**2.1 Anatase-dominant matrix in Ge/TiO2 thin films prepared by rf sputtering**

The present study employed a new method of preparing Ge/TiO2 films using a composite target of a Ge chip set on a TiO2 disk, and their composition has been thoroughly changed. Figure 2-1(a) depicts the X-ray diffraction (XRD) pattern of Ge/TiO2 thin films as a function of Ge concentration. In this case, the additional oxygen ratio in argon is kept constant at 0%. Labels A through E indicate Ge concentrations of 0, 1.9, 6.8, 8.1, and 21at.% by adopting 0, 1, 2, 3, and 21 Ge chips. XRD patterns first exhibited an amorphous state in as-deposited films, and several diffraction peaks began to appear at 723 K when the post-annealing temperature was raised from 673 to 873K in 50K steps. These peaks were assigned to TiO2, and the films were therefore crystallized at around 723K (not shown here). A single-phase rutile structure is observed at a Ge concentration of 0at.% in the figure, corresponding to simple preparation of pure TiO2 thin film. In our preliminary experiment for preparing the TiO2 thin films, a singlephase anatase structure was obtained for oxygen ratios exceeding 0.5% and the successive post-annealing treatment. An insufficient oxygen ratio thus seems to cause formation of the rutile structure. Next, with a slight addition of Ge in the pattern of B, distinct diffraction peaks of anatase structure begin to appear, and the (101) Bragg reflection is dominant. Further addition of Ge, as seen in patterns C and D, produces different behavior in orientation, increasing the peak intensity at (004) reflection of the anatase structure. Finally, dominant, broad peaks of Ge can be observed with excess Ge addition in pattern E. The average size of the Ge nanogranules is estimated to be about 6.6nm based on the full-width at half maximum of the XRD peak employing Scherrer's equation (Scherrer, 1918). According to the variation of Ge concentration, the anatase structure is favorably promoted in patterns B, C, and D.

the substances for nanocrystal and matrix are also selected following thermodynamic insolubility. The HWD technique, which is a kind of thermal evaporation, causes unintentional increase of the substrate-temperature due to the thermal irradiation. Hence, simultaneous HWD evaporation from multiple resources often produces solid solution [e.g., Pb1-*x*Ca*x*S (Abe & Masumoto, 1999)]. Hence, package synthesis of the composite thin film needs insolubility material system. The bulk PbSe-ZnSe system, for instance, is found to phase-separate at thermal equilibrium state (Oleinik et al., 1982). It is therefore expected that PbSe nanocrystals phase-separate from the ZnSe matrix in spite of the simultaneous

Accordingly, the two thermodynamic material-designs, heat of formation for rf sputtering and insolubility system for HWD, are employed here for package synthesis of composite thin film. This chapter focuses on one-step physical synthesis of Ge/TiO2 composite thin films by rf sputtering and PbSe/ZnSe composite thin films by HWD, as candidate materials

TiO2 mainly has crystal structures of rutile, anatase and brookite. It is believed that the anatase structure is favorable for the matrix, since carrier mobility and photoconductivity in the anatase structure exceed those in the rutile structure (Tang et al., 1994). It is difficult to forecast how the crystal structure of the TiO2 matrix will be formed in such composite films. In fact, Ge/TiO2 films prepared by rf sputtering employing a mixture target of TiO2 and Ge powder hitherto contained anatase- and rutile -structure almost equally (Chatterjee, 2008). Hence, it is investigated here that the composition of Ge/TiO2 films is thoroughly varied for preparing the anatase structure of the TiO2 matrix while retaining vis-NIR absorption of Ge quantum dots.

The present study employed a new method of preparing Ge/TiO2 films using a composite target of a Ge chip set on a TiO2 disk, and their composition has been thoroughly changed. Figure 2-1(a) depicts the X-ray diffraction (XRD) pattern of Ge/TiO2 thin films as a function of Ge concentration. In this case, the additional oxygen ratio in argon is kept constant at 0%. Labels A through E indicate Ge concentrations of 0, 1.9, 6.8, 8.1, and 21at.% by adopting 0, 1, 2, 3, and 21 Ge chips. XRD patterns first exhibited an amorphous state in as-deposited films, and several diffraction peaks began to appear at 723 K when the post-annealing temperature was raised from 673 to 873K in 50K steps. These peaks were assigned to TiO2, and the films were therefore crystallized at around 723K (not shown here). A single-phase rutile structure is observed at a Ge concentration of 0at.% in the figure, corresponding to simple preparation of pure TiO2 thin film. In our preliminary experiment for preparing the TiO2 thin films, a singlephase anatase structure was obtained for oxygen ratios exceeding 0.5% and the successive post-annealing treatment. An insufficient oxygen ratio thus seems to cause formation of the rutile structure. Next, with a slight addition of Ge in the pattern of B, distinct diffraction peaks of anatase structure begin to appear, and the (101) Bragg reflection is dominant. Further addition of Ge, as seen in patterns C and D, produces different behavior in orientation, increasing the peak intensity at (004) reflection of the anatase structure. Finally, dominant, broad peaks of Ge can be observed with excess Ge addition in pattern E. The average size of the Ge nanogranules is estimated to be about 6.6nm based on the full-width at half maximum of the XRD peak employing Scherrer's equation (Scherrer, 1918). According to the variation of

**2.1 Anatase-dominant matrix in Ge/TiO2 thin films prepared by rf sputtering** 

Ge concentration, the anatase structure is favorably promoted in patterns B, C, and D.

evaporation from PbSe- and ZnSe-resource.

for quantum dot solar cell.

