Superconductivity in heavily boron-doped silicon carbide

Abstract

The discoveries of superconductivity in heavily boron-doped diamond in 2004 and silicon in 2006 have renewed the interest in the superconducting state of semiconductors. Charge-carrier doping of wide-gap semiconductors leads to a metallic phase from which upon further doping superconductivity can emerge. Recently, we discovered superconductivity in a closely related system: heavily boron-doped silicon carbide. The sample used for that study consisted of cubic and hexagonal SiC phase fractions and hence this led to the question which of them participated in the superconductivity. Here we studied a hexagonal SiC sample, free from cubic SiC phase by means of x-ray diffraction, resistivity, and ac susceptibility.

Introduction

The possibility to achieve a superconducting phase in wide-band-gap semiconductors was suggested in 1964 by Cohen in Ge and GeSi [1]. Right after the prediction, several semiconductor-based compounds were indeed found to be superconducting at rather low temperatures and high doping concentrations. In the last decade, superconductivity was found in doped silicon clathrates [2–4] crystallizing in a covalent tetrahedral sp³ network with a bond length similar to that in diamond. In 2004, type-II superconductivity was found in highly boron-doped diamond (C : B) [5], the cubic carbon modification with a large band gap. The boron (hole) concentration of the sample was reported to be about n=1.8×10²¹cm⁻³ with a critical superconducting transition temperature T_c≈4.5 K and an upper critical field strength H_c2≈4.2 T. At higher doping concentrations n=8.4×10²¹ cm⁻³, T_c was found to increase to about 11.4 K and H_c2 to about 8.7 T [6, 7]. In 2006, type-II superconductivity was discovered in its next-period neighbor in the periodic system cubic silicon (Si : B) at boron concentrations of about n=2.8×10²¹ cm⁻³ [8]. However, the critical temperature is only 0.4 K and the upper critical field 0.4 T³.

In 2007, we found superconductivity in the stoichiometric composition of carbon and silicon: heavily boron-doped silicon carbide (SiC : B) [9]. One interesting difference between these three superconducting systems is the well-known polytypism in SiC meaning that SiC exhibits various ground states of slightly different energy. More than 200 such structural modifications are reported [10]. There is only one cubic ‘C’ modification labeled as 3C-SiC (zincblende = diamond structure with two different elements) or β-SiC. All other observed unit cells are either hexagonal ‘H’ (wurtzite or wurtzite related) or rhombohedral ‘R’, labeled as mH-SiC or α-SiC and mR-SiC, respectively. The variable m indicates the number of carbon and silicon bilayers which are needed to form the unit cell. The most important hexagonal modifications are 2H-SiC, which is the only pure hexagonal polytype, and 4H- and 6H-SiC, which consist of cubic and hexagonal bonds. The two relevant modifications for this paper are 3C- and 6H-SiC shown in figure 1. For a more comprehensive introduction to SiC see [11] and references therein. We note here that all SiC polytypes break inversion symmetry which is known to give rise to quite unconventional superconducting scenarios, e. g. in heavy-fermion compounds, in contrast to the inversion-symmetry conserving systems C : B and Si : B. However, we do not believe that any exotic superconducting scenario applies to SiC : B because of the comparably light elements carbon and silicon.

Figure 1.

(a) Unit cell of cubic 3C-SiC. The planes mark the three C–Si bilayers forming the unit cell (stacking sequence: ABC – …along 〈111〉 (dotted arrow)). The tetrahedral bond alignment of diamond is emphasized demonstrating the close relation to that structure. (b) Four unit cells of hexagonal 6H-SiC. The six bilayers needed for the unit cell are again denoted by planes (stacking sequence ABCACB – …along 〈001〉 (dotted arrow)). For the drawings the software Vesta was used [12].

