JOURNAL OF APPLIED PHYSICS 109, 034105 共2011兲
Surface passivation of crystalline silicon by plasma-enhanced chemical vapor deposition double layers of silicon-rich silicon oxynitride and silicon nitride Johannes Seiffe,1,a兲 Luca Gautero,1 Marc Hofmann,1 Jochen Rentsch,1 Ralf Preu,1 Stefan Weber,2 and Rüdiger A. Eichel2 1
Fraunhofer Institute for Solar Energy Systems (ISE), Heidenhofstrasse 2, D-79110 Freiburg, Germany Institute of Physical Chemistry, Albert-Ludwigs-Universität Freiburg, Albertstr. 21, D-79104 Freiburg, Germany
2
共Received 2 August 2010; accepted 11 December 2010; published online 3 February 2011兲 Excellent surface passivation of crystalline silicon 共c-Si兲 is desired for a number of c-Si based applications ranging from microelectronics to photovoltaics. A plasma-enhanced chemical vapor deposition double layer of amorphous silicon-rich oxynitride and amorphous silicon nitride 共SiNx兲 can provide a nearly perfect passivation after subsequent rapid thermal process 共RTP兲 and light soaking. The resulting effective minority carriers’ lifetime 共ef f 兲 is close to the modeled maximum on p-type as well as on n-type c-Si. Restrictions on the RTP of passivated surfaces, typical of other common passivation schemes 共e.g., amorphous Si兲, are relieved by this double layer. Harsher thermal treatments can be adopted while still obtaining salient passivation. Furthermore, characterization of the same, such as, surface photovoltage, capacitance voltage, and electron paramagnetic resonance, enables the reproducibility and the understanding of the passivation scheme under test. It is shown that the strong quality of surface passivation is ensured by a mechanism that emits electrons from shallow donor states in the passivation layer system and therefore creates a positive field effect. © 2011 American Institute of Physics. 关doi:10.1063/1.3544421兴 I. INTRODUCTION
Reducing recombination losses at any crystalline silicon 共c-Si兲 surface is of particular interest for improving minority carrier devices like c-Si solar cells. As the c-Si photovoltaic industry aims to adopt thinner wafers in order to achieve cost reductions, surface passivation is of growing importance for the front as well as for the rear surface. For contacting solar cells with screen printed contacts, a short fast-firing process at a wafer temperature Twafer ⬎ 800 ° C for several seconds is commonly used. The advantage of enduring this firing process ensures a successful integration of a passivation into a solar cell production line. Additionally, low-temperaturedeposited passivation layers with high deposition rates are envisaged to reduce fabrication costs. A state-of-the-art surface passivation layer for n-type silicon 共bulk or diffused emitter兲 is amorphous hydrogenated silicon nitride 共here abbreviated as SiNx兲 deposited via plasma-enhanced chemical vapor deposition 共PECVD兲. SiNx is known to develop positive charges in contact with silicon leading to accumulation on n-type and inversion on p-type silicon.1 It can be adjusted in refractive index and thickness and hence can be adapted as an antireflection-coating to improve light trapping. Good surface passivation is possible for optimized films.2,3 Several new low-temperature surface passivation layers have been examined in recent years. Excellent results were obtained with amorphous hydrogenated silicon 共a-Si:H兲 共Ref. 4兲 or amorphous hydrogenated silicon carbide a兲
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a-SiCx : H 共Refs. 5 and 6兲 but both surface passivation layers show a very low temperature stability. An additional capping layer of PECVD silicon oxide 共a-SiOx兲 or PECVD SiNx significantly improves the thermal stability of a-Si:H 共Refs. 7 and 8兲 or a-SiCx : H.9 A good firing stability with lower but for many devices sufficient, surface passivation is given by a PECVD double layer of thick a-SiOx 共several hundred nanometers兲 capped with SiNx.10 Amorphous aluminum oxide 共AlOx兲 traps negative charges in the dielectric and induces accumulation on p-type silicon surfaces. Hence it is a promising surface passivation layer for the rear of p-type solar cells.11 Commonly, this layer is produced by atomic layer deposition, which is a low-temperature technique but with very low deposition rates, making its industrial feasibility thus still questionable. However, an AlOx deposition with PECVD has recently been demonstrated to permit an excellent surface passivation.12 In this work, a double-layer stack of an amorphous hydrogenated silicon-rich oxynitride 共short: SiriON兲 layer capped with SiNx, both deposited via PECVD, is investigated. The passivation scheme was already introduced briefly in Ref. 13 and allows an excellent thermally stable passivation quality on p-type, and in particular on n-type silicon. The electric origin of the surface passivation is examined in this work. As a result, it will be shown that the layer presumably emits electrons from shallow donor states in the passivation layer. The resulting positive charge density leads to a strong field effect passivation and makes the passivation especially interesting for n-type silicon surfaces.