**2. Ge/TiO2 composite thin films** 

Fig. 2.1. (a) XRD patterns of Ge/TiO2 composite films versus Ge concentrations. () indicates anatase structure, and (○), rutile structure. (b) Same patterns versus additional oxygen ratio in argon. () indicates anatase structure, and (○), rutile structure (b) (after Abe et al., 2008b).

Figure 2-1(b) depicts the XRD pattern of Ge/TiO2 thin films as a function of the additional oxygen ratio in argon. In this case, the oxygen ratio is varied from 0 to 0.4%, and the number of Ge chips is kept constant at 2. When the ratio is increased to 0.1%, the (004) Bragg reflection becomes more prominent as seen in the figure. A further increase of the oxygen ratio then indicates weakness. An anatase-dominant structure with strong intensity at (004) reflection is thus observed at an oxygen ratio of 0.1%. We cannot observe an XRD peak of Ge in the pattern within the precision of our experiment technique, possibly due to the relatively low Ge concentration of 5.8at.%. This c-axis growth behavior in an anatase-dominant structure seems to be unique even though the composite film is deposited on a glass substrate. Thus, the crystal structure of TiO2 matrix is found to be changed with respect to the Ge number and the oxygen ratio as illustrated in Figs. 2-1(a) and 2-1(b).

One-Step Physical Synthesis of Composite Thin Film 153

structure. They can favorably cover the desirable energy region for high conversion efficiency (Loferski, 1956). Therefore, it should be pointed out that valuable characteristics of vis-NIR absorption and anatase-dominant structure of TiO2 matrix are simultaneously retained in the Ge/TiO2 composite thin films as a result of compositional optimization. Ge addition is first motivated to demonstrate the quantum size effect, then, it is worthy of note that its addition also effectively controls the crystal structure of the TiO2 matrix. Consequently, a single phase of anatase structure cannot be obtained. However, extensive progress can be made in structural formation of the TiO2 matrix as a result of exhaustive compositional investigation. Based on these results, Ge/TiO2 thin films having an anatasedominant structure of TiO2 matrix and vis-NIR absorption should also be regarded as

01234

Fig. 2.3. Typical optical absorption spectra of Ge/TiO2 composite films with anatase-

**2.2 Solubility range and energy band gap of powder-synthesized Ti1-***x***Ge***x***O2 solid** 

As a reason for the vis-NIR absorption, the quantum size effect probably appeared owing to the presence of Ge nanogranules. However, a ternary solid solution of Ti1-*x*Ge*x*O2 is possibly formed as a matrix during the postannealing, and the solubility range of Ge and its energy band gap are hitherto unclear. Therefore, the reason for the vis-NIR absorption requires further investigation. To demonstrate whether the matrix exhibits the vis-NIR absorption, powder synthesis of a ternary Ti1-*x*Ge*x*O2 solid solution is carried out. Specifically, the Ge/TiO2 composite thin film contains multiple phases, and it is then difficult to focus on the matrix characteristics. In this section, Ti1-*x*Ge*x*O2 solid solution is powder-synthesized, and the fundamental properties of solubility range of Ge and the energy band gap are investigated to clarify whether the ternary solid solution exhibits the

Photon energy / eV

5.8 6.8 Ge(at%) 8.1 8.7

> Anatase TiO2

candidate materials for quantum dot solar cell.

0

dominant structure of TiO2 matrix (after Abe et al., 2008b).

2

Absorbance1/2

**solution** 

vis-NIR absorption.

4

Fig. 2.2. Compositional plane of crystal structure of TiO2 matrix in Ge/TiO2 composite films. (○) indicates anatase structure, and (▲), rutile structure. (■) indicates coexistence of anatase and rutile structure. In particular, (□) indicates anatase-dominant structure with strong intensity at (004) reflection (after Abe et al., 2008b).

The relation between the analyzed composition of the films and the structure of TiO2 matrix is summarized in Fig. 2-2 based on these results. The stoichiometric composition of TiO2 is also plotted as a dotted line. The single phase of anatase structure (○) can be seen in the figure, but its visible absorption is quite weak. These films therefore do not achieve the present objective. A mixed phase containing anatase- and rutile -structure (■) appears in a wide range of Ge concentrations. In particular, an anatase-dominant structure with strong (004) reflection (□) is found at a Ge concentration of 6 to 9at.% near the stoichiometric composition of TiO2. The optical absorption will be discussed using the following figure. The rutile structure (▲) is observed at a relatively high Ge concentration range. In these films, diffraction peaks of Ge nanogranules were observed at the same time [Fig. 2-1(a)]. Accordingly, the anatase-dominant structure with strong (004) reflection (□) is regarded to be the most optimized structure in the present study. As a further optimization, total gas pressure was varied from 2mTorr to 10mTorr in the optimized composition range. The (004) Bragg reflection was maximized at a gas pressure of 6mTorr; however, a slight amount of rutile structure still remained.

