**3.1. Crystal structures of bismuth chalcogenides**

The crystal structures of bismuth chalcogenides (e.g., Bi2Te3, Bi2Se3, and Bi3Se2Te) are usually described by a hexagonal cell consisting of 15 layers of atoms stacking along the *c*-axis with a sequence shown below [17], as shown in **Figure 4a** and **b**.

**Figure 4.** Crystal structures of (a) Bi2Te3, (b) Bi2Se3, and (c) Bi3Se2Te in the form of (Bi2)*m*(Bi2Se2Te)*n* (*m* = 1, *n* = 2) homologous series. The unit cells are marked with black thick boxes. (d) X-ray diffraction patterns of the typical TE bismuth chalcogenide thin films grown at 300°C on SiO2/Si substrates.

A 5-atomic-layer-thick lamellae of -(Te(1)-Bi-Te(2)-Bi-Te(1))- or -(Se(1)-Bi-Se(2)-Bi-Se(1))- is called a quintuple layer, QL, in which the Te(1)-Bi and Bi-Te(2) or Se(1)-Bi and Bi-Se(2) are ionic-covalent bonds. Because of the weak binding (i.e., Van der Waals force) between Te or Se layers, bismuth chalcogenides could be cleaved easily along the plane perpendicular to the *c*-axis. It also induces the anisotropic thermal/electrical transport properties. For example, the thermal conductivity along the plane perpendicular to the *c*-axis (~1.5 W m−1 K−1) is nearly two times higher than that along the *c*-axis direction (~0.7 W m−1 K−1) [17, 18].

The crystal structures of Bi3Se2Te can be formed by ordered stacking of Bi2Se2Te and Bi2 building blocks, that is, (Bi2)*m*(Bi2Se2Te)*n* (*m* = 1, *n* = 2) [19, 20], in which the covalently connected double layers of bismuth (Bi–Bi) lie between two QL (Se-Bi-Te-Bi-Se) blocks (**Figure 4c**); the (Bi–Bi)

strictly alternates with two QL (Se–Bi–Te–Bi–Se) blocks [9, 20]. **Figure 4d** shows the typical XRD patterns of Bi2Te3, Bi2Se3, and Bi3Se2Te thin films grown on SiO2/Si substrates at *T*S = 300°C. They exhibit the dominance of (0 0 1) family planes of the rhombohedral phases of Bi2Te3 (PDF#82-0358), Bi2Se3 (PDF#33-0214), and Bi3Se2Te (JCPDS 00-053-1190), indicating that the films are highly c-axis oriented (i.e., textured films).

### **3.2. Introduction to thermoelectrics and applications**

Thermoelectric materials are solid-state energy converters in which the combination of thermal, electrical, and semiconducting properties allows them to be used to convert waste heat into electricity or electrical power directly into cooling and heating [21].

### *3.2.1. The thermoelectric figure of merit (ZT)*

pulse [14]. For the growth of Bi2Te3 thin films, *T*<sup>S</sup> was varied from room temperature (30°C) to 380°C and the Ar ambient pressure (*PAr*) was at 80 Pa. The number of laser pulses was 12,000 and the deposition took 40 min. The average growth rate was approximately 0.52 Å/pulse [15]. For the growth of Bi-Se-Te thin films, the depositions were at *T*S of 200–350°C and a helium ambient pressure (*P*He) of 0.027–86.7 Pa. The number of laser pulses was 9000 and the deposition

The crystal structures of bismuth chalcogenides (e.g., Bi2Te3, Bi2Se3, and Bi3Se2Te) are usually described by a hexagonal cell consisting of 15 layers of atoms stacking along the *c*-axis with a

**Figure 4.** Crystal structures of (a) Bi2Te3, (b) Bi2Se3, and (c) Bi3Se2Te in the form of (Bi2)*m*(Bi2Se2Te)*n* (*m* = 1, *n* = 2) homologous series. The unit cells are marked with black thick boxes. (d) X-ray diffraction patterns of the typical TE bismuth

A 5-atomic-layer-thick lamellae of -(Te(1)-Bi-Te(2)-Bi-Te(1))- or -(Se(1)-Bi-Se(2)-Bi-Se(1))- is called a quintuple layer, QL, in which the Te(1)-Bi and Bi-Te(2) or Se(1)-Bi and Bi-Se(2) are ionic-covalent bonds. Because of the weak binding (i.e., Van der Waals force) between Te or Se layers, bismuth chalcogenides could be cleaved easily along the plane perpendicular to the *c*-axis. It also induces the anisotropic thermal/electrical transport properties. For example, the thermal conductivity along the plane perpendicular to the *c*-axis (~1.5 W m−1 K−1) is nearly two times

The crystal structures of Bi3Se2Te can be formed by ordered stacking of Bi2Se2Te and Bi2 building blocks, that is, (Bi2)*m*(Bi2Se2Te)*n* (*m* = 1, *n* = 2) [19, 20], in which the covalently connected double layers of bismuth (Bi–Bi) lie between two QL (Se-Bi-Te-Bi-Se) blocks (**Figure 4c**); the (Bi–Bi)

took 15 min. The average growth rate was approximately 0.6 Å/pulse [16].

60 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

**3. Thermoelectric bismuth chalcogenide thin films**

**3.1. Crystal structures of bismuth chalcogenides**

chalcogenide thin films grown at 300°C on SiO2/Si substrates.

higher than that along the *c*-axis direction (~0.7 W m−1 K−1) [17, 18].

sequence shown below [17], as shown in **Figure 4a** and **b**.

The performance of the thermoelectric materials is often denoted as figure of merit *Z* whose unit is K–1 or *ZT* with the dimensionless unit [17, 22].

$$ZT = \frac{\alpha^2 \sigma}{\kappa} T = \frac{\alpha^2 \sigma}{\kappa\_\varepsilon + \kappa\_\perp} T \tag{2}$$

where *σ*, *α*, *κ*, and *T* are the electrical conductivity, Seebeck coefficient, thermal conductivity, and absolute temperature, respectively. The total thermal conductivity can be split into a lattice contribution (*κL*) and an electronic contribution (*κE*). The quantity *α*<sup>2</sup> *σ* is commonly used to represent the thermoelectric power factor (*PF*).

The efficiency of a thermoelectric device is directly related to *ZT*. For power generation, the maximum efficiency (*η*) is expressed by [23]

$$\eta = \frac{T\_h - T\_c}{T\_h} \cdot \frac{\sqrt{1 + Z\overline{T}} - 1}{\sqrt{1 + Z\overline{T}} + \frac{T\_c}{T\_h}} \tag{3}$$

and for air-conditioning or refrigeration, the coefficient of performance is [23]

$$\text{COP} = \frac{T\_c}{T\_h - T\_c} \cdot \frac{\sqrt{1 + Z\overline{T}} - \frac{T\_h}{T\_c}}{\sqrt{1 + Z\overline{T}} + 1} \tag{4}$$

where *Th* and *Tc* are the hot-end and cold-end temperatures of the thermoelectric materials, respectively, and is the average temperature of *Th* and *Tc*. Therefore, the enhanced *ZT* value of TE materials is important to increase the COP for practical applications.

### *3.2.2. Conflicting properties in thermoelectric materials*

Maximizing *ZT* is challenging due to the interdependence of the TE parameters. An increased power factor *α2 σ* by optimizing the carrier concentration *n* and/or a reduced lattice thermal conductivity *κL* by introducing the scattering centers are necessary to enhance *ZT* value. The dependences of these parameters with scattering factor *r*, carrier effective mass *m\** , carrier mobility *μ*, and their interconnectivity limits the *ZT* to about 1 in large bulk materials [24].

The electrical conductivity (*σ*) and electrical resistivity (*ρ*) are related to *n* through the carrier mobility *μ*:

$$1/\rho = \sigma = \text{ue}\mu\tag{5}$$

The Wiedemann-Franz Law [2] states that the electronic contribution to the thermal conductivity is proportional to the electrical conductivity (*σ*) of the materials, with the relationship being

$$
\kappa\_e = L\sigma T = \text{me}\mu L\,T\tag{6}
$$

where *e* is electron charge, and *L* is the Lorenz factor of 2.48 × 10−8 J 2 /K2 C2 for free electrons and this can vary particularly with carrier concentration [2].

The kinetic definition of *α* is the energy difference between the average energy of mobile carriers and the Fermi energy [25]. An increase in *n* leads to the increase in both the Fermi energy and the average energy, but the former increases more rapidly than the latter and thus results in a decrease in *α* value and a reduction factor of *α*<sup>2</sup> *n*. Thus, in attempting to increase *ZT* for most of the homogeneous materials, the carrier concentration (*n*) increases electrical conductivity (*σ*) but reduces the Seebeck coefficient (*α*). For this reason, in metals and degenerate semiconductors (energy-independent scattering approximation), the Seebeck coefficient can be expressed as [2]:

$$\alpha = \frac{8\pi^2 k\_B^2}{3eh^2} m^\* T \left(\frac{\pi}{3n}\right)^{2/3} \tag{7}$$

The high *m\** causes the Seebeck coefficient to rise according to Eq. (7). High *m\** materials generally possess low *μ* which limits the enhancement of power factor by (*m\** )3/2*μ*. Noticeably, the defect scatters are not only the phonons but also the electrons which lead to reduce *κL* as well as *μ*. Therefore, the ratio of *μ/κL* determines the improvement in *ZT* [17, 24]. Although the increase in the ratio is usually experimentally achieved through a greater reduction in *κL* rather than that in *μ*, some fundamental issues in this mechanism are not understood well [24].

**Figure 5** shows the compromise between large *α* and high *σ* in thermoelectric materials that must be struck to maximize the figure of merit *ZT*. Meanwhile, the low carrier concentration will result in lower electrical conductivity with decreasing *ZT*. The *ZT* and *PF* peaks typically occur at carrier concentrations between 1019 and 1021 carriers per cm3 (depending on the material system), which fall in between common metals and semiconductors, that is, the concentrations found in heavily doped semiconductors [2].

**Figure 5.** Maximizing the efficiency (*ZT*) of a thermoelectric device involves a compromise of thermal conductivity (*κ*, plotted on the *y*-axis from 0 to a top value of 10 W m−1 K−1) and Seebeck coefficient (*α*, 0–500 μV K−1) with electrical conductivity (*σ*, 0–5000 Ω−1 cm−1) [2].

### *3.2.3. Overview of thermoelectric applications*

*3.2.2. Conflicting properties in thermoelectric materials*

power factor *α2*

mobility *μ*:

being

can be expressed as [2]:

The high *m\**

Maximizing *ZT* is challenging due to the interdependence of the TE parameters. An increased

conductivity *κL* by introducing the scattering centers are necessary to enhance *ZT* value. The

The Wiedemann-Franz Law [2] states that the electronic contribution to the thermal conductivity is proportional to the electrical conductivity (*σ*) of the materials, with the relationship

The kinetic definition of *α* is the energy difference between the average energy of mobile carriers and the Fermi energy [25]. An increase in *n* leads to the increase in both the Fermi energy and the average energy, but the former increases more rapidly than the latter and thus

*ZT* for most of the homogeneous materials, the carrier concentration (*n*) increases electrical conductivity (*σ*) but reduces the Seebeck coefficient (*α*). For this reason, in metals and degenerate semiconductors (energy-independent scattering approximation), the Seebeck coefficient

è ø

the defect scatters are not only the phonons but also the electrons which lead to reduce *κL* as well as *μ*. Therefore, the ratio of *μ/κL* determines the improvement in *ZT* [17, 24]. Although the increase in the ratio is usually experimentally achieved through a greater reduction in *κL* rather than that in *μ*, some fundamental issues in this mechanism are not understood well [24].

**Figure 5** shows the compromise between large *α* and high *σ* in thermoelectric materials that must be struck to maximize the figure of merit *ZT*. Meanwhile, the low carrier concentration

2/3

causes the Seebeck coefficient to rise according to Eq. (7). High *m\** materials

æ ö <sup>=</sup> ç ÷

*2 2 B \* 2 π k <sup>π</sup> α mT eh 3n*

8

generally possess low *μ* which limits the enhancement of power factor by (*m\**

where *e* is electron charge, and *L* is the Lorenz factor of 2.48 × 10−8 J

and this can vary particularly with carrier concentration [2].

results in a decrease in *α* value and a reduction factor of *α*<sup>2</sup>

mobility *μ*, and their interconnectivity limits the *ZT* to about 1 in large bulk materials [24]. The electrical conductivity (*σ*) and electrical resistivity (*ρ*) are related to *n* through the carrier

dependences of these parameters with scattering factor *r*, carrier effective mass *m\**

62 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

*σ* by optimizing the carrier concentration *n* and/or a reduced lattice thermal

1 / *ρ σ neμ* = = (5)

= = *<sup>e</sup> κ LσT neμLT* (6)

<sup>3</sup> (7)

2 /K2 C2

*n*. Thus, in attempting to increase

, carrier

for free electrons

)3/2*μ*. Noticeably,

TE devices have unique features: no moving parts, substantially less maintenance, quiet operation, high power density, low environmental impact, and high reliability [26]. Commercial use has been made mostly from Peltier thermoelectric cooling (TEC) effect, such as in small refrigerator devices used for camping and outdoor activities, automotive climate control seats, and localized cooling at the hot spots of chips. **Figure 6** gives an overview of the present and potential applications of thermoelectric generators (TEGs) [27]. Indeed, TEGs have been used for the power in miniaturized autarkic sensor systems, automotive waste heat recovery systems, ventilated wood stove, heating systems, water boilers, and heat recovery in industry.

**Figure 6.** Overview of the potential applications of thermoelectric generators [27].
