- Email: [email protected]
Band edge absorption, carrier recombination and transport measurements in 4H-SiC epilayers
Materials Science and Engineering B61 – 62 (1999) 197 – 201
Band edge absorption, carrier recombination and transport measurements in 4H-SiC epilayers V. Grivickas a,*, J. Linnros b, P. Grivickas b, A. Galeckas a,b a
Institute of Material Research and Applied Sciences, Vilnius Uni6ersity, Sauletekio 10, 2054 Vilnius, Lithuania Department of Electronics, Royal Institute of Technology, Electrum 229, S-164 40, Kista-Stockholm, Sweden
b
Abstract A depth-resolved technique based on probe-pump free carrier absorption (FCA) is especially useful for measurements in thin layers. This technique is used here to characterize optical and electrical properties under a wide range of injection levels, 1014 – 1018 cm − 3, in low-doped n-type 4H-SiC epilayers. Our results reveal valuable anisotropy of the band-band absorption at the photon energy about 0.2 eV above the indirect band gap. While the absorption coefficient is found nearly independent of the injection level. The ambipolar carrier diffusion coefficient is measured by an FCA-detected transient grating. Carrier diffusion length, bulk lifetime and surface recombination velocity is also estimated. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Free carrier absorption; Band-band absorption; Carrier diffusion; Surface recombination; 4H-SiC
1. Introduction During the last decade the interest in SiC for electronic devices has increased rapidly. Recently, lowdoped 4H-SiC epilayers grown by chemical vapor deposition (CVD) on n-type doped substrates have permitted the best structural quality and a ms-long carrier lifetime [1]. Since 4H-SiC also has a higher-thanother-SiC-polytypes electron mobility, with a lower anisotropy in the effective mass tensor, this material is favored in many device applications. Coupled with the availability of low-doped epilayers at a reasonable cost, 4H-SiC, thus, has been adopted as the best current choice for future power device developement. A limited number of studies have been conducted to investigate optical and electronic properties of 4H-SiC under high injection conditions [2 – 4]. As a result, there is still a great deal of uncertainty regarding many fundamental parameters. No wonder that device simulators up to now employ incomplete and unverified models, mainly adopted from the quantitative data available for crystalline silicon. We attempt to characterize some properties of 4H-SiC epilayers applying depth-resolved FCA sampling of excess carriers injected * Corresponding author. Fax: +370-2-767313. E-mail address: [email protected] (V. Grivickas)
by the short laser pulse. The versatility of the FCA technique allows (i) to study anisotropy of the bandband absorption near band edge, and (ii) to investigate carrier recombination and transport parameters accurately [5,6]. In this paper, we present a compilation of the recent results obtained applying various FCA methods.
2. Experimental The measurements were carried out on thick (30–90 mm) low-doped n-type 4H-SiC epilayer grown by a hot-wall CVD on nitrogen-doped ( 1019 cm − 3) commercial n + -substrates [7]. Epilayers were n-type, with the residual doping either about 4× 1015 or 7×1014 cm − 3. Specimens of 0.4–1 mm width have been sawed from the samples of each group, the side-walls of the stripes were then polished to optical quality. No specific treatment of surfaces was performed. The results carried out on oxidized samples will be presented separately, in an accompanying paper [8]. For electron-hole (e-h) pair excitation we have used 2.5 ns duration pulses of the third harmonic Nd:YAG laser (Coherent Infinity) at 355 nm wavelength with an extremely uniform beam profile. The repetition rate of the pulses was varied between 20 and 100 Hz. A
0921-5107/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 9 8 ) 0 0 5 0 1 - 7
198
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
focused infrared cw probe beam of 1.3 mm wavelength and of 3 mW power was exploited to monitor the photo-induced FCA. The FCA transients were detected by a fast photon-detector and processed by a wide-band digital oscilloscope [2 – 6]. For most measurements a time resolution better than 10 ns is maintained. High temperature measurements were performed in normal atmosphere with the sample placed on a heating holder. FCA signals have been calibrated to the overall photon density injected into the material. The induced change of absorption is proportional to the excess injected carrier concentration, as shown in Fig. 1. The proportionality stems from a constant electron-hole (e-h) pair absorption cross-section seh =4.5·10 − 17 cm2 which can be adequately described by the classical Drude-Zener theory of the FCA process [2]. In-depth scanning was provided by focusing the beam up to diameter 3.5 mm and with a subsequent translation of the specimen by 1 mm increment. Carrier distribution and relaxation either across or along the epilayer was investigated applying two different optical configurations of the experiment. Further details on depth-resolved FCA measurements can be found in Ref. [5,8]. In addition, we also performed Fourier transient grating (TG) measurements. The method uses a laser pulse projected through a semi-transparent grid pattern to excite a sinusoidal excess carrier grating within the specimen. The interdiffusion of carriers was then monitored by FCA of a focused probe beam. The spatial Fourier transform was calculated at each sampling time following the excitation pulse. The decay of the fundamental frequency component represents a characteristic TG erasure time, which is related to the carrier diffusivity. Explicit description of the TG technique was given in Ref. [9].