In the above sections, the structural optimization of the TiO2 matrix in the Ge/TiO2 composite films was focused. Next, we shall investigate the optical properties. Figure 2-3 depicts the typical optical absorption spectra of Ge/TiO2 thin films thus optimized. For comparison, the spectrum of TiO2 thin film is also presented in the figure. Ge has an indirect band-gap structure (Macfarlane et al., 1957), and the square root of absorbance is employed. As seen in the figure, the onset absorption can be confirmed at around 1.0eV in contrast to UV absorption of TiO2 thin films due to its energy band gap of 3.2eV in the anatase

Fig. 2.2. Compositional plane of crystal structure of TiO2 matrix in Ge/TiO2 composite films. (○) indicates anatase structure, and (▲), rutile structure. (■) indicates coexistence of anatase and rutile structure. In particular, (□) indicates anatase-dominant structure with strong

The relation between the analyzed composition of the films and the structure of TiO2 matrix is summarized in Fig. 2-2 based on these results. The stoichiometric composition of TiO2 is also plotted as a dotted line. The single phase of anatase structure (○) can be seen in the figure, but its visible absorption is quite weak. These films therefore do not achieve the present objective. A mixed phase containing anatase- and rutile -structure (■) appears in a wide range of Ge concentrations. In particular, an anatase-dominant structure with strong (004) reflection (□) is found at a Ge concentration of 6 to 9at.% near the stoichiometric composition of TiO2. The optical absorption will be discussed using the following figure. The rutile structure (▲) is observed at a relatively high Ge concentration range. In these films, diffraction peaks of Ge nanogranules were observed at the same time [Fig. 2-1(a)]. Accordingly, the anatase-dominant structure with strong (004) reflection (□) is regarded to be the most optimized structure in the present study. As a further optimization, total gas pressure was varied from 2mTorr to 10mTorr in the optimized composition range. The (004) Bragg reflection was maximized at a gas pressure of 6mTorr; however, a slight amount of

In the above sections, the structural optimization of the TiO2 matrix in the Ge/TiO2 composite films was focused. Next, we shall investigate the optical properties. Figure 2-3 depicts the typical optical absorption spectra of Ge/TiO2 thin films thus optimized. For comparison, the spectrum of TiO2 thin film is also presented in the figure. Ge has an indirect band-gap structure (Macfarlane et al., 1957), and the square root of absorbance is employed. As seen in the figure, the onset absorption can be confirmed at around 1.0eV in contrast to UV absorption of TiO2 thin films due to its energy band gap of 3.2eV in the anatase

intensity at (004) reflection (after Abe et al., 2008b).

rutile structure still remained.

structure. They can favorably cover the desirable energy region for high conversion efficiency (Loferski, 1956). Therefore, it should be pointed out that valuable characteristics of vis-NIR absorption and anatase-dominant structure of TiO2 matrix are simultaneously retained in the Ge/TiO2 composite thin films as a result of compositional optimization. Ge addition is first motivated to demonstrate the quantum size effect, then, it is worthy of note that its addition also effectively controls the crystal structure of the TiO2 matrix. Consequently, a single phase of anatase structure cannot be obtained. However, extensive progress can be made in structural formation of the TiO2 matrix as a result of exhaustive compositional investigation. Based on these results, Ge/TiO2 thin films having an anatasedominant structure of TiO2 matrix and vis-NIR absorption should also be regarded as candidate materials for quantum dot solar cell.

Fig. 2.3. Typical optical absorption spectra of Ge/TiO2 composite films with anatasedominant structure of TiO2 matrix (after Abe et al., 2008b).

### **2.2 Solubility range and energy band gap of powder-synthesized Ti1-***x***Ge***x***O2 solid solution**

As a reason for the vis-NIR absorption, the quantum size effect probably appeared owing to the presence of Ge nanogranules. However, a ternary solid solution of Ti1-*x*Ge*x*O2 is possibly formed as a matrix during the postannealing, and the solubility range of Ge and its energy band gap are hitherto unclear. Therefore, the reason for the vis-NIR absorption requires further investigation. To demonstrate whether the matrix exhibits the vis-NIR absorption, powder synthesis of a ternary Ti1-*x*Ge*x*O2 solid solution is carried out. Specifically, the Ge/TiO2 composite thin film contains multiple phases, and it is then difficult to focus on the matrix characteristics. In this section, Ti1-*x*Ge*x*O2 solid solution is powder-synthesized, and the fundamental properties of solubility range of Ge and the energy band gap are investigated to clarify whether the ternary solid solution exhibits the vis-NIR absorption.

