Research of p-i-n Junctions Based on 4H-SiC Fabricated by Low-Temperature Diffusion of Boron

Novel method of boron diffusion at low temperatures between 1150 and 1300°C is used for the formation of both p-i SiC junction and i-region in one technological process. As the junction formation conditions in this method are essentially different from those in the conventional diffusion (low temperatures and process of diffusion are accompanied by formation of structure defects), it is of special interest to identify advantages and disadvantages of a new method of diffusion. Developed SiC p-i-n junction diodes have fast switching time, and the duration of the reverse recovery current is less than 10 ns with a breakdown voltage of 120–140V. Fabricated diodes possess capability to operate at temperatures up to 300°C. As the temperature of diffusion process is lower than the melting temperature of silicon, this new technology allows fabrication of diodes on the base of SiC/Si epitaxial structures.


Introduction
Silicon carbide-(SiC-) based devices have number of advantages over traditional silicon and gallium arsenide analogues. One of such advantages is high operating temperature of SiC devices [1][2][3], which makes this material very promising for power and extreme electronics [2][3][4][5][6][7]. Another important feature of SiC is high saturation velocity of electrons [8], which enables SiC-based devices to operate at high frequencies (RF and microwave). An important characteristic of diodes for power and pulse application is the switching time. For SiC diode with an area of 100 × 100 µm 2 , switching time (t s ) is ∼20 ns [9] (silicon diodes have t s ∼100 ns [10]). Previously, it has been shown in [11] that the base region of SiC diodes doped by aluminum has a deep level with ionization energy E C −1.45 eV and a trapping level with ionization energy E C −0.16 eV, which is observed due to nitrogen impurity. Capture processes and thermal activation of electrons associated with these levels can greatly influence duration of current relaxation of SiC p-n junction. Currently, power diodes based on silicon carbide made by diffusion technology have maximal breakdown voltage ∼700 V for 4H polytype and ∼1000 V for the 6H polytype of silicon carbide [12,13].
Previously, it has been shown that to fabricate diodes with high breakdown voltage (more than 2000 V), highly resistive i-region of SiC p-i-n diodes needs to be created by epitaxial growth of thin SiC layer (free from micropipe defects) [14][15][16]. Afterwards (second technological step), pregion of SiC p-i-n diodes is formed by thermal diffusion at temperatures > 2050°C or ion implantation of SiC by aluminum [17,18] and boron [17]. It is worth mentioning that heavily doped SiC crystal fabricated by ion implantation (with concentration of impurities up to 10 19 cm −3 ) should be annealed at a temperature of ∼1800°C to remove the defects [3,18]. Extremely high-temperature processing (>2050°C) needed during thermal diffusion [19][20][21] or after ion implantation [3,18] may increase the production cost. Very high blocking voltage over 26.9 kV for such structures with epilayer (n + -n − epilayer/n + epilayer/n + substrate) has been achieved in [21]. e most important process steps in SiC devices manufacturing are formation of p-n junction and lowresistance ohmic contact. e p-region of SiC diodes can be conventionally formed by thermal diffusion of shallow impurity (at T > 2000°C) or ion implantation of aluminum in SiC with concentrations up to 10 19 cm −3 [9,22]. For layers heavily doped by ion implantation, it is necessary to perform thermal treatment (at T > 1600°C) to anneal radiation defects [3]. e materials used as impurity sources during diffusion are as follows: diborane B 2 H 6 gas [23] (diffusion from gas phase) and wafer of boron nitride [24] or borosilicate glass (diffusion from solid state). Conventional diffusion processes are usually carried out in a vacuum or inert atmosphere. Extremely high temperatures (over 2000°C) are necessary during conventional diffusion process to form p-n SiC [19][20][21].
Low-temperature (900-950°C) diffusion of boron and phosphorus in single-crystal silicon carbide was studied in [25,26]. Obtained high concentrations of up to 10 21 cm −3 are explained by prevailing role of silicon vacancies in the process of diffusion of these impurities [27]. e mechanism of thermal diffusion in silicon carbide is quite complex as the crystal has two sublattices (silicon and carbon). Previously, Gao et al. and Lebedev [20,28] studied boron diffusion on 6H-SiC in the temperature range between 2000 and 2200°C and have demonstrated that there are two types of boron solubility depending on the position of boron atoms in the carbon or silicon sublattice. According to Girka and Mokhov [29], the concentration of carbon vacancies at these temperatures in silicon carbide is very high (from 3 × 10 17 to 5 × 10 17 cm −3 ) and, according to Gao et al., carbon vacancies exert a strong influence on the diffusion of boron. In the silicon sublattice, the boron solubility (∼6 × 10 19 to 9 × 10 19 cm −3 ) is approximately 10 times higher than that in the carbon sublattice (from 1 ×10 18 to 10 × 10 18 cm −3 ) [30].
Several factors can influence thermal diffusion process such as surface conditions, chemical treatments, concentration of defects in carbon, and silicon sublattices. at is why conventional thermal diffusion is regarded as an old and unstable technology for fabricating p-n SiC junction. is paper describes a novel method to diffuse boron at temperatures between 1150 and 1300°C that has been used for formation of p-i junction and i-region in one technological process. Characteristics of fabricated p-i-n 4H-SiC structures are presented. Diffusion temperature is lower than the melting temperature of silicon, and this new technology can be used to fabricate diodes based on the SiC/Si epitaxial structures. As the conditions of junction formation in this method are essentially different from those in the conventional diffusion (low temperatures and process of diffusion are accompanied by formation of structure defects), it is interesting to identify the advantages and disadvantages of a new method of diffusion.

