1. Introduction

Silicon carbide has long been known for its many industrial uses. In recent years high-purity single-crystal SiC has found applications in a number of cutting-edge technologies, including semiconductor electronics, optics, and as substrate for growing graphene. There are over 200 crystalline forms of SiC [1]. Of these, the hexagonal polytype 4H-SiC has been found to be the most suitable for a wide variety of applications. It also has the important advantage in that it can be grown as large boules of very high optical quality and few crystal defects.

Hexagonal silicon carbide is a wide bandgap semiconductor crystal belonging to the point group symmetry $C_{6v}^4-P{6}_{3}mc$ and has positive birefringence (i.e. the refractive index is larger for the e-wave than for the o-wave, n_e > n_o). It is one of the hardest high-performance materials available, second only to diamond; and also possesses superior resistance to harsh environments, such as high temperature and pressure. The different polytypes of hexagonal SiC are variations of the same chemical compound that are identical in two dimensions and differ in the third. Thus, they can be viewed as layers stacked in a certain sequence, or combinations of two stacking sequences, with a periodicity of N double layers in the stacking direction [1, 2]. Among these, 6H-SiC (N = 6) and 4H-SiC (N = 4) are the most common ones.

Pure SiC is colorless and highly transparent in the visible; hexagonal SiC forms are birefringent. The optical properties of 4H-SiC for o- and e-wave have been investigated in the visible between 467–691 nm [3], and later in the near-infrared covering 0.4–2.3 μm and 3–6 μm [4]. The main transparency window of 4H-SiC was found to extend between 0.37–5.6 μm [4]. SiC has a high optical damage threshold: up to 80 GW/cm² under excitation by 10 ns pulses from an Nd:YAG laser at 1.064 μm [1]. A summary of SiC properties for various polytypes and a bibliography of the available literature can be found on [5].

Hexagonal SiC is also highly transparent in the millimeter-wave and THz regions. Despite this, scarce data are available on its optical properties at these frequencies, and then only for the o-wave, due to the widespread prevalence of SiC wafers cut orthogonally to the crystal axis. Because of its low loss, polycrystalline high-purity semi-insulating 4H-SiC has been studied for applications in RF devices and circuits: a loss tangent of 2×10⁻⁵ was reported at 131.5 GHz [6], 6×10⁻⁵ at 135 GHz [7], ≈10⁻³ at 0.1–0.6 THz [8], and 10⁻⁶ at 1 THz [9]. High transparency was reported in 6H-SiC at 0.5–3 THz [10] and between 40–120 μm (2.5–7.5 THz) [11]. A strong Reststrahlen band was observed in 4H-SiC at 6–15 μm (20–50 THz) [12]; all available data confirm that outside this region hexagonal SiC is highly transparent.

Over the past decades, numerous examples of coherent THz sources have been demonstrated using difference frequency generation (DFG) in phase matchable (anisotropic) nonlinear crystals [13, 14]. In order to achieve high conversion efficiency, the nonlinear crystal must possess low optical loss at both pump and THz frequencies, high optical damage threshold, and a large nonlinear coefficient. In addition, it is advantageous for the crystal to have high hardness, to allow cutting in an arbitrary direction and polishing to a high optical finish. Although 4H-SiC has only moderate nonlinearity, it abundantly satisfies all other requirements, and therefore appears to be a highly attractive candidate for THz generation.

The possibility of type-II phase matching (PM) in SiC for wavelengths longer than 2.0 μm was first predicted for an unknown (probably 6H) polytype [15]. In a later study mid-IR DFG was demonstrated in 4H-SiC at 3.90–5.60 μm [4]. Second-order nonlinear coefficients were measured in both 4H- and 6H-SiC at 1 μm [16, 17]. At THz frequencies, non-phase matched optical rectification was demonstrated in 6H-SiC [10]. It is known, however, that DFG into the THz range requires relatively low values of birefringence, as explained in [18], such as found in hexagonal SiC.

4H-SiC has very promising properties for THz applications, including extremely low loss, ultrabroad transparency window, very high optical damage threshold, moderate nonlinearity and birefringence. Its THz optical properties therefore deserve detailed study. In this paper we report measurements of o- and e-wave optical properties of 4H-SiC at frequencies <0.1–20 THz. DFG into the THz range up to 15 THz (20 μm) is predicted to be possible.