One-Step Physical Synthesis of Composite Thin Film 155

0.0 0.1 0.2 0.3 0.4 0.5

x

2.8 3.0 3.2 3.4

Photon energy / eV

Fig. 2.6. Typical optical absorption spectra of Ti1-*x*Ge*x*O2 solid solution vs Ge concentration

Next, the solubility limit of Ge in the Ti1-*x*Ge*x*O2 is determined through the variation of the lattice constant. Figure 2-5 depicts the lattice constant of the Ti1-*x*Ge*x*O2 solid solution as a function of *x*. Here, the lattice constant of the tetragonal system is estimated from the (200) and (002) reflections. Their peak intensities were found to be relatively weak (Fig. 2-4), but the peak position can be distinctly determined from Lorentzian fitting of the spectra, containing a measurement error of about 0.06 deg in 2 as a result of four repetitive measurements. Accordingly, the lattice constant results in containing a maximum calculation error of about 0.0006 nm. In the preliminary experiment, a mass reduction during the heat treatment was found to be less than 0.1% in standard powders of TiO2 and GeO2, suggesting a small amount of sublimation. The nominal content of Ge is therefore employed here as a composition of the product. It is clearly seen in the figure that the lattice constant in both reflections is first decreased linearly in proportion to *x*, and becomes constant irrespective of *x* in the range exceeding 0.25. According to Vegard's law (Vegard, 1921), an on-setting composition *x* to deviate from the linearity is regarded as a solubility

Fig. 2.5. Lattice constant of Ti1-*x*Ge*x*O2 solid solution vs Ge concentration (after Abe , 2009).

*x*=0 *x*=0.04 *x*=0.1

(002)

*x*=0.2 *x*=0.25 *x*=0.3

GeO2

(200)

0.293 0.294 0.295 0.296 0.454 0.455 0.456 0.457 0.458 0.459 0.460 0.461 0.462

> *Ti1-xGex O2*

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

(K-M function )0.5

(after Abe , 2009).

Lattice constant / nm

Fig. 2.4. Typical powder XRD patterns of Ti1-*x*Ge*x*O2 solid solution with respect to *x*. Filled circle indicates GeO2 (after Abe , 2009).

In a previous section, Ge nanogranules and TiO2 matrix were thermally crystallized at an annealing temperature of 873K (Abe et al., 2008). Accordingly, a similar temperature of 923K was preliminary adopted to synthesize the Ti1-*x*Ge*x*O2 solid solution. In this case, four samples (*x* = 0.05, 0.1, 0.2, and 0.3) were mixed and heat-treated for 20 days to achieve thermal equilibrium. However, a single phase of the Ti1-*x*Ge*x*O2 solid solution could not be obtained, forming two phases of GeO2 and anatase-structured TiO2 according to the XRD pattern. For reference, there was a slight decrease in the lattice constant at *x*=0.05 estimated from the (004) reflection of anatase structure in comparison with those of the TiO2 standard powder, and gradually increased with increasing *x* in the range exceeding 0.05. Thus, the solubility limit of Ge was found to be quite narrow (less than 0.05) at 923K. In addition, no energy shift of the optical absorption edge can be seen with respect to *x*. Therefore, an adequately high temperature of 1273K is alternatively adopted here in anticipation of a wide solubility range of Ge.

Figure 2-4 depicts typical powder XRD pattern of the Ti1-*x*Ge*x*O2 solid solution. In the range below 0.1, all the XRD peaks can be assigned to rutile structure and shift toward greater angle as *x* increases owing to the difference in ionic radii between Ti and Ge (Shannon, 1976; Takahashi et al., 2006). In addition, an XRD peak of GeO2 cannot be observed within the precision of the experimental technique. Such peak shift was also observed on the TiO2- GeO2 solid solution synthesized through sol-gel method within a Ge concentration range below 10 mol% (Kitiyanan et al., 2006) or 1.5 mol% (S. Chatterjee & A. Chatterjee, 2006). It is suggested that the present sample possibly forms a solid solution of Ti1-*x*Ge*x*O2. The solubility range of Ge is therefore found to be enlarged as a result of elevating the temperature from 923 to 1273K. The standard powder of TiO2 employed here has anatase structure, since the matrix of the Ge/TiO2 composite thin films had anatase-dominant structure (Abe et al., 2008b). However, the product thus powder-synthesized resulted in rutile structure because of phase transition from anatase to rutile at 973K (The Mark Index, 1968). In contrast, the GeO2 peaks, which are indicated by a filled circle, begin to appear in the range exceeding 0.3. Their peak positions seem to remain the same with respect to *x*, suggesting no solubility range of Ti in GeO2 at 1273 K. The two phases of the Ti1-*x*Ge*x*O2 and GeO2 are therefore formed in such concentration range.

