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Deep-level transient spectroscopy in the depletion zone of boron-doped homoepitaxial diamond films
Diamond and Related Materials 9 (2000) 1041–1045 www.elsevier.com/locate/diamond
Deep-level transient spectroscopy in the depletion zone of borondoped homoepitaxial diamond films P. Muret *, C. Saby, F. Pruvost, A. Deneuville Laboratoire d’E´tudes des Proprie´te´s E´lectroniques des Solides, CNRS, B.P. 166, F-38042 Grenoble Cedex 9, France
Abstract Investigation of deep levels in the depletion zone of boron-doped homoepitaxial diamond films is achieved from analysis of the transient responses of Schottky junctions. The active layer consists of a homoepitaxial film grown by microwave plasma decomposition of a very small percentage of B H mixed with CH in hydrogen on synthetic Ib diamond substrates. Rectifying 2 6 4 contacts are implemented with either aluminium, gold or erbium after suitable pre- and post-treatments. Reverse-current transients due to the thermal emission of holes from deep-level traps into the valence band are recorded and analysed with a Fourier transform deep-level transient spectroscopy (Fourier DLTS ) procedure as a function of temperature up to 520°C. At each temperature, a thermal emission time constant is extracted. Arrhenius diagrams are deduced. A deep level at 1.40±0.07 eV above the valence band is detected in samples that have been submitted to a 800°C annealing in ultrahigh vacuum. Another deep level at 1.16±0.03 eV above the valence band exists only if an oxygen radio-frequency plasma treatment is applied to the sample before the Schottky contact deposition. Thermal capture cross-sections are also deduced. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Boron-doped homoepitaxial diamond films; Current deep-level transient spectroscopy (current DLTS); Hole traps; Schottky junctions
1. Introduction Improving the knowledge about defects and their origin is a necessary issue for the progress of large-gap semiconductors. In most cases, either point defects, such as foreign atoms, vacancies and their combination which form complex defects, or extended defects at the interfaces or interphases induce a detrimental effect on the electronic properties. Several charge states of one defect can generate deep levels in the forbidden band gap that can affect the electrical properties of elementary devices. For diamond, experimental data extracted from electrical responses are very scarce in the literature and have been obtained only in the cases of natural or highpressure and high-temperature synthetic diamond [1]. Because of the large value of the band gap and ionisation energies of the carriers trapped in deep states, radiative transitions are often thought to be the most probable. But the phonon energy in diamond also makes phononassisted non-radiative transitions occur. Characteristic times may be very long near room temperature except for the boron acceptors themselves [2] but, if an appropriate temperature range is used, the resulting charge * Corresponding author. Fax: +33-476-88-79-88. E-mail address: [email protected] (P. Muret)
variations can be detected from capacitance transients or current transients by deep-level transient spectroscopy (DLTS ) in Schottky junctions with typical times of a few seconds or less. The present work reports results of deep-level current transient spectroscopy obtained in several boron-doped homoepitaxial diamond films. Analysis of data yields the ionisation energy and thermal capture cross-section of two hole traps.