Superconducting properties of SiC : B

In the discovery paper [9], we used a multiphase polycrystalline boron-doped SiC sample which contained three different phase fractions: 3C-SiC, 6H-SiC, and unreacted Si. The charge-carrier concentration of this particular sample was estimated to 1.91×10²¹ holes cm⁻³ [9]. The critical temperature, at which we observe a sharp transition in resistivity and ac susceptibility, is ∼1.45 K. The critical field strength amounts to H_c≈115 Oe, much lower than those of the two parent compounds C : B and Si : B. A big surprise was the finding that SiC : B is a type-I superconductor as indicated by a clear hysteresis between data (resistivity and ac susceptibility) measured upon cooling from above T_c to the lowest accessible temperature and a subsequent warming run in different applied external DC magnetic fields. This is in clear contrast to the reported type-II behaviour of C : B and Si : B [5, 7, 8] (see footnote 3). Another surprise is the low residual resistivity ρ₀=60 μΩ cm at T_c, which is unexpected for an impure semiconductor-based system, i. e., for a multi phase polycrystalline sample. Above T_c, the system features a metallic-like temperature dependence with a positive slope of dρ/dT in the whole temperature range up to room temperature and a residual resistivity ratio RRR=ρ(300 K)/ρ₀ of about 10. These observations are again in contrast, especially to C : B, which exhibits a more or less temperature independent resistivity with ρ₀≈2500 μΩ cm and RRR≈1. In a subsequent specific-heat study [11], using the same sample, we found a very small normal-state Sommerfeld parameter γ_n≈0.29 mJ mol⁻¹ K⁻¹. Moreover, we could clearly demonstrate that SiC : B is a bulk superconductor, as indicated by a specific-heat jump at about 1.45 K coinciding with the critical temperature T_c estimated from resistivity and ac susceptibility data. The jump in the specific heat is rather broad reflecting the multiphase polycrystalline character of the sample used. In addition, there is a third remarkable surprise. The electronic specific heat c_el/T exhibits a strictly linear temperature dependence below its jump down to the lowest so-far accessed temperature ∼0.35 K and extrapolates almost identical to 0 for T→0. The jump height is estimated to Δc_el/γ_nT_c≈1, which is only 2/3 of the expectation in the Bardeen–Cooper–Schrieffer theory (BCS) of a weak-coupling superconductor and is close to the value theoretically expected for a superconducting gap with nodes [13, 14]. However, a strictly linear temperature dependence is only expected well below T_c, where the superconducting gap is nearly temperature independent. When approaching T_c, the specific heat should deviate from c_el/T∝T due to the reduction of the gap magnitude. We note here that the assumption of a BCS-like scenario with a residual contribution to the specific heat γ_res, e.g., due to non-superconducting parts of the sample, yields a reasonable description of the data, too, with γ_res≈0.14 mJ mol⁻¹ K⁻¹, see [11]. The jump height in this scenario is 1.48, almost matching the BCS expectation of 1.43. In the description of the specific heat, assuming a linear c_el/T, no residual contribution is needed. A respective fit to the data yields γ_res≈0 mJ mol⁻¹ K⁻¹, as suggested by the almost perfect extrapolation of the data down to 0 for T→0. These results for γ_res for the two approaches imply a superconducting volume fraction of about 100% for the nodal gap scenario and about 50% for the BCS-like scenario.

In [15], we reported that the hexagonal phase fraction is superconducting and exhibits a similar linear temperature dependence of the electronic specific heat c_el/T in the superconducting state and also a reduced jump height. In this paper, we focus on this particular sample referred to as 6H-SiC in more detail and discuss the H–T phase diagram derived from ac susceptibility data. We give an evaluation of the Ginzburg–Landau parameter and compare these results with those obtained for the aforementioned ‘mixed’ sample used in [9] and [11] referred to as 3C/6H-SiC.