20 30 40 50 60 70

2 / deg

(210)

(111)

Fig. 2.4. Typical powder XRD patterns of Ti1-*x*Ge*x*O2 solid solution with respect to *x*. Filled

In a previous section, Ge nanogranules and TiO2 matrix were thermally crystallized at an annealing temperature of 873K (Abe et al., 2008). Accordingly, a similar temperature of 923K was preliminary adopted to synthesize the Ti1-*x*Ge*x*O2 solid solution. In this case, four samples (*x* = 0.05, 0.1, 0.2, and 0.3) were mixed and heat-treated for 20 days to achieve thermal equilibrium. However, a single phase of the Ti1-*x*Ge*x*O2 solid solution could not be obtained, forming two phases of GeO2 and anatase-structured TiO2 according to the XRD pattern. For reference, there was a slight decrease in the lattice constant at *x*=0.05 estimated from the (004) reflection of anatase structure in comparison with those of the TiO2 standard powder, and gradually increased with increasing *x* in the range exceeding 0.05. Thus, the solubility limit of Ge was found to be quite narrow (less than 0.05) at 923K. In addition, no energy shift of the optical absorption edge can be seen with respect to *x*. Therefore, an adequately high temperature of 1273K is alternatively adopted here in anticipation of a wide

Figure 2-4 depicts typical powder XRD pattern of the Ti1-*x*Ge*x*O2 solid solution. In the range below 0.1, all the XRD peaks can be assigned to rutile structure and shift toward greater angle as *x* increases owing to the difference in ionic radii between Ti and Ge (Shannon, 1976; Takahashi et al., 2006). In addition, an XRD peak of GeO2 cannot be observed within the precision of the experimental technique. Such peak shift was also observed on the TiO2- GeO2 solid solution synthesized through sol-gel method within a Ge concentration range below 10 mol% (Kitiyanan et al., 2006) or 1.5 mol% (S. Chatterjee & A. Chatterjee, 2006). It is suggested that the present sample possibly forms a solid solution of Ti1-*x*Ge*x*O2. The solubility range of Ge is therefore found to be enlarged as a result of elevating the temperature from 923 to 1273K. The standard powder of TiO2 employed here has anatase structure, since the matrix of the Ge/TiO2 composite thin films had anatase-dominant structure (Abe et al., 2008b). However, the product thus powder-synthesized resulted in rutile structure because of phase transition from anatase to rutile at 973K (The Mark Index, 1968). In contrast, the GeO2 peaks, which are indicated by a filled circle, begin to appear in the range exceeding 0.3. Their peak positions seem to remain the same with respect to *x*, suggesting no solubility range of Ti in GeO2 at 1273 K. The two phases of the Ti1-*x*Ge*x*O2 and

(200)

(301)

(002)

(220)

(211)

*Ti1-xGex O2*

GeO2

(310)

0

GeO2 are therefore formed in such concentration range.

1000

circle indicates GeO2 (after Abe , 2009).

solubility range of Ge.

2000

3000

4000

intensity (arb. unit)

5000

 *x* 0.4 0.3 0.1 0.04

0.02

(110)

(101)

6000

7000

Fig. 2.5. Lattice constant of Ti1-*x*Ge*x*O2 solid solution vs Ge concentration (after Abe , 2009).

Fig. 2.6. Typical optical absorption spectra of Ti1-*x*Ge*x*O2 solid solution vs Ge concentration (after Abe , 2009).

Next, the solubility limit of Ge in the Ti1-*x*Ge*x*O2 is determined through the variation of the lattice constant. Figure 2-5 depicts the lattice constant of the Ti1-*x*Ge*x*O2 solid solution as a function of *x*. Here, the lattice constant of the tetragonal system is estimated from the (200) and (002) reflections. Their peak intensities were found to be relatively weak (Fig. 2-4), but the peak position can be distinctly determined from Lorentzian fitting of the spectra, containing a measurement error of about 0.06 deg in 2 as a result of four repetitive measurements. Accordingly, the lattice constant results in containing a maximum calculation error of about 0.0006 nm. In the preliminary experiment, a mass reduction during the heat treatment was found to be less than 0.1% in standard powders of TiO2 and GeO2, suggesting a small amount of sublimation. The nominal content of Ge is therefore employed here as a composition of the product. It is clearly seen in the figure that the lattice constant in both reflections is first decreased linearly in proportion to *x*, and becomes constant irrespective of *x* in the range exceeding 0.25. According to Vegard's law (Vegard, 1921), an on-setting composition *x* to deviate from the linearity is regarded as a solubility

One-Step Physical Synthesis of Composite Thin Film 157

having a rutile structure for the powder and an anatase structure for the composite films. Therefore, the matrix of the composite film possibly formed a solid solution of Ti1-*x*Ge*x*O2. Subsequently, optical absorption should be investigated regardless of whether the solid

Figure 2-6 plots the optical absorption spectra of the powder-synthesized Ti1-*x*Ge*x*O2 solid solution. These spectra are derived from the square root of Kubelka-Munk function (Kubelka & Munk, 1931) because of the indirect band gap structure of TiO2 (Macfarlane et al., 1957). For comparison, the spectrum of GeO2 is also shown. It is clearly seen that the GeO2 is appreciably transparent in the measured range from 2.7 to 3.5 eV, whereas the optical absorption edge of the Ti1-*x*Ge*x*O2 can be clearly observed at approximately 3 eV, and shift to the greater energy region as *x* increases. Therefore, the solid solution of Ti1-*x*Ge*x*O2 is

