Nitrogen doping concentration as determined by

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Received 16 April 1996; accepted for publication 31 May 1996. Low-temperature photoluminescence PL spectroscopy is used for determination of the nitrogen.
Nitrogen doping concentration as determined by photoluminescence in 4H– and 6H–SiC I. G. Ivanov,a) C. Hallin, A. Henry,b) O. Kordina,b) and E. Janze´n Department of Physics and Measurement Technology, Linko¨ping University, S-581 83 Linko¨ping, Sweden

~Received 16 April 1996; accepted for publication 31 May 1996! Low-temperature photoluminescence ~PL! spectroscopy is used for determination of the nitrogen doping concentration in noncompensated 4H– and 6H–SiC by comparing the intensity of nitrogen-bound exciton ~BE! lines to that of the free exciton ~FE!, the latter being used as an internal reference. The results are compared with a previous work performed for the case of 6H–SiC only. A line-fitting procedure with the proper line shapes is used to determine the contribution of the BE and FE lines in the PL spectrum. The ratio of the BE zero-phonon lines ~R 0 and S 0 in 6H, Q 0 in 4H! to the FE most intensive phonon replica around 77 meV exhibits very well a direct proportional dependence on the doping as determined by capacitance–voltage (C – V) measurements for both polytypes. The use of fitting procedure which takes into account the real line shapes, the influence of the spectrometer transfer function, and the structure of the PL spectrum in the vicinity of the FE replica allows us determination of the N-doping concentration by PL for doping levels in the region 1014 cm23 –331016 cm23 for 4H– and 1014 cm23 –1017 cm23 for 6H–SiC. Above these levels the free-exciton related emission is not observable. © 1996 American Institute of Physics. @S0021-8979~96!06917-4#

I. INTRODUCTION

The specific physical and electronic properties of SiC make it one of the most promising semiconductors for use in future electronic devices, especially in those applications where operation at high power, high speed, extreme temperatures, or high radiation levels is needed. Many applications require the growth of thick, high-quality layers with low doping concentration and long carrier lifetimes. This has led to significant progress in the technologies for both bulk and epitaxial growth in the past few years. Growth of highquality epitaxial layers of 6H– and 4H–SiC by means of chemical vapour deposition ~CVD! has been reported.1,2 Among several characterization techniques, the lowtemperature photoluminescence ~PL! is considered as one of the most informative tools for nondestructive and rapid qualitative characterization of the grown materials. At the present, most features of a PL spectrum at low temperature from 6H– and 4H–SiC are well understood. This includes the series of lines originating from the recombination of excitons bound to the principal donor ~nitrogen, N! and acceptor ~Al! impurities, as well as the emission arising from some other impurities, such as Ti and H.3–6 Recently, the PL spectrum of the Ga acceptor in 4H–, 6H–, and 3C–SiC has been reported.7 Thus, in many cases the PL provides qualitative information about the impurities in the material. Quantitative estimations of the impurity concentration, however, are not possible without correlating the emissions of the extrinsic, impurity related to some intrinsic. Fortunately, in pure SiC layers which became available a few years ago,1,2 mainly because of the rapid development of the CVD growth technique, the lines related to the freeexciton ~FE! radiative recombination can be observed. These a!

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b!

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J. Appl. Phys. 80 (6), 15 September 1996

latter lines can be used as an internal reference to which the emission from the impurities should be compared. Such an approach was developed in Refs. 8 and 9 for the case of 6H–SiC. By correlating the ratio R of the nitrogen-related R 0 and S 0 lines divided by the FE-related I77 line, measured by PL ~see Sec. II!, to the carrier concentration n determined by capacitance–voltage (C – V) electrical measurements at room temperature, the authors derive an empirical equation which allows evaluation of the nitrogen doping concentration evaluation only by measuring the PL.9 The present article deals with a similar calibration for the case of 4H–SiC, as well as with some refinement for the case of 6H–SiC. In Sec. II the sample preparation and the experimental setup for PL measurements are described. Section III explains the line-fitting procedure used to accurately determine the contribution of the different lines in the PL spectrum. The results and some discussion are presented in Sec. IV. II. EXPERIMENT

