Transient-Enhanced Diffusion of Implanted Aluminum in 4H-SiC

. Semiconductor devices rely on the incorporation of donor and acceptor atoms into the crystal lattice to form locally doped regions. For dopant atoms incorporated into SiC by ion implantation, a high-temperature annealing step is required to achieve electrical activation. This annealing step is accompanied by redistribution of the implanted atoms. The influence of the annealing parameters on dopant redistribution is crucial when aiming for ever smaller device dimensions. In this work, we present a consistent analysis of the diffusion of Al implanted in 4H-SiC after high-temperature annealing at 1650 °C and 1800 °C for different annealing times. We identify the equilibrium diffusion coefficient at long annealing times from Al profiles obtained by SIMS analyses for both annealing temperatures. The temperature dependence is determined using an Arrhenius representation. This allows to quantify the equilibrium diffusion lengths for the actual temperature profiles, including heating and cooling rates. We find that the measured diffusion lengths for short annealing times are larger than expected from equilibrium diffusion and attribute the excess length to transient enhanced diffusion. Comparing the transient diffusion lengths of room-temperature and 500 °C-implanted samples, we conclude that the transient behavior is likely related to residual crystal damage induced during the implantation process.


Introduction
The reported diffusivities of Al as one of the main acceptor doping species in SiC are exceptionally low [1,2] at typical processing temperatures, orders of magnitude lower than in Si [3].This renders doping of SiC by in-diffusion from the vapor phase impractical.Therefore, incorporating dopant atoms by ion implantation is the preferred process.To achieve electrical activation of implanted dopant atoms, a high-temperature annealing step is required to facilitate the incorporation of dopants on lattice sites.During the annealing step, dopant atoms undergo redistribution, altering the asimplanted profiles.Knowledge of the dopant distribution after annealing processes is essential for accurate modeling of semiconductor device performance.
Early investigations on the diffusion of Al implanted into 6H-SiC were examined by Lucke et al. [4].They observed significant out-diffusion and redistribution of Al atoms and related these effects to the presence of radiation-induced defects.A first temperature dependence of the diffusion coefficient of implanted Al upon annealing in a furnace was given by Tajima et al. [2].They observed asymmetric broadening of the implanted peak profile towards the sample surface and reported enhanced diffusion of Al into the crystal bulk.In both investigations, a total dose surpassing the amorphization threshold was employed [5].
The reports mentioned above share the common implication of transient-enhanced diffusion of implanted Al occurring during the thermal annealing process.However, the presence of transient effects for Al in 4H-SiC implanted at room and moderate temperatures for concentrations below the amorphization threshold has not been clarified so far.In order to determine the contribution of transient effects to the overall redistribution, the diffusion occurring in thermal equilibrium needs to be established first.To extract the equilibrium diffusion coefficient  at 1650 °C and 1800 °C, the profile broadening after a sequence of increasing annealing times was measured.Imposing the diffusion coefficient follows an Arrhenius relationship, the temperature dependence () can be obtained and the expected broadening for the applied temperature profile () can be calculated.The diffusion length related to transient-enhanced effects can be assessed by quantifying the deviation from the measurements.

Experimental Details
To investigate the diffusion effects, a single Al peak was implanted at an energy of 300 keV with a dose of 1.6×10 14 cm -2 .Implantations were performed at room temperature and at 500 °C into 1×10 16 cm -3 N-doped epitaxial layers grown on 4° miscut n-type 4H-SiC substrates.The ion beam was oriented perpendicular to the sample surface, resulting in an effective implantation angle of 4° from [0001] towards [112 ̅ 0].The implantation resulted in a peak concentration of about 1×10 19 cm -3 .Part of the samples were subsequently annealed at 1650 °C or 1800 °C for 3, 10, 30 or 100 min.The furnace annealing was performed with a heating rate around 20 °C min -1 , while the cooling rate exhibited an exponential decrease with a time constant of approximately 100 min.To protect the SiC surface from degradation, the samples were annealed with a graphite capping layer [6].Aluminum concentration profiles of as-implanted and annealed samples were obtained by SIMS (secondary ion mass spectrometry) analysis on a CAMECA IMS SC Ultra instrument under ultra-high vacuum of 4×10 -10 mbar.High spatial and concentration resolution was achieved with oxygen primary ions and high incidence angle bombardment [7].The impact energy was 500 eV, the raster size was 250×250 µm 2 , and the analysis area was limited to 200×200 µm 2 .To achieve a better signal-to-noise ratio, five separate experiments were performed on each sample and the results were averaged.