2. Preparation of diamond films and contacts Homoepitaxial boron-doped diamond films were grown by microwave-plasma-assisted chemical vapour deposition (MWCVD) on synthetic Ib (100) crystals [3,4]. The deposition conditions were 30 torr of a mixture containing 4% CH in hydrogen and a ratio of 4 [B]/[C ] in the range 0.05 to 8000 ppm, giving boron concentrations that span the range 5×1016 to 1021 cm−3. Crystalline quality was testified by a 1332 cm−1 Raman peak with a full-width at half-maximum height of less than 3 cm−1. The hole conductivity is provided by boron acceptors, with a typical compensation ratio of 10% for samples doped with 2×1017 B cm−3 [4]. In this study, the doping concen-
0925-9635/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0 9 25 - 9 63 5 ( 9 9 ) 00 3 6 7- 2
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P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
tration of the samples was between 5×1016 and 2×1017 B cm−3. Schottky contacts were made with several surface preparation procedures and metals: either erbium, aluminium or gold. In the first case, the contact formation demands an oxygen-free diamond surface. So, the samples provided with the erbium contact (sample #1) were rehydrogenated before metal deposition under conditions identical to those utilised for growth of the diamond film without methane, after the sulfo-chromic treatment described below. Then, they were heated a first time up to 800°C in ultrahigh vacuum ( UHV ) after the deposition of two monolayers of erbium and a second time after the deposition of 20 nm of erbium and silicon in the ratio 1:2 for the formation of the disilicide [5]. Rectification ratios of three orders of magnitude can be obtained up to 500°C [5]. In contrast, the diamond surface of the aluminium and gold diodes was treated only with the sulfo-chromic mixture, the NH OH/H O mixture (both at 90°C ) and finally the 4 2 2 HF/HNO mixture and aqua regia in order to remove 3 non-diamond phases and hydrogen at the surface. Additionally, some aluminium samples were treated by a radio-frequency (RF ) oxygen plasma at 200°C before aluminium deposition by sputtering (sample #2). Other aluminium or gold diodes that underwent neither a high-temperature treatment in UHV nor an RF oxygen plasma are labelled samples #3. Circular or square diodes with dimensions between 100 and 300 mm were defined by electron-beam photolithography or through a mask. Ohmic contacts were obtained either with polycrystalline Mo C or with silver paste. Below 600°C, 2 the absence of total ionisation of boron acceptors in the neutral zone of the diode makes the series resistance vary with temperature (some tens or hundreds of kV at room temperature and about one kV at 500°C ). This makes capacitance measurements difficult, except at frequencies typically less than 100 Hz, but in this case sensitivity is too low. So current transient measurements are preferred here because they are not dependent on the series resistance.
a transient current that superimposes on the standing state. The characteristic time of the transient depends strongly on temperature. An example of a transient recorded in a metal–diamond diode is displayed in Fig. 1. Applying Shockley–Read–Hall and Fermi–Dirac statistics leads to an exponential variation of the electron occupancy function f of the deep trap, governed by the T simple equation given below. Here, the problem is restricted to p-type semiconductors in the dark and majority carrier traps because this hypothesis matches the case of diamond where the equilibrium band curvature at Schottky junctions does not exceed half the band gap: df T =e (1−f )−c pf . p T p T dt
(1)
Capture and emission coefficients, c and e , respectively, p p are related through the equilibrium form of Eq. (1) where the left member is zero, p being the free hole concentration in the semiconductor valence band. Multiphonon capture and emission are indeed possible even in large-gap semiconductors, especially in diamond, because the phonon energy is much larger than in narrower-gap semiconductors, so that the ratio of the ionisation energy over the phonon energy remains in the same range. This ionisation energy, G =G −G , is the Tm m+1 m difference between the free energy of N centres charged T with either (m+1) or m carriers. It comprises an enthalpy term labelled E −E , an entropy term DS T V (configuration and vibration) quoted with the parameter c=exp(DS/k), k being the Boltzmann constant and E V
3. Analysis of current transients In metal–ideal semiconductor junctions, a reversebias voltage pulse coming after a zero or forward bias involves a constant reverse current because minority carriers generally have a negligible effect. But if deep levels are present, they can emit their carrier into semiconductor bands within the extension of the depletion zone which results from turning back to reverse bias. Then, after the end of a filling pulse which increases the hole concentration momentarily, favouring the capture of holes by traps, thermal emission from traps induces
Fig. 1. Plot of the transient reverse current recorded at 475 K after the filling pulse in sample #2 after 100 averages with a time window t =6.2 s, a reverse bias voltage of 1.5 V and a pulse voltage level at w 1 V, giving a difference of only 0.5 V. The transient amplitude is much less than the steady reverse current. As testified by the Fourier analysis described in the text, a single exponential is sufficient here to account for the transient, the eventual shorter and longer ones being inefficient at the time scale used here.