The 4H– and 6H–SiC epilayers were grown in a hotwall CVD reactor described elsewhere.10 The layers were grown on n 1 substrates from CREE Research Inc. to a thickness ranging between 20 and 40 mm. Different n-type doping concentrations ~up to 1017 cm23! were achieved by small additions of nitrogen into the hydrogen carrier gas. For the C – V measurements, gold Schottky contacts ~1 mm in diameter! were deposited on the layers. An ohmic backside contact was achieved by gluing a large surface on the backside with silver paint. The luminescence spectra were taken at 2 K with a double SPEX Model 1404 monochromator equipped with 1200 grooves/mm gratings. Unless specified otherwise, a resolution of 0.5 Å ~100 mm slits! was used. The samples were excited by the 334.5 nm UV line of an Ar ion laser, using a power of 10 mW moderately focused

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© 1996 American Institute of Physics

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are determined by the actual number and energies of the phonons ~24 in 4H- and 36 in 6H-polytype!. Some selection rules restrict the number of observable replicas. Thus, most of the other lines, observed in the spectrum, are phonon replicas either to the P 0 ~N at hexagonal site!, or to the FE. Some of the strongest replicas are marked in Fig. 1 with the letter P or I, denoting P 0 or FE replica, respectively, and an index showing the energy shift ~in meV! between the replica and the zero-phonon line, equal to the energy of the momentum conserving phonon. The FE replicas can be recognized by their asymmetric line shape, as a consequence of the Maxwellian distribution of the velocities of the free excitons in an indirect band-gap semiconductor.11,12 Some weak replicas can be observed from Q 0 ~in 4H! and R 0 , S 0 ~in 6H!, corresponding to N located at a cubic site. They have negligible intensity, because the corresponding exciton binding energies are larger than that for the N at hexagonal site. This results in much lower probability for a phonon-assisted recombination, than a recombination when the impurity atom takes the momentum itself. The same argument explains the much higher intensity of the ‘‘deeper’’ zero-phonon lines ~Q 0 in 4H, R 0 and S 0 in 6H! than the intensity of the ‘‘shallower’’ P 0 line. In Ref. 9 the authors propose the use of R 0 and S 0 lines as a measure of the nitrogen content in 6H–SiC, since P 0 is ‘‘more forbidden’’ and its intensity might be more sensitive to stresses in the layer. They define the following ratio: R5 FIG. 1. Low-temperature PL spectra of high-quality CVD-grown epilayers of 4H–SiC ~a! and 6H–SiC ~b!.

on the sample to a spot diameter of approximately 100 mm. The power density at the sample surface was therefore about 30 W/cm2. III. GENERAL CONSIDERATION

Typical spectra for 4H– and 6H–SiC are shown in Figs. 1~a! and 1~b!, respectively. P 0 , Q 0 in Fig. 1~a! @P 0 , R 0 , S 0 in Fig. 1~b!# denote the zero-phonon lines, associated to the direct ~without the assistance of phonons! recombination of excitons bound to neutral nitrogen donors in 4H– and 6H– SiC, respectively.3 The number of bound excitons seen, two in 4H and three in 6H–SiC, corresponds to the number of inequivalent carbon sites which can be occupied by a N-atom in these polytypes. Since all known SiC polytypes are indirect band gap semiconductors, the direct recombination of an electron-hole pair forming a free exciton ~FE! is forbidden due to the quasi-momentum conservation law. The recombination of a FE is possible with the creation of a phonon which accommodates the difference in momentum and consumes a part of the energy of the FE recombination, equal to the energy of the phonon itself. If the exciton is bound to an impurity ~say, N!, either the impurity itself or a phonon can accomplish the momentum conservation during recombination. The former process gives rise to the zero-phonon lines, mentioned above, and the latter to various phonon assisted recombinations, the number and energy positions of which J. Appl. Phys., Vol. 80, No. 6, 15 September 1996