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described by the Shockley–Read–Hall 共SRH兲 statistics. To describe a distribution of traps, the extension of Simmons and Taylor has to be considered.15 The recombination mechanism is represented by energy-dependent capture and emission probabilities of charge carriers by the defect states.16 This dependency and the continuous distribution of states are best taken into account in the estimation of the recombination rate with an integration along the energy bandgap as follows:17
II. SURFACE PASSIVATION
At the c-Si surface, the abrupt ending of the crystal structure leads to a continuous distribution of states in the energy bandgap.14 The density of these states is typically denoted as Dit. States between the valence-band top-edge energy EV and the conduction-band bottom-edge energy EC can act as recombination centers for mobile charge carriers in the silicon. The recombination rate of an interband state is
Uit = 共ns ps − n2i 兲
冕
EC
EV
−1 p 共兲
冋
thDit共兲
冉 冊册
− Ei ns + ni exp k BT
+
−1 n 共兲
with the capture cross sections for electrons and holes n and p, respectively, the thermal velocity of electrons th, the intrinsic carrier density ni, Boltzmann constant kB, temperature T, and the mobile charge carrier densities at the surface ns and ps, which in general differ from the ones inside the silicon bulk nb and pb. This is mainly due to charges trapped in surface defects 共charge density Qit兲 or in the passivation layer 共charge density Q fix兲, which have to be balanced by a redistribution of mobile charge carriers in the silicon, resulting in an effective charge density Qsc as follows: − Qsc = Q fix + Qit .
共2兲
The induced electric field causes a band bending toward the surface, which is described by the potential 共z兲 defined as
F共兲 =
冑
冋
冉
− Ei ps + ni exp − k BT
ns = nb exp关兴, ps = pb exp关− 兴,
共6兲
Surface recombination is normally not described by the recombination rate Us; instead, the surface recombination velocity S = Us / ⌬ns is defined. It is difficult to determine experimentally the recombination rate at the surface, therefore, the effective surface recombination Sef f is considered instead17 Sef f 共⌬nbulk兲 =
Us共⌬nbulk兲 + Usc共⌬nbulk兲 . ⌬nbulk
共7兲
共1兲
the difference between the intrinsic energy level in the bulk Ei.bulk and at a certain distance z from the surface Ei共z兲 共Ref. 14兲 1 共z兲 = 关Ei.bulk − Ei共z兲兴 q
共3兲
with the elementary charge q. The dependency between the surface potential = 共0兲 and Qsc is given by the following:14 Qsc = ⫿ 共nb + pb兲DF共兲
共4兲
with the charge carrier densities in the silicon bulk nb and pb, the extrinsic Debye length D and the space charge function F defined as
2 兵pb共exp关− 兴 +  − 1兲 + nb共exp关兴 −  − 1兲其 pb + nb
with  = q / 共kBT兲. Finally ns and ps are calculated from the charge-carrier densities inside the bulk via the following:
冊册
d
共5兲
This term includes all recombination channels throughout the space charge region and the surface, which, through the geometrical dependency of the SCR on the injection, show a dependence of the excess charge carrier density upon the bulk ⌬n. A passivation layer is applied to minimize surface recombination. As can be followed from Eq. 共1兲, increased surface passivation is a consequence of following two effects: 共i兲 the reduction in recombination-active interface states, and 共ii兲 any strong imbalance of majority and minority charge carrier densities at the silicon surface. The first effect is achieved by saturation of silicon dangling bonds at the crystal surface, the second by charges which are trapped at defects at the interface or in the near passivation layer.18 These charges build up an electric field repelling the mobile
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charge carriers with the same sign from the surface. Depending on the doping type of the silicon substrate, the repelled charges could be majority carriers, which results in a depletion or inversion condition at the surface; or minority carriers, leading to an accumulation condition. The accumulation is in many cases advantageous at solar cell surfaces.19 The inversion presents the inconvenience of an enhanced SRH recombination in the depletion region, situated between the inversion layer and the bulk. This effect appears especially at low injection levels 共⌬n ⬍ 1015 cm−3兲.20,21 The experimental determination of the surface recombination velocity is usually done by measuring the effective charge carrier lifetime17
ef f 共⌬nav兲 =
⌬nav U共⌬nav兲
共8兲
with the average excess charge-carrier injection in the sample ⌬nav and the total recombination in the sample U. State-of-the-art for determining ef f is a quasi-steady-statephotoconductance measurement,22 which measures ⌬nav via the excess conductivity of the sample with an inductive coil after excitation with a flash light. The recombination rate is then determined from transient decay, in quasistatic condition or in a generalized mode. For reasonably high effective lifetimes on symmetrically passivated samples, the dependence between ef f and Sef f is given by the following:23 Sef f =
