InSe is an interesting layer-structured III-VI group semiconductor with a moderately direct band gap, high electron mobility, and pronounced photoluminescent response, thus showing diverse potential applications in the fields of photovoltaics, optics, thermoelectrics, and so on^{[1⇓⇓⇓⇓⇓⇓⇓-9]}. For example, Han et al.^[1] reported InSe as one of the most promising materials with absolute advantages in field-effect transistors (FETs) due to its high electron mobility and stable material properties. Cao et al.^[2] announced hBN-encapsulated atomically thin InSe allowed high-quality optics and electron transport devices. Yu et al.^[3] found that multilayer InSe-based diode showed a high forward rectification ratio over 10³ without gate-modulation at room temperature, which was superior to most multilayer van der Waals heterojunctions (vdWHs) devices. Cui et al.^[4] revealed that InSe doped with Sn achieved a thermoelectric figure of merit ZT = 0.23 at 830 K by increasing the carrier concentration from ~10¹⁴ cm^-3 to ~10¹⁵ cm^-3, highlighting its potential as a thermoelectric material. Recently, it is reported that single-crystalline InSe exhibits a remarkable plastic deformability that is rarely observed in inorganic semiconductors, offering a new avenue towards flexible/hetero-shaped electronic devices^[10⇓-12]. Therefore, it is convinced that the research on InSe semiconductor will develop fast in the future.

Large-size crystal is essential to studying the structure and properties of InSe semiconductors. On the one hand, it can reflect the nearly intrinsic structures, defects, and properties. On the other hand, the big crystal is an important raw material to prepare mono- or few layer materials by e.g., mechanical exfoliation. However, it should be noted that the preparation of large-size InSe crystal is difficult due to the inconsistent melting of In and Se elements and the peritectic reactions between InSe/In₆Se₇/In₄Se₃ according to the In-Se phase diagram^[5]. Up to now, a lot of approaches have been developed to produce InSe crystals, such as the Czochralski method, horizonal gradient freeze method, low temperature liquid phase method, vapor transfer method, vertical Bridgman method, and so on^[6]. However, it remains a persistent challenge to produce large or high-quality InSe crystals. For instance, Chevy et al.^[13] ever produced InSe crystal from the stoichiometric solution by using the Czochralski method, but many parasitic nucleations appeared on the (001) faces of the crystal. Tang et al.^[14] explored a low temperature liquid phase method using InSe_0.77 solution and Se gas source as raw materials, resulting in the inclusion of a significant amount of In elements in the crystals. Medvedeva et al.^[15] reported that the InSe crystal produced via the vapor transfer method was only 0.3 mm× 0.3 mm×0.1 mm in size and some In₆Se₇ phases were embodied. In recent years, the vertical Bridgman method was considered a feasible way for bulk InSe crystals preparation. As an example, a ϕ14 mm×40 mm boule with large area InSe crystal was successfully obtained from a stoichiometric melt^[16]. Moreover, a ϕ25 mm×75 mm ingot was also fabricated from the In_0.52Se_0.48 non-stoichiometric solution in our previous work^[10], which displayed a high mole percentage of InSe crystal due to the peritectic reaction in the melt. Frankly speaking, in order to meet the rapidly growing demand for academic research and applications, the development of novel methods for large-size InSe crystal growth remains an urgent challenge.

In this work, a zone melting method is introduced for InSe crystal preparation. Compared to the traditional vertical Bridgman method, this technique has obvious advantages of low cost and solid-liquid interface optimization during crystallization, which has been successfully employed for many kinds of semiconductor crystals fabrication in the past, such as GaAs, SnSe, Mg₃Sb₂, ZnTe, and so on^{[17⇓⇓-20]}. Ultimately, a boule with dimensions of ϕ27 mm×130 mm is produced, and a pile of large area slab-like InSe crystals are smoothly peeled from the ingot along the cleavage plane. Furthermore, the crystal structure, optical, electrical and thermal properties are also characterized. The obtained results indicate that the zone melting method is indeed an effective way for large-size InSe crystal growth which can be used for research and applications in the future.