P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
the valence-band edge. The equilibrium form of Eq. (1) leads to the emission coefficient e (which is also the p reciprocal time constant of the transient) under some conditions that are given below: e =cs v N exp p p p V =cs
p
A
E −E V T kT
A
B B
E −E 16pm1 k2 T , p T2 exp V h3 kT
(2)
where T is the absolute temperature, v the thermal p velocity of holes, s the capture cross-section of the trap p (and c =s v ), h Planck’s constant and m1 the effecp p p p tive mass of holes for conduction in the valence band. In the depletion zone, the emission term dominates in Eq. (1) and this fact justifies that e is the reciprocal p time constant of the transient after a filling pulse at zero or forward bias voltage, which sets conditions where the capture term in Eq. (1) dominates momentarily. The transient regime may be detected from measurements of either the depletion-layer capacitance or current [6 ]. It follows the same law as the occupancy function f T mainly if the emission coefficient is homogeneous in the probed part of the depletion zone and if the trap concentration N is weaker than the shallow impurity T concentration N . Thus, measuring the thermal emission A coefficient e as a function of temperature T allows one p to deduce the enthalpy E −E (the so-called trap depth) T V and the product of the capture cross-section s and c p from a plot of ln(e T−2) or ln(e−1 v N ). p p p V The exponential transient, which is the solution of Eq. (1) with the e (1−f ) term alone, is recorded here p T generally with 512 samples along the whole time window t and averaged with numerous repetitions at each w temperature to improve the signal-to-noise ratio ( Fig. 1). Then, various cosine and sine Fourier coefficients of the transients, a and b respectively for the n n nth order, are calculated and displayed. In a first method, the time constant e−1 can be calculated from three p formulae using these independent coefficients if the transient is assumed to be exponential: either b w n, 2pn a n
(3a)
S
a −a k n a n2−a k2 n k
(3b)
S
kb −nb n k nk(b k−b n) k n
(3c)
t
t w 2p or t w 2p
[7]. It is of considerable advantage that these equations use only ratios of coefficients and neither amplitude nor
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offset. Hence a temperature dependence of the transient amplitude does not influence the time constant, unlike standard DLTS methods. Moreover, the coherence of the various time constants calculated from Eqs. (3a), (3b) and (3c) and several orders n or couples n, k is a severe check of the conformity of the experimental transient to the exponential law. Otherwise, a dispersion appears and it is preferable to apply a second method which relies on the location of the maximum in the plot of the various Fourier coefficients as a function of temperature. Each of them passes through a maximum at a distinct temperature ( like in Fig. 3), which is related to the reciprocal time constant e in a unique way in p the case of an exponential transient. This second method is an extension of the standard DLTS which uses only one correlation function, either box-car or square wave, whereas the present Fourier DLTS method utilises up to 16 sine, cosine or more complex correlation functions to derive as many coefficients. When a multi-exponential or another law arises due to some dispersion of the emission coefficient, non-negligible capture or recombination coefficients, or non-linear effects, it is reasonable to assume that one time constant still dominates and that the temperature law displays its maximum close to the value that would be obtained in the pure exponential case. Either the first or the second method permits one to plot the Arrhenius law related to Eq. (2) with more data than in standard DLTS even with only one time window t and much more data with several time w windows (see Figs. 2 and 4).
4. Hole traps in homoepitaxial boron-doped diamond films If sufficiently high temperatures are reached in lightly boron-doped diamond, thermal emission of carriers from deep levels can be observed through transient regimes of the reverse capacitance or current (Fig. 1). It shows an observable transient regime due to the thermal emission of holes if the temperature is such that e−1 is close to the time window t . Some preliminary p w results have appeared previously [8] but with limited ranges of t and kinds of sample. In Fig. 2, the Arrhenius w plot of the product of v N with the measured e−1 in p V p sample #1, deduced from Eqs. (3a), (3b) and (3c) with t ranging from 40 ms to 10 s and temperatures between w 660 and 800 K, fits a straight line which gives the capture cross-section s =3×10−17 cm2 (assuming c=1) and an p ionisation enthalpy of 1.40±0.07 eV. This last value agrees with the onset of photocapacitance in natural IIb diamond (1.4 eV ) [9] and may be also compared with that deduced from photocapacitance in synthetic IIb diamond (1.25 eV ) [1]. These values may be assigned to a defect, only electrically active in samples that have
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P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
Fig. 2. Arrhenius plot of the product of the time constant e−1 , the p thermal velocity of holes v and the effective density of states N in p V the valence band. It fits a straight line where the slope gives the ionisation enthalpy E −E =1.40±0.07 eV and the intercept with the vertiT V cal axis yields the capture cross-section s =3×10−17 cm2 if the p entropy parameter c is unity, for the sample type #1. The time windows t used here are typically between 40 ms and 10 s, giving rise to detectaw ble exponential transients in the range 660–800 K, with reverse bias and filling pulse voltages at 4 V and 0 V, respectively.