Experimental
Single-crystal sample of silicon carbide has been grown at Cree, Inc., by physical vapor transport (PVT) method with a relatively low concentration of growth defects: N dislocations 10 4 cm −2 and N micropipes ∼10-10 2 cm −2 for 4H polytype of n-SiC. ickness of the sample (4 × 4 mm 2 ) is ∼300-600 μm, and specific resistance is between 3.6 and 20 Ω·cm. e samples have been etching in KOH solution with UV light stimulation. Unlike to reactive ion etching, the UV light stimulated etching does not create defects and allows fabrication of a smooth soft surface [31].
e diffusion process has been carried out at inert atmosphere (to create a flow of vacancies of Si and C from the crystal surface into the bulk of the sample [38]). Increased concentration of Si and C vacancies allows increase of the diffusion constant and solubility of impurity up to 10 20 cm −3 (depth of p-area reaches up to 2-3 μm) [37,38]. Low disintegration of SiC surface is expected, and the diffusion temperature in our method is between 1150 and 1300°C, which is lower compared to the conventional diffusion.
It should be noted that, in the works of Bagraev et al. [40,41] for the formation of ultra-shallow p + -n junctions (with depth of 10 nanometers) at low diffusion temperatures of 900°C, the flux of silicon vacancies was created at the SiC-SiO 2 interface. In our case, the flux of V C carbon and V Si silicon vacancies was created by surface oxidation. Below, we describe briefly the mechanism of formation of V C and V Si vacancies.
In [42], it is described that, at temperatures 1100-1400°C, SiC exhibits two types of oxidation behavior, "active" and "passive," depending upon the ambient oxygen potential. At high oxygen pressures, "passive" oxidation occurs, wherein a protective film of SiO 2 (s) is formed on the surface by the reaction At low oxygen potentials, severe "active" oxidation occurs due to the formation of gaseous products according to the following reactions: Active oxidation of SiC occurs only at oxygen pressures lower than ∼3·10 −4 atm at 1400°C. As seen from (2) and (3), surface oxidation of silicon carbide in these conditions leads to production flow of both carbon and silicon vacancies from the surface into the bulk of the crystal (may be mostly of carbon vacancies). Obviously, the vacancy concentration in this case can be much higher as compared with the introduction of vacancies by irradiation.
Our technological experiments show that, during diffusion process, the vacancies of Si and C penetrate into volume deeper than doping impurity. Deep penetration of vacancies leads to formation of i-region. So, in one technological process, both p-and i-regions are formed ( Figure 1).

