Scandium nitride (ScN) has emerged as a promising material in various fields due to its exceptional characteristics, including high mechanical strength, hardness, high melting point, high thermal stability, and wide bandgap. This work investigates the thermal behavior of ScN by the measurement of its coefficient of linear thermal expansion (TEC). A (111)-oriented ScN thin film on a (111)-oriented Si substrate is used for the measurements. The lattice parameter is determined using x-ray diffraction, and in situ measurements are performed at elevated temperatures of up to 923 K. The expansion of the material with increasing temperature is modeled using Debye's phonon dispersion. The fitted lattice parameters are used to calculate the TEC, which we measured to be ( 6.61 ± 0.60 ) × 10 6 K 1 at 300 K. Thus, the value is 1.37 × 10 6 K 1 lower than the value published by Tahri et al. [J. Phys.: Condens. Matter 24, 035401 (2011)]. who simulated the TEC for a ScN bulk crystal. This work contributes to the knowledge on thermal properties of ScN and paves the way for further research in this field.

In recent years, ScN has attracted increasing attention in the research community due to its exceptional characteristics, which include high mechanical strength, high hardness, high thermal stability, a high melting point of 2600 °C, an indirect bandgap of 1.14 eV ( Γ X), and a direct one (XX) of ( 2.2 ± 0.2 ) eV.2–5 These properties lead to potential applications in many fields such as electronics, optoelectronics, and thermoelectrics. Scandium nitride (ScN) crystallizes in the rock salt structure, and its unstrained lattice parameter at 0 K is determined to be a = ( 4.5 ± 0.05) Å using calculations based on both the local density approximation and the generalized gradient approximation.1,6–8 When (111)-oriented, it is an excellent fit to GaN(0001), with a lattice mismatch of less than 1%.9,10 Adamski et al.10 have been able to determine a high polarization discontinuity of 1.358 cm 2 at the ScN(111)/GaN(0001) interface. This leads to the accumulation of a two-dimensional electron gas with a high charge carrier density of up to 8.5 × 10 14 cm 2 at the interface.10 This value is around 100 times higher than that of the state-of-the-art AlGaN/GaN heterostructures11 and thus could become very interesting for tunnel junctions or contacts. Furthermore, ScN is very suitable as the semiconductor in metal–semiconductor junctions. ZrN and HfN, which are transition metal nitrides with metallic properties and crystallize in the rock salt structure as well, are often used as the metal. The lattice mismatches between HfN and ScN and between ZrN and ScN are only 0.5%12 and 1.5%,13 respectively. Therefore, the epitaxial growth of ScN on these metals is highly favorable. This is not the case with most of the other semiconductor nitrides, as they predominantly grow in the wurtzite or zinc blende structure.4,14 In addition to the aforementioned technologies, research is also being conducted into the potential utilization of ScN as a dislocation reductor in GaN-based devices such as LEDs or lasers15 and for Schottky diodes.4 

As ScN is such a versatile material, understanding its thermal behavior is crucial for optimizing its performance and reliability in the wide variety of devices mentioned beforehand. The coefficient of linear thermal expansion (TEC) is a fundamental property that indicates the change in length with temperature. It has been determined for most materials and common semiconductors. For example, at 300 K GaN has the TECs α a = 5.6 × 10 6 K–1 and α c = 3.3 × 10 6 K–1 for the lattice parameters a and c, respectively.16 At the same temperature, AlN in the wurtzite structure has a lower TEC of α a = 3.04 × 10 6 K–1 and α c = 2.23 × 10 6 K–1.17 For AlN in the rock salt structure, simulations resulted in a TEC of α a = 8.05 × 10 6 K–1 also at 300 K.18 Excessive thermal expansion or contraction can cause stresses and strains within the material, which in turn can lead to cracks or unwanted dislocations. Materials can be heated for a variety of reasons, including power dissipation from a component or growth processes where temperatures can reach up to 850 °C.19,20 Accurate measurement of the TEC can ensure the unimpaired function of a device over the long term and prevent potential performance degradation. Furthermore, by measuring the TEC of ScN, important information on the fundamental behavior of the material is gathered, which in turn is relevant for understanding its thermodynamic properties. Based on these insights, further material models can be established and theories explored. This includes, for example, the thermal behavior of the promising solid solution alloy AlScN in the rock salt structure. Tahri et al.1 have already performed simulations on the TEC of a ScN bulk crystal as a function of temperature. However, on the measured value for ScN thin films, no data has been published yet. Therefore, in this work, the expansion of ScN(111) thin films was investigated by in situ measurements of the in-plane and out-of-plane lattice parameters a 111 and a 002, respectively.