Just for reference, the band gap can be estimated from a linear extrapolation to zero of the optical absorption edge, and is then summarized in Fig. 2-7(a). Error bars indicative of the possible variation in energy gap are used to plot the data. The energy band gap increases monotonically from 2.98 to 3.03 eV with respect to *x*, and becomes constant in the range exceeding 0.25. The energy shift is therefore achieved to be 0.05 eV at a solubility limit of 0.23. In fact, the Ge/TiO2 composite thin films were compositionally optimized at a relatively low Ge concentration of 6 to 9at.% (Abe et al., 2008b), which indicates the total amount of Ge contained in both the matrix and the nanogranules. Hence, the energy shift in the matrix of the composite thin film is considered to be negligibly small (less than 0.01 eV). From these results, the matrix of the Ge/TiO2 composite thin films possibly formed a solid solution of Ti1-*x*Ge*x*O2 during the post annealing, but did not exhibit the vis-NIR absorption. Figure 2-7(b) depicts the optical absorption spectra of the Ge/TiO2 thin film and a solid solution of the Ti1-*x*Ge*x*O2 powder. Here, Ge concentration in the film was analyzed to be 8.7 at.%, and a similar concentration of *x*=0.1 in the powder was also presented for comparison. The absorption spectrum of the Ti1-*x*Ge*x*O2 powder was obtained by means of the Kubelka-Munk function (Kubelka & Munk, 1931) through a diffused reflectance spectrum. The vis-NIR absorption was clearly observed in the Ge/TiO2 film, while an optical absorption edge of the synthesized powder was observed at UV region. It was therefore concluded that the

In the previous sections, valuable characteristics of the vis-NIR absorption and the anatasedominant structure of TiO2 matrix were simultaneously retained in the Ge/TiO2 composite thin films. However, it was unclear whether the vis-NIR absorption (Fig. 2-3) was due to the presence of Ge nanogranules, since an X-ray diffraction peak of Ge was not observed in the optimized composition range. In this section, we have investigated the presence of Ge nanogranules embedded in the anatase-dominant structure of TiO2 thin films, and clarified

Figure 2-8 depicts the size distribution of nanogranules in the Ge/TiO2 composite thin films. These profiles were estimated from small angle X-ray spectroscopy (SAXS) analysis of Guinier fitting for an experimental result (the inset in Fig.2-8). In this case, Ge chips of 3 and the oxygen ratio of 0.3% was adopted during the deposition, and Ge concentration was analyzed to be 8.7at.%, and the film exhibited the vis-NIR absorption [Fig. 2-7(b)]. In the pinhole-collimated apparatus of SAXS measurement, X-ray was injected perpendicularly to the film surface, providing in-plane structural characteristic. As can be seen in the figure, the

solution exhibits the vis-NIR absorption.

found to unexhibit the vis-NIR absorption.

Ti1-*x*Ge*x*O2 solid solution unexhibited such vis-NIR absorption.

**2.3 Quantum size effect of Ge in TiO2 matrix** 

the reason for the vis-NIR absorption.

limit of Ge. It is therefore determined to be 0.23 0.01 at 1273 K, having 0.22 at (200) and 0.24 at (002) reflection. Thus, the two-phase region consistently involves the fixed composition of Ti0.77Ge0.23O2 and GeO2. It can be clearly explained in terms of Gibb's phase rule. Specifically, the number of degrees of freedom is simply estimated to be 1, since the present ternary system has a component of 2. Thus, the state of the system is completely fixed at a given temperature of 1273K. Based on these results, the relation between the lattice constant *L* (nm) and *x* in the solubility range is expressed as follows: *L*=0.4595-0.0162*x* at (200) reflection and *L*=0.2960-0.0075*x* at (002) reflection.

Fig. 2.7. (a) Energy band gap of Ti1-*x*Ge*x*O2 solid solution at room temperature vs Ge concentration. (b) Absorption spectra of the Ge/TiO2 thin film and a solid solution of the Ti1-*x*Ge*x*O2 powder (after Abe , 2009).

In comparison, the lattice constant of the matrix in the Ge/TiO2 composite thin films also decreased with increasing Ge concentration, ranging from 0.9495 to 0.9400nm estimated from the (004) reflection of anatase structure. In this case, the postannealing was performed at 873K for 60min. Such decreasing tendency of the lattice constant is the same as those of the Ti1-*x*Ge*x*O2 powder despite the fact that the crystal structure is different in both samples,

limit of Ge. It is therefore determined to be 0.23 0.01 at 1273 K, having 0.22 at (200) and 0.24 at (002) reflection. Thus, the two-phase region consistently involves the fixed composition of Ti0.77Ge0.23O2 and GeO2. It can be clearly explained in terms of Gibb's phase rule. Specifically, the number of degrees of freedom is simply estimated to be 1, since the present ternary system has a component of 2. Thus, the state of the system is completely fixed at a given temperature of 1273K. Based on these results, the relation between the lattice constant *L* (nm) and *x* in the solubility range is expressed as follows: *L*=0.4595-0.0162*x* at

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Ge/TiO2

 thin film (Ge:8.7at%)

x

Ge0.1Ti0.9O2 solid solution powder

Photon energy / eV

In comparison, the lattice constant of the matrix in the Ge/TiO2 composite thin films also decreased with increasing Ge concentration, ranging from 0.9495 to 0.9400nm estimated from the (004) reflection of anatase structure. In this case, the postannealing was performed at 873K for 60min. Such decreasing tendency of the lattice constant is the same as those of the Ti1-*x*Ge*x*O2 powder despite the fact that the crystal structure is different in both samples,

Fig. 2.7. (a) Energy band gap of Ti1-*x*Ge*x*O2 solid solution at room temperature vs Ge concentration. (b) Absorption spectra of the Ge/TiO2 thin film and a solid solution of the

1234

a)

b)

(200) reflection and *L*=0.2960-0.0075*x* at (002) reflection.