not been grown in hydrogen or that have lost some hydrogen after annealing in UHV at 800°C, as one can expect in sample #1 [10]. Indeed, this trap is hardly evidenced in sample #3 that was grown in hydrogen but not heated at such temperatures afterwards. Other sample treatments and DLTS investigations, such as depth profile, are in progress to clarify this point. Unlike the samples #1 and #3, a new deep level is detected in sample #2 which has undergone an oxygen RF plasma treatment. The Fourier coefficients of the
Fig. 4. Arrhenius plot of the product of v N with the measured p V e−1 deduced from the T values for sample type #2, giving an ionisation p m enthalpy of 1.16±0.03 eV and a capture cross-section of 4×10−15 cm2 (t =2 and 20 s for triangles, 5 s for squares, 200 s for w circles).
corresponding transient can be measured in the range 440–540 K (Fig. 3), very different from the first one. As an example, the first sine Fourier coefficients are displayed in Fig. 3 for two t values, each one showing a w maximum at a distinct temperature. Using about 12 coefficients and the second method described in Section 3 for plotting an Arrhenius diagram ( Fig. 4), an ionisation enthalpy of 1.16±0.03 eV above the valence band and a capture cross-section s =4×10−15 cm2 (assuming c= p 1) are deduced ( Fig. 4). Such a deep level is certainly due to the influence of the oxygen RF plasma treatment applied to this sample, since it did not appear in samples #1 and #3 that were not subjected to such a process but only the oxidising sulfo-chromic mixture. The ion bombardment inherent to RF plasma might result in shallow implantation of oxygen which in turn could change the profile of other impurities like hydrogen due to a modification of the thermodynamic surface barrier [10]. Release of the compensation of some deeper defects may result. Future work is needed to check this hypothesis.
5. Conclusions
Fig. 3. First sine Fourier coefficient b of current transients like that 1 of Fig. 1, recorded with t of 20 s (circles) and 2 s (squares), plotted w as a function of the temperature in a sample of type #2. The longer the time window t , the lower the temperature T at the curve w m maximum.
In this work, we demonstrated that current transients can be detected in MWCVD boron-doped homoepitaxial diamond junctions if appropriate temperature and time window ranges are utilised. Fourier analysis of the reverse-current transients after a filling pulse is carried out. The method is able to check the exponential character of the transient and, in any case, to deliver Arrhenius plots with much more data than standard DLTS methods. For the first time, purely electrical transient signals due to the thermal emission of holes from traps have
P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
been detected and analysed in lightly boron-doped homoepitaxial diamond films. The ionisation enthalpy and capture cross-section of the corresponding levels are extracted safely. A deep level 1.40±0.07 eV above the valence band appears and seems to be common to many diamond crystals. Another deep level 1.16±0.03 eV above the valence band is characteristic of samples to which an oxygen RF plasma treatment had been applied before the Schottky contact deposition. This study demonstrates that electrical transient regimes taking place in junctions are a powerful tool for the investigation of defects even in large-gap semiconductors like diamond, and that care must be exercised in the treatments used for preparing devices made of epitaxial diamond thin films.
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References [1] R. Zeisel, C. Nebel, M. Stutzmann, J. Appl. Phys. 84 (1998) 6105. [2] H. Sato, H. Tomokage, H. Kiyota, T. Ando, Diamond Relat. Mater. 7 (1998) 167. [3] E. Gheeraert, A. Deneuville, J. Mambou, Diamond Relat. Mater. 7 (1998) 509. [4] J.-P. Lagrange, A. Deneuville, E. Gheeraert, Diamond Relat. Mater. 7 (1998) 1390. [5] P. Muret, F. Pruvost, C. Saby, E. Lucazeau, T.A. Nguyen Tan, E. Gheeraert, A. Deneuville, Diamond Relat. Mater. 8 (1999) 961. [6 ] E. Meijer, H.G. Grimmeiss, Semicond. Sci. Technol. 7 (1992) 188. [7] S. Weiss, R. Kassing, Solid State Electron. 31 (1988) 1733. [8] P. Muret, E. Gheeraert, A. Deneuville, Phys. Stat. Sol. (a) 174 (1999) 129. [9] M.W. Geis, J.C. Twichell, IEEE Trans. ED 44 (1997) 1514. [10] J. Chevallier, D. Ballutaud, B. Theys, F. Jomard, A. Deneuville, E. Gheeraert, F. Pruvost, Phys. Stat. Sol. (a) 174 (1999) 73.
