**2. Cubic Silicon Carbide (3C-SiC): Structure and Material Properties for Power Electronic Application**

The cubic form of SiC, coined '3C-SiC', is one of many stable polytypes characterised by its wide bandgap and bilayer stacking sequence of ABCABC . . . [7]. The resulting structure is a pure zinc-blende exhibiting an energy band gap of 2.3–2.4 eV [8], lower compared to other major SiC polytypes, but with a higher electron mobility and saturation velocity owing to its higher degree of symmetry. Although 3C-SiC has a smaller energy bandgap compared to its wide bandgap counterparts such as 4H-SiC and GaN, this material displays isotropy for many of the desired power device material characteristics such as avalanche coefficients and high electron mobility [9,10]. Another advantage of 3C-SiC is its relatively large thermodynamic stability meaning that bulk material can be grown at reduced thermal budgets (below 1500 ◦C). Table 1 shows the important physical and electrical properties of 3C-SiC compared to other commercial power device materials such

as Si, GaN and 4H-SiC. Likewise included are promising oxide and nitride ultra-WBG materials. The 3C-SiC intrinsic carrier concentration (~10−<sup>1</sup> cm−<sup>3</sup> ) is several orders of magnitude lower than in Si, but not as low as 4H-SiC or GaN. Moreover, 3C-SiC has a thermal conductivity three times that of Si. Consequently, 3C-SiC devices should have lower leakage currents with the ability to operate at moderately higher temperatures when compared to Si and GaN. Other key aspects are the reasonable critical electric field value resulting in a higher breakdown of the material. On analysis of these material properties, 3C-SiC is a promising semiconductor for power semiconductor devices in the region of 600–1000 V. On reflection, there exists the possibility to obtain a targeted breakdown voltage (VB) with thinner, more highly doped drift layers, which results in a significant reduction of the specific on-resistance (RON) compared to Si devices. Therefore, devices that are smaller and more efficient can be fabricated, minimizing both the static and dynamic losses.

**Table 1.** Appropriate physical and electrical properties of cubic silicon carbide (3C-SiC) compared to other wide bandgap materials (data taken at 300 K).


Note: <sup>a</sup> is mobility along a-axis, <sup>c</sup> is mobility along c-axis, \* refers to an estimated value and \*\* refers to the 2DEG mobility.

> The 3C-SiC Baliga figure of merit (BFOM) and BFOM for high-frequency, high-power unipolar switches (BHFFOM) [11] are 140 and 25, respectively. These values seem very modest compared to the equivalent values for more advanced WBG power semiconductors such as 4H-SiC and GaN. These key performance indicators for power semiconductors quantify the minimum conduction loss during DC operation (BFOM) and the minimum conduction loss at high frequencies (BHFFOM). Indeed, examination of these values suggests that lower resistance devices are possible based on 4H-SiC and GaN when compared to 3C-SiC. However, this advantage must be weighed against power device reliability and field lifetime within a converter application. In this regard, 3C-SiC is the clear winner, benefitting from a favourable metal-oxide-semiconductor (MOS) interface when compared to its 4H-SiC counterpart. The bandgap value (Eg) for 3C-SiC was reported by Bimberg et al. [12] and later by Goldberg et al. [8] (see Table 1). Figure 1 shows the conduction band offsets of the major power semiconductors with silicon dioxide (SiO2). From the figure it is seen that the band offset (ΦB) between 3C-SiC and SiO<sup>2</sup> is 3.7 eV. This is significantly larger when compared to the other power semiconductors with their values ranging between 2.7 eV–3.2 eV.

> The ramifications of this important property are realised in terms of reduced gate leakage current for a given oxide electric field. The important current transport mecha

nism which relates to this physical parameter is the Fowler-Nordheim (F-N) tunnelling mechanism. The F-N tunnelling current is given by:

$$J\_{FN} = \frac{A}{\Phi\_B} E\_{\text{ox}}{}^2 \exp\left(-\frac{B\Phi\_B^{3/2}}{E\_{\text{ox}}}\right) \tag{1}$$

where *Eox* is the oxide electric field, Φ*<sup>B</sup>* is the barrier height and A, B are constant values. It can be seen that due to F-N tunnelling the oxide electric field value must be reduced by 2–3 times in 4H-SiC compared to the 3C-SiC system.

**Figure 1.** Major power semiconductors' band structure for 3C-SiC, 4H-SiC, 6H-SiC and silicon, illustrating band offsets with silicon dioxide (SiO<sup>2</sup> ).

Fardi and Van Zeghbroeck [13] developed an empirical breakdown field model based on the breakdown voltage and field values that were obtained from published experimental data [14,15]. This proved to be more than adequate for 3C-SiC device design, having matched electrical breakdown characteristics to many published reports. Moreover, the model has been utilised in commercial 2-dimensional device design suites [16–18]. Fitting these impact ionisation coefficients to the electric field and substituting into the impact ionisation integral leads to closed-form solutions of the breakdown voltage and depletion layer width. These material parameters allow for the initial stages of power device design. The closed-form solutions for the breakdown voltage and parallel-plane depletion region width are given as:

$$BV\_{PP} = 7.88 \times 10^{14} N\_D^{-3/4} \tag{2}$$

$$\mathcal{W}\_{\rm PP} = 9.12 \times 10^{10} \text{N}\_{\rm D}^{-7/8} \tag{3}$$

where *BVPP* is the breakdown voltage, *N<sup>D</sup>* is the doping concentration and *WPP* is the parallel-plane depletion region width. The breakdown voltage and depletion region widths predicted by Equations (2) and (3), respectively, are shown in Figure 2.

**Figure 2.** (**a**) Parallel plane breakdown voltage (*BVPP*) and (**b**) depletion width (*WPP*) as a function of doping (*ND*) for 3C-SiC.

#### **3. Processing Technology for 3C-SiC**