Fig. 2. The band-band absorption of the third harmonic YAG laser light (3.495 eV) vs. temperature for two indicated polarizations. Injection level is maintained at 1017 cm − 3. Inset shows the absorption coefficient for E Ú 20° at different injection levels and T= 300 K.
3. Results
3.1. Band-band absorption Intrinsic band-band absorption produces damping in the direction of the incoming light in passing through a medium from point x1 to another point x2 I(x2)= I(x1)· exp(− abb x2 − x1 )
(1)
where I(x) denotes the photon flux of the pump beam inside the sample at x. Consequently, electrons and holes are created by the pump light in relation to number of absorbed photons per unit area producing the instant gradient of the excess carriers Dn(x,t)= Dn(0,t) exp(−abb x),
Dn(x,t)= Dp(x,t), (2)
Fig. 1. Free carrier absorption vs. concentration of injected carriers in a 32 mm thick 4H-SiC. Proportionality stands from e-h pair absorption cross-section seh. Carrier excitation is provided by 0.355 wavelength and 2.5 ns duration pulses, photo-induced changes in absorption are probed at 1.3 mm wavelength.
where a characteristic exponential slope is given by the band-band absorption coefficient abb. The instant gradient may last for a time interval of about t=10–50 ns depending on actual values of carrier lifetime and diffusivity. We have performed FCA measurements from the polished sample side-wall to deduce instant gradients, see inset to Fig. 2. Photon energy E=3.495 eV used in this experiment gives 0.2 eV excess energy above the indirect band gap of 4H-SiC (Eg :3.28 eV at 300 K). At this energy, phonon-assisted optical transition between G-point and M points are responsible for
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
the absorption. Furthermore, since material is a hexagonal polytype, we expect optical anisotropy for polarization different from E Þ c where uniaxial c-axis is along (0001), the growth direction of the epilayer [10]. Apart the geometry for E Þ c, we also tested E Ú 20° c polarization at the Brewster’s angle incidence. Fig. 2 demonstrates the absorption measurements at a constant injection of 1017 cm − 3 in the temperature range T= 297–514 K for E Þ c and for E Ú 20° c cases. Error bars, however, are larger for E Þ c measurements because of the limited (40 mm) thickness of the epilayer. Increase in the absorption is observed which can be approximated by a power-law function as shown in Fig. 2 by two lines: for E Ú 20° c, as abb(T)=16.5×{T − 244.4 K}0.6 cm − 1 and, for E Þ c, as abb(T)=0.428×{T K}1.1 cm − 1. A clear anisotropy is observed between the two polarizations, with a changing of sign at about 360 K. This behavior is likely to be a consequence of the overlap of the optical transitions resulting between three uppermost valence bands, which are altered by the crystal-field splitting of about 73 meV and the spin-orbit splitting of about 7 meV, into two lowest conduction band minima which are separated by about 120 meV [10]. Due to increasing phonon function and reduction of the band gap with T [11], contribution from the transitions to the upper conduction band is expected to increase abruptly. Therefore, an exact interpretation with a fine bandband structure of 4H-SiC would require more experimental work to be performed at different excitation wavelengths. In the inset to Fig. 2 is shown the instant gradient of excess carriers for polarization E Ú 20° c at four injection levels covering the range Dn =(3 × 1015 –1.4× 1018) cm − 3. The resultant fit gives values ranging within abb =159–169 cm − 1 with a standard error of dabb 9 5 cm − 1. (The small deviation of the slope above 1018 cm − 3 in Fig. 2 is caused by the influence of Auger recombination rate [4].) This means that abb at this particular wavelength is nearly independent of the injection level. Similar behavior is observed around the edge of the indirect band gap in Si [12]. This may be a striking feature where no absorption enhancement due to filling of the band states and due to dynamic shrinkage of the band gap occurs but which has not been definitely identified in any indirect type semiconductor.