R 0 1S 0 , I77

~1!

where R 0 , S 0 , and I77 are the corresponding line intensities, multiplied by the full width at half maximum ~FWHM!, i.e., a quantity that is proportional to the area below each line. This same argument suggests the use of Q 0 line only for the case of 4H–SiC, and we define the ratio R5

Q0 , I76.4

~2!

where the quantities Q 0 and I76.4 have the same definition ~the intensity times the linewidth! as above in Eq. ~1!. The most intense FE replica in the spectrum, recorded from an ~0001!-oriented crystal, is the I77 ~I76.4! for 6H– and 4H– SiC, respectively, and it is chosen as the internal reference in Eqs. ~1! and ~2!. In the present study we use a line-fitting procedure in order to determine more accurately the contribution of the selected lines @bound exciton BE or FE related# in the spectrum. This also allows the separation of the free-exciton emission from the background and some overlapping lines, which is crucial at higher doping levels when the FE ~I77 or I76.4! has an intensity comparable to those of the replicas in its vicinity. The manual processing of the lines in such cases is difficult and less accurate. The use of correct line shapes for each of the fitted lines is discussed below. It is known that the emission lines due to FE recombination in an indirect band-gap semiconductor are accurately described by the following line shape ~sometimes called Maxwellian!:11,12 Ivanov et al.

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FIG. 2. The narrow spectral regions in the vicinity of I76.4 in the PL spectrum of 4H ~a!, and I77 in 6H ~b!, which are fitted in accordance to the procedure described. In both cases, spectra for two doping concentrations are shown, the higher ~from the bottom in both figures! illustrating the overlapping of the lines. R 46 in Fig. 2~b! @not resolved from I77# has actually the same intensity as S 46, which can be observed in spectra taken from high-doped samples without FE emission, and should be taken into account. The fits are also shown by a smooth solid line, in most cases overlapping with the spectrum. The question marks represent unknown lines.

F ~ E ! } AE exp

S

D

E2E 0 , kT

~3!

where F(E) is the line intensity as a function of the photon energy E, E 0 is the threshold energy, k is the Boltzmann constant, and T is the temperature. In Ref. 12 a very good agreement between the line shape given by Eq. ~3! and the experimentally recorded spectrum in Si is demonstrated. However, for the case of SiC, the spectral resolution @i.e., the linewidth of the spectrometer transfer function ~STF!# is comparable to the linewidth of the FE-related lines, and the STF must be taken into account. Thus, for the fitting of FErelated lines in both 4H and 6H we use the convolution I(E) of Eq. ~3! with the spectrometer transfer function T(E) I~ E !5

E

`

2`

F ~ t ! •T ~ E2 t ! d t .

~4!

The spectrometer transfer function T(E) can be considered to be triangular T~ E !5

H

12 u E u /DE,

2DE,E,DE

0

otherwise.

~5!

The parameter DE, i.e., the linewidth ~FWHM! of the STF, is the actual resolution and is known from the slit settings. For each FE-related line, therefore, there are three parameters to be determined by the fit, namely, the amplitude, the threshold energy E 0 , and the linewidth s 5kT eff which might differ from the factor kT in Eq. ~3! on account of the local heating caused by the incident laser beam. If more than one FE-related line is fitted, as is the case with 6H–SiC @see Fig. 2~b!#, the same value of s is, however, used. For the line shape of the BE zero-phonon lines and their replicas we choose a Lorentzian @it must be convoluted with the STF, Eq. ~5!#, with a common linewidth for all the fitted lines. Similar to the FE-related lines, the amplitudes, the peak positions, and the common linewidth of the BE-related 3506