Deep-level transient spectroscopy in the depletion zone of borondoped homoepitaxial diamond films P. Muret *, C. Saby, F. Pruvost, A. Deneuville Laboratoire d’E´tudes des Proprie´te´s E´lectroniques des Solides, CNRS, B.P. 166, F-38042 Grenoble Cedex 9, France
Abstract Investigation of deep levels in the depletion zone of boron-doped homoepitaxial diamond films is achieved from analysis of the transient responses of Schottky junctions. The active layer consists of a homoepitaxial film grown by microwave plasma decomposition of a very small percentage of B H mixed with CH in hydrogen on synthetic Ib diamond substrates. Rectifying 2 6 4 contacts are implemented with either aluminium, gold or erbium after suitable pre- and post-treatments. Reverse-current transients due to the thermal emission of holes from deep-level traps into the valence band are recorded and analysed with a Fourier transform deep-level transient spectroscopy (Fourier DLTS ) procedure as a function of temperature up to 520°C. At each temperature, a thermal emission time constant is extracted. Arrhenius diagrams are deduced. A deep level at 1.40±0.07 eV above the valence band is detected in samples that have been submitted to a 800°C annealing in ultrahigh vacuum. Another deep level at 1.16±0.03 eV above the valence band exists only if an oxygen radio-frequency plasma treatment is applied to the sample before the Schottky contact deposition. Thermal capture cross-sections are also deduced. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Boron-doped homoepitaxial diamond films; Current deep-level transient spectroscopy (current DLTS); Hole traps; Schottky junctions
1. Introduction Improving the knowledge about defects and their origin is a necessary issue for the progress of large-gap semiconductors. In most cases, either point defects, such as foreign atoms, vacancies and their combination which form complex defects, or extended defects at the interfaces or interphases induce a detrimental effect on the electronic properties. Several charge states of one defect can generate deep levels in the forbidden band gap that can affect the electrical properties of elementary devices. For diamond, experimental data extracted from electrical responses are very scarce in the literature and have been obtained only in the cases of natural or highpressure and high-temperature synthetic diamond [1]. Because of the large value of the band gap and ionisation energies of the carriers trapped in deep states, radiative transitions are often thought to be the most probable. But the phonon energy in diamond also makes phononassisted non-radiative transitions occur. Characteristic times may be very long near room temperature except for the boron acceptors themselves [2] but, if an appropriate temperature range is used, the resulting charge * Corresponding author. Fax: +33-476-88-79-88. E-mail address: [email protected] (P. Muret)
variations can be detected from capacitance transients or current transients by deep-level transient spectroscopy (DLTS ) in Schottky junctions with typical times of a few seconds or less. The present work reports results of deep-level current transient spectroscopy obtained in several boron-doped homoepitaxial diamond films. Analysis of data yields the ionisation energy and thermal capture cross-section of two hole traps.
2. Preparation of diamond films and contacts Homoepitaxial boron-doped diamond films were grown by microwave-plasma-assisted chemical vapour deposition (MWCVD) on synthetic Ib (100) crystals [3,4]. The deposition conditions were 30 torr of a mixture containing 4% CH in hydrogen and a ratio of 4 [B]/[C ] in the range 0.05 to 8000 ppm, giving boron concentrations that span the range 5×1016 to 1021 cm−3. Crystalline quality was testified by a 1332 cm−1 Raman peak with a full-width at half-maximum height of less than 3 cm−1. The hole conductivity is provided by boron acceptors, with a typical compensation ratio of 10% for samples doped with 2×1017 B cm−3 [4]. In this study, the doping concen-
0925-9635/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0 9 25 - 9 63 5 ( 9 9 ) 00 3 6 7- 2
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P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
tration of the samples was between 5×1016 and 2×1017 B cm−3. Schottky contacts were made with several surface preparation procedures and metals: either erbium, aluminium or gold. In the first case, the contact formation demands an oxygen-free diamond surface. So, the samples provided with the erbium contact (sample #1) were rehydrogenated before metal deposition under conditions identical to those utilised for growth of the diamond film without methane, after the sulfo-chromic treatment described below. Then, they were heated a first time up to 800°C in ultrahigh vacuum ( UHV ) after the deposition of two monolayers of erbium and a second time after the deposition of 20 nm of erbium and silicon in the ratio 1:2 for the formation of the disilicide [5]. Rectification ratios of three orders of magnitude can be obtained up to 500°C [5]. In contrast, the diamond surface of the aluminium and gold diodes was treated only with the sulfo-chromic mixture, the NH OH/H O mixture (both at 90°C ) and finally the 4 2 2 HF/HNO mixture and aqua regia in order to remove 3 non-diamond phases and hydrogen at the surface. Additionally, some aluminium samples were treated by a radio-frequency (RF ) oxygen plasma at 200°C before aluminium deposition by sputtering (sample #2). Other aluminium or gold diodes that underwent neither a high-temperature treatment in UHV nor an RF oxygen plasma are labelled samples #3. Circular or square diodes with dimensions between 100 and 300 mm were defined by electron-beam photolithography or through a mask. Ohmic contacts were obtained either with polycrystalline Mo C or with silver paste. Below 600°C, 2 the absence of total ionisation of boron acceptors in the neutral zone of the diode makes the series resistance vary with temperature (some tens or hundreds of kV at room temperature and about one kV at 500°C ). This makes capacitance measurements difficult, except at frequencies typically less than 100 Hz, but in this case sensitivity is too low. So current transient measurements are preferred here because they are not dependent on the series resistance.