High-purity In and Se elements (>99.99%) with the mole ratio of 0.52 : 0.48 were used as start materials and the total weight was about 342.48 g. Fig. 1(a) shows the dependence of weight percentage of In and Se on temperature measured by thermogravimetry equipment (TG-DTA 8121, Japan). It is found the weight of In kept stable in the range of 300-1000 K. However, there is a significant loss of Se beginning at 620 K, and it is completely exhausted near 790 K. Based on this knowledge, a rocking method is introduced for polycrystal synthesis. The In and Se elements were loaded into a ϕ27 mm quartz ampoule that was sealed with <10^-3 Pa vacuum and then placed into a 1020 K rocking furnace. After the start materials were melted and soaked for 10 min, the furnace was worked at a rate of 30 r/min for half an hour to promote the reaction sufficiently. Then, the furnace was cooled to room temperature naturally. InSe crystal growth was carried out by a homemade zone melting furnace, as the schematic diagram described in Fig. 1(b). A quartz crucible containing the prepared In_0.52Se_0.48 polycrystal was placed into the furnace and supported by an Al₂O₃ block. A pair of Pt/Pt-10%Rh thermocouples were installed near the bottom of quartz crucible for temperature indication. The furnace temperature was controlled at ~970 K, a sufficiently high temperature for InSe crystal preparation. After the polycrystal was melted and soaked for 10 h, InSe crystal growth was gradually executed at a rate of 0.6 mm/h under a temperature gradient of ~30 K/cm. Finally, the furnace was cooled to room temperature at a rate of 40-50 K/h.

The crystal density (ρ) was measured via the Archimedes principle. The phase structure was analyzed by X-ray diffractometer (Bruker D8, Germany) using Cu Kα radiation (λ=0.15406 nm) at room temperature. The crystal composition was measured by energy dispersive spectrometer (Oxford Instruments, Britain). The transmittance was examined by ultraviolet visible near infrared spectrophotometer (LAMBDA, China). The crystal dislocations were revealed by using the acid solution (30 g K₂Cr₂O₇, 50 mL concentrated H₂SO₄ and 300 mL distilled water), and then observed by normal optical microscope (FLY-L3230, China) and white light confocal microscope (ZEISS Smart Proof 5, Germany). The electrical conductivity was tested by thermoelectric measurement equipment (ULVAC-RIKO, ZEM-3) from room temperature to 800 K, and the thermal diffusivity (D) was characterized through a laser flash method (Netzsch, LFA-457, Germany) over 300-800 K.

According to the In-Se phase diagram in Fig. 2, the inconsistent melting of In and Se elements and the peritectic reactions between InSe/In₆Se₇/In₄Se₃ make the initial mole ratio crucial for obtaining pure phased InSe single crystals. In detail, if In and Se elements are weighted according to their standard stoichiometric ratio, In₆Se₇ will firstly crystallize near 630 ℃ (as the red dotted line indicated), followed by the production of InSe when the temperature is lowered to ~600 ℃, where a peritectic reaction occurs between In₆Se₇ and the solution. However, when the non-stoichiometric melt In_0.52Se_0.48 is cooled to ~600 ℃, InSe will firstly form and part of them will transfer to In₄Se₃ through another peritectic reaction at around 550 ℃ (as the blue dotted line indicated). It should be noted that the window passage for InSe fabrication from non-stoichiometric solution is much narrow. Chevy et al.^[13] reported the upper limit of Se was 45.0% (in atomic) and the lower limit was only 34.4% (in atomic). Nevertheless, Imai et al.^[21] modified the In-Se phase diagram depending on the careful composition design and differential thermal analysis (DTA). Ultimately, the window passage was adjusted to 38.0%-48.3% (in atomic). Therefore, a non-stoichiometric In_0.52Se_0.48 solution, rather than stoichiometric InSe, provides a more feasible and effective way to grow large-sized InSe crystal.

The narrow high temperature zone of the furnace is much valuable for InSe crystal preparation. As previous literature reported, InSe crystal has a low thermal conductivity compared to those of GaAs, InSb, GaSb, etc^{[17,22⇓ -24]}. Therefore, it is anticipated that a large amount of crystallization latent heat will accumulate near the solid-liquid interface during the crystal growth, leading to a concave interface that might introduce kinds of defects in the crystal, such as inclusions, twinning, heavy dislocations, parasitic nucleations, etc^[25-26]. Fortunately, the narrow temperature zone is beneficial for solid-liquid interface optimization as the latent heat can be conducted along both up and down directions simultaneously.

Fig. 3(a) exhibits the as-grown ingot just taken out from the quartz ampoule. It is about ϕ27 mm×130 mm in dimensions, the largest size so far. Table 1 lists the growth results of InSe crystals by different methods in the past years. The ingot can be divided into two parts according to the peritectic reaction principle. The powder XRD patterns from middle and top parts of the ingot are indexed to be hexagonal InSe (PDF#34-1431) and In₄Se₃ (PDF#51-0808) phases, respectively, as shown in Fig. 3(b). In addition, some In elements (PDF#05-0642) are detected in the In₄Se₃ matrix because the crystal grows from an In-rich solution. Such residual In phase is a common problem that also happened in the vertical Bridgman method using the same In_0.52Se_0.48 compound as raw material^[27]. Fig. 3(c) illustrates the transfer relationship between InSe and In₄Se₃ phases during crystal growth. When In_0.52Se_0.48 solution is moved from high temperature zone to the temperature gradient zone, InSe phase would firstly crystallize, then the In₄Se₃ phase will gradually grow up through the reaction between InSe and the In-rich solution. The final mole percentage of InSe in the whole ingot is calculated to be ~83% according to the following formula^[21]:

Where M_InSe is the InSe weight, M_Ingot is the ingot weight, C₀= 48% is the initial Se content, C_InSe= 50% is the mole percentage of Se in InSe, and C_p= 38% is the lower limit of Se among the window passage range.