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lines are determined by the fit. The choice of a Lorentzian is merely because we anticipate a homogeneous broadening of the lines. However, this choice is of no importance since the linewidth of BE-related lines appears to be much less than the spectral resolution DE, and the result of the convolution with the STF ~5! is very close to the STF itself. In the case of 4H–SiC we are able to fit the spectrum in the vicinity of the I76.4 line with five lines, as shown in Fig. 2~a!. Only one of them, i.e., I76.4 itself is considered as a FE replica. In the case of 6H–SiC @see Fig. 2~b!#, the corresponding part of the spectrum is fitted with four lines, two of which are FE related. Our data provides strong evidence that I77 in 6H is in fact a doublet, because the intensities of the main line and its counterpart @the shoulder marked I76 in Fig. 2~b!# are very well correlated, the ratio of their amplitudes being A 77/A 76'1061, as determined by the fit of the spectra of more than 40 samples. The background in the narrow spectral regions shown in Figs. 2~a! and 2~b!, which is caused by a broad luminescence from the substrate, was fitted with a straight line. The Q 0 line in 4H, as well as R 0 , S 0 lines in 6H were also fitted in order to determine their amplitude and linewidth. However, since the linewidth for these lines is much less than the resolution, as mentioned earlier, the actual linewidth cannot be determined precisely, and it is worthwhile to use the apparent linewidth ~FWHM! for both for the zerophonon lines and the FE line in the determination of the ratio R. By ‘‘apparent’’ we mean the full width at half maximum ~FWHM! of the recorded line, which is, of course, a function of the spectrometer resolution. Thus, we define the quantities, involved in formulas ~1! and ~2! R 0 5A R0 •FWHMR0 ,

S 0 5A S0 •FWHMS0 ,

Q 0 5A Q0 •FWHMQ0 ,

and Ix5A Ix •FWHMIx ,

~6!

where A R0 , A S0 , A Q0 , and A Ix are the amplitudes of the corresponding lines, and FWHMR0 , FWHMS0 , FWHMQ0 , and FWHMIx are their apparent linewidths ~full width at half maximum!. I x denotes I76.4 in 4H and I77 in 6H. Then Eq. ~1! exactly coincides with the definition in Ref. 9, and our results for 6H are comparable with those from Ref. 9. The spectral resolution affects both the amplitudes and the apparent linewidths of the selected lines. Within the definition ~6!, therefore, we must check whether the ratio R is influenced by the spectral resolution, or not. This was done for both 6H and 4H samples, the resolution being varied between 0.25 and 1 Å. We can consider these limits as reasonable, since for larger slit settings R 0 , S 0 , and other lines in 6H or 4H are not well resolved and the spectrum gradually becomes rough. Two extreme cases are illustrated in Fig. 3. Figure 3 also shows a significant increase of the FE-related lines with respect to the bound-exciton zero-phonon lines as the slits are opened, however no variation of the ratio R calculated for different slit settings was observed. The results are summarized in Table I. IV. RESULTS AND DISCUSSION

Let us consider now the variation of the ratio R with the donor concentration n as determined by C – V measurements Ivanov et al.

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FIG. 3. A part of a PL spectrum of 6H–SiC, recorded from the same spot of the sample, under the same conditions but with different resolution. Figure 3 illustrates the change in the relative intensities of the I77 and the R 0 , and S 0 lines.

for 4H– and 6H–SiC. The results are presented in Fig. 4. Figure 4~b! ~6H–SiC! presents both our results and the results from Ref. 9, illustrating the excellent agreement between these two sets of measurements. It is convenient to process and present the data in double logarithmic scale in order to retain comparable weights for low and high values of n ~see Fig. 4!. It can be seen that the dependence, ln~R! vs ln(n), can be fitted well with a straight line, that is, R varies as a power of n: R}n a . In Ref. 9 the value a'0.9 is found from a fit. This value is very close to 1, which corresponds to a direct proportional dependence of R upon n. The fit of our data for 6H and 4H gave values of a even closer to 1, which was a reason to suppose that the deviation of a from 1 is occasional and the data can be fitted equally well with a simple direct-proportional dependence ~7!