a transient current that superimposes on the standing state. The characteristic time of the transient depends strongly on temperature. An example of a transient recorded in a metal–diamond diode is displayed in Fig. 1. Applying Shockley–Read–Hall and Fermi–Dirac statistics leads to an exponential variation of the electron occupancy function f of the deep trap, governed by the T simple equation given below. Here, the problem is restricted to p-type semiconductors in the dark and majority carrier traps because this hypothesis matches the case of diamond where the equilibrium band curvature at Schottky junctions does not exceed half the band gap: df T =e (1−f )−c pf . p T p T dt
(1)
Capture and emission coefficients, c and e , respectively, p p are related through the equilibrium form of Eq. (1) where the left member is zero, p being the free hole concentration in the semiconductor valence band. Multiphonon capture and emission are indeed possible even in large-gap semiconductors, especially in diamond, because the phonon energy is much larger than in narrower-gap semiconductors, so that the ratio of the ionisation energy over the phonon energy remains in the same range. This ionisation energy, G =G −G , is the Tm m+1 m difference between the free energy of N centres charged T with either (m+1) or m carriers. It comprises an enthalpy term labelled E −E , an entropy term DS T V (configuration and vibration) quoted with the parameter c=exp(DS/k), k being the Boltzmann constant and E V
3. Analysis of current transients In metal–ideal semiconductor junctions, a reversebias voltage pulse coming after a zero or forward bias involves a constant reverse current because minority carriers generally have a negligible effect. But if deep levels are present, they can emit their carrier into semiconductor bands within the extension of the depletion zone which results from turning back to reverse bias. Then, after the end of a filling pulse which increases the hole concentration momentarily, favouring the capture of holes by traps, thermal emission from traps induces
Fig. 1. Plot of the transient reverse current recorded at 475 K after the filling pulse in sample #2 after 100 averages with a time window t =6.2 s, a reverse bias voltage of 1.5 V and a pulse voltage level at w 1 V, giving a difference of only 0.5 V. The transient amplitude is much less than the steady reverse current. As testified by the Fourier analysis described in the text, a single exponential is sufficient here to account for the transient, the eventual shorter and longer ones being inefficient at the time scale used here.