2. 4H-SiC sample preparation and measurement

The samples of hexagonal 4H-SiC polytype were supplied by Norstel (Sweden), and were grown by the high temperature chemical vapor deposition (HTCVD) technique. It is a CVD technique using purified gas precursors, such as silane and ethylene, as source material. The precursors, diluted in a carrier gas, are continuously fed into an open vertical graphite crucible at a temperature above 2000 °C. Undoped material is very pure and electrically semi-insulating with resistivity of >10⁷ Ω·cm. Standard material used by industry is today 100 mm diameter and with a micropipe density clearly below 5 cm⁻². Other technological details can be found elsewhere [19]. Visually, the material is colorless and completely transparent. As a result, the high-resistivity 4H-SiC, combining low micropipe and high purity, can provide an enabling material for optical applications.

The samples were one 2″ wafer with an average thickness of 352.5 μm and a total thickness variation (TTV) of 2.0 μm; and two cubes with thickness of 5.69±0.01 mm and 5.72±0.01 mm. One of the cubes was cut such that the measurement direction was parallel to the c-axis (θ=0°), whereas the other was perpendicular to the c-axis (θ=90°). This made it possible to measure both o-wave and e-wave transmission.

Measurements at 0.1–4 THz were performed using a time-domain spectrometer (TDS) described elsewhere [20]. The Fourier transform spectrometer (FTS) used to carry out measurements at 2–20 THz was a Bruker Vertex 80/80v. Only the wafer could be measured using the FTS, due to the small dimensions and large optical thickness of the cubic samples.

3. THz optical properties

Figure 1(a) shows power transmission (I_incident /I_transmitted) in the 4H-SiC wafer measured by TDS at 0.1–4 THz (blue trace) and by FTS at 2–20 THz (green trace); it is seen that there is good coincidence between the two measurements. The FTS trace shows etalon oscillations due to the formation of a standing wave in the SiC wafer. The oscillation amplitude remains large and nearly constant up to about 7 THz, indicating low absorption loss in this region. At higher frequencies of 10–15 THz the gradual reduction in the oscillation amplitude signals increasing absorption.

 

Fig. 1 Power transmission (a) and refractive index (b) in 4H-SiC measured by TDS and FTS. Transmission curves (a) are calculated from Fresnel reflection losses using refractive index values shown in (b). The FTS refractive index (b) was calculated from the frequency spacing of etalon oscillations shown in figure (a).

Download Full Size | PDF

The FTS oscillation period allows the refractive index to be calculated from the Fabry-Perot relation Δf = c/2nd, where Δf is the frequency difference between two adjacent peaks or valleys, c is the speed of light, d is the sample thickness, and n is the linear refractive index of the material. The refractive index calculated from the FTS data in Fig. 1(a) is shown in Fig. 1(b), together with values measured directly by TDS, which are also presented separately in detail in Fig. 2(a). Again, there is good coincidence between the two sets of data. It is seen that the refractive index begins to rise strongly at around 7 THz, signaling the onset of anomalous dispersion and indicating the approaching edge of an absorption band due to phonon resonances.

 

Fig. 2 Refractive index of 4H-SiC measured by TDS (a). Also shown are uncertainty limits due to the uncertainty in the sample thickness (±1 μm). Refractive indices (b) n_o and n_e of 4H-SiC: green lines represent measurement data from this work.

Download Full Size | PDF

Using the refractive index data from Fig. 1(b), power transmission due to Fresnel reflection losses can be calculated from T = (1 − R)², where R = [(n − 1)/(n + 1)]²; this is also shown in Fig 1(a). It is seen that transmission measured directly by TDS overlaps closely with the calculated Fresnel transmission, confirming that absorption losses in this frequency region are very low (although they cannot be quantified on the basis of these data). The absorption coefficient could not be measured by TDS, because it was below the detection threshold of 1 cm⁻¹. Likewise, calculated Fresnel transmission lies close to the mean value of the etalon oscillations up to ≈7 THz, also confirming that the low optical absorption region extends to those frequencies.