冉
1 W 1 − 2 ef f bulk
冊
共9兲
with the wafer thickness W and the charge carrier lifetime in the silicon bulk bulk. This charge carrier lifetime depends on SRH recombination at defects in the crystal and on the intrinsic radiative and Auger recombination processes. For the intrinsic recombination processes several models have been published, leading to different bulk共⌬n兲 curves.20,24–26 If high-quality float-zone silicon is used, bulk can be estimated properly by considering only the intrinsic recombination processes. In this work, the model of Kerr and Cuevas25 is used to compare with the achieved lifetimes. In addition to the determination of Sef f , experimental access to the parameters Dit, Q fix, and n/p, which describe the passivation mechanisms, is not easy. For passivation layers exhibiting a good electrical insulation like thermally grown silicon oxide, the Dit and Q fix can be deduced from capacitance voltage 共CV兲 measurements and n/p could be evaluated by deep-level transient spectroscopy. However, for passivation layers that provide a charge-carrier penetration into or through the layer, the extraction of the desired parameters usually fails. So, for silicon-rich SiNx layers, which are often used for passivation purposes, CV measurements are difficult because leakage currents are too high. Contacting the sample with a Hg-probe enables very small areas compared to evaporated Al contacts, and therefore, decreases the leakage problem. If a measurement is possible, it typically shows hysteresis effects because of trapped charges after voltage application.21 For a-Si:H-passivated samples, several new characterization tools have been investigated in recent years. Surface photovoltage 共SPV兲 measurements are used for di-
rect access to the surface potential or to determine Dit.27 The formation of defect states at the passivation layer or at the interface may be monitored by means of electron paramagnetic resonance 共EPR兲 spectroscopy provided the defects are paramagnetic. This condition particularly holds for silicon dangling bond states at thermally grown SiOx,28 or at SiNx passivated surfaces.29 From the different characterization methods a quite good understanding of the state densities at the SiOx / c-Si interface and the SiNx / c-Si interface has been developed, which is summarized in detail in regard to surface passivation in the book by Aberle.17 For these dielectric layers, the interface defect states are mainly due to silicon dangling bonds. The dangling bond states are nonbonding orbitals at a silicon atom, which can be charged positively 共unoccupied state兲, neutrally 共occupied with one electron兲, or negatively 共occupied with two electrons兲. Only the neutral state includes an unpaired electron spin and thus shows a paramagnetic resonance. The energy level of a dangling bond state depends on the kind of atoms that are back-bonded to the silicon atom. The •SiSi3-defect lies energetically inside the silicon band gap and therefore is attributed as the major surface recombination center. In the dielectric, the dangling bond atoms are mostly backbonded to more electronegative atoms like oxygen or nitrogen, which increase the energy level of the corresponding dangling bond states and thus can result in fixed positive charges. At the SiOx / c-Si-interface this leads typically to a charge density of Q fix ⬇ 5 ⫻ 1010 – 2 ⫻ 1011 cm−2 located in the first few nanometers of SiOx.17 For SiNx, typical values are Q fix ⬇ 1 ⫻ 1011 – 5 ⫻ 1012 cm−2 in about 20 nm from the interface.17 Due to the discontinuity of the atomic structure at the interface, besides the dangling bond defects, atomic bonds, and bonding angles will be stretched or compressed. This leads to a continuous broadened energy distribution for the defect states as well as for the energy bands. The latter results in the so-called “band-tail states,” which are particularly present in amorphous silicon30 but also occur in amorphous silicon nitride, silicon oxide, or oxynitride.31 Unpaired electrons trapped in the conduction band tail could be detected by its paramagnetic resonance.32 As the band-tail states are shallow localized states at the band edges, the paramegnetic resonance signal is quite similar to the resonance of electrons in neutral shallow donor states caused by dopant impurities in c-Si or a-Si:H. This means there is a narrow resonance peak near the conduction electron resonance at g = 1.9995.33 Finally, for silicon-rich passivation layers a charge carrier penetration from the silicon into the passivation layer has to be taken into account. Therefore charge carrier trapping and recombination processes have to be considered not only at the interface but also inside the passivation layer.34 The most reasonable model to avoid this problem is to define an effective surface, which includes interface states at the actual interface and in the accessible region in the passivation layer. This model of an effective interface has to be kept in mind when the origin of defects in this work will be discussed.