P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
the valence-band edge. The equilibrium form of Eq. (1) leads to the emission coefficient e (which is also the p reciprocal time constant of the transient) under some conditions that are given below: e =cs v N exp p p p V =cs
p
A
E −E V T kT
A
B B
E −E 16pm1 k2 T , p T2 exp V h3 kT
(2)
where T is the absolute temperature, v the thermal p velocity of holes, s the capture cross-section of the trap p (and c =s v ), h Planck’s constant and m1 the effecp p p p tive mass of holes for conduction in the valence band. In the depletion zone, the emission term dominates in Eq. (1) and this fact justifies that e is the reciprocal p time constant of the transient after a filling pulse at zero or forward bias voltage, which sets conditions where the capture term in Eq. (1) dominates momentarily. The transient regime may be detected from measurements of either the depletion-layer capacitance or current [6 ]. It follows the same law as the occupancy function f T mainly if the emission coefficient is homogeneous in the probed part of the depletion zone and if the trap concentration N is weaker than the shallow impurity T concentration N . Thus, measuring the thermal emission A coefficient e as a function of temperature T allows one p to deduce the enthalpy E −E (the so-called trap depth) T V and the product of the capture cross-section s and c p from a plot of ln(e T−2) or ln(e−1 v N ). p p p V The exponential transient, which is the solution of Eq. (1) with the e (1−f ) term alone, is recorded here p T generally with 512 samples along the whole time window t and averaged with numerous repetitions at each w temperature to improve the signal-to-noise ratio ( Fig. 1). Then, various cosine and sine Fourier coefficients of the transients, a and b respectively for the n n nth order, are calculated and displayed. In a first method, the time constant e−1 can be calculated from three p formulae using these independent coefficients if the transient is assumed to be exponential: either b w n, 2pn a n
(3a)
S
a −a k n a n2−a k2 n k
(3b)
S
kb −nb n k nk(b k−b n) k n
(3c)
t
t w 2p or t w 2p
[7]. It is of considerable advantage that these equations use only ratios of coefficients and neither amplitude nor
1043
offset. Hence a temperature dependence of the transient amplitude does not influence the time constant, unlike standard DLTS methods. Moreover, the coherence of the various time constants calculated from Eqs. (3a), (3b) and (3c) and several orders n or couples n, k is a severe check of the conformity of the experimental transient to the exponential law. Otherwise, a dispersion appears and it is preferable to apply a second method which relies on the location of the maximum in the plot of the various Fourier coefficients as a function of temperature. Each of them passes through a maximum at a distinct temperature ( like in Fig. 3), which is related to the reciprocal time constant e in a unique way in p the case of an exponential transient. This second method is an extension of the standard DLTS which uses only one correlation function, either box-car or square wave, whereas the present Fourier DLTS method utilises up to 16 sine, cosine or more complex correlation functions to derive as many coefficients. When a multi-exponential or another law arises due to some dispersion of the emission coefficient, non-negligible capture or recombination coefficients, or non-linear effects, it is reasonable to assume that one time constant still dominates and that the temperature law displays its maximum close to the value that would be obtained in the pure exponential case. Either the first or the second method permits one to plot the Arrhenius law related to Eq. (2) with more data than in standard DLTS even with only one time window t and much more data with several time w windows (see Figs. 2 and 4).
4. Hole traps in homoepitaxial boron-doped diamond films If sufficiently high temperatures are reached in lightly boron-doped diamond, thermal emission of carriers from deep levels can be observed through transient regimes of the reverse capacitance or current (Fig. 1). It shows an observable transient regime due to the thermal emission of holes if the temperature is such that e−1 is close to the time window t . Some preliminary p w results have appeared previously [8] but with limited ranges of t and kinds of sample. In Fig. 2, the Arrhenius w plot of the product of v N with the measured e−1 in p V p sample #1, deduced from Eqs. (3a), (3b) and (3c) with t ranging from 40 ms to 10 s and temperatures between w 660 and 800 K, fits a straight line which gives the capture cross-section s =3×10−17 cm2 (assuming c=1) and an p ionisation enthalpy of 1.40±0.07 eV. This last value agrees with the onset of photocapacitance in natural IIb diamond (1.4 eV ) [9] and may be also compared with that deduced from photocapacitance in synthetic IIb diamond (1.25 eV ) [1]. These values may be assigned to a defect, only electrically active in samples that have
1044
P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
Fig. 2. Arrhenius plot of the product of the time constant e−1 , the p thermal velocity of holes v and the effective density of states N in p V the valence band. It fits a straight line where the slope gives the ionisation enthalpy E −E =1.40±0.07 eV and the intercept with the vertiT V cal axis yields the capture cross-section s =3×10−17 cm2 if the p entropy parameter c is unity, for the sample type #1. The time windows t used here are typically between 40 ms and 10 s, giving rise to detectaw ble exponential transients in the range 660–800 K, with reverse bias and filling pulse voltages at 4 V and 0 V, respectively.