In this study, we employ a 100 nm thick (111)-oriented ScN thin film that was sputtered onto a Si(111) substrate for measurements. The sample is securely mounted to the DHS 1100 Domed Hot Stage of Anton Paar GmbH with a graphite dome screwed onto it. The chamber is then evacuated to a high vacuum of 5 × 10 8 bar using a turbomolecular pump (TPS mini of Agilent Technologies) to minimize possible oxidation and other reactions of the sample with air. We determine the lattice parameter a by using x-ray diffraction (XRD). For that a X'Pert3 MRD of Malvern Panalytical GmbH with a hybrid monochromator 2xGE(220), a 1°/32 slit to focus the x-ray radiation, a PIXcel3D Medipix 3 detector, and copper- K α 1-radiation with a wavelength of λ = 1.5406 Å are utilized. In situ determinations of the lattice parameters are subsequently performed at higher temperatures. The heating rate is set at 200 K/min with a waiting time of five minutes at the measurement temperature. This is to allow enough time for the heat to spread uniformly across the sample. In addition to the ScN reflexes, the 111 reflex of the Si substrate is measured as well. As the expansion of Si is already well studied and known, we use the measured lattice parameter to determine the temperature of the sample. Therefore, the obtained value is compared to the data measured by Okada et al.21 

Although only one lattice parameter is required to describe the cubic rock salt structure, both symmetric (111 reflex) and asymmetric (002 reflex) 2 θ-scans are performed. Due to a high lattice mismatch of 17.31% between Si(111) and ScN(111), a coincidence site lattice is formed.22 By measuring different reflexes, possible strains can be determined. Figure 1 shows the unit cell of ScN, specifying the lattice parameter and directions. From the plane spacing d hkl, the lattice parameter is determined using the formula a = d hkl · h 2 + k 2 + l 2.23 For the measurement of the 111 reflex, the plane spacing d 111 is equal to one third the spatial diagonal of the unit cell, and a is the average of three possibly varying lattice parameters. For measurements through an asymmetric reflex h00, 0 k 0, or 00l, the lattice parameter corresponds directly to a multiple of the measured plane spacing. This value is therefore not averaged over different edge lengths of the cubic unit cell but specifies a particular lattice parameter. A difference in the lattice parameters determined using the 111 reflex and the ones determined using the 002 reflex would indicate that the growth of the ScN thin film is strained on the Si.

FIG. 1.

Unit cell of rock salt ScN indicating lattice parameter a, [100], [010], [001], and [111] direction.

FIG. 1.

Unit cell of rock salt ScN indicating lattice parameter a, [100], [010], [001], and [111] direction.

Close modal
The expansion of a solid with rising temperature is related to the increasing lattice vibrations of the crystal. Thus, for curve fitting, it is reasonable to use a model based on Debye's phonon dispersion as follows:24,
(1)
The Debye function f ( θ D T ) is defined as follows:24,
(2)
Here, a0 is the lattice parameter at 300 K, and αmax is the TEC that the curve asymptotically approaches. The fitting parameters a0 and αmax are determined using the least squares method, and T is the temperature. The Debye temperature at 300 K θ D , 0 is calculated using the following equation:25,
(3)
where h is Plank's quantum of action, k B is Boltzmann's constant, N A is Avogadro's constant, the molar masses are M Sc = 44.956 g mol and M N = 14.007 g mol, and the number of atoms per unit cell is n rs = 8 for the rock salt structure. The mass density of ScN can be determined by ρ = 4 · ( M Sc + M N ) N A · a 3,25 which we calculated to be ρ = 4.24 g cm 3. To approximate the average sound velocity v m, longitudinal and traversal sound velocity v l and v t are required,25,
(4)
with
(5)
and
(6)
where G is the shear, and B is the bulk modulus. Further calculations and simulated values of the elastic coefficients Cij can be taken from Wu et al.6 For ScN, we evaluated a Debye temperature of θ D , 0 = 882 K. To include the isochoric anharmonicity of the phonons, a temperature-dependent Debye temperature is introduced and expressed by26,
(7)
where γ ( T ) represents the Grüneisen parameter. The values employed in the model were derived from simulations conducted by Tahri et al.1 Despite the consideration of anharmonic effects, their impact on thermodynamic characteristics is rather small for temperatures lower than the melting point (2600 °C).24,27
Through the fitted lattice parameters at different temperatures, the linear thermal expansion coefficient α can be ascertained,28 
(8)
where da(T) describes the change of the lattice parameter caused by the change of temperature dT. The term a ( T d T ) refers to the lattice parameter before the temperature change.