*Ti1-xGex O2*

2.98

0.0

0.5

1.0

1.5

Absorbance0.5

Ti1-*x*Ge*x*O2 powder (after Abe , 2009).

2.0

2.5

3.0

2.99

3.00

3.01

Energy band gap / eV

3.02

3.03

3.04

having a rutile structure for the powder and an anatase structure for the composite films. Therefore, the matrix of the composite film possibly formed a solid solution of Ti1-*x*Ge*x*O2. Subsequently, optical absorption should be investigated regardless of whether the solid solution exhibits the vis-NIR absorption.

Figure 2-6 plots the optical absorption spectra of the powder-synthesized Ti1-*x*Ge*x*O2 solid solution. These spectra are derived from the square root of Kubelka-Munk function (Kubelka & Munk, 1931) because of the indirect band gap structure of TiO2 (Macfarlane et al., 1957). For comparison, the spectrum of GeO2 is also shown. It is clearly seen that the GeO2 is appreciably transparent in the measured range from 2.7 to 3.5 eV, whereas the optical absorption edge of the Ti1-*x*Ge*x*O2 can be clearly observed at approximately 3 eV, and shift to the greater energy region as *x* increases. Therefore, the solid solution of Ti1-*x*Ge*x*O2 is found to unexhibit the vis-NIR absorption.

Just for reference, the band gap can be estimated from a linear extrapolation to zero of the optical absorption edge, and is then summarized in Fig. 2-7(a). Error bars indicative of the possible variation in energy gap are used to plot the data. The energy band gap increases monotonically from 2.98 to 3.03 eV with respect to *x*, and becomes constant in the range exceeding 0.25. The energy shift is therefore achieved to be 0.05 eV at a solubility limit of 0.23. In fact, the Ge/TiO2 composite thin films were compositionally optimized at a relatively low Ge concentration of 6 to 9at.% (Abe et al., 2008b), which indicates the total amount of Ge contained in both the matrix and the nanogranules. Hence, the energy shift in the matrix of the composite thin film is considered to be negligibly small (less than 0.01 eV). From these results, the matrix of the Ge/TiO2 composite thin films possibly formed a solid solution of Ti1-*x*Ge*x*O2 during the post annealing, but did not exhibit the vis-NIR absorption. Figure 2-7(b) depicts the optical absorption spectra of the Ge/TiO2 thin film and a solid solution of the Ti1-*x*Ge*x*O2 powder. Here, Ge concentration in the film was analyzed to be 8.7 at.%, and a similar concentration of *x*=0.1 in the powder was also presented for comparison. The absorption spectrum of the Ti1-*x*Ge*x*O2 powder was obtained by means of the Kubelka-Munk function (Kubelka & Munk, 1931) through a diffused reflectance spectrum. The vis-NIR absorption was clearly observed in the Ge/TiO2 film, while an optical absorption edge of the synthesized powder was observed at UV region. It was therefore concluded that the Ti1-*x*Ge*x*O2 solid solution unexhibited such vis-NIR absorption.

### **2.3 Quantum size effect of Ge in TiO2 matrix**

In the previous sections, valuable characteristics of the vis-NIR absorption and the anatasedominant structure of TiO2 matrix were simultaneously retained in the Ge/TiO2 composite thin films. However, it was unclear whether the vis-NIR absorption (Fig. 2-3) was due to the presence of Ge nanogranules, since an X-ray diffraction peak of Ge was not observed in the optimized composition range. In this section, we have investigated the presence of Ge nanogranules embedded in the anatase-dominant structure of TiO2 thin films, and clarified the reason for the vis-NIR absorption.

Figure 2-8 depicts the size distribution of nanogranules in the Ge/TiO2 composite thin films. These profiles were estimated from small angle X-ray spectroscopy (SAXS) analysis of Guinier fitting for an experimental result (the inset in Fig.2-8). In this case, Ge chips of 3 and the oxygen ratio of 0.3% was adopted during the deposition, and Ge concentration was analyzed to be 8.7at.%, and the film exhibited the vis-NIR absorption [Fig. 2-7(b)]. In the pinhole-collimated apparatus of SAXS measurement, X-ray was injected perpendicularly to the film surface, providing in-plane structural characteristic. As can be seen in the figure, the

One-Step Physical Synthesis of Composite Thin Film 159

region with spherical geometry corresponds to Ge nanogranule, and their lattice image can be clearly seen. The average size is estimated to be about 2nm. Furthermore, their average size is also estimated to be about 5nm by SAXS analysis. These estimated sizes are found to be close each other, and the Ge nanogranules are sufficiently small to create the quantum size effect because of the exciton Bohr radius of 24.3nm in Ge (Maeda et al., 1991). Therefore, the shift of optical absorption (Fig. 2-3) is reasonably due to the Ge nanogranules embedded