R5A•n,

the only parameter A which is determined by the leastsquares method

F

1 A5exp N

N

( ~ ln R i 2ln n i !

i51

G

~8!

,

where N is the number of experimental data points which can be enumerated by the index i; Ri and n i are the values of R ~determined by the PL spectrum! and n ~determined by C – V measurements! for each sample. The dependence ~7! is plotted in Fig. 4 for both 6H- and 4H–SiC. The corresponding values of A for 4H ~A4H! and 6H ~A6H! are determined to be

TABLE I. The ‘‘slit dependence’’ of the ratio R. Sample\slits→ ↓ ~mm! 6H, 4H,

R5 R5

50

100

150

200

0.299 0.345

0.315 0.366

0.302 0.354

0.311 0.349

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FIG. 4. The logarithmic plot of the ratio R vs the doping concentration n, for 4H– ~a!, and 6H–SiC ~b!. The solid lines represent the least-squares fit of our data ~circles! by means of the direct-proportional dependence ~7!. The triangles and the dashed line in Fig. 4~b! are the data points and the fit from Ref. 9. The cross represents a compensated sample.

1/A4H55.231014 cm23 ,

1/A6H51.131015 cm23 .

~9!

The presented data show that the nitrogen doping concentration n can be determined from the PL spectrum by means of the reverse of Eq. ~7!, n5A 21 •R, for n in the limits 1014 cm23,n,1017 cm23 for 6H, and 1014 cm23,n,331016 cm23 for 4H–SiC. For higher doping levels the FE-related lines cannot be observed in the PL spectra. The accuracy can be estimated to be about 10%, although some deviations in the order of 30% can be observed in both Figs. 4~a! and 4~b!. Most probably the formula can be successfully applied for doping concentrations below 1014 cm23 as long as the nitrogen-related lines are detectable. However, there exists a restriction for the applicability of this simple method, namely, the material should be uncompensated. This is also discussed in Ref. 9, where a sample is considered as uncompensated if the Al-related lines in the wavelength region 4125–4135 Å in 6H–SiC are not observed. Being the principal acceptor impurity, aluminium is normally introduced unintentionally during the growth, although in much lower concentration than the nitrogen, and its spectrum can always be observed, the maximum intensity being around 1/5 ~1/2! of the intensity of the P 0 line in 6H– and 4H–SiC, respectively. This is the case for all the Ivanov et al.

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samples grown under normal growth conditions, among them are the samples for which the data in Fig. 4 are presented. Figure 4 also provides evidence that all these samples can be regarded as uncompensated, as will be clear from the following. The aluminium concentration can become comparable to that of the nitrogen under certain growth conditions, such as high carbon-to-silicon ratios.13 We have observed an increase of the relative contribution of the FE-related lines in the PL spectrum with increasing Al content as detected by the intensity of the Al-related lines. This is probably due to a partial compensation of the N donors. Since the probability for binding an exciton is higher for neutral donors, the decrease of their concentration due to the compensation results in an increase of the FE concentration. A further increase of the Al concentration leads to a decrease and even disappearance of the FE emission, since now the Al acceptor becomes significant in the capture of the FEs. Therefore, for a compensated or for a p-type material formulas ~1! and ~2! are not expected to work correctly. One can expect, therefore, that if there is a compensation due to the unintentional doping with Al, it should be better revealed at low N-doping concentrations. However, in our data presented in Fig. 4, no trend can be seen for larger deviations from the plotted line in the region of low doping concentration, neither for 6H, nor for 4H samples. This allows us to conclude that in all these cases the samples can be considered as uncompensated, and provides a practical criterion for a classification of a sample as uncompensated. Namely, we can compare the maximum intensity of the Alrelated lines, IAl , with the P 0 line in both polytypes. If it is below the values IAl