THE EFFECT OF PLASMON-PHONON INTERACTION ON THE IR REFLECTIONS SPECTRA OF ZNO FILMS GROWN ON DIFFERENT SUBSTRATES

In this section, the application of theoretical approach developed for ZnO bulk materials and described above for crystals with different carrier concentrations will be demonstrated for ZnO films grown on different substrates, that is, semiconductor and dielectric (Kor- sunska et al., 2019; Melnichuk, Melnichuk, Korsunska, et ah, 2019; Melnichuk, Melnichuk, Tsykaniuk, et ah, 2019). It will be shown that this method allows determining the optical and electrophysical properties of the films taking into account plasmon-phonon interaction between film and substrate. Such study was reported for the films grown on Si, AbOj, and Si0₂ substrates by magnetron sputtering or by atomic layer deposition (Korsunska et ah. 2019; Melnichuk, Melnichuk, Korsunska. et ah, 2019; Melnichuk, Melnichuk, Tsykaniuk, et ah, 2019; Venger et ah, 2016; Venger. Melnichuk, Pasechnik, & Sukhenko, 1997).

It should be noted that for some applications of ZnO films, it is required to achieve high electron conductivity. In this case, the doping with trivalent elements (such as Al, Ga. and In) was usually used (see for instance, Hu & Gordon. 1992; Igasaki & Saito, 1991; Minarni, Sato, Imamoto, & Takata, 1992). At the same time, the use of trivalent rare-earth elements allows not only to achieve high ZnO film conductivity, but also to obtain specific luminescence properties (Elfakir, Douayar, & Diaz et ah, 2014; Fang et ah. 2005; Guillaume, Labbe, & Frilay et ah, 2018; Hastir, Kohli, & Singh, 2017; Korsunska et ah, 2019, 2020; Ziani, Davesnne, & Labbe et ah,

2014). However, in most cases such films are highly textured (Figure 7.19) that causes some difficulties in the observation of the correlation between doping level and film conductivity. Recently, it was shown that the use of IR reflection method allows to obtain this information, for instance, for Tb-doped and/or (Eu.Tb)-codoped ZnO films (Korsunska et ah, 2019. 2020).

Figure 7.19 shows typical AFM images of the surface of undoped (a) and Tb-doped films (b d) grown on different substrates. The influence of terbium doping on surface topography is clearly illustrated by the images for undoped (a) and Tb-doped (c) films grown on Si (001) substrates. Instead of smooth surface of the undoped ZnO film, the film grown on Si substrate shows clusters with lateral sizes of 0.5-1.6 pm separated by trenches with a depth of 50-190 nm. Besides, the nano-granular fine structure of the clusters can also be distinguished on the surfaces of both films.

Generally, theoretical calculations of specular IR reflection spectra inherent to the absorbing film deposited onto “semi-infinite” semiconductor substrate (such as silicon) are performed within the range of residual rays of ZnO using formula

where A = 2(cjc/2 + Л1Л2); В = 2(ч1ъ — С = 2(qq2 — Л1Л2); D = 2(q/i2 + qik)

FIGURE 7.19 AFM images of the surface of different samples: ZnO/Si (a), ZnO-Tb/Al₂0₃ (b), ZnO-Tb/Si (c), and ZnO-Tb/Si0₂ (d)

Z>2 = (4яу;2г/шт)/Л and «i(^i), n₂(k₂), and и₃(А'₃) are the refractive indexes (extinction coefficient) of air, ZnO, and substrate, respectively; dfu_m is the thickness of ZnO film.If the ZnO film is grown on Si substrate, then for the calculation of the n₂ and из, the dielectric permittivity is considered as a function with additive contribution of active optical phonons (vr) and plasmons (v_/;) in the film and substrate according to Eq. (7.27). For further calculation, the parameters for ZnO were taken from Table 7.2, whereas for Si substrate c₀ = - 11.4

and v_L = vj = 520.9 cm~' are considered.