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Type of conductivity of doped layers and silicon carbide single crystals has been tested by hot probe (thermoprobe) method [43].
Distribution of electrically active impurities in SiC crystal has been measured by spreading resistance method after polishing the samples at an angle of 3°. e distribution of boron in very thin region near surface is obtained by using capacitance-voltage (C-V) measurements of Ni-p-SiC Schottky barriers.
ese methods allow obtaining of the distribution of electrically active impurities in the crystal, whereas the depth pro ling by SIMS gives information on the total content of impurity including impurity atoms in nonactive interstitial sites and in inclusions of secondary phase in crystal.
Current-voltage (I-V) characteristics have been measured by a standard scheme using digital devices. e concentration of shallow impurities has been determined based on the capacitance-voltage (C-V) characteristics [44]. Impedance measurements have been carried out at di erent frequencies with the amplitude of the AC signal at 20 mV, while permanent bias has also been applied to the structure. Switching time for 4H-SiC<B> diode structures has been measured on a special impulse stand [45].

Results and Discussions
It is well known that spreading resistance method allows measuring of the distribution of electrically active impurity only. Boron impurity distribution (up to 2 µm) for one of the 4H-SiC<B> samples measured by spreading resistance method on the angle polished samples is shown in Figure 2. As the di usion is stimulated by the ow of carbon and silicon vacancies generated on the surface of SiC crystal, the concentration of defects becomes very high near the surface.
To study the distribution of boron in the region near the surface (on top of p-region), Ni-p-3C-SiC Schottky barriers have been fabricated and their C-V characteristics have been measured. As one can see in Figure 3, boron di usion stimulated by the ow of Si and C vacancies shows high solubility of ∼10 20 cm −3 , although this value is practically unreachable by other doping technologies. Ion implantation technology also allows achieving high concentration of impurities such as aluminum. However, to anneal the defects, additional thermal treatment is necessary [3]. Another observed interesting feature is the quasiperiodic distribution of boron in some samples. is might be due to the interaction of the di using impurities and point defects at high concentration, and it is probably related to some synergistic processes in di usion.
Since di usion takes place under conditions of surface oxidation in air at a xed temperature, the concentration of vacancies on the surface is determined only by the temperature, and the reproducibility of the process is quite high (50-80%). Figure 4 shows the current-voltage characteristics of p-i-n junction in 4H-SiC<B> (p-n junction area is 6 mm 2 ).
For samples with a thickness of 300-400 μm, the breakdown voltage occurs to be within the range of 120-140 V. us, the variation of the breakdown voltage between the samples is no more than 20 V (about 15% of the maximal value). e nonlinearity coe cient (I for /I rev ) at 25 V is about 100.
Such a low value of breakdown voltage is mainly due to the in uence of dislocations (N d ∼10 4 cm −2 ) and micropipes (N m ∼10-10 2 cm −2 ) in the studied SiC crystals. It has been reported previously [47] that, with a screw dislocation concentration of ∼10 4 cm −2 , maximum breakdown voltage (V b ) between 350 and 400 V can be reached. is breakdown voltage can be improved in several ways, for example, by improving lowtemperature di usion technology, by formation of mesastructure, and by surface passivation But to get a signi cantly high breakdown voltage, it is necessary to use SiC crystal free from micropipes and lower concentration of dislocations.
e growth of forward current is observed at voltage values higher than 10 V. On the ohmic section of the I-V characteristics, resistance of di erent junctions is between 15 and 20 Ohms, which indicates the presence of a highresistance layer between p-and n-regions.
is assumption is also con rmed by capacitance measurements: for reverse applied voltage, the capacitance is 9-12 pF ( Figure 5). High-resistance layer leads to large losses, and this is a disadvantage of this technology which must be eliminated in the future.
ickness W of i-layer has been evaluated by the known formula C εε 0 S/W (C is the capacitance of diode, ε 9.7 is the dielectric constant of silicon carbide, ε 0 is the electric constant, S is the layer area, and W is the thickness of layer), showing that, in SiC diode samples, W ∼39-40 μm. According to the well-known expression L ∼ D · t √ (where L is the di usion length, D is the di usion constant, and t 30 minutes is the di usion time), the di usion constant must be D ∼2 × 10 −9 cm 2 /s.