Experiment

The details of the sample preparation of sample 3C/6H-SiC are given in [9], sample 6H-SiC was synthesized in a similar way. The charge-carrier concentration of this sample is 0.25×10²¹ holes cm⁻³ as estimated from a Hall effect measurement. The electrical resistivity was measured by a conventional four-probe technique using a commercial system (Quantum Design, PPMS). Ac susceptibility measurements were performed using a mutual-inductance method in a commercial ³He refrigerator (Oxford Instruments, Heliox) inserted into a standard superconducting magnet applying a small ac field of H_ac=0.01 Oe-rms at a frequency of 3011 Hz in zero and several finite dc magnetic fields H_dc parallel to H_ac.

Results

Figure 2 (a) shows the powder x-ray diffraction patterns of boron-doped 6H-SiC (this work) and 3C/6H-SiC : B [9]. The sample 6H-SiC : B is also a multiphase polycrystalline compound with two different SiC modifications. We detect mainly hexagonal 6H-SiC (∼63% of the sample) and a much smaller phase fraction of rhombohedral 15R-SiC (about 9%)⁴. In addition, we find some unreacted silicon, too. In spite of the substantial boron doping, as evidenced by the high charge-carrier concentration, the lattice parameter changes only little. Thus boron only substitutes for carbon in SiC : B, as discussed in [9]. Due to this small change of the lattice parameter, we cannot obtain any information on the homogeneity of the doping from the x-ray diffraction data.

Figure 2.

(a) Powder x-ray diffraction patterns of boron-doped 6H-SiC. Three phases, 6H-SiC, 15R-SiC, and silicon, are identified. There is no indication for a cubic SiC modification in this sample. The respective data for 3C/6H-SiC : B from [9] is shown in panel (b), for comparison.

Figure 3 presents the resistivity of 6H-SiC : B (blue symbols) (a) up to room temperature and (b) around the superconducting transition. The respective data for 3C/6H-SiC : B (red symbols) from [9], multiplied by 10, are shown for comparison, too. The resistivity exhibits a metallic-like behaviour, i. e., dρ/dT>0, in the whole examined temperature range above T_c. However, a linear temperature dependence is observed only in a very small temperature range 60–120 K. The slope decreases at higher temperatures. Below approximately 1.5 K, a clear drop to zero-resistance with a transition width of about 25 mK is found indicating the onset of a superconducting phase. The residual resistivity is ρ₀≈1.2 mΩ cm and the residual resistivity ratio estimates to RRR≈4.7.

Figure 3.

Resistivity vs. temperature of 6H-SiC : B (blue symbols) (a) up to room temperature and (b) around T_c. The sample used exhibits a metallic-like temperature dependence in the whole examined temperature range above T_c. At T_c, we detect a sharp drop to zero resistance. The respective data for 3C/6H-SiC : B from [9] are shown for comparison (red symbols), too. Please note that the resistivity data of 3C/6H-SiC : B is multiplied by 10. The dotted line marks the transition; see text.

Figure 4 summarizes the results of our ac susceptibility measurements on sample 6H-SiC : B. The data for sample 3C/6H-SiC : B from [9] are included for comparison. In panels (a) and (c) the real parts and in (b) and (d) the imaginary parts of χ_ac=χ′+ i·χ″ are shown. The measurements were performed upon cooling and warming at constant H_dc as well as upon sweeping H_dc up and down at constant temperature. The temperature dependence of the in-field susceptibility data was taken as follows: The external dc magnetic field was set above T_c. Then the temperature was reduced down to approx. 300 mK and subsequently increased above T_c. Figure 4 shows the results of temperature sweeps (solid lines: cooling run, dashed lines: warming run) for H_dc=0, 20, 40 and 60 Oe. In zero field, a single sharp transition with a T_c of about 1.5 K is observed in good agreement with the resistivity data. In finite magnetic fields (‘in-field’), a hysteresis between cooling and subsequent warming run appears as can be clearly seen in both χ′ and χ″ (figures 4 (a) and (b)). The arrows in panel (a) denote the temperature sweep direction for H_ac=60 Oe. This in-field first-order phase transition is known as supercooling effect and is an indication of a type-I superconductor with a Ginzburg–Landau parameter κ_GL⩽0.417 [16–18]. We observed a similar hysteresis in field-dependent data measured at constant temperature, too. In case of a supercooled type-I superconductor, the observed critical field upon warming gives the thermodynamical critical field H_c(T). The Ginzburg–Landau parameter is discussed in more detail in the next section.