199
yields to extraction of room temperature ambipolar diffusion coefficient D= 3.89 0.5 cm2 s − 1. This value is lower than the expected value 4.9 cm2 s − 1, obtained from Einstein’s relation by using the best room temperature electron and hole mobility published values (see for example Ref. [13]). The reason for this could be a reduction of carrier mobilities, especially of the minority carriers, which for all our measurements are holes. We are planing to extend our transient grating measurements in other samples as well as in a wider temperature range to provide more quantitative picture. Providing different injections for our TG experiments, we observed that the extracted ambipolar diffusion is slowly decreasing from about 4 down to 3 cm2 s − 1 with increasing carrier density from Dn =1016 to 1017 cm − 3. Similar behavior of the ambipolar diffusivity reduction also has been previously studied in crystalline Si [9]. In Si, we have interpreted this dependence by a combined effect from (i) the dynamic band gap shrinkage; (ii) the indirect influence from electron-hole scattering; and (iii) the excitonic effect [14]. While there may be a similar models invoked for explanation of this dependence in 4H-SiC, we note again that more experimental results should be obtained at injection above 1017 cm − 3 and at different temperatures.
3.3. Recombination and diffusion length Previously we observed a strong correlation between the effective carrier lifetime in 4H-SiC and epitaxial layer thickness in the sample. This correlation is evidence of the influence of the surface recombination. In thick epilayers average statistical lifetime is typically approaching 2 ms. Contribution from the surface recombination has been resolved by FCA scanning across epilayer [4,8].
3.2. Ambipolar diffusi6ity The data displayed in Fig. 3 show that an almost ideally shaped sinusoidal excess carrier grating can be created within the epilayer of the sample. For this excitation level of 1016 cm − 3 and TG period of L=79 mm, the diffusion erasure time in this case is 0.46 ms, by a factor of 1.5 faster than a corresponding effective recombination lifetime measured in this sample. This
Fig. 3. Temporal developments of excess carrier transient grating in 4H-SiC epilayer at various elapsed times. Erasure of the grating is related to both carrier recombination and diffusion. Grating period L =79 mm is indicated.
200
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
very good agreement can be obtained. Modeling has accounted for surface recombination which increases from 4×103 to 3×104 cm s − 1 with increasing injection level while the true bulk lifetime remains almost constant tb = 1.9–2.2 ms. The dependence of the carrier diffusion length as a function of the injection level is summarized in Fig. 5. Diffusion length of about Ld = 30 mm can be assumed as a typical value for high carrier injection in 4H-SiC epilayer.
4. Conclusions
Fig. 4. Temporal developments of excess carrier distributions in a vinicity of the lateral surface of a 90 mm thick 4H-SiC epilayer. Symbols indicate different elapsed times. The injected laser light is directed from the left side. Curves represent theoretical modeling using continuity equation.