not been grown in hydrogen or that have lost some hydrogen after annealing in UHV at 800°C, as one can expect in sample #1 [10]. Indeed, this trap is hardly evidenced in sample #3 that was grown in hydrogen but not heated at such temperatures afterwards. Other sample treatments and DLTS investigations, such as depth profile, are in progress to clarify this point. Unlike the samples #1 and #3, a new deep level is detected in sample #2 which has undergone an oxygen RF plasma treatment. The Fourier coefficients of the
Fig. 4. Arrhenius plot of the product of v N with the measured p V e−1 deduced from the T values for sample type #2, giving an ionisation p m enthalpy of 1.16±0.03 eV and a capture cross-section of 4×10−15 cm2 (t =2 and 20 s for triangles, 5 s for squares, 200 s for w circles).
corresponding transient can be measured in the range 440–540 K (Fig. 3), very different from the first one. As an example, the first sine Fourier coefficients are displayed in Fig. 3 for two t values, each one showing a w maximum at a distinct temperature. Using about 12 coefficients and the second method described in Section 3 for plotting an Arrhenius diagram ( Fig. 4), an ionisation enthalpy of 1.16±0.03 eV above the valence band and a capture cross-section s =4×10−15 cm2 (assuming c= p 1) are deduced ( Fig. 4). Such a deep level is certainly due to the influence of the oxygen RF plasma treatment applied to this sample, since it did not appear in samples #1 and #3 that were not subjected to such a process but only the oxidising sulfo-chromic mixture. The ion bombardment inherent to RF plasma might result in shallow implantation of oxygen which in turn could change the profile of other impurities like hydrogen due to a modification of the thermodynamic surface barrier [10]. Release of the compensation of some deeper defects may result. Future work is needed to check this hypothesis.
5. Conclusions
Fig. 3. First sine Fourier coefficient b of current transients like that 1 of Fig. 1, recorded with t of 20 s (circles) and 2 s (squares), plotted w as a function of the temperature in a sample of type #2. The longer the time window t , the lower the temperature T at the curve w m maximum.
In this work, we demonstrated that current transients can be detected in MWCVD boron-doped homoepitaxial diamond junctions if appropriate temperature and time window ranges are utilised. Fourier analysis of the reverse-current transients after a filling pulse is carried out. The method is able to check the exponential character of the transient and, in any case, to deliver Arrhenius plots with much more data than standard DLTS methods. For the first time, purely electrical transient signals due to the thermal emission of holes from traps have
P. Muret et al. / Diamond and Related Materials 9 (2000) 1041–1045
been detected and analysed in lightly boron-doped homoepitaxial diamond films. The ionisation enthalpy and capture cross-section of the corresponding levels are extracted safely. A deep level 1.40±0.07 eV above the valence band appears and seems to be common to many diamond crystals. Another deep level 1.16±0.03 eV above the valence band is characteristic of samples to which an oxygen RF plasma treatment had been applied before the Schottky contact deposition. This study demonstrates that electrical transient regimes taking place in junctions are a powerful tool for the investigation of defects even in large-gap semiconductors like diamond, and that care must be exercised in the treatments used for preparing devices made of epitaxial diamond thin films.
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References [1] R. Zeisel, C. Nebel, M. Stutzmann, J. Appl. Phys. 84 (1998) 6105. [2] H. Sato, H. Tomokage, H. Kiyota, T. Ando, Diamond Relat. Mater. 7 (1998) 167. [3] E. Gheeraert, A. Deneuville, J. Mambou, Diamond Relat. Mater. 7 (1998) 509. [4] J.-P. Lagrange, A. Deneuville, E. Gheeraert, Diamond Relat. Mater. 7 (1998) 1390. [5] P. Muret, F. Pruvost, C. Saby, E. Lucazeau, T.A. Nguyen Tan, E. Gheeraert, A. Deneuville, Diamond Relat. Mater. 8 (1999) 961. [6 ] E. Meijer, H.G. Grimmeiss, Semicond. Sci. Technol. 7 (1992) 188. [7] S. Weiss, R. Kassing, Solid State Electron. 31 (1988) 1733. [8] P. Muret, E. Gheeraert, A. Deneuville, Phys. Stat. Sol. (a) 174 (1999) 129. [9] M.W. Geis, J.C. Twichell, IEEE Trans. ED 44 (1997) 1514. [10] J. Chevallier, D. Ballutaud, B. Theys, F. Jomard, A. Deneuville, E. Gheeraert, F. Pruvost, Phys. Stat. Sol. (a) 174 (1999) 73.