Figure 4.

Temperature dependence of the ac susceptibility χ_ac of 6H-SiC. In (a) the real part χ ′ and in (b) the imaginary part χ ″ are shown. The respective data for 3C/6H-SiC : B from [9] is shown in panels (c) and (d), for comparison. The dotted line in panels (a) and (c) signals the zero-field transition temperature. The arrows in panels (a) and (c) denote the temperature sweep direction; see text.

From these data, we derived the H–T phase diagram of 6H-SiC : B shown in figure 5(a). The phase diagram of 3C/6H-SiC : B from [9] is shown in panel (b) for comparison. The critical temperature was estimated from the shielding-fraction data (χ′). Here we define T_c as the temperature at which the absolute value of χ′ decreased by 1% of the total difference in the signal between the normal and the superconducting state. This procedure was applied to the data obtained upon decreasing and increasing temperature. The resulting two lines are the lower supercooling field phase line H_sc(T) and the higher lying critical field phase line H_c(T). The black dashed lines are fits to the data applying the empirical formula H_c(T)=H_c(0)[1−(T/T_c(0))^α] yielding for T→0 a supercooling field of H_sc(0)=(90±5) Oe with α=1.3, which can be identified as the upper limit of the intrinsic supercooling limit. The thermodynamical critical field was estimated to H_c(0)=(110±5) Oe, again with α=1.3.

Figure 5.

(a) H–T phase diagram of 6H-SiC : B. The dashed lines are fits to the data; see text. The respective data for 3C/6H-SiC : B from [9] is shown in panel (b), for comparison. The lower phase lines H_sc correspond to the ‘supercooling’ effect; see text.

Discussion

Next, we briefly compare the newly presented with the previously published data [9], which is included to the figures 2–5, and, together with the results of respective specific-heat studies in [11, 15], discuss the superconducting parameters.

The comparison of the resistivity data in figure 3 reveals that 6H-SiC : B (ρ₀=1200 μΩ cm) is the much dirtier crystal, as indicated by the different RRR values of 5 (6H-SiC : B) and 10 (3C/6H-SiC : B). Please note, that the data of 3C /6H-SiC : B (ρ₀=60 μΩcm) is multiplied by a factor of 10 in figure 3. Obviously, the transition width is smaller for the cleaner 3C/6H-SiC : B sample (∼15 mK compared to ∼25 mK). Surprisingly, the difference in the charge-carrier concentration does not affect the onset temperature of superconductivity which is ∼1.5 K for both samples, see the dashed line in figure 3.

As seen in figure 4, both samples exhibit a clear supercooling behaviour, which is usually observed in clean systems like type-I elemental superconductors. In both compounds, the shielding signal is strong and robust, and the shielding fraction is almost field independent, although the hysteresis is more pronounced in 3C/6H-SiC : B as seen in the H–T phase diagrams (figure 5). The thermodynamical critical field strength H_c≈ 110–115 Oe is almost identical, too. The additional features at the low-temperature side of χ″ are likely due to superconducting grains with a slightly lower critical temperature. Remembering the comparably higher purity of sample 3C/6H-SiC : B, it is surprising that these features are much less pronounced in 6H-SiC : B. Assuming that both phase fractions in 3C/6H-SiC : B are superconducting, which will be discussed next, one might speculate that the cubic phase fraction has a lower T_c leading to these features. However, this conclusion is in contradiction with the observation of only one single sharp transition in the χ′ data of that sample.