Another feature which is strong evidence for surface recombination is illustrated here in Fig. 4. It depicts a set of carrier temporal distributions measured after the excitation pulse against distance from the lateral sample surface. While the right side is not affected by any sample boundary (only first 150 mm of the material is shown), carriers propagate with time to the bulk of the epilayer because of the build-in gradient (the initial gradient, see section 3.1). On the other hand, in a vicinity of the left surface, carrier slope is progressively developed with increasing time because of a combined effect of diffusion flow in presence of a pronounced surface recombination sink. Accordingly, total process of carrier redistribution is extremely sensitive to an actual value of the surface recombination and the length which carriers penetrate during an average lifetime. In this work we have provided continuous theoretical modeling of excess carrier distributions for data of Fig. 4, applying numerical analysis of continuity equation. One-dimensional approximation is here applicable due to the experiment geometry. Density dependent values of ambipolar diffusion coefficient have been adopted from our TG measurements. Average lifetime was taken from experimental transient at the distance of 100 mm from the surface, i.e. where influence of surface recombination is negligible (see Fig. 4). Surface recombination was treated as a free parameter. No other simplifications for the calculation were made. Solid lines in Fig. 4 show the result of the best fit to the experimental data. At this point it can be noted that
We have shown that depth- and time-resolved FCA is an effective technique for the study of band-band optical absorption and of carrier recombination and diffusion in low-doped 4H-SiC at high injection levels. For the first time we have determined anisotropy of the optical absorption close to the indirect band gap. Ambipolar carriers diffusion coefficient at room temperature was measured applying FCA-detected transient grating technique. Using experimentally defined parameters, and providing numerical modeling of carrier distributions within the epitaxial layer, we have been able to quantify carrier diffusion length, surface recombination and bulk carrier lifetimes.
Acknowledgements Financial support of this work was provided by Asea Brown Boveri (ABB) and from Visby program of Swedish Baltic fund.
Fig. 5. Carrier diffusion length LD = Dt b vs. injection level in a 90 mm thick 4H-SiC.
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
References [1] J.P. Bergman, Diam. Relat. Mater. 6 (1997) 1324. [2] A. Galeckas, V. Grivickas, J. Linnros, H. Bleichner, C. Hallin, J. Appl. Phys. 81 (1997) 3522. [3] A. Galeckas, J. Linnros, V. Grivickas, U. Lindefelt, C. Hallin, Appl. Phys. Lett. 71 (1997) 3269. [4] V. Grivickas, A. Galeckas, J. Linnros, Lith. J. Phys. 37 (1997) 555. [5] V. Grivickas, J. Linnros, A. Galeckas, Mater. Sci. Forum 264 – 268 (1998) 529. [6] A. Galeckas, J. Linnros, V. Grivickas, U. Lindefelt, C. Hallin, Mater. Sci. Forum 264–268 (1998) 533.
.
201
[7] O. Kordina, C. Hallin, A. Henry, J.P. Bergman, I.G. Ivanov, A. Ellison, N.T. Son, E. Jenzen, Phys. Stat. Sol. (b) 202 (1997) 321. [8] A. Galeckas, J. Linnros, M. Frischolz, K. Rottner, V. Grivickas, see this volume. [9] J. Linnros, V. Grivickas, Phys. Rev. B 50 (1994) 16943. [10] W.R. Lambrecht, S. Limpijumnong, S.N. Rashkeev, B. Segall, Phys. Stat. Sol. (b) 202 (1997) 5. [11] A. Itoh, T. Kimoto, H. Matsunami, Jpn. J. Appl. Phys. 35 (1996) Pt. 1, 4375. [12] K.G. Svantesson, N.G. Nilson, J. Phys. C 12 (1980) 3837. [13] R. Mickevicius, H. Zhao, Phys. J. Appl. Phys. 83 (1998) 3161. [14] V. Grivickas, J. Linnros, A. Galeckas, V. Bikbajevas, Proc. 23rd Int. Conf. Phys. Semicond., World Scientific, Singapore, Vol. 1 (1996) pp. 91.