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FIG. 1. Sketch of the symmetrically passivated samples with the SiriON/ SiNx double layer.
III. EXPERIMENTAL A. Sample preparation
In this work the surface passivation characteristics of a silicon-rich PECVD silicon oxynitride 共SiriON兲 capped with PECVD silicon nitride 共SiNx兲 is investigated. Both layers were deposited in an industrial type inline-PECVD system 共Roth&Rau SiNA XS兲 with a linear-antenna microwave plasma excitation 共2.45 GHz兲. The process gases for the SiriON layer are silane 共SiH4兲, hydrogen 共H2兲, and nitrous oxide 共N2O兲 in a gas-flux ratio leading to a refractive index of n = 2.9 at 630 nm. The layer was deposited with a thickness of about 30 nm. Subsequently, a SiNx-layer with a thickness of about 70 nm was deposited on top using the same plasma reactor with SiH4 and ammonia 共NH3兲 as process gases. The gas-flux ratio was chosen to achieve a refractive index of n = 2.15. The substrates were high-quality float zone silicon wafers with shiny etched surfaces. The wafers were cleaned by oxidation in 69 wt %-HNO3 at 110 ° C for 10 min, and oxide removal in diluted hydrofluoric acid 共1 wt %-HF, 1 min兲. The passivation is investigated on pand n-type silicon. For both of these, a doping level leading to a resistivity of = 1 ⍀ cm was chosen. This equates to an acceptor 共boron兲 concentration of NA = 1.5⫻ 1016 cm−3 for p-type and a donor 共phosphorus兲 concentration ND = 5 ⫻ 1015 cm−3 for n-type. The thickness of the wafers is W = 250 m, except for the EPR measurements for which the wafers were ground down to W = 100 m and lower doped p-type silicon 共 = 8 ⍀ cm兲 was used. For the photoconductance decay measurements and the EPR investigations, the wafers were passivated symmetrically on both surfaces as sketched in Fig. 1. For the SPV characterization and the CV measurements only one side was passivated as the other side has to be contacted. After the deposition the samples were exposed to a high temperature step. A single wafer RTP system 共SHS10, ASTElectronic兲 was used, as an accurate temperature control is possible with this system. The temperature ramp is based on a typical contact firing step for screen printed contacts in the production of silicon solar cells This includes a burn out plateau at about 450 ° C for 30 s followed by a short firing peak for about 3 s.35 The temperature of this peak reaches about 820 ° C in solar cell production but was varied for the presented investigations between 650 and 850 ° C. Figure 2 shows exemplarily the used temperature ramp with a set
FIG. 2. Temperature ramp of a sample fired at 850 ° C. The ramp is adapted to a firing process which enables screen printed pastes to contact both solar cell sides. By setting the peak temperature to 860 ° C, the sample temperature is at 共850⫾ 5兲 ° C for 3 s.
peak temperature of 860 ° C for 3 s. It can be seen that the real wafer temperature fits the targeted temperature of 850 ° C in a range of ⫾5 ° C. Subsequently the samples fired at 650 ° C were exposed to light soaking with a common halide lamp, reaching a luminance of about 10 000 lx. The samples fired at 850 ° C are additionally annealed at 350 ° C for 10 min on a standard hotplate in ambient air. B. Effective lifetime measurements
To determine the surface passivation quality, the effective charge carrier lifetime ef f of the samples was measured using a commercially available lifetime tester 共WCT-100, Sinton兲 as described elsewhere.22 The measurements were performed in the transient measurement mode, except for one measurement with ef f ⬍ 150 s, which was done in the generalized mode.36 The accuracy of the measured effective lifetime with the used system is well discussed in Ref. 37. The greatest contribution to uncertainty is given by the used mobility model for charge carriers in the silicon. This uncertainty leads to a systematic error depending on material and test device in use; hence it is of no consequence for the comparison of different surface passivations on the same substrate measured for this work. After including the mobility uncertainty, the data are exactly in a range of 8.6% for transient measurements and 10.9% for quasistatic ones.37 When comparing different measurements in this work, the data are accurate in a range of 3% for transient and 4.5% for quasistatic measurements.37 As in this paper only surface recombination is of interest, high-quality float-zone silicon is used. This material, in good approximation, exhibits only the intrinsic recombination processes known as radiative and Auger recombination. As the same material is used for the various measurements presented, the directly measured ef f is sufficient for the comparison of the surface recombination. The bulk resulting from the general parameterization of Kerr et al.25 is plotted as reference 共see Figs. 3 and 4兲. C. SPV measurements
SPV measurements were performed to examine the surface potential . The measurement principle is described elsewhere38 and will be briefly outlined here. The passivated
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sample is illuminated by a short intense laser pulse 关 = 910 nm, pulse duration 150 ns, maximum intensity 1019 photons/ 共cm2 s兲兴, creating a high generation of excess charge carriers. This leads to a flattening of the bands at the surface, which changes the potential compared to the silicon bulk. The voltage between the surface and the silicon bulk under illumination U ph is measured capacitively via a transparent conductive front contact 共transparent conductive oxide TCO兲 on top of an insulating slab of mica. Assuming flat bands under illumination, the surface potential in the dark is calculated as the negative of U ph corrected with the Dember potential VD as follows:39
= − U ph + VD .