At the time of writing [9], we were not sure which of the two SiC phase fractions (3C or 6H) is responsible for the superconductivity in this system. The comparison of figures 2 (a) and (b) clearly demonstrates that there is no indication for a cubic phase fraction in sample 6H-SiC : B and hence the hexagonal modification of SiC : B is a bulk superconductor. Very recent data on 3C-SiC : B implies that also the cubic modification participates in the superconductivity [19]. The unreacted silicon in our samples is likely to be an insulating phase fraction with no electronic and almost no phononic contributions to the specific heat at low temperatures. Therefore, a residual contribution caused by this phase fraction cannot easily explain the values for γ_res found in the specific-heat analysis assuming a BCS-like scenario given in [11, 15], as mentioned in the Introduction. However, a possible inhomogeneous distribution of boron doping can be responsible for parts of the sample remaining normal-conducting 3C- and/or 6H-SiC leading to a residual contribution.

Together with the analysis of the specific-heat data, we are able to estimate the superconducting parameters for 6H-SiC : B as described in detail for 3C/6H-SiC : B in [11]. The parameters for both systems are summarized in table 1. Here, the Ginzburg–Landau parameter is derived from the experimental values of the charge-carrier concentration n, the critical temperature T_c, and the Sommerfeld parameter of the normal-state specific heat γ_n. Using the values given in table 1 yields κ_GL=7. This is much higher than the value suggested by the observation of a supercooling effect κ_GL⩽0.417 and the finding for 3C/6H-SiC : B, i. e. κ_GL=0.35. The values of T_c and γ_n are similar for both samples, but the charge-carrier concentration of 6H-SiC : B is about one order of magnitude smaller than that of 3C/6H-SiC : B, and indeed, this is the crucial parameter. The Ginzburg–Landau parameter is defined as κ_GL=λ/ξ, compare the discussion in [11]. The penetration depth depends on the charge-carrier concentration as λ∝1/n^2/3, the coherence length as ξ∝n^2/3 and hence κ_GL∝1/n^4/3. Using a charge-carrier concentration of about 2×10²¹ cm⁻³ yields a Ginzburg–Landau parameter of the right order of magnitude. Therefore the determination of n needs further clarification.

Table 1.

Normal-state (left) and superconducting state properties (right) of 6H-SiC : B (this work) and 3C/6H-SiC (taken from [11]). The parameters ℓ, ξ(0), and λ(0) are the mean-free path and the superconducting penetration depth and coherence length.

	6H-SiC : B	3C/6H-SiC : B		6H-SiC : B	3C/6H-SiC : B
n (cm−3)	0.25×1021	1.91×1021	Tc(0) (K)	1.5	1.45
γn (mJ mol−1 K−2)	0.349	0.294	Hc(0) (Oe)	110	115
Δcel/γnTc	1	1	Hsc(0) (Oe)	90	80
ρ0 (μΩ cm)	1200	60	ξ(0) (nm)	78	360
RRR	5	10	λ(0) (nm)	560	130
ℓ (nm)	2.7	14	κGL(0)	7	0.35

Summary

In summary, we present a study of mainly hexagonal boron-doped 6H-SiC, without any indication of a cubic 3C phase fraction, by means of x-ray diffraction, resistivity, and ac-susceptibility measurements. We compare these results with those obtained for a sample containing noteworthy fractions of both, the 3C- and the 6H-SiC modification. Both samples are bulk type-I superconductors as suggested by the H–T phase diagrams, i. e. the finding of a pronounced supercooling indicated by an in-field first-order phase transition and recent specific-heat studies, revealing a clear jump at T_c. The sample consisting of both SiC phase fractions contained a one order of magnitude higher charge-carrier concentration and exhibited a lower residual resistivity. The Ginzburg–Landau parameter for the hexagonal SiC sample is much higher than expected for a type-I superconductor with a strong supercooling effect. This could be due to an erroneous determination of the charge-carrier concentration and needs further clarification. Taking all data together, we have strong indications that boron-doped cubic as well as hexagonal SiC are bulk superconductors.