Band edge absorption, carrier recombination and transport measurements in 4H-SiC epilayers V. Grivickas a,*, J. Linnros b, P. Grivickas b, A. Galeckas a,b a
Institute of Material Research and Applied Sciences, Vilnius Uni6ersity, Sauletekio 10, 2054 Vilnius, Lithuania Department of Electronics, Royal Institute of Technology, Electrum 229, S-164 40, Kista-Stockholm, Sweden
b
Abstract A depth-resolved technique based on probe-pump free carrier absorption (FCA) is especially useful for measurements in thin layers. This technique is used here to characterize optical and electrical properties under a wide range of injection levels, 1014 – 1018 cm − 3, in low-doped n-type 4H-SiC epilayers. Our results reveal valuable anisotropy of the band-band absorption at the photon energy about 0.2 eV above the indirect band gap. While the absorption coefficient is found nearly independent of the injection level. The ambipolar carrier diffusion coefficient is measured by an FCA-detected transient grating. Carrier diffusion length, bulk lifetime and surface recombination velocity is also estimated. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Free carrier absorption; Band-band absorption; Carrier diffusion; Surface recombination; 4H-SiC
1. Introduction During the last decade the interest in SiC for electronic devices has increased rapidly. Recently, lowdoped 4H-SiC epilayers grown by chemical vapor deposition (CVD) on n-type doped substrates have permitted the best structural quality and a ms-long carrier lifetime [1]. Since 4H-SiC also has a higher-thanother-SiC-polytypes electron mobility, with a lower anisotropy in the effective mass tensor, this material is favored in many device applications. Coupled with the availability of low-doped epilayers at a reasonable cost, 4H-SiC, thus, has been adopted as the best current choice for future power device developement. A limited number of studies have been conducted to investigate optical and electronic properties of 4H-SiC under high injection conditions [2 – 4]. As a result, there is still a great deal of uncertainty regarding many fundamental parameters. No wonder that device simulators up to now employ incomplete and unverified models, mainly adopted from the quantitative data available for crystalline silicon. We attempt to characterize some properties of 4H-SiC epilayers applying depth-resolved FCA sampling of excess carriers injected * Corresponding author. Fax: +370-2-767313. E-mail address: [email protected] (V. Grivickas)
by the short laser pulse. The versatility of the FCA technique allows (i) to study anisotropy of the bandband absorption near band edge, and (ii) to investigate carrier recombination and transport parameters accurately [5,6]. In this paper, we present a compilation of the recent results obtained applying various FCA methods.
2. Experimental The measurements were carried out on thick (30–90 mm) low-doped n-type 4H-SiC epilayer grown by a hot-wall CVD on nitrogen-doped ( 1019 cm − 3) commercial n + -substrates [7]. Epilayers were n-type, with the residual doping either about 4× 1015 or 7×1014 cm − 3. Specimens of 0.4–1 mm width have been sawed from the samples of each group, the side-walls of the stripes were then polished to optical quality. No specific treatment of surfaces was performed. The results carried out on oxidized samples will be presented separately, in an accompanying paper [8]. For electron-hole (e-h) pair excitation we have used 2.5 ns duration pulses of the third harmonic Nd:YAG laser (Coherent Infinity) at 355 nm wavelength with an extremely uniform beam profile. The repetition rate of the pulses was varied between 20 and 100 Hz. A
0921-5107/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 9 8 ) 0 0 5 0 1 - 7
198
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
focused infrared cw probe beam of 1.3 mm wavelength and of 3 mW power was exploited to monitor the photo-induced FCA. The FCA transients were detected by a fast photon-detector and processed by a wide-band digital oscilloscope [2 – 6]. For most measurements a time resolution better than 10 ns is maintained. High temperature measurements were performed in normal atmosphere with the sample placed on a heating holder. FCA signals have been calibrated to the overall photon density injected into the material. The induced change of absorption is proportional to the excess injected carrier concentration, as shown in Fig. 1. The proportionality stems from a constant electron-hole (e-h) pair absorption cross-section seh =4.5·10 − 17 cm2 which can be adequately described by the classical Drude-Zener theory of the FCA process [2]. In-depth scanning was provided by focusing the beam up to diameter 3.5 mm and with a subsequent translation of the specimen by 1 mm increment. Carrier distribution and relaxation either across or along the epilayer was investigated applying two different optical configurations of the experiment. Further details on depth-resolved FCA measurements can be found in Ref. [5,8]. In addition, we also performed Fourier transient grating (TG) measurements. The method uses a laser pulse projected through a semi-transparent grid pattern to excite a sinusoidal excess carrier grating within the specimen. The interdiffusion of carriers was then monitored by FCA of a focused probe beam. The spatial Fourier transform was calculated at each sampling time following the excitation pulse. The decay of the fundamental frequency component represents a characteristic TG erasure time, which is related to the carrier diffusivity. Explicit description of the TG technique was given in Ref. [9].