共10兲
With the SPV setup applied for the determined photovoltages, an accuracy of ⫾5 mV is expected. D. Capacitance-voltage measurement
CV measurements are a well-known technique to investigate the interface between a dielectric layer and a silicon substrate. By using a mercury probe with a dot size of A = 0.0031 cm2, it is possible to measure on the silicon rich and therefore leaky SiNx layer investigated here. The curves are recorded at room temperature 共28 ° C兲 using a quasistatic or a high-frequency pulsed voltage ramp with a pulse length p = 10−4 s in a range from 共−15兲 – 共+10兲 V. A voltage ramp in the range from 共−40兲 – 共+40兲 V is performed in highfrequency conditions using a 75 kHz sine signal. Flatband capacitance CFB = C共 = 0兲 is given by the following:40 CFB =
i
i d+ Si
冑
kBTSi N Aq 2
.
共11兲
From the associated flatband voltage VFB the Q fix can be calculated as follows:40 Q fix =
冋
Ci ⌬ MS VFB − qA q
册
共12兲
with the capacitance of the insulator Ci and the work function difference ⌬ MS = M − Si − 共EC − EF兲.
共13兲
The work function of Hg is given as M = 4.475 eV, the electron affinity of silicon is Si = 4.05 eV, and the difference between the conduction band edge and the Fermi level for 1 ⍀ cm p-type silicon EC − EF = 0.92 eV. 41
To increase the investigated passivated surface in the resonator, silicon wafers were ground down to about 100 m. After deposition, the wafers were broken into small plates with sizes between 1.5⫻ 14 and 4 ⫻ 14 mm2. To remove silicon dust from the breaking, the plates were cleaned in 30 wt %-KOH for 2 min at 80 ° C, followed by a short dip in diluted HCl. Subsequently, a stack of 13 plates was stuck on a Teflon stick and inserted in the cylindrical resonator. Owing to this procedure, the investigated passivated area added up to about 12 cm2. Because of the comparatively high conductivity in the silicon at room temperature, critical coupling of the microwave resonator was only achieved for temperatures below 50 K. Most of the measurements were thus performed at 20 K. Temperature control was enabled by a helium gas flow cryostat 共Oxford兲 in conjunction with a temperature controller 共Oxford, ITC 503s兲. Considering the temperature dependence in the available interval, the paramagnetic behavior of the paramagnetic susceptibility owing to electrons located at defects in the passivation layer or at the interface follows Curie’s law as follows:
Curie共T兲 = NCurie S
g20B2 4kBT
共14兲
with the number of spins NS, the magnetic susceptibility 0, and the Bohr magneton B. Hence the number of spins in the sample can be determined by comparison with a Curie spin standard. If delocalized electrons contribute to the resonance signal, Fermi–Dirac statistics have to be taken into account, leading to Pauli paramagnetism. The susceptibility can be approximated for small temperatures 共T Ⰶ T f ; T f : Fermitemperature兲 by the following temperature independent expression:
Pauli共T兲 = NPauli S
g20B2 . 4kBT f
共15兲
The contribution of Pauli electrons can be derived from the temperature dependence of the EPR signal. Beyond the intensity of a given resonance, also its lineshape function may be considered. This is particularly pronounced when observing resonances from conduction electrons. If the conductivity is high enough to absorb the microwave radiation inside the sample, the characteristic skin depth of the sample becomes smaller than the sample thickness. Correspondingly, the resonant conduction electrons carry the magnetization between regions of different microwave intensities leading to a distortion of the resonance signal and resulting in an asymmetric curve. This is known as Dyson effect.42
E. EPR spectroscopy
EPR measurements were conducted at X-Band microwave frequencies 共9.7 GHz, Bruker ElexSys 680兲 using a dielectric-ring resonator. The magnetic field was determined using an NMR-Gaussmeter 共Bruker ER 035M兲 and calibrated with a DPPH-standard 共g = 2.0036兲. The paramagnetic susceptibility of the samples under study has been determined by comparison with a galvinoxyl spin-standard, enabling the estimation of observed spins per area.