For the simulation of 1R reflection spectra for the ZnO film situated on sapphire (A1₂0₃) substrate, the dielectric permittivity of A1₂0₃ versus the frequency can be taken accounted for four-oscillator model

where - high-frequency dielectric constant of sapphire for E±C Дf.j - the strength of the /th oscillator; v_Ti - the frequency of transversal optical vibration of /th oscillator; уд - damping constant of the /th oscillator. In the case of Si0₂ substrate, the model with four oscillators for noncrystalline quarts was also used. The parameters for sapphire and quarts substrates are collected in Table 7.9.

The simulation of the R(v) spectra can be performed versus carrier concentration, film thickness, plasmon, and phonon damping coefficients. As an example, Figure 7.20 shows simulated R(v) spectra versus carrier concentration. The simulation was performed with Eqs. (7.28) and (7.29) for the Zn0/Al₂0₃ structure for the film thickness of 500 nm (Figure 7.20a) and 675 nm (Figure 7.20b) that correspond to experimental values. Phonon damping

TABLE 7.9

The parameters of Al₂O_t and Si0₂ substrates used for the R(v) simulation

Substrate AI2O3 single crystal, ElC	Parameter fbe /th oscillator
j= 1	384	0.2	0.015
./=2	442	2.8	0.01
у=з	571	3.1	0.2
./ = 4	634	0.2	0.02
Si02 (JGS1 type)
;'= 1	457	0.95	0.015
./■=2	810	0.05	0.1
у=з	1072	0.6	0.06
./ = 4	1160	0.15	0.04

FIGURE 7.20 Simulated (lines) and experimental (symbols) R(v) spectra for conductive undoped (a, c) and Tb-doped ZnO (b, d) films. Parameters of simulation are as follows: the thickness and phonon damping coefficient are d = 500 nm, y_fj_ = 20 cm ¹ (a, c) and d = 675 nm, y_fJ_ = 20 cm ¹ (b, d), respectively, (a, b) v_pj = Vi. ⁼ 100-500 cm"¹ (curves 1-5); (c) v_pj_ = 400 cm y_pi = 870 cm¹; (d) v_pj_ = 350 cm^-1 and y_pJ_ = 250 cm'¹

coefficient was fixed уy_x = 20 cm^-1 for both films. The frequency and damping coefficient of plasmons were varied from v_p± = 100 cm^-1 and y_pJ_ = 100 cm^-1 (curve 1) up to v_pJ_ = 500 cm^-1 and y_pJ_ - 500 cm^-1 (curve 5) with a scanning step of 100 cm^-1.

It is seen that the increase of carrier concentration (variation of the v_p) in conductive undoped film results in the significant deformation of the R(v) dependence in the range of 100-1200 cm^-1 (Figure 7.21a) followed by the decrease of the R(v) value, for instance, down to 0.8 at v = 680 cm^-1 and to 0.4 at v = 510 cm^-1. This fact can be applied for the estimation of the concentration and mobility of free carriers in ZnO films (Melnichuk, Mel- nichuk, Tsykaniuk, et al., 2019). At the same time, the variation of phonon damping coefficient у/ in ZnO film affects the reflection spectra mainly in the vicinity of TO phonon frequency (v_T = 412 cm^-1), whereas in other spectral ranges its influence is negligible.

For Tb-doped ZnO film (Tb content is about 3 at.%), the increase of the v_pA_ and y_pA_ values causes the increase of the slope of R(v) curves in the 600-900 cm^-1 spectral range that corresponds to an increase of electron concentration. The appearance of a shoulder at about 890-900 cm^-1 is due to higher film thickness (Melnichuk, Melnichuk, Tsykaniuk. et ah, 2019).

The experimental and simulated spectra are compared in Figure 7.20c, d. For conductive undoped ZnO film, the best fitting was obtained for y^ - 25 cm^-1, v_/;J_ = 400 cm^-1, and y_/;J_ = 870 cm^-'(Figure 7.20c). The electron concentration, mobility, and conductivity were estimated to be n₀ = 1.83 x 10¹⁸cm^-3, p = 258cnr V^-1 x s^-1 and a = 76Q^-1 x cm^-1, respectively. For the Tb-doped ZnO film (Figure 7.20d), these parameters were as follows: yn = 20cm^-1, v_ps_i = 350cm^-1, and y_pA_ - 250cm^-1, n₀ - 1.03 x Ю¹⁸ cm^-3, p = 89.7 cm V^-1 s^-1 and a = 202 Q^-1 x cm^-1. It is seen that the electron concentration is nearly the same in both films. This allows concluding that Tb incorporation does not change essentially the electron concentration in ZnO in spite of the fact that Tb³⁺ is the donor. This effect was explained by the formation of some defects acting as charge compensator for Tb^,+ ions (Melnichuk. Melnichuk, Korsunska, et ah, 2019). Another reason can be the dependence of the conductivity on Tb concentration as it was reported by Elfakir et ah (2014). It was shown that the increase of Tb content up to 1 at.% results in the higher film conductivity, while for higher Tb content (up to 5 at.%), the decrease of conductivity was observed. It should be noted that both experimental and theoretical curves are in good agreement. This confirms the reliability of the parameters of bulk ZnO and the possibility of their use for the study of textured ZnO films.

