The deep-level drain current transient spectroscopy (Id-DLTS) measurements of Al-doped SiC metal–oxide–semiconductor field-effect transistors (MOSFETs) strongly suggest that the reduction in the channel mobility at low temperatures is related to a shallow trap detectable at 70 K. Using the Shockley–Reed–Hall (SRH) theory, the level of this trap has been extracted to be around 0.15 eV below the conduction band minimum of SiC. Density functional theory (DFT) calculations of Al Si N C Al Si and Al Si O C Al Si defect complexes have found one configuration of the Al Si O C Al Si complex, which has a charge transition level within the SRH extracted trap level range. Therefore, we suggest that these Al Si O C Al Si defects are likely candidates for traps responsible for the channel mobility reduction.

The 4 H- SiC polytype of silicon carbide with a 3.26 eV bandgap1 is a very promising semiconductor. It has a high critical breakdown field and thermal conductivity2 and is used within metal–oxide–semiconductor field-effect transistor devices (MOSFETs) for high-power, high-temperature electronics.3 Unfortunately, the performance of 4 H- SiC MOSFET devices does not yet meet expectations compared to bulk SiC. However, device performance can be further improved upon by improvement of inversion channel field-effect mobilities. The mobilities within current 4 H- SiC devices average around 1–50  cm 2 V 1 s 1,4,5 whereas the reachable bulk electron and hole mobilities of 4 H- SiC are approximately 1020 and 95  cm 2 V 1 s 1, respectively, at 300 K.6 

Generally, p-type regions within 4 H- SiC MOSFETs are created via high-energy ion implantation of Al in SiC wafers. Within 4 H- SiC, the Al acceptor level (depending on the Si sub-lattice site occupied) is E V + 0.198 / E V + 0.201 eV,7,8 which is considerably deeper than the levels of p dopants in other semiconductors (e.g., level of E V + 0.045 eV B in Si9). Al-induced level in 4 H- SiC can be made shallower by increasing the concentrations of implanted Al10 to improve the conductivity of the device by producing higher distributions of mobile holes.11 However, recent evidence suggests that a heavier p-doping of the devices may further reduce channel mobilities due to the formation of defects at the SiC/ SiO 2 interface. In particular, analysis of subthreshold slope characteristics, after NO post-oxidation anneal, as a function of temperature, detected subthreshold slope deterioration at 13 K related to interfacial defects, extracted to be within 0.01 eV of E C.12 Densities of these interfacial defects are found to double, and almost quadruple, upon an increase of 1 to 2 orders of magnitude in implanted Al concentration, while effective mobility is seen to plummet by 70–80  cm 2 V 1 s 1.12,13 This suggests that mobility reduction is a direct consequence of high Al implantation concentration in 4 H- SiC. High Al implantation concentration in 4 H- SiC has also been associated with impurity-induced conduction mechanisms, such as variable-range hopping conduction14 and impurity band conduction.15 Impurity band conduction, in particular, is believed to be caused by precipitation of Al clusters,10 which have been verified to form by secondary ion mass spectrometry (SIMS) of highly doped layers of 4 H- SiC.16 Attempts to find another p-type impurity with a shallower acceptor level than Al proved unsuccessful despite the theoretical efforts of wide p-type impurity screening studies.17 Therefore, attention turned to identifying the Al-related mobility-affecting defects, so that effective mitigation techniques can be used to reduce device performance-hindering defects.

Usually, up to 99% of interface state density can be reduced through passivation via nitridation during post-oxidation anneal (POA) under an NO atmosphere.18 Theoretical simulations suggest that NO molecules are able to diffuse through 6- and 7-member rings of amorphous SiO 2 via interstitial migration during the anneal process.19 On the SiC side of the interface, N concentrations of 0.1 of a monolayer have been detected at approximately 2 and 3 nm from the interface20 alongside signatures of C Si N and Si C N bond environments21 after NO anneal. Low-energy muon-spin-rotation spectroscopy (LE- μSR) measurements have also indicated that unintentional doping can occur in SiC upon NO anneal, with an increase in carrier concentration of almost two orders of magnitude observed.22 