IV. RESULTS A. Effective lifetime measurements
Figures 3 and 4 show the measured effective lifetime for p-type and n-type silicon after the deposition, after a high temperature step at 650 or 850 ° C and after subsequent light soaking 共for the 650 ° C samples兲 and after subsequent an-
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FIG. 3. Effective minority charge carrier lifetime measurements for p-type silicon 共 = 1 ⍀ cm兲 passivated with the SiriON/ SiNx double layer stack, after different temperature and illumination treatments. The modeled bulk lifetime 共Ref. 26兲 is plotted as reference 共solid line兲.
nealing at 350 ° C 共for the 850 ° C samples兲. For comparison, the intrinsic bulk lifetime bulk calculated by the Kerr model was plotted.25 After firing the samples at 650 ° C, a quite good passivation quality was already reached for p- and n-type. This was improved by subsequent illumination for 10 min, resulting in effective carrier lifetimes exceeding 2 ms for the p-type and 5 ms for the n-type silicon. Both are in the region of the approximated intrinsic bulk lifetime for the used material. It can be seen that for the n-type silicon, the effective lifetime follows the calculated bulk lifetime very closely down to ⌬n = 1014 cm−3, equating to Sef f ⬍ 0.3 cm/ s. For the p-type silicon the effective lifetime fits the bulk lifetime down to ⌬n = 1015 cm−3 共Sef f ⬍ 1.5 cm/ s兲, then starts to significantly diverge from Kerr’s bulk lifetime expression. This behavior suggests that the surface is in inversion below the passivation for the p-type silicon and therefore the recombination in the space charge region affects the surface passivation at low injection.21 After firing the samples at 850 ° C, the effective lifetime for the p-type silicon is limited to values of about 0.7 ms 共Sef f ⬇ 12 cm/ s兲 in high injection, decreasing to about 0.4 ms 共Sef f ⬇ 26 cm/ s兲 in low injection. An additional annealing improves the effective lifetime to about 1 ms 共Sef f ⬇ 7 cm/ s兲 in high injection and 0.7 ms 共Sef f ⬇ 13 cm/ s兲 in low injection. For the n-type samples, the additional annealing does not result in a positive effect.
FIG. 4. Effective minority charge carrier lifetime measurements for n-type silicon 共 = 1 ⍀ cm兲 passivated with the SiriON/ SiNx double layer stack, after different temperature and illumination treatments. The modeled bulk lifetime 共Ref. 26兲 is plotted as reference 共solid line兲.
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FIG. 5. Effective carrier lifetime measurement for one sample after firing at 700 ° C, illumination from the first side for 15 min and after illumination from the second side for 15 min.
Instead a decrease of the effective lifetime after firing, namely from 2 ms 共Sef f ⬇ 2 cm/ s兲 to about 1 ms 共Sef f ⬇ 10 cm/ s兲, is observed after the subsequent annealing at 350 ° C. As well as for the p- and n-types, the effective lifetime measured with the single SiNx layer used as capping in the double layer passivation was plotted for reference and shows the significant gain for the surface passivation by the thin SiriON-interface layer. A better understanding of the light-induced improvement of the surface passivation was achieved by a simple test. Comparing the effect of illumination from one side on the symmetrically passivated samples with the effect by illuminating the other side after the lifetime measurement, it could be distinguished whether the upgrading results from a direct impact of photons in the passivation layer or from the impact of the prolonged high charge carrier injection acting from the silicon on the passivation. In the first case, the illumination from one side will only lead to a small upgrade in performance, as only one surface would gain a better surface passivation. Considering that the carrier diffusion length in the silicon Lbulk is much larger than the wafer thickness W 共for both materials Lbulk ⬎ 2000 m兲, the rear side would dominate the recombination. The possibility that photons from infrared irradiation crossing the whole wafer activate the backside with the first illumination as well is considered very improbable, as the energies are too low to affect the atomic structure of the passivation layer. So only after illuminating the second side would the effective lifetime be significantly increased. In the second case the improvement would act on both surfaces at once by illuminating only one side 共again as the diffusion length is larger than the wafer thickness兲. In Fig. 5 the result of this test is shown for one exemplary sample. It can clearly be seen that the activation happens after the first illumination step, and so the impact of the charge carrier injection on the passivation layer has to be considered as the reason for the upgrading effect. Furthermore, a small decrease in the effective lifetime is seen after the illumination of the second surface. The effect is almost inside the expected measurement uncertainty but perhaps it indicates an additional light induced effect that harms passivation. As yet, an extensive UV-stability test for this passivation layer has not been performed.