Fig. 2. The band-band absorption of the third harmonic YAG laser light (3.495 eV) vs. temperature for two indicated polarizations. Injection level is maintained at 1017 cm − 3. Inset shows the absorption coefficient for E Ú 20° at different injection levels and T= 300 K.
3. Results
3.1. Band-band absorption Intrinsic band-band absorption produces damping in the direction of the incoming light in passing through a medium from point x1 to another point x2 I(x2)= I(x1)· exp(− abb x2 − x1 )
(1)
where I(x) denotes the photon flux of the pump beam inside the sample at x. Consequently, electrons and holes are created by the pump light in relation to number of absorbed photons per unit area producing the instant gradient of the excess carriers Dn(x,t)= Dn(0,t) exp(−abb x),
Dn(x,t)= Dp(x,t), (2)
Fig. 1. Free carrier absorption vs. concentration of injected carriers in a 32 mm thick 4H-SiC. Proportionality stands from e-h pair absorption cross-section seh. Carrier excitation is provided by 0.355 wavelength and 2.5 ns duration pulses, photo-induced changes in absorption are probed at 1.3 mm wavelength.
where a characteristic exponential slope is given by the band-band absorption coefficient abb. The instant gradient may last for a time interval of about t=10–50 ns depending on actual values of carrier lifetime and diffusivity. We have performed FCA measurements from the polished sample side-wall to deduce instant gradients, see inset to Fig. 2. Photon energy E=3.495 eV used in this experiment gives 0.2 eV excess energy above the indirect band gap of 4H-SiC (Eg :3.28 eV at 300 K). At this energy, phonon-assisted optical transition between G-point and M points are responsible for
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
the absorption. Furthermore, since material is a hexagonal polytype, we expect optical anisotropy for polarization different from E Þ c where uniaxial c-axis is along (0001), the growth direction of the epilayer [10]. Apart the geometry for E Þ c, we also tested E Ú 20° c polarization at the Brewster’s angle incidence. Fig. 2 demonstrates the absorption measurements at a constant injection of 1017 cm − 3 in the temperature range T= 297–514 K for E Þ c and for E Ú 20° c cases. Error bars, however, are larger for E Þ c measurements because of the limited (40 mm) thickness of the epilayer. Increase in the absorption is observed which can be approximated by a power-law function as shown in Fig. 2 by two lines: for E Ú 20° c, as abb(T)=16.5×{T − 244.4 K}0.6 cm − 1 and, for E Þ c, as abb(T)=0.428×{T K}1.1 cm − 1. A clear anisotropy is observed between the two polarizations, with a changing of sign at about 360 K. This behavior is likely to be a consequence of the overlap of the optical transitions resulting between three uppermost valence bands, which are altered by the crystal-field splitting of about 73 meV and the spin-orbit splitting of about 7 meV, into two lowest conduction band minima which are separated by about 120 meV [10]. Due to increasing phonon function and reduction of the band gap with T [11], contribution from the transitions to the upper conduction band is expected to increase abruptly. Therefore, an exact interpretation with a fine bandband structure of 4H-SiC would require more experimental work to be performed at different excitation wavelengths. In the inset to Fig. 2 is shown the instant gradient of excess carriers for polarization E Ú 20° c at four injection levels covering the range Dn =(3 × 1015 –1.4× 1018) cm − 3. The resultant fit gives values ranging within abb =159–169 cm − 1 with a standard error of dabb 9 5 cm − 1. (The small deviation of the slope above 1018 cm − 3 in Fig. 2 is caused by the influence of Auger recombination rate [4].) This means that abb at this particular wavelength is nearly independent of the injection level. Similar behavior is observed around the edge of the indirect band gap in Si [12]. This may be a striking feature where no absorption enhancement due to filling of the band states and due to dynamic shrinkage of the band gap occurs but which has not been definitely identified in any indirect type semiconductor.