If, in fact, unintentional nitrogen doping is occurring through anneal, then devices could potentially be considered to have been “unintentionally co-doped” via Al implantation and NO anneal to create defect complexes that cause the ionization energy of either the acceptor or donor to become shallower.23 Experimentally, traps related to Al and N double implantation have been located as shallow as E V + 0.27 eV and E C 0.15 eV within junction diodes.24 However, when unintentional, co-doping may occur due to aggregation of defects related to different p- and n-type impurities introduced into the system through separate device creation steps. In particular, there is a likelihood that, during POA, NO molecules can interact with precipitated clusters of Al atoms at the SiC / SiO 2 interface to form defect complexes, such as Al N Al and Al O Al.

To further assess the effect of Al concentration on device channel field-effect mobility, we performed deep level transient spectroscopy measurements for SiC MOSFETs with increasing concentrations of Al dopants after post-oxidation anneal in a NO atmosphere. A new shallow trap band, correlated with both the increase in Al concentration and the decrease in channel mobility, is identified near the conduction band. Analysis of the electronic structure of different configurations of Al N Al and Al O Al defect complexes using density functional theory (DFT) calculations supports their relevance to the identified mobility reduction and suggests potential candidates for the new shallow trap states. In Sec. II, we describe the experimental and theoretical methods used in this work. In Sec. III, we present the experimental findings and the results of theoretical calculations. Discussion and conclusions are given in Sec. IV.

For this study, similar test structures as in Ref. 25 were used. In the SiC n-MOSFET test structures used in this work, the p-type body regions were formed by ion implantation of A l, while the drain and source were formed by ion implantation of N. The SiO 2 gate oxide was formed by chemical vapor deposition, which was followed by a POA in a NO atmosphere at high temperature.

In order to gain a better understanding of the shallow traps at the interface between SiC and SiO 2, measurements were carried out at cryogenic temperatures. According to the non-radiative multiphonon (NMP) transitions model, most trap bands have strongly temperature-dependent capture and emission time constants.26 At sufficiently low temperatures, these time constants are large enough for trapping effects to become measurable within experimentally accessible time windows. Drain current, Id, deep level transient spectroscopy (Id-DLTS), a variant of DLTS, has been used to measure the trapping effects within our test structures. In standard capacitance DLTS, voltage pulses are applied to the device under test as a deviation from the steady state, and the resulting capacitance transients are measured from the transition backwards.27–29 In Id-DLTS, the same principle applies, but here drain current transients are measured instead of capacitance. The change of drain current can be translated into a change of threshold voltage with the help of transfer characteristics, out of which a number of states can be estimated.

In this work, for Id-DLTS, a stress bias of 0 V and a recovery bias of 8 V are applied for 10 s, respectively, using a lockin amplifier. These bias conditions result in the movement of the device Fermi level from midgap to conduction band edge. Therefore, electron capture by trap states close to the conduction band is measured. The temperature was ramped with a constant heating rate of 0.5 K/min in order to account for the long stress times. Since the threshold voltage strongly shifts for wide range temperature sweeps, transfer characteristics were re-measured at regular time frames. From the temperature-dependent transfer characteristics, a temperature-dependent field effect mobility was extracted and correlated with the Id-DLTS defect signals.

Γ-point spin polarized density functional theory (DFT) calculations were performed using the Gaussian Plane Wave method,30 as implemented in the CP2K code.31 The PBE0-TC-LRC32 density functional with 27% Hartree–Fock exchange and the exchange cutoff radius of 2 Å was used in all calculations. We used a cut-off energy of 600 Ry on a 448 atom 7 × 4 × 1 supercell of orthorhombic C m c 2 1 4 H- SiC structure.33 All atomic species involved in the simulations were described using Geodecker, Teter, and Hutter (GTH) pseudopotentials34–36 and the DZVP-MOLOPT-SR-GTH37 and the DZP-UZH Auxiliary Density Matrix Method38 basis sets. Optimization of the geometry of the 7 × 4 × 1 supercell (SC) gives the primitive cell lattice constants of a = 3.09 Å and c = 10.06 Å and a single electron bandgap of 3.31 eV. These characteristics, as well as the Si C bond lengths between 1.88 and 1.9 Å, and bond angles of 109.5 ° for perfect 4 H- SiC are all in good agreement with the experimental results.1,39

To investigate defect aggregation, the Al Si, N C, and O C substitutional defects were combined to create Al Si N C Al Si and Al Si O C Al Si defect complexes. The site-occupation disorder, SOD, package40 was used to identify nonequivalent geometry configurations within the confines of the 8-atom 4 H- SiC primitive unit cell, in which one or both Al Si substitutes are directly bonded to the N C / O C placement, for each defect complex. The inequivalent configurations of defect complexes are shown in Fig. 1. These were determined by first finding inequivalent positions of the substitutional site C, resulting in two configurations for each complex. These correspond to substitution of N / O in the hexagonal ( C ( HEX )) and cubic ( C ( CUB )) carbon sublattice sites to create O C ( HEX ) (pale red atoms)/ N C ( HEX ) (navy blue atoms) and O C ( CUB ) (deep red atoms)/ N C ( CUB ) (dark blue atoms) defects. Each of these configurations was then searched for inequivalent combinations of two Al atoms substituting into Si ( HEX ) and Si ( CUB ) sublattice sites, producing Al Si ( HEX ) (peach pink atoms) and Al Si ( CUB ) (orchid pink atoms) defects. This resulted in a total of four inequivalent configurations per defect complex. The first of these configurations, termed O Al 1/ N Al 1 for simplicity, consists of two Al Si ( HEX ) atoms and an O C ( HEX ) / N C ( HEX ) atom to which one of the Al Si ( HEX ) atoms is bonded to. The second configuration, O Al 2 / N Al 2, also has an O C ( HEX ) / N C ( HEX ) atom bonded to an Al Si ( HEX ) atom as well as an Al Si ( CUB ) atom. The third and fourth configurations consist of an O C ( CUB ) / N C ( CUB ) atom bonded an Al Si ( HEX ) atom in O Al 3 / N Al 3 and an Al Si ( CUB ) atom in O Al 4 / N Al 4. In both O Al 3 / N Al 3 and O Al 4 / N Al 4, there is also an Al Si ( HEX ) atom separated by either a C atom or a C Si bond from the other substitutional atoms. The geometry of each inequivalent configuration was optimized in a 448-atom 7 × 4 × 1 supercell of 4 H- SiC.

FIG. 1.

Defect complex inequivalent geometry configurations. (a) Central 8-atom 4 H- SiC unit cell taken from the 448-atom 4 H- SiC 7 × 4 × 1 SC, within which configurations (b) O Al 1, (c) O Al 2, (d) O Al 3, and (e) O Al 4 for Al Si O C Al Si and (f) N Al 1, (g) N Al 2, (h) N Al 3, and (i) N Al 4 for Al Si N C Al Si were found with SOD.40 Si is yellow; C is cyan; Al is pink; O is red; N is blue; paler shades are HEX sublattice sites; darker shades are CUB sublattice sites. Figure created using VMD.41 

FIG. 1.

Defect complex inequivalent geometry configurations. (a) Central 8-atom 4 H- SiC unit cell taken from the 448-atom 4 H- SiC 7 × 4 × 1 SC, within which configurations (b) O Al 1, (c) O Al 2, (d) O Al 3, and (e) O Al 4 for Al Si O C Al Si and (f) N Al 1, (g) N Al 2, (h) N Al 3, and (i) N Al 4 for Al Si N C Al Si were found with SOD.40 Si is yellow; C is cyan; Al is pink; O is red; N is blue; paler shades are HEX sublattice sites; darker shades are CUB sublattice sites. Figure created using VMD.41 

Close modal

Since each Al substitution induces a hole within the system, and 1(2) extra electron(s) are also introduced by the substitution of N(O), neutral defect configurations were calculated with doublet(singlet) multiplicity. Therefore, all Al Si O C Al Si configurations have equal numbers of electrons in both α and β spins, and all Al Si N C Al Si configurations possess a hole within the β spin.

Characterization of these defect complexes to establish their relevance as potential candidates of mobility-impeding defect states has been carried out by calculating the following characteristics. Formation energy, E f 0 [ D ]:

(1)
where X refers to N for the Al Si N C Al Si complex and O for the Al Si O C Al Si complex; E [ D 0 ] is the total energy of the defect in the neutral charge state; n Si, n C, n Al, and n X correspond to the number of Si, C, Al, and X atoms within the defect supercell; and μ SiC bk is the total energy per unit formula of perfect 4 H- SiC,42 calculated to be 262.4 eV.

Chemical potentials μ Si bk and μ C bk are taken to be the total energies of crystalline silicon [ E ( Si silicon ) = 107.2 eV] and diamond [ E ( C diamond ) = 154.7 eV] per formula unit. To be able to investigate whether aggregation of impurity-related defects could be occurring unintentionally within MOSFET device fabrication, chemical potentials of Al, N, and O have been taken from the experimental device fabrication sources of AlH 3 ( g ) [ μ Al = E ( AlH 3 )- 3 μ H = 55.0 eV] and NO ( g ) [ μ O = E ( NO ) 1 2 E ( N 2 ) = 435.7 eV; μ N = E ( NO ) 1 2 E ( O 2 ) = 269.4 eV].

Charge transition levels (CTLs):

(2)
where δ ϵ f is the Fermi energy above the valence band maximum of defect-free 4 H- SiC, ε V B M,43 at which the formation energies of two charge states, q 1 and q 2 ( q 1 > q 2), intersect.44,45 The potential alignment correction, Δ V Nap, is the yz planar average of the scalar potential shift between the 7 × 4 × 1 D 0 and 7 × 4 × 1 SiC b k supercells.46 The anisotropic Lany–Zunger correction47 has been used for the charge correction term, E corr, based upon 4 H- SiC’s static dielectric constants, ε 0 C = 9.66 and ε 0 C = 10.03,48 and the Madelung potential method.47 

All defect configurations were calculated in the neutral ( 0) and single negative ( ) charge states. The / 0 charge transition level is commonly referred to as thermal ionization energy (IE). This is the thermal energy required either to create a hole in the valence band via population of an unoccupied bandgap state close to the valence band maximum or to excite an electron into the conduction band from a bandgap state close to the conduction band minimum. Binding energy, E b:

How readily two or more simple defects will combine together if they all transpire within a sample. The energy of combining Al Si ( HEX ), X C ( CUB ) (where X is either N or O), and Al Si ( CUB ) to create the Al Si ( HEX ) X C ( CUB ) Al Si ( CUB ) complex defect configuration is calculated as2 
(3)

This is simply the difference in formation energy of the complex defect and the sum of the formation energies of each individual defect within the complex. A positive binding energy indicates that it is more favorable for the individual defects to stay separated, rather than to combine together.

Inverse Participation Ratio, I P R ( ψ n ):

The KS orbital localization is carried out using the inverse participation ratio (IPR) of KS orbitals, IPR ( ψ n ). CP2K implements atom-centered basis sets ( ψ n ( r ) = i N c n i ϕ i ( r )) with ϕ i basis functions that allows simple quantification of eigenvector localization. IPR is defined as49 
(4)

KS orbitals within the valence and conduction bands are almost always highly delocalized with very small IPR values. Due to this, highly delocalized states in general are considered “band-like.” KS orbitals that are partially or highly localized within the calculation supercell are seen to give higher IPR values.

Figure 2(a) shows the Id-DLTS spectrum measured in the temperature range from 40 to 100 K. The signal of the trap distribution scales directly with the Al channel doping concentration at the interface between SiC and SiO 2, suggesting the origin of the trap signal is either the Al dopant or an Al-related defect. At the highest concentration of Al, a trap density of 4 × 10 11 cm 2 is obtained. In our measurements, the Fermi level is positioned between the midgap and the conduction band edge. Therefore, despite Al ionization (which corresponds to a level close to the valence band) being observed slightly above 100 K within temperature-dependent CV measurements for comparable temperature ramping rates, this signal is not a direct result of dopant ionization. Thus, these results clearly indicate the existence of other Al-related traps.

FIG. 2.

(a) Id-DLTS spectrum showing trap density as a function of temperature and doping concentration (conc. 1 < conc. 2 < conc. 3 < conc. 4). With increasing doping concentration, an increasing trap density is measured. (b) Drain current as a function of the measurement temperature extracted for V Grec V t h , 303 K = const at V D = 0.05 V. A dip in the current is observed around 70 K.

FIG. 2.

(a) Id-DLTS spectrum showing trap density as a function of temperature and doping concentration (conc. 1 < conc. 2 < conc. 3 < conc. 4). With increasing doping concentration, an increasing trap density is measured. (b) Drain current as a function of the measurement temperature extracted for V Grec V t h , 303 K = const at V D = 0.05 V. A dip in the current is observed around 70 K.

Close modal

Upon comparison of the DLTS spectrum with the behavior of the temperature dependence of field effect mobility at around 70 K, the DLTS peak correlates with a significant change in the mobility curve trace seen in Fig. 3. Moreover, a closer analysis of the temperature effect on drain current around 70 K shows a dip in the drain current at the exact same temperature as the observed Id-DLTS peak [Fig. 2(b)]. Combining these observations, we conclude that this specific trap distribution is detrimental to device performance, particularly channel mobility at low temperatures.

FIG. 3.

Field effect mobility as a function of temperature. Around 70 K, the mobility starts decreasing.

FIG. 3.

Field effect mobility as a function of temperature. Around 70 K, the mobility starts decreasing.

Close modal

This trap band is not related to the interfacial defects identified by subthreshold slope characteristics, as it has been detected at a 57 K higher temperature. We note that a similar trap distribution was found at the same temperature within earlier cryogenic measurements using thermal dielectric relaxation current (TDRC). These measurements also demonstrated a correlation between the TDRC trap distribution and Al implantation.50 However, although the TDRC and DLTS peaks occur at the same temperature, they do not necessarily belong to the same trap distribution. This is because only charge emission close to the conduction band edge is captured by TDRC, whereas both capture and emission effects can be extracted from DLTS, depending on the measurement conditions. Using the TDRC emission process transformation equations,51 the TDRC peak is extracted to occur at E C 0.13 eV.50 

Using the Shockley–Read–Hall (SRH) theory,52,53 an activation energy of 0.155 ± 0.025 eV is obtained for the Id-DLTS trap. In contrast, the TDRC emission barrier is slightly lower. This indicates that the trap distributions of the TDRC and Id-DLTS peaks are, in fact, unrelated to each other, despite being detected at the same temperature. It also verifies the independence of the sub-threshold slope interfacial defects and the Id-DLTS trap band. Moreover, defects responsible for the Id-DLTS trap band occur much less frequently than those responsible for the TDRC trap and the sub-threshold slope characteristics state. Their densities were measured at 5 × 10 12 cm 250 and 1 × 10 14–4 × 10 14 cm 2,12,13 respectively.

Therefore, the Id-DLTS measurements conducted here have identified a new, slightly less predominant set of Al-related defects that also negatively impact device channel mobilities. Such Al related defects could result from the interaction of implanted Al ions with N and O atoms present at SiC/ SiO 2 interfaces as a result of POA in NO. In the following, we investigate theoretically whether such complexes could be responsible for the shallow defect states reported here. The formation mechanism of these defects will not be addressed here because of the complex nature of implantation and post-oxidation anneal. We note that the properties of one of the Al Si N C Al Si complexes have been calculated in Ref. 54.

The investigated configurations of the X Al n [ X = { N , O }, n = { 1 , 2 , 3 , 4 }] Al Si N C Al Si and Al Si O C Al Si defect complexes are shown in Fig. 1. Table I summarizes the ionization energies and structural characteristics of these configurations along with the calculated formation ( E f 0) and binding ( E b) energies and the IPR analysis of each configuration in the neutral charge state. Calculations are spin polarized, which means the sign of the IPR value is dependent on the wavefunction spin state. Therefore, for the Al Si O C Al Si configurations, whose β spin IPR values are the negatives of their α spin values, only positive IPR values are given. For Al Si N C Al Si configurations, given values are negative, since the defect states are solely in the β spin state.

TABLE I.

Calculation results for the X Al n [X = {N, O}, n = {1, 2, 3, 4}] AlSiNCAlSi and AlSiOCAlSi defect complex configurations. E f 0 [ X Al n ] is the formation energy [eV] of the defect complex; ΔxSi→Al is the displacement (Å) of substituting Al within the Si lattice site and Δ xC→X is the displacement (Å) of substituting O or N within the C lattice site; Δ xmax is the max displacement (Å) of nearest neighboring atoms to the substitution sites; Eb is the binding energy (eV) of the complex configuration; and IE is the −/0 CTL ionization energy (eV) of the defect and is given with respect to both the top of the valence band (EV +) and the bottom of the conduction band (Ec −). IPR analysis results include the single electron KS energy level (eV) [ ϵ ( ψ DS ); relative to that of the valence band maximum] of the defect state and its IPR value, |IPR(ψDS)|.

Computational results for defect
X Aln E f 0 [X Al n]Δ xSi→AlΔ x C XΔ x maxEbIE [eV]IPR analysis
X, n =[eV][Å][Å][Å][eV]EV +EC − ϵ ( ψ DS ) [eV]|IPR(ψDS)|
N,1 −3.55 0.02 0.13 0.16 −4.07 0.15 3.16 0.19 −0.0329 
N,2 −4.10 0.03, 0.01 0.14 0.12 −4.61 0.12 3.19 0.07 −0.0120 
N,3 −3.57 0.03 0.10 0.15 −4.01 0.10 3.21 0.13 −0.0152 
N,4 −3.43 0.02, 0.04 0.12 0.19 −3.87 0.25 3.06 0.49 −0.0716 
O,1 −2.96 0.04, 0.06 0.14 0.15 −6.65 2.96 0.35 3.12 0.0241 
O,2 −3.98 0.05, 0.09 0.18 0.11 −7.68 3.20 0.11 3.23 0.0085 
O,3 −2.93 0.04, 0.11 0.15 0.16 −6.55 3.17 0.14 2.94 0.0376 
O,4 −2.71 0.07, 0.10 0.17 0.17 −6.32 2.88 0.43 2.91 0.0373 
Computational results for defect
X Aln E f 0 [X Al n]Δ xSi→AlΔ x C XΔ x maxEbIE [eV]IPR analysis
X, n =[eV][Å][Å][Å][eV]EV +EC − ϵ ( ψ DS ) [eV]|IPR(ψDS)|
N,1 −3.55 0.02 0.13 0.16 −4.07 0.15 3.16 0.19 −0.0329 
N,2 −4.10 0.03, 0.01 0.14 0.12 −4.61 0.12 3.19 0.07 −0.0120 
N,3 −3.57 0.03 0.10 0.15 −4.01 0.10 3.21 0.13 −0.0152 
N,4 −3.43 0.02, 0.04 0.12 0.19 −3.87 0.25 3.06 0.49 −0.0716 
O,1 −2.96 0.04, 0.06 0.14 0.15 −6.65 2.96 0.35 3.12 0.0241 
O,2 −3.98 0.05, 0.09 0.18 0.11 −7.68 3.20 0.11 3.23 0.0085 
O,3 −2.93 0.04, 0.11 0.15 0.16 −6.55 3.17 0.14 2.94 0.0376 
O,4 −2.71 0.07, 0.10 0.17 0.17 −6.32 2.88 0.43 2.91 0.0373 

Charge transition level (CTL) diagrams for O and N containing complexes are shown in Fig. 4, and the positions of CTLs with respect to the top of the valence band ( E V +) and the bottom of the conduction band ( E c ) are also given in Table I. These CTL values are equal to thermal ionization energies of these defect states into respective bands. One can see that the 0 and charge states for both complexes are the most stable in the full Fermi level range. Our results for the Al Si N C Al Si complex are in qualitative agreement with those obtained in Ref. 54 using the LDA approximation in a much smaller periodic cell.

FIG. 4.

Formation energies (eV) calculated for the (a) , , 0, and + charge states of Al Si N C Al Si configurations and the (b) , 0, +, and + + charge states of Al Si O C Al Si configurations. Solid lines illustrate the stable charge states of each configuration found within the 4H-SiC bandgap (VBM and CBM represented by the gray vertical dotted line). Stable charge transition levels are annotated in black notation. Dashed lines and brown notations highlight where a charged state is meta-stable and the charge transition levels between meta-stable states.

FIG. 4.

Formation energies (eV) calculated for the (a) , , 0, and + charge states of Al Si N C Al Si configurations and the (b) , 0, +, and + + charge states of Al Si O C Al Si configurations. Solid lines illustrate the stable charge states of each configuration found within the 4H-SiC bandgap (VBM and CBM represented by the gray vertical dotted line). Stable charge transition levels are annotated in black notation. Dashed lines and brown notations highlight where a charged state is meta-stable and the charge transition levels between meta-stable states.

Close modal

The most stable, shallowest / 0 CTLs with respect to the edges of the conduction and valence band are found for the OAl2 and NAl2 configurations, respectively. This aligns with these two configurations having defect states with the closest single-electron KS energy levels to the band edges, which are within 3 and 5 meV, respectively, of their / 0 CTL ionization energies. These two configurations also have the lowest IPR values, indicating that NAl2 and O Al2 are significantly more delocalized and “band-like” than the other Al Si N C Al Si and Al Si O C Al Si configurations. We note that the bottom of the 4H-SiC conduction band is dominated by Si p-states with IPR values of 0.0016 and the top of the valence band is dominated by C p-states with IPR values of 0.0039. The IPR values for the defect states shown in the right column of Table I are an order of magnitude larger, indicating that these defect states are more localized.

he NAl2 and OAl2 configurations also stand out as they are 0.5 and 1 eV lower than their respective defect configuration counterparts in both formation and binding energies. These configurations have the lowest binding energies because their defect states are more delocalized. Differences in energy between configurations are likely due to differences in structural distortions of the lattice induced by impurities at substitutional sites. The values of the lattice site displacements of Al ( Δ x Si Al) and N / O ( Δ x C X), as well as the maximum displacements of the nearest neighbouring atoms ( Δ x max), of each neutral configuration are also shown in Table I. The negative defect binding energies indicate that, if Al Si and N C / O C are separately present within 4H-SiC, it is more energetically favorable for them to aggregate. When binding energies between the two defect complexes are compared, the Al Si O C Al Si configurations are found to have lower energies. This can be explained by the approximately 3.74 and 1.39 eV higher bond dissociation energies of the Si–O and Al–O bonds compared to the Si–N and Al–N bonds,55–57 respectively, as stronger bonds are formed more favorably.

Id-DLTS results strongly point to channel mobility decreasing at low temperatures with the formation of a shallow trap detectable at 70 K. Using SRH theory, the level of this trap has been extracted to be roughly E c 0.15 eV. The results shown in Table I demonstrate that all Al Si N C Al Si complexes have their 0/ CTLs close to the top of the valence band and that NAl4 is the only Al Si N C Al Si configuration that has a higher ionization energy than the single Al dopant. The results for Al Si N C Al Si complexes can be viewed as Al p-dopants perturbed by a N C Al Si dipole.

Applying the same approach to Al Si O C Al Si complexes explains why Al CTLs have been shifted close to the bottom of the conduction band by the perturbation induced by negatively charged O C Al Si dipoles. OAl2’s ionization energy coincides with the maximum activation energy extracted for the Id-DLTS trap, and the ionization energy of OAl3 sits comfortably within the energy range of the trap. The calculated CTLs suggest that these defects are good candidates to explain the Id-DLTS data presented above. However, the extracted Id-DLTS trap level cannot be directly compared with CTLs. This is due to the neglect of relaxation energy within the Shockley–Read–Hall theory.26 

To calculate relaxation energies for these configurations, the relationship between total energy and relaxation coordinate must be examined for both the neutral and negative charge states. Since OAl2 has the shallowest CTL with respect to the conduction band minimum and is also the most favorable Al Si O C Al Si configuration in both formation and binding energies, its neutral and negative charge state structures were analyzed in more detail.

The OAl2 configuration (and the NAl2 configuration) contains Al Si ( HEX ) and Al Si ( CUB ) substitutional sites that are both directly bonded with the O C ( HEX ) [ N C ( HEX )] substitutional site to create Al Si ( HEX ) O C ( HEX ) Al Si ( CUB ) [ Al Si ( HEX ) N C ( HEX ) Al Si ( CUB )] bonds, as can be seen in Fig. 5. Compared to the other configurations—where the complex is split up into an Al Si- O C bond and a single Al Si separated by either a Si–C bond or a C atom—the neutral OAl2 configurations are seen to have the largest O lattice site displacements and also the smallest nearest neighbor displacements. This results in OAl2 having the shortest Al Si ( HEX ) O C ( HEX ) bond by 0.03 Å. In the negative charge state of OAl2, directions and magnitudes of atomic displacements differ from those in neutral OAl2 state, as seen in Fig. 5.

FIG. 5.

Nearest neighbor relaxed geometry structures of (a) neutral OAl2 and (b) negative OAl2. Si is yellow, C is cyan, Al is pink, and O is red. Lighter and darker shades represent HEX and CUB sublattice sites, respectively. Atom transparency is graded with proximity to substitutional atom, increasing from first to second nearest neighbors. Configurational atomic displacements are represented by triangles colored by size of displacement (Å) (according to the color bar) and point in the direction of this displacement. In (a), modal lengths (Å) for each individual substitutional atom-nearest neighbor bond type are given. Bonds with lengths not equal to their bond type’s modal length are in italics. In (b), only bonds who’s length differs in the negative charge state are stated—unless there is a modal length change, these lengths will be in italics.

FIG. 5.

Nearest neighbor relaxed geometry structures of (a) neutral OAl2 and (b) negative OAl2. Si is yellow, C is cyan, Al is pink, and O is red. Lighter and darker shades represent HEX and CUB sublattice sites, respectively. Atom transparency is graded with proximity to substitutional atom, increasing from first to second nearest neighbors. Configurational atomic displacements are represented by triangles colored by size of displacement (Å) (according to the color bar) and point in the direction of this displacement. In (a), modal lengths (Å) for each individual substitutional atom-nearest neighbor bond type are given. Bonds with lengths not equal to their bond type’s modal length are in italics. In (b), only bonds who’s length differs in the negative charge state are stated—unless there is a modal length change, these lengths will be in italics.

Close modal

Our calculations demonstrate that these capture relaxation energies are within 0.15 eV due to delocalized nature of electronic states and cannot affect the qualitative alignment between configuration CLTs and the Id-DLTS trap level because only 1/4 of the relaxation energy contributes to the capture energy.26 

To conclude, the DFT calculations suggest that the Al Si O C Al Si complex is a good candidate to explain the Id-DLTS data presented. All Al Si O C Al Si configurations are found to have 0/ CTLs close to the bottom of the conduction band, with OAl2 and OAl3, in particular, having ionization energies that align with the energy range of the trap. However, the positions of CTLs can be affected by the dependence of the 4H-SiC bandgap on the exposed facet as well as by the presence of interface states with a- SiO 2 detected in Refs. 5 and 18. The results of our calculations conducted in the bulk of 4H-SiC suggest that further studies at the interfaces could be useful to provide more accurate predictions.

N.S. would like to acknowledge EPSRC and Infineon Technologies, Austria for financial support. Via our membership of the UK’s HEC Materials Chemistry Consortium, which is funded by EPSRC (EP/X035859), this work has been completed using the ARCHER2 UK National Supercomputing Service (http://www.archer2.ac.uk). A.S. would like to acknowledge support from the EPSRC Grant No. EP/R034540/1.

The authors have no conflicts to disclose.

N. Smith: Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). J. Berens: Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). G. Pobegen: Supervision (equal); Writing – review & editing (equal). T. Grasser: Supervision (equal); Writing – review & editing (equal). A. Shluger: Supervision (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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