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Let us evaluate the di usion constant of vacancy by using the following expression [48]: where D 0 is the preexponential factor, E m is the migration energy, k is the Boltzmann constant, and T is the temperature. According to [48] devoted to atomistic study of intrinsic defect migration, the value D 0 for 3C-SiC is approximately (1-3) × 10 −3 cm 2 /s, and E m for carbon and silicon vacancies are approximately 4.1 eV and 2.35 eV, respectively. In our nonequilibrium conditions, activation energy of vacancy di usion has to be near activation energy of boron impurity (0.8-1.3 eV). en, according to (4), the di usion constant of vacancy ranges from 10 −9 to 10 −8 cm 2 /s, which is in good agreement with the above experimental value ∼2 × 10 −9 cm 2 /s. High-resistance region, most likely formed by defects created during the di usion, has inhomogeneous distribution of the carrier density. e distribution of impurity concentration can be evaluated by using the following expressions [44]: where C is the capacitance of junction, ε S is the dielectric constant of the silicon carbide, N(W) is the concentration of impurity at W, and W is the depth of depletion region. As it can be seen from expression (5), the slope of (1/C 2 ) function is decreased with increasing impurity concentration. According to data presented in Figure 6, the carrier concentration between i-layer and n-area of SiC increases from 10 16 to 5 × 10 17 cm −3 (impurity concentration in the substrate of silicon carbide). e fabricated structure is layer stack of boron-doped p-region up to 2-3 µm with maximal concentration between 10 19 -10 21 cm −3 and high resistive i-region which is created by defects related with deep penetration of Si and C vacancies into volume of crystal during di usion. During the di usion process, the Si and C vacancies penetrate into volume deeper than doping impurity. Deep penetration of vacancies leads to formation of i-region.
us, in one technological process, both the p-and iregions are formed.
Fabricated diode structures have been further studied by impedance measurements at relatively low frequencies 5,000, 10,000, 15,000, and 20,000 Hz (Figure 7). Assuming the parameters of the structures do not change in this frequency range, the data can be used for the development of equivalent circuits and evaluation of capacitance, series resistance, and other parameters of diode. Figure 8 shows the equivalent circuit of our structure (based on the equivalent circuit of the p-i-n diode) and a simpli ed circuit for the forward and reverse bias [49].
Equivalent circuit for this p-i-n junction consists of diffusion capacity C dif , parallel R pi (p-i transition resistance), series base, and ohmic contact resistance. For reverse voltage, the simpli ed diagram consists of C pi , R pi , C i , and R i of p-i and i-n junctions, as well as high-resistance layer (Figure 8). It should be stated here that the sign i represents high resistance region but not the region with intrinsic conductivity.
For forward bias, the C dif with parallel R pi has conductivity S: where jωC dif is the capacitance conductivity (j −1 √ means that capacitance changes the phase of AC). Impedance is Total impedance for direct bias is Let us transform this expression into the canonical form: Module of this impedance is For the reverse bias, the same method can be used to obtain an expression

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where ω is the frequency, C dif is the e ective di usion capacity, R pi is the junction resistance, R S is the series resistance, and R i is the resistance to high-resistance layer. By computer tting of expression (12) to impedance, the measured di usion capacity data are evaluated for applied direct voltage 10 V, which occurs to be in the range from 80 pF to 1300 pF at a forward current from 100 μA to 2.4 mA (Figure 9).
In this case, the value R S includes both high-resistance layer and resistance of i-n junction which makes the value to vary from 4 to 100 Ohms. e well-known expression for the di usion capacity is as follows: where τ p is the lifetime of minority carriers, J is the forward current through the diode, k is the Boltzmann constant, T is the temperature, and q is the electron charge. e lifetime of minority carriers estimated by using expression (14) is between 10 and 21 ns. Even though expression (12) cannot be used for computer tting as tting parameter R pi is not constant and slightly depends on frequency, the conducted tting shows that the capacity of a high-resistance layer is between 3 and 12 pF (evaluated from tting procedure) which is also con rmed by measuring the capacity ( Figure 5). Resistance value R i has varied considerably from 550 to 850 Ohms. e resistivity of the high-resistance layer occurs to be between 90 and 130 Ω·m and depends on the applied voltage and current through the structure.
is value is much lower than the value of intrinsic resistivity of silicon carbide. Here, it is necessary to mention that more experimental data points (not less than 20 data points) are required to fully prove this. Our measurements include only four frequencies which makes the values that p