199
yields to extraction of room temperature ambipolar diffusion coefficient D= 3.89 0.5 cm2 s − 1. This value is lower than the expected value 4.9 cm2 s − 1, obtained from Einstein’s relation by using the best room temperature electron and hole mobility published values (see for example Ref. [13]). The reason for this could be a reduction of carrier mobilities, especially of the minority carriers, which for all our measurements are holes. We are planing to extend our transient grating measurements in other samples as well as in a wider temperature range to provide more quantitative picture. Providing different injections for our TG experiments, we observed that the extracted ambipolar diffusion is slowly decreasing from about 4 down to 3 cm2 s − 1 with increasing carrier density from Dn =1016 to 1017 cm − 3. Similar behavior of the ambipolar diffusivity reduction also has been previously studied in crystalline Si [9]. In Si, we have interpreted this dependence by a combined effect from (i) the dynamic band gap shrinkage; (ii) the indirect influence from electron-hole scattering; and (iii) the excitonic effect [14]. While there may be a similar models invoked for explanation of this dependence in 4H-SiC, we note again that more experimental results should be obtained at injection above 1017 cm − 3 and at different temperatures.
3.3. Recombination and diffusion length Previously we observed a strong correlation between the effective carrier lifetime in 4H-SiC and epitaxial layer thickness in the sample. This correlation is evidence of the influence of the surface recombination. In thick epilayers average statistical lifetime is typically approaching 2 ms. Contribution from the surface recombination has been resolved by FCA scanning across epilayer [4,8].
3.2. Ambipolar diffusi6ity The data displayed in Fig. 3 show that an almost ideally shaped sinusoidal excess carrier grating can be created within the epilayer of the sample. For this excitation level of 1016 cm − 3 and TG period of L=79 mm, the diffusion erasure time in this case is 0.46 ms, by a factor of 1.5 faster than a corresponding effective recombination lifetime measured in this sample. This
Fig. 3. Temporal developments of excess carrier transient grating in 4H-SiC epilayer at various elapsed times. Erasure of the grating is related to both carrier recombination and diffusion. Grating period L =79 mm is indicated.
200
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
very good agreement can be obtained. Modeling has accounted for surface recombination which increases from 4×103 to 3×104 cm s − 1 with increasing injection level while the true bulk lifetime remains almost constant tb = 1.9–2.2 ms. The dependence of the carrier diffusion length as a function of the injection level is summarized in Fig. 5. Diffusion length of about Ld = 30 mm can be assumed as a typical value for high carrier injection in 4H-SiC epilayer.
4. Conclusions
Fig. 4. Temporal developments of excess carrier distributions in a vinicity of the lateral surface of a 90 mm thick 4H-SiC epilayer. Symbols indicate different elapsed times. The injected laser light is directed from the left side. Curves represent theoretical modeling using continuity equation.
