidence: 55 °, 65 °, and 75 °.

Figure 2

Electron concentration $N_H$ (a) mobility ${\mu }_H$ (b) and resistivity ρ (c) for ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films doped with TM dopants (Ti, W, Mo, and Zr) with increasing dopant concentration $N_d$. Dashed lines are guide to the eyes.

Figure 3

Temperature dependence of (a) Electron concentration (b) Mobility and (c) resistivity of ∼1%–2% TM doped ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films with high mobilities. Data for ITO is shown in open symbol for comparison.

Figure 4

Complex dielectric function of ${\mathrm{In}}_2{\mathrm{O}}_3$:Mo thin films showing (a) the real dielectric function and (b) imaginary part of the dielectric function with the variable $N_{\mathrm{Hall}}$. The inset of Fig. 3 shows the extrapolation of the plasma energy of the thin films.

Figure 5

(a): The plasma wavelength obtained from SE analysis as a function of the resistivity for different ${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{TM}$ samples, Previous experimental reported plasma energy of several TCOs are also shown [21, 22] (b) The high-frequency dielectric constant of thin films vs $N_{\mathrm{Hall}}$ obtained from the intercept of the plot of ${\varepsilon }_1$ vs $1/\left(E^2+{\mathrm{\Gamma }}^2\right)$.

Figure 6

Electron effective mass, $m^{*}$ for ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films with different dopants as a function of $N_H$, accuracies are $\sim \pm 5\%$, where $m_{\mathrm{o}}$ is the free electron mass. The black solid line is the best fit for the data from Mo and Zr doped while the black dashed line is the best fit for Ti- and W doped ${\mathrm{In}}_2{\mathrm{O}}_3$ samples of the conduction band nonparabolicity equation. The best fit curves were obtained for samples with $N_H<5\times {10}^{20}\mathrm{c}{\mathrm{m}}^{\text{−}3}$.

Figure 7

Optical mobility of TM doped ${\mathrm{In}}_2{\mathrm{O}}_3$ obtained from the SE analysis as a function of Hall mobility.

Figure 8

(a) Absorption coefficient of Mo doped ${\mathrm{In}}_2{\mathrm{O}}_3$ for samples different $N_{\mathrm{Hall}}$. (b) Free carrier absorption for values of TM doped ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films at an IR wavelength of 1300 nm.

Figure 9

(a) Optical transmission intensity of TM doped ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films with thickness, $t=150$ nm for different resistivity ($\mathrm{\Omega }$-cm), ${\mathrm{In}}_2{\mathrm{O}}_3:\mathrm{Sn}$ thin films obtained at similar condition are also shown. (b) Refractive index $n$ at 600 nm wavelength of the ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films doped with various dopants obtained from SE Analysis.

Figure 10

Optical band gap of TM doped ${\mathrm{In}}_2{\mathrm{O}}_3$ thin films vs $N_{\mathrm{Hall}}$ obtained from the second derivative the real part of the dielectric function, $d^2{\varepsilon }_1/d{E}^2$. The inset shows $d^2{\varepsilon }_1/d{E}^2$ of a ${\mathrm{In}}_2{\mathrm{O}}_3$:Ti sample as a function of photon energy with the black arrow indicating the optical band-gap energy value.