FIGURE 7.21 The IR reflection spectra of Tb-doped ZnO films grown on A1₂0₃ (1), Si (2), and Si0₂ (3) substrates and their corresponding simulation (curves 1 -3'). The spectra are shifted in vertical direction for clarity

It is interesting that direct current conductivity was also studied by Melnichuk, Melnichuk, Korsunska, et al. (2019). However, significantly different values were obtained. The planar electrical conductivity was about 10^-7—10^-8 Q^_l x cm^-1, which is much lower than the values obtained from the measurements of IR reflectance spectra. This difference was explained by the presence of high-resistive spaces between ZnO columns that was confirmed by structural characterization of the films (Korsunska et al., 2019; Melnichuk, Melnichuk, Korsunska, et al., 2019). Thus, IR reflectance spectra are useful for the investigation of conductivity of nonhomogeneous systems. Note also that in the case of Si substrate (in contrast to insulated one), the sheet resistance can be influenced by the substrate conductivity, while IR reflectance allows extracting the conductivity values of ZnO film and substrate, separately.

The experimental IR reflection spectra of Tb-doped ZnO films grown on different substrates are shown in Figure 7.21. To simulate these spectra in the range of residual rays, the approach described above was also applied.

The best fitting of experimental data for Tb-doped film grown on different substrates was obtained using the parameters shown in Table 7.10. The calculation of carrier concentrations and their mobility was performed with the uncertainty less than 1%.

It should be noted that all Tb-doped samples were prepared in the same deposition run. The analysis of the IR reflection spectra shows that the concentration of electrons in Tb- ZnO films on different substrates lies in the range of n₀ - 10^{1 s}— 10¹⁹ cm^-3. It was found that Tb³⁺ luminescence does not correlate with the Tb³⁺ content. It was concluded that the Tb incorporation into ZnO host requires Tb ions’ association with other charge-compensating lattice defects or impurities. Besides, such doping provokes some film disordering and formation of intrinsic defects in ZnO lattice. The higher is the Tb concentration, the higher is the number of compensating defects, thus resulting in unchanged conductivity.

The results described above show the effect of substrate material, including Si, SiOn, and A1₂0₃, on structural, optical, and electrical properties of Tb-doped ZnO films. The doping with Tb ions results in the formation of highly textured films with the micro-clusters of 0.5-1.6 pm diameter consisted of ZnO columns oriented perpendicularly to substrate surface and separated by deep tranches. The width of these tranches depends on the type of substrate, being the largest in the Tb-ZnO/AF0₃ one. Besides, the Tb-ZnO/AF0₃ film is found to consist of two layers with different morphologies, only the upper part being of column structure.The investigation described above shows the utility of this nondestructive approach for the estimation of the conductivity of ZnO columns as well as the concentration and mobility of free carriers. The experimental results are well simulated using self-consistent parameters of ZnO and substrate for required orientation. This method allows analyzing the electrical parameters in textured materials that contain high-conductive crystallites separated by high-resistive regions when planar conductivity gives incorrect results.

TABLE 7.10

Parameters of the films extracted from simulation of the IR reflection spectra presented in Figure 7.21

Sample
ZnO-Tb/AbOj	350	250	30	1.4 x K)18	89
ZnO-Tb/SiCb	600	2500	80	4.14 x 1018	89
ZnO-Tb/Si	1150	880	18	1.52 x 1019	254
ZnO/Si	950	650	50	1.03 x 1019	344