Another feature which is strong evidence for surface recombination is illustrated here in Fig. 4. It depicts a set of carrier temporal distributions measured after the excitation pulse against distance from the lateral sample surface. While the right side is not affected by any sample boundary (only first 150 mm of the material is shown), carriers propagate with time to the bulk of the epilayer because of the build-in gradient (the initial gradient, see section 3.1). On the other hand, in a vicinity of the left surface, carrier slope is progressively developed with increasing time because of a combined effect of diffusion flow in presence of a pronounced surface recombination sink. Accordingly, total process of carrier redistribution is extremely sensitive to an actual value of the surface recombination and the length which carriers penetrate during an average lifetime. In this work we have provided continuous theoretical modeling of excess carrier distributions for data of Fig. 4, applying numerical analysis of continuity equation. One-dimensional approximation is here applicable due to the experiment geometry. Density dependent values of ambipolar diffusion coefficient have been adopted from our TG measurements. Average lifetime was taken from experimental transient at the distance of 100 mm from the surface, i.e. where influence of surface recombination is negligible (see Fig. 4). Surface recombination was treated as a free parameter. No other simplifications for the calculation were made. Solid lines in Fig. 4 show the result of the best fit to the experimental data. At this point it can be noted that
We have shown that depth- and time-resolved FCA is an effective technique for the study of band-band optical absorption and of carrier recombination and diffusion in low-doped 4H-SiC at high injection levels. For the first time we have determined anisotropy of the optical absorption close to the indirect band gap. Ambipolar carriers diffusion coefficient at room temperature was measured applying FCA-detected transient grating technique. Using experimentally defined parameters, and providing numerical modeling of carrier distributions within the epitaxial layer, we have been able to quantify carrier diffusion length, surface recombination and bulk carrier lifetimes.
Acknowledgements Financial support of this work was provided by Asea Brown Boveri (ABB) and from Visby program of Swedish Baltic fund.
Fig. 5. Carrier diffusion length LD = Dt b vs. injection level in a 90 mm thick 4H-SiC.
V. Gri6ickas et al. / Materials Science and Engineering B61–62 (1999) 197–201
References [1] J.P. Bergman, Diam. Relat. Mater. 6 (1997) 1324. [2] A. Galeckas, V. Grivickas, J. Linnros, H. Bleichner, C. Hallin, J. Appl. Phys. 81 (1997) 3522. [3] A. Galeckas, J. Linnros, V. Grivickas, U. Lindefelt, C. Hallin, Appl. Phys. Lett. 71 (1997) 3269. [4] V. Grivickas, A. Galeckas, J. Linnros, Lith. J. Phys. 37 (1997) 555. [5] V. Grivickas, J. Linnros, A. Galeckas, Mater. Sci. Forum 264 – 268 (1998) 529. [6] A. Galeckas, J. Linnros, V. Grivickas, U. Lindefelt, C. Hallin, Mater. Sci. Forum 264–268 (1998) 533.
.
201
[7] O. Kordina, C. Hallin, A. Henry, J.P. Bergman, I.G. Ivanov, A. Ellison, N.T. Son, E. Jenzen, Phys. Stat. Sol. (b) 202 (1997) 321. [8] A. Galeckas, J. Linnros, M. Frischolz, K. Rottner, V. Grivickas, see this volume. [9] J. Linnros, V. Grivickas, Phys. Rev. B 50 (1994) 16943. [10] W.R. Lambrecht, S. Limpijumnong, S.N. Rashkeev, B. Segall, Phys. Stat. Sol. (b) 202 (1997) 5. [11] A. Itoh, T. Kimoto, H. Matsunami, Jpn. J. Appl. Phys. 35 (1996) Pt. 1, 4375. [12] K.G. Svantesson, N.G. Nilson, J. Phys. C 12 (1980) 3837. [13] R. Mickevicius, H. Zhao, Phys. J. Appl. Phys. 83 (1998) 3161. [14] V. Grivickas, J. Linnros, A. Galeckas, V. Bikbajevas, Proc. 23rd Int. Conf. Phys. Semicond., World Scientific, Singapore, Vol. 1 (1996) pp. 91.