To obtain the lattice parameters, we repeatedly measured the 111 reflex and the 002 reflex. Figure 2 shows the averaged 2 θ / θ-scans of the 111 reflex at each measured temperature. As expected, the 2 θ values decrease with increasing temperature, demonstrating that the lattice parameter expands. Because a solid expands more per temperature step at higher temperatures than at lower temperatures, the distances between two scans increase with increasing temperature.29 At 923 K, less intensity can be seen, which may indicate a starting oxidation or another reaction with residual atoms present in the vacuum.

FIG. 2.

2 θ / θ-scans of the 111 reflex of ScN at every measuring temperature, smoothed by the moving average with four points per window.

FIG. 2.

2 θ / θ-scans of the 111 reflex of ScN at every measuring temperature, smoothed by the moving average with four points per window.

Close modal

The decreasing intensity results in a comparatively high error of 0.011 Å of the last point of measuring at 923 K, as shown in Fig. 3. This figure presents the lattice parameters of ScN as a function of temperature from 300 to 1000 K. The symmetric reflex measured at 300 K yields a lattice parameter of a 111 = ( 4.5187 ± 0.0012 ) Å, which is only slightly smaller (0.0007 Å) than the lattice parameter of a 2 = ( 4.5194 ± 0.0037) Å measured via the 002 reflex at the same temperature. The almost equally sized lattice parameters suggest that the ScN thin film is not noticeably strained.

FIG. 3.

Measured lattice parameters of ScN at different temperatures from 300 to 1000 K. The orange rhombuses mark the lattice parameters measured via the 111 reflex and the blue circles measured using the 002 reflex. The dashed lines picture the Debye fits.

FIG. 3.

Measured lattice parameters of ScN at different temperatures from 300 to 1000 K. The orange rhombuses mark the lattice parameters measured via the 111 reflex and the blue circles measured using the 002 reflex. The dashed lines picture the Debye fits.

Close modal

The fitting parameters a0 and αmax, as well as the TEC at 300 K, are summarized in Table I. The standard deviations for αmax and α ( T ) are in the range of 10 12 10 14 K 1, which is significantly smaller than the value itself, so the errors are not reported. At a temperature of approximately 850 K, the two fits intersect, and a 111 becomes larger than a 2 from that point on. According to these results, the thin film expands less in-plane than out-of-plane. This is illustrated in Fig. 4, which shows the temperature-dependent TECs determined from the Debye fits. Also, the simulated result of Tahri et al.1 is included as the dashed green graph in the figure.

TABLE I.

Used fitting parameters α max and a0 as well as the TEC at 300 K.

Lattice parameter a0 in (Å) α max in ( 10 6 K 1) α ( 300 K ) in 10 6 K 1
a 111  4.513 ± 0.001  9.672  6.738 
a 002  4.516 ± 0.002  9.672  6.192 
Lattice parameter a0 in (Å) α max in ( 10 6 K 1) α ( 300 K ) in 10 6 K 1
a 111  4.513 ± 0.001  9.672  6.738 
a 002  4.516 ± 0.002  9.672  6.192 
FIG. 4.

Temperature-dependent TEC α from 300 to 1000 K of ScN determined through the 111 reflex (orange) and 002 reflex (blue) and simulated by Tahri et al.1 (green dashed line) as well as from Si21 (red dashed line).

FIG. 4.

Temperature-dependent TEC α from 300 to 1000 K of ScN determined through the 111 reflex (orange) and 002 reflex (blue) and simulated by Tahri et al.1 (green dashed line) as well as from Si21 (red dashed line).