Co-sputtering thus employed in the above section is useful for forming a composite thin film consisting of semiconductor nanocrystals embedded in a matrix because of its simple preparation process and consequent low cost. In the material design, based on the heat of formation, nanocrystal and matrix are clearly phase-separated in spite of the co-deposition from multiple sources (Abe et al., 2008b; Ohnuma et al., 1996). However, it is generally found that sputtering techniques often damage a film due to contamination of the fed gas and high-energy bombardment of the film surface. Thermal evaporation in a high-vacuum atmosphere seems to be better as a preparation technique from the point of view of film quality. In addition, the present study focuses on the insolubility of the material system, since simultaneous evaporation from multiple sources often provides a solid solution (Nill,

Fig. 3.1. HWD apparatus used in the study. It consists of four electric furnaces for substrate,

The PbSe-ZnSe system is a candidate for the composite. In the bulk thermal equilibrium state, the mutual solubility range is quite narrow, less than 1mol%, at temperatures below 1283K (Oleinik et al., 1982). In addition, a composite thin film of PbSe nanocrystal embedded in ZnSe matrix is capable of exhibiting the quantum size effect because of the relatively large exciton Bohr radius of 46nm in PbSe (Wise, 2000) and the relatively wide band gap of 2.67eV in ZnSe (Adachi & Taguchi, 1991). Hence, the optical gap of PbSe nanocrystals will probably be tuned to the maximum solar radiation spectrum. The

in Ti1-*x*Ge*x*O2 matrix.

**3. PbSe/ZnSe composite thin films** 

et al., 1973; Holloway & Jesion, 1982; Abe & Masumoto, 1999).

wall, source-1, and source-2 (after Abe, 2011).

size profile distributed broadly, and mean radius of nanogranules was estimated to be 1.9 nm (3.8nm in diameter), ranging the radius from ~0.5 to 8nm. The SAXS analysis therefore strongly suggested that nanoscale material was embedded in the film, possibly attributing to Ge nanogranules or another phase of the Ti1-*x*Ge*x*O2 matrix. Successively, the size of Ti1 *<sup>x</sup>*Ge*x*O2 matrix was estimated by HREM.

Fig. 2.8. Size distribution of nanogranules derived from the SAXS analysis. The inset depicts SAXS spectrum (after Abe et al., 2008c).

Fig. 2.9. (a) HREM image of anatase structure of the matrix in Ge/TiO2 thin films (Abe et al., 2008c). (b) HREM image of Ge nanogranules embedded in the matrix (after Abe et al., 2008b).

Figure 2-9(a) presents the HREM image of the anatase-structured matrix at an oxygen ratio of 0.3%. Lattice image of the anatase structure was clearly observed, and size of their grains was estimated to be ~30nm. The size exceeded that of the nanogranules estimated by SAXS. Figure 2-9(b) presents an HREM image of Ge nanogranules embedded in Ge/TiO2 composite film at a Ge concentration of 8.7at.%. In the figure, the slightly bright contrast

size profile distributed broadly, and mean radius of nanogranules was estimated to be 1.9 nm (3.8nm in diameter), ranging the radius from ~0.5 to 8nm. The SAXS analysis therefore strongly suggested that nanoscale material was embedded in the film, possibly attributing to Ge nanogranules or another phase of the Ti1-*x*Ge*x*O2 matrix. Successively, the size of Ti1-

02468

r / nm

Fig. 2.8. Size distribution of nanogranules derived from the SAXS analysis. The inset depicts

Fig. 2.9. (a) HREM image of anatase structure of the matrix in Ge/TiO2 thin films (Abe et al., 2008c). (b) HREM image of Ge nanogranules embedded in the matrix (after Abe et al.,

Figure 2-9(a) presents the HREM image of the anatase-structured matrix at an oxygen ratio of 0.3%. Lattice image of the anatase structure was clearly observed, and size of their grains was estimated to be ~30nm. The size exceeded that of the nanogranules estimated by SAXS. Figure 2-9(b) presents an HREM image of Ge nanogranules embedded in Ge/TiO2 composite film at a Ge concentration of 8.7at.%. In the figure, the slightly bright contrast


Log I(q) (arb. unit)

100

q / nm-1

*<sup>x</sup>*Ge*x*O2 matrix was estimated by HREM.

Frequency (normalized)

SAXS spectrum (after Abe et al., 2008c).

2008b).

0.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

region with spherical geometry corresponds to Ge nanogranule, and their lattice image can be clearly seen. The average size is estimated to be about 2nm. Furthermore, their average size is also estimated to be about 5nm by SAXS analysis. These estimated sizes are found to be close each other, and the Ge nanogranules are sufficiently small to create the quantum size effect because of the exciton Bohr radius of 24.3nm in Ge (Maeda et al., 1991). Therefore, the shift of optical absorption (Fig. 2-3) is reasonably due to the Ge nanogranules embedded in Ti1-*x*Ge*x*O2 matrix.