Results and Discussion
The measured Al profiles of the as-implanted and annealed samples for an implantation temperature of 500 °C are shown in Fig. 1a.No out-diffusion or surface segregation can be observed.The calculation of the cumulative dose depicted in Fig. 1b indicates that the total dose is conserved upon annealing.We therefore conclude that the SiC surface with a carbon capping layer acts as a highly reflecting barrier for diffusing Al atoms.

Formation of Solid-State Structures
The Al profiles were analyzed first using the approach of Malherbe et al. [8], by fitting of Gaussian functions subjected to Fickian diffusion under the assumption of a perfectly reflecting surface.In this case, the dopant concentration  at location  at time  of an initial Gaussian profile with peak concentration  0 , mean peak position   and broadening of standard deviation ∆  subjected to diffusion with constant  for time  is given by The initial as-implanted profile cannot be accurately described by a Gaussian function due to its asymmetric shape [2], whereas it is better described by a Pearson IV distribution [9].To increase the accuracy of the fit, the profile data considered was restricted from 230 nm to a depth corresponding to a concentration of 1×10 16 cm -3 on the bulk side of the peak.Employing this procedure, the profiles can be described by Eq. 1, as depicted in Fig. 1a.
Applying the analytical solution of a diffused Gaussian profile (Eq. 1) to a measured profile annealed for a time  at the temperature of the annealing plateau, only an effective diffusion coefficient  eff can be obtained, as the heating and cooling rates are neglected.However, annealing a second sample for time  2 >  1 , the additional broadening within the timeframe  1 to  2 between the two samples can be attributed to diffusion at the plateau temperature alone.Temperature profiles () for different annealing times are shown in Fig. 2. To extract the effective diffusion coefficient attributed to the timeframe  1 to  2 , a Gaussian fit to the experimental profile obtained after time  1 is used as the initial profile.From this, a diffused Gaussian profile (Eq. 1) is fitted to the experimental profile after annealing for time  2 , with the time  of the fit corresponding to  =  2 −  1 .We employed the same procedure to the profile obtained after time  2 and compared the broadening to the profile obtained from the sample annealed for time  3 with  =  3 −  2 .The effective diffusion coefficients found this way are shown as a function of plateau annealing time in Fig. 3.According to our investigation, the effective diffusion coefficient associated with the net broadening between the measured profiles approaches a constant value at a given temperature.The method was verified then by solving Fick's law of diffusion numerically.This allowed also to confirm that the diffusion process could be excellently reproduced by a constant diffusion coefficient despite the fact that a significant part of the profile is extrinsic.

Solid State Phenomena Vol. 359
The effective diffusion coefficients related to  1 (10 min at 1650 °C and 3 min at 1800 °C) shown in Fig. 3 include the profile broadening during the heating and cooling phases.As the effective diffusion coefficients obtained between the timeframes  1 to  2 and  2 to  3 are of similar value, we conclude that they represent diffusion in thermal equilibrium.The equilibrium diffusion coefficients found for annealing at 1650 °C and 1800 °C in this way are expected to follow an Arrhenius law.The temperature dependence of diffusion in thermal equilibrium  eq () is compared to reported diffusion data [1,2] in Fig. 4. The temperature dependence of the experimentally determined diffusion coefficients in thermal equilibrium found in this work can be described by the Arrhenius expression (Eq. 2)