Close modal

At a temperature of 300 K, the TECs of the ScN thin film are found to be α 111 = 6.612 × 10 6 K 1 and α 2 = 6.072 × 10 6 K 1. In the case of a bulk crystal, one would assume an isotropic behavior of the lattice parameters. Here, the difference of 0.540 × 10 6 K 1 in the expansion along the two crystal directions may be attributed to the interaction between the ScN thin film and the Si substrate. Given that the TEC differs between the [111] and [002] directions, we infer a subtle influence of the Si substrate on the in-plane TEC. As the Si substrate has a lower thermal expansion coefficient ( α S i ( 300 K ) = 2.63 × 10 6 K 1),21 it compressively strains the ScN atoms in-plane by not allowing the thin film to expand as much in the horizontal direction as predicted by simulations for the bulk ScN. However, the TEC along [002] in the ScN thin film is more than twice as large as that of silicon, suggesting a significant degree of independence from substrate-induced thermal strain. The compressive effect is not observed along the [111] direction perpendicular to the surface, where atoms can expand more freely in the vertical direction because they are not bound to other layers. Consequently, we observe a higher TEC value along the [111] direction. At 300 K, in Tahri et al.'s1 study, the values exceed that of α 111 by around 1.4 × 10 6 K 1. Although the substrate may contribute to the lower experimental TEC values compared to Tahri et al.'s simulated values, a parallel investigation involving rs-TiAlN showed similar discrepancies. In the study, the TiAlN film was separated from the substrate for lattice parameter measurements using powder XRD, and the thermal expansion was obtained both experimentally as well as through simulations. Following the TiAlN study, we plotted the ratio ( a a 0 ) a 0 in % in Fig. 5 to highlight the differences between experimental and simulated values. The results showed similar discrepancies of up to 0.1% between the experimental and simulated values, highlighting the difficulties in accurately predicting thin film behavior through theoretical calculations alone.30 

FIG. 5.

Temperature-dependent a ( T ) a 0 a 0 ratio from 300 to 1000 K of ScN determined through the 111 reflex (orange) and 002 reflex (blue) and simulated by Tahri et al.1 (green).

FIG. 5.

Temperature-dependent a ( T ) a 0 a 0 ratio from 300 to 1000 K of ScN determined through the 111 reflex (orange) and 002 reflex (blue) and simulated by Tahri et al.1 (green).

Close modal

Overall, our measurements provide valuable insights into the thermal expansion behavior of ScN thin films between 300 and 1000 K.

In conclusion, this study investigates the thermal expansion behavior of ScN thin films by measuring the coefficient of linear thermal expansion. The results shed light on the thermal properties of ScN and enhance our understanding of its fundamental behavior. We were able to measure two temperature-dependent TECs, one along the [111] direction and one along the [002] direction, obtaining values of α 111 = 6.612 × 10 6 K 1 and α 2 = 6.072 × 10 6 K 1 at 300 K, respectively. The values rise up to α 111 = 9.307 × 10 6 K 1 and α 2 = 8.551 × 10 6 K 1 at 900 K. The measured TECs enable the optimization of ScN growth processes and ScN-based devices, ensuring their long-term functionality and preventing performance degradation due to thermal stresses. Furthermore, the knowledge gained from these measurements aids in the development of material models and theories related to ScN's thermodynamic properties. Continued research in this area will further advance the utilization of ScN in various applications, including electronics, optoelectronics, and thermoelectrics.

This work was supported by the Gips-Schüle-Stiftung and the German Science Foundation (DFG) that supported this work through the Priority Programme SPP 2312 (GaNius—Energy Efficient Power Electronics) under the Project Nos. 441885089 and 462722619.

The authors have no conflicts to disclose.

L. Ciprian: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (lead); Writing – original draft (lead). S. Mihalic: Conceptualization (equal); Formal analysis (supporting); Investigation (supporting); Supervision (equal); Validation (equal); Visualization (supporting); Writing – review & editing (equal). C. Lüttich: Resources (equal). F. Hörich: Resources (equal). E. Wade: Visualization (supporting); Writing – review & editing (equal). B. Christian: Funding acquisition (equal); Project administration (equal); Visualization (supporting). A. Dadgar: Project administration (equal); Resources (equal). O. Ambacher: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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