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TABLE I. Measured surface potential and calculated Qsc for samples passivated with single SiNx and with the SiriON/ SiNx double layer.
Sample SiNx as deposited SiNx fired SiNx fired at 700 ° C and illuminated SiriON/ SiNx as deposited SiriON/ SiNx fired SiriON/ SiNx fired at 700 ° C and illuminated
FIG. 6. The surface passivation slightly decreases after the illumination over time but stays at a high level.
The high level of surface passivation exhibits a slight degradation with time, as is shown in Fig. 6. The effective lifetime of an exemplary sample kept in the dark after the illumination has decreased from initial 1.3 ms to about 1 ms after 33 days. The decay in the effective lifetime is observed to be similar for all samples passivated with the double layer stack; however, the passivation remains at a high level.
B. SPV measurement
Figure 7 shows the measured surface potentials for two p-type silicon samples: one coated with the single SiNx layer and one coated with the SiriON/ SiNx stack system. For both samples was determined for the “as deposited” state, after a firing step at 700 ° C and after subsequent illumination for 10 min. First it can be seen that for all samples an inversion condition is measured, which confirms the properties of SiNx on p-type silicon1 and is to be expected for the SiriON/ SiNx stack system. For the SiNx passivated sample, the surface potential slightly increases with the firing step from 733 to 760 mV, whereby for the SiriON/ SiNx the surface potential increases from 645 to 720 mV. As seen before for the effective lifetime, the intense illumination causes a change in the surface potential for the SiriON/ SiNx passivated sample. It increases further to 755 mV. Table I shows the surface densities Qsc in q / cm2 calculated for the measured surface potentials using Eq. 共4兲.
FIG. 7. Surface potentials measured with SPV for a SiriON/ SiNx-passivated sample in comparison to a SiNx passivated sample: as deposited, after firing at 700 ° C and after illumination for 10 min.
共mV兲
Qsc 共⫻1011 cm−2兲
734⫾ 5 760⫾ 5 760⫾ 5 645⫾ 5 720⫾ 5 755⫾ 5
−3.9⫾ 0.1 −4.1⫾ 0.1 −4.1⫾ 0.1 −3.48⫾ 0.05 −3.76⫾ 0.05 −4.1⫾ 0.1
C. CV-measurements
In Fig. 8 the CV characteristics for the fired single SiNx layer are plotted. The single SiNx layer shows a hysteresis effect, so that an exact determination of the flatband voltage or the interface state density Dit is not possible. In high frequency one curve is plotted after a positive voltage stress 共+10 V for 2 min兲 and one after a negative voltage stress 共⫺10 V for 2 min兲. The calculated fixed charge densities for these measurements, according to formula 共11兲, are compiled in Table II. The effect of charge trapping by applying a voltage is a known effect for SiNx layers,43 in which open silicon bonds in the Si3N4 network form chargeable traps, the socalled K-centers. In addition, a quasistatic 共low frequency LF兲 curve was recorded after the negative voltage stress. It can be seen that the inversion capacitance exceeds the accumulation capacitance. This is likely due to the inversion channel conductivity, which increases the effective area contributing to the capacitance.44 For the SiriON/ SiNx double layer 共fired at 700 ° C and illuminated for 15 min兲, it is not possible to achieve an accumulation condition at the surface for the possible voltage range 共Fig. 9兲. The high-frequency curve is measured starting with a sweep from 0 to +40 V, which results in a deep depletion, and continuing with a sweep from +40 to ⫺40 V, for which the capacitance stays at the depletion level. The low-frequency measurement is only possible between ⫺10 and +10 V, due to charge leakage through the layers at higher biases. In this range the capacitance indicates the inversion level. As with the SiNx, an increased effective area could be affecting the inversion capacitance; therefore, the capacitance of the passivation layer Ci cannot be evaluated
FIG. 8. HF- and LF-capacitance-voltage characteristic of a SiNx layer fired at 700 ° C on p-type silicon 共 = 1 ⍀ cm兲 with a mercury probe 共dot size A = 3.1⫻ 10−3 cm2兲.