R pi
Forward bias Reverse bias  Advances in Materials Science and Engineering we have obtained to be an estimation rather than exact value. e oscillogram of the current switching diode based on 4H-SiC<B> is shown in Figure 10. Switching of diodes has been performed from forward current (I 0.25 mA) to reverse voltage 60 V. As one can see from Figure 10, the diodes have very fast switching time and duration of the reverse recovery current (of the order of 10 ns) for junctions with an area of approximately 6 mm 2 .
If we assume that the transition process is determined by the capacity of the junction (capacitive processes) [48] and this time is proportional to t r RC, where R is the series resistance and Cis the capacity of the junction, then the relaxation time t r should be less than 1 ns. However, it has been shown earlier [11] that transition processes involving nonequilibrium carriers in silicon carbide are determined by the level of trapping (EK 2 with energy E C − 0.16 eV) and by the duration of the reverse recovery current which is >20 ns. is level is ascribed to the donor impurity of nitrogen and the observed concentration pro le of silicon carbide diode associated with the di usion of nitrogen as background impurities. As the switching time in our diodes is fast (∼10 ns), it can be assumed that in our samples the concentration of these centres (with the trapping levels near the middle of the gap) is relatively low. e measured switching time is su ciently close to the lifetime of minority carriers (10-20 ns) which has been evaluated by using di usion capacity of junction. e Maxwell relaxation can also in uence the switching process. Estimate shows that, for speci c resistance between 90 and 130 Ω·m, Maxwell relaxation time is between 5 and 7 ns (τ μ εε 0 /σ, where ε is the dielectric constant of the silicon carbide, ε 0 is the electric constant, and σ is the conductivity of a semiconductor).
us, the estimations of RC time relaxation, lifetime of minority carriers, and Maxwell relaxation time of the current do not contradict our experimental data.
It should be noted that the reverse branch of I-V characteristics of diodes does not have sharp breakdown region. at is why current of around 100 mA is believed to be the beginning of breakdown process. e dependence of reverse voltage at 100 mA U (I R 100 mA) versus temperature is shown in Figure 11. It can be seen from Figure 11 that the diodes have rectifying properties up to 300°C.   Figure 9: e results of computer tting to experimental data on impedance at direct (a and b) and at reverse voltage (c and d) for some samples.
A fundamental property of the p-i-n diode is its i-region ambipolar carrier lifetime τ, which represents the average time during which an electron-hole pair exists in the i-region of the diode [50].
A common method of measuring the pin diode : carrier lifetime is by forward biasing the device with a known current (I F ) and then extracting a known reverse current (I R ) during the turn-o phase. is method is named the reverse recovery method, and the carrier lifetime can be estimated by using the following expression in the framework of this method [51]: where t rr is the reverse recovery time. According to Figure  10, τ is close to Maxwell relaxation time. us, diodes having small switching time and duration of the reverse recovery current <10 ns, breakdown voltage from 120 to 140 V, and capable of operating at temperatures up to 300°C were developed.
A clear advantage of this new method is the fast switching time. We believe that it is caused by a decrease in the concentration of the traps. e disadvantage of our technology is a small breakdown voltage, which can be eliminated by using SiC samples without micropipe defects. A more serious challenge is the intermediate high-resistivity layer that increases losses. To prevent formation of this layer, further research is needed.
is fabricated SiC diodes can be potentially used in mobile phones, DSC, lighting, Notebook PCs, HDD, PPC, and power supplies for communication devices [52].

Conclusion
New method of boron di usion at low temperatures between 1150 and 1300°C has been used for formation of both SiC p-i junction and i-region in one technological process. As the conditions of junction formation in this method is essentially di erent from the conventional di usion (low temperatures and process of di usion is accompanied by formation of structure defects), it is of special interest to identify advantages and disadvantages of new method of di usion.
Developed SiC p-i-n diodes have fast switching time, and duration of the reverse recovery current is less than 10 ns with a breakdown voltage of 120-140 V. Fabricated diodes possess capability to operate at temperatures up to 300°C. As the temperature of di usion process is lower than the melting temperature of silicon, this new technology allows fabrication of diodes based on the SiC/Si epitaxial structures.

Conflicts of Interest
e authors declare that they have no con icts of interest.