The refractive index was obtained from the TDS data by applying Fourier Transform and then calculating the frequency-dependent refractive index from the phase of the normalized amplitude spectrum using the standard approach [21]. The ordinary refractive index was measured by TDS in both the wafer and the two cube samples, and the results from all three samples were found to be in close agreement. These are shown in Fig. 2(a), where the ordinary refractive index is seen to be 3.14 at 1 THz and 3.15 at 4 THz (with a systematic uncertainty of ±0.02). Previous measurements on 4H-SiC reported its ordinary refractive index as 3.10 at 0.5 THz [22, 23], measured by DFTS (dispersive FTS); 3.16 at 0.131 THz [6], and 3.10 at 0.135 THz [7], both measured by the resonator method. There appears to be, therefore, a fair agreement between these results, given that the uncertainties of DFTS and resonator measurements are generally larger than those achieved by TDS.

The refractive index n_e was measured by TDS in the cube sample that was cut orthogonally to the c-axis, and is also shown in Fig. 2(a). It is 3.24 at 2 THz, giving birefringence of 0.09.

The values of dielectric constants in 6H-SiC are commonly taken to be valid also for 4H-SiC [5]. The refractive index of 6H-SiC has been reported as 3.17 [24] and 3.0 [10] at 2 THz, both measured by TDS; and 3.13 at 2.5 THz measured by a rotating etalon [11]. It appears that the refractive indices of 4H-SiC and 6H-SiC are indeed close; more detailed measurements with higher precision are required to determine accurately the differences between them.

4. Phase matching for THz generation

The 2^nd-order nonlinear susceptibility coefficients in hexagonal SiC are related to the optical electric field components: $P_x^{{\omega }_1\pm {\omega }_2}=2d_{15}{E}_x{E}_z$, $P_x^{{\omega }_1\pm {\omega }_2}=2d_{15}{E}_y{E}_z$, and $P_x^{{\omega }_1\pm {\omega }_2}=d_{31}{E}_x^2+d_{31}{E}_y^2+d_{33}{E}_z^2$, where d ₁₅ = d ₃₁. If Kleinman symmetry relations are valid, the 2^nd-order nonlinear efficiency for interactions involving one e- and two o-waves (ooe, eoo, oeo) is d _eff = d ₁₅ sinθ [25]. Otherwise, d _eff = d ₃₁ sinθ for ooe interaction and d _eff = d ₁₅ sinθ for oeo.

Using dispersion equations for 4H-SiC, valid in its transparency window at 0.37–5.6 μm [4], combined with the measured data from this work, new dispersion equations were designed for the entire transparency range of 4H-SiC from 370 nm up to 1 mm:

Equations (1) and (2) can be used to calculate the PM condition for DFG of near IR into the THz range, as shown in Fig. 3(a). It is seen that by using a pump laser at ≈1 μm, type II PM for THz generation by DFG occurs at small angles, which significantly reduces the walk-off effect.

 

Fig. 3 PM curves (a) for eo → o type of DFG to THz for the pump wavelengths at 800 nm (Ti:Sapphire), 1064 nm (Nd:YAG), and 1550 nm (Er). Generalized PM diagrams for ooe type of three-wave interaction in 4H-SiC (b). For example, at the tilt of 20° (cyan line) a DFG output of 100 μm requires pump wavelengths of ≈1 μm.

Download Full Size | PDF

In Fig. 3(b) it is seen that by using pump lasers in the transparency window of 4H-SiC, DFG can be achieved in a broad THz band of <0.3–18 THz. Moreover, due to the high optical damage threshold and moderate nonlinearity of 4H-SiC, THz generation can be performed at high pump intensities, with the consequent improvement in conversion efficiencies [26].

5. Conclusion

Optical properties of 4H-SiC grown by HTCVD were studied by TDS at 0.1–4 THz and by FTS at 2–20 THz. A high-transparency region was confirmed between <0.1–10 THz. The ordinary refractive index was measured at 0.1–17 THz and the extraordinary refractive index at 0.2–3 THz; giving birefringence of 0.09 at 2 THz. The absorption coefficient in the high-transparency region could not be measured because it was below the detection threshold. Using the measured refractive index data combined with published results, the refractive indices for o-wave and e-wave were approximated in the form of Sellmeier equations for the entire transparency range. DFG in the range <0.3–18 THz was found to be possible using pump wavelengths at 0.8–1.5 μm (where 4H-SiC is also highly transparent). The extremely low absorption coefficient, high damage threshold, and possibility for phase matching make 4H-SiC highly suited for high-power THz optics and generation. In particular, generation of difficult-to-access 6–10 THz frequencies appears to be possible.