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TABLE II. Fixed charge densities Q fix calculated from CV measurements for the single SiNx layer and the estimated lower limit for the SiriON/ SiNx double layer after firing at 700 ° C, illumination and degradation.
Sample SiNx after ⫺10 V for 2 min SiNx after +10 V for 2 min SiriON/ SiNx
A 共cm2兲
Ci 共⫻10−11 F兲
CFB 共⫻10−11 F兲
VFB 共V兲
Q fix 共⫻1012 cm−2兲
0.003 15 0.003 15 0.003 15
22 22 ⬃16.3
21 21 ⬃16.0
⫺10 ⫺2.5 ⬍共−40兲
4.1 0.9 ⬎13
from this measurement with certainty. It could only be estimated by assuming the same ratio of the effective areas in inversion and accumulation as for the SiNx. With this estimation, a lower limit for the fixed charge density can be calculated as Q fix ⬎ 1.3⫻ 1013 cm−2 共see Table II兲. Remembering that the surface space charge evaluated from the SPV measurements is on the order of 1011 cm−2 共see Table I兲, a huge number of trapped electrons, which could be emitted into the silicon by applying the negative voltage, has to be assumed. In contrast to the measurement of the SiNx sample, those electrons are directly emitted during the voltage sweep and no hysteresis effect occurs. D. EPR spectroscopy
To investigate the formation of paramagnetic interface or surface defect states, EPR spectroscopy is a sensitive technique with detection limit of about 1011 spins. The corresponding X-band 共9.5 GHz兲 spectra are shown in Figs. 10 and 11 for p-type silicon passivated with a single SiNx layer 共Fig. 10兲, or with a SiriON/ SiNx double layer system 共Fig. 11兲 before and after a firing step at 700 ° C and illumination for 10 min. The estimated spin densities are given in Table III. First, the possible presence of silicon dangling-bond states at the passivated silicon surfaces is discussed. The corresponding resonances typically are centered in a range between g = 2.0043 and g = 2.0058, which translates at X-band frequencies to a magnetic field range between 345.5 and 345.8 mT. Obviously, for the here studied SiriON/ SiNx-double layer, the amount of such defects is be-
FIG. 9. HF- and LF-capacitance-voltage characteristics of a SiriON/ SiNx layer fired at 700 ° C and illuminated for 15 min on p-type silicon 共 = 1 ⍀ cm兲 with a mercury probe 共dot size A = 3.1⫻ 10−3 cm2兲. The HFmeasurement was done by a sweep from 0 to +40 V and then from +40 V to ⫺40 V. The SiriON/ SiNx double layer stays in depletion over the whole voltage range. For the LF-measurement, the leakage of the layer exhibits only a measurement between +10 and ⫺10 V, indicating the inversion capacitance.
low the EPR detection limit. For the SiNx sample a small resonance band in this range is observable but difficult to distinguish from noise. As the here investigated surfaces are all in inversion, the silicon dangling bond interface states will mainly be negatively charged by interface trapped electrons. Therefore the dangling bond orbitals will be occupied by two electrons and in turn are not paramagnetic. From EPR measurements it is difficult to draw conclusions for the dangling bond state density at the interface without considering the surface band bending. On the other hand, instead of the trapped electrons in dangling-bond states, electrons in shallow donor states formed by overcoordinated atoms or stretched bonds in band-tails could be detected. The observed strong resonance at g = 1.9991⫾ 0.0003 for the SiNx sample in the “as deposited” state is presumably owing to such defects. For SiNx in the “as deposited” state, a high defect density in its bulk typically leads to a high positive fixed charge density Q fix and a high interface state density, and hence, to a high number of interface trapped electrons. A temperature step like the firing is known to reduce the defect states in SiNx and at the interface.21 The atomic structure will be relaxed and so also the band tails will be strongly reduced. The EPR resonance shows a decrease in the trapped electrons with g = 1.9991⫾ 0.0003 from NS = 7.4⫻ 1011 cm−2 to NS = 1.2⫻ 1011 cm−2, which could be explained by the detailed behavior. For the SiriON/ SiNx double layer passivation, electrons in shallow donor states and/or band-tail states could be observed as well 共Fig. 11兲. With g = 1.9998⫾ 0.0003, the surface states differ from the states of the SiNx layer. In contrast to the SiNx sample, for the double layer sample the signal did not decrease as much after firing. Moreover the signal
FIG. 10. EPR signals of SiNx passivated p-type silicon before and after a firing step at 700 ° C. A signal of electrons in shallow donor states nearly disappears with the high temperature treatment