InSe is a layered structure material: the monolayer is composed of Se-In-In-Se atomic planes through strong covalent/ionic bonds while the layers are connected via the weak van der Waals interactions. Therefore, InSe crystal can be readily exfoliated. A pile of slab-like InSe crystals are smoothly peeled from the ingot along the cleavage plane. Fig. 4(a) is a typical specimen with an area of about ϕ27 mm× 50 mm. Fig. 4(b) exhibits the slab has good single-crystalline character as only (00l) peaks are detected in the XRD pattern examined on the cleavage plane. Here, attention should be paid to the wrinkled crystal surfaces and its step configurations, which are mainly attributed to the soft mechanical property and layered structure of InSe when they are manually processed. Fig. 4(c) shows a piece of mirror-like InSe wafer and a fresh flake is disclosed by tweezers. The new exposed surface is analyzed by SEM and the layered morphology is clearly observed in Fig. 4(d). Fig. 4(e) shows the EDS mappings reveal In and Se elements are uniformly distributed in the matrix. The EDS line scan diagram in Fig. 4(f) further verifies the crystal has a high composition homogeneity. Based on these results, it is convinced the zone melting method is indeed a competitive technique for large-size InSe crystal fabrication.

The transmittance spectrum of a 0.8 mm thickness (001) wafer is given in Fig. 5(a). It is totally opaque below 1020 nm relates to its absorption edge. However, as the wavelength is gradually increased to 1060 nm, the transmittance (T) undergoes a sharp increase. After that, the growth of T is gentle and ultimately reaches the highest of 55.1% at 1800 nm. This result means InSe crystal has nice near infrared transmittance. Based on this transmittance spectrum, the band gap energy E_g of InSe can be deduced by Equation (2)^[18]:

Here h is the Planck’s constant, v is the frequency of incident photon, C is a constant for direct transition, and α is the absorption coefficient can be gained by:

Where d is the wafer thickness and T is the transmittance. Finally, the dependence of (αhv)² on hv is drawn in Fig. 5(b) and E_g is deduced to be ~1.22 eV that agrees well with the previous studies^[15,23].

Fig. 6(a) shows the relationship of electrical conductivity (σ) with temperature along (001) plane. It is noted here that the σ is not detected below 450 K which implies the InSe crystal has high resistance near room temperature. The σ is kept on a low level before 600 K, and the smallest value is about 0.58 S·m^-1 at 450 K. However, as temperature surpasses 600 K, the σ suddenly rises and finally reaches a biggest value of 1.55×10² S·m^-1 at 800 K. Such electrical conductivity variation tendency is mainly attributed to the intrinsic semiconducting transport behavior of InSe. As for the thermal transport behavior, the thermal diffusion D perpendicular to (001) plane is studied, as shown in Fig. 6(b). When temperature is increased from 300 K to 800 K, the D is reduced more than half from 0.79 mm²/s to 0.33 mm²/s. However, as temperature is back to 300 K, the D returns to 0.72 mm²/s that implies InSe has good thermal diffusion reversibility. Based on the D, the thermal conductivity κ can be obtained by Equation (4)^[37]:

Where N is the number of atoms in InSe molecular formula, R is the molar gas constant, ρ= 5.568 g/mm³ is the measured density and M is molecular weight of InSe. Obviously, the temperature-κ curve would display a similar shape compared with that of thermal diffusion. The average κ at 300 K is about 1.08 W·m^-1·K^-1 and the lowest value is 0.48 W·m^-1·K^-1 at 800 K which is consistent with the other reported results^[23]. InSe is a typical van der Waals layer-structured semiconductor and is easy to cleave along the in-plane direction, leading to difficulty in obtaining flake along the out-of-plane directions. To the best of our knowledge, the in-plane thermal conductivity for bulk InSe is not available so far, and this remains to be addressed in the future. The measured electrical and thermal behaviors in this work provide significant reference for InSe crystal application.

In summary, a ϕ27 mm×130 mm InSe crystal has been successfully prepared using a zone melting method from non-stoichiometric In_0.52Se_0.48 solution based on the peritectic reaction of In-Se system. The productivity ratio of InSe crystal is about 83%. The as-grown InSe crystal shows a layered crystal structure and the In/Se elements are uniformly distributed. The band gap energy is determined as ~1.22 eV via the transmittance spectrum. The crystal has a highest electrical conductivity of 1.55×10² S·m^-1 along (001) and a lowest thermal conductivity of 0.48 W·m^-1·K^-1 perpendicular to (001) near 800 K.