Formation of Solid-State Structures
It is similar to the one reported by Tajima et al. [2], despite differences in the experimental conditions.However, we find no indications for higher diffusion in the tail region of the profile as reported by Tajima et al. [2].These discrepancies could be attributed to the room-temperature implantation they employed, exceeding the amorphization threshold, as well as their use of annealing without a carbon capping layer.In general, in agreement with previous reports [2], we find that diffusion below 1800 °C is more pronounced than reported by Mokhov et al. [1] for diffusion from the vapor phase, characterized also by a significantly lower activation energy.The different slopes might be a consequence of a change in the diffusion mechanisms as the temperature ranges of the investigations do not overlap.
The total diffusion length  eq expected from diffusion in thermal equilibrium can be calculated from Eq. 3, considering the actual temperature profile () by taking into account both a steady heating rate and an exponential cooling phase, as provided above.
(Eq. 3) We find that the diffusion lengths of thermal equilibrium diffusion for the shortest annealing times including the contributions of the heating and cooling phases are about 19 nm and 32 nm for annealing at 1650 °C (10 min) and 1800 °C (3 min), respectively.The corresponding actual diffusion lengths can be calculated from the effective diffusion coefficients given in Fig. 3 and account to about 30 nm and 40 nm for annealing at 1650 °C and 1800 °C, respectively.The difference between the equilibrium and actual diffusion lengths are about 10 nm, independent of the annealing temperature, which corresponds to an increase in diffusion length by about 50% and 30% for annealing at 1650 °C and 1800 °C, respectively.We attribute this difference to transient-enhanced diffusion phenomena.It is noteworthy that the transient effects almost completely cease within the shortest annealing duration studied at both temperatures.Finally, we compare Al depth profiles of room-temperature and 500 °C implanted samples in Fig. 5.The profiles of the as-implanted state show no significant difference after room-temperature implantation compared to implantation at 500 °C.Extrapolating the temperature dependence for diffusion of Al during high-temperature implantation provided by Usov et al. [10] for the temperature range of 1300 °C to 1800 °C to a temperature of 500 °C, the calculated diffusion length associated to an implantation time of 1 min is in the sub-nanometer regime and cannot be resolved in our measurements.However, the transient diffusion of Al they observed in the profile tail regions during high-temperature implantation is absent in this form in our samples after high-temperature annealing.This points to a different mechanism leading to transient-enhanced diffusion during implantation at high temperatures compared to annealing of implanted profiles at high temperatures.One cause might be a significantly higher concentration of continuously generated intrinsic defects as found for hightemperature implantation of boron in silicon [11].
After annealing at 1800 °C for 3 min, the broadening of the room-temperature implanted sample is significantly larger compared to the sample implanted at 500 °C, as shown in Fig. 5.The associated actual diffusion length is about 57 nm, with a transient diffusion length of about 25 nm when compared to the diffusion length of 32 nm in thermal equilibrium.The excess transient length after room-temperature implantation is almost three times the length after implantation at 500 °C.Since implant damage can be assumed to anneal out at least in part during implantation at elevated temperatures, we take this as an indication that the transient diffusion behavior of Al is related to residual crystal damage induced during the implantation process.
To better understand the mechanism of transient-enhanced diffusion and to determine the temperature range of transient effects, conducting additional experiments at lower temperatures is essential.In addition, further clarification of the influence of the implanted dose, implantation energy, beam current, and heating rates on the observed transient effects is required.

Summary
In summary, we present a consistent analysis of the temperature dependence of equilibrium diffusion of aluminum implanted in 4H-SiC by means of high-resolution SIMS.In addition, we identify transient-enhanced diffusion as a likely reason for additional diffusive broadening during an initial period.Furthermore, we compare diffusion of room-temperature and 500 °C-implanted samples.The more pronounced transient behavior observed for the lower implantation temperature indicates a relation to residual crystal damage induced by the implantation process.Further investigations are necessary to clarify the migration paths involved in the diffusion mechanism of aluminum.

Fig. 1 .
Fig. 1.Aluminum depth profiles obtained by SIMS analysis for samples implanted at 500 °C.a) As-implanted (diamond) or annealed at 1650 °C (closed symbols) and 1800 °C (open symbols) for various annealing times, where only every fifth datapoint is shown for reasons of readability.The lines are corresponding simulation results.b) Calculated cumulative dose for conditions: as-implanted (continuous line), 1650 °C 100 min (dashed line) and 1800 °C 30 min (dotted line).

Fig. 2 .
Fig. 2. Schematic of temperature profiles () with linear heating rate and exponential cooling rate for different plateau annealing times   .

Fig. 3 .
Fig. 3. Effective diffusion coefficients  eff associated to the net broadening between the measured Al profiles obtained by the method described in the text after annealing at 1650 °C (closed symbol) or 1800 °C (open symbol) as a function of the plateau annealing time.Dotted lines serve as a guide to the eye.

Fig. 5 .
Fig. 5. Comparison of room-temperature (closed symbols) and 500 °C (open symbols) implanted Al depth profiles after implantation (square) and after annealing at 1800 °C for 3 min (circle), where only every fifth datapoint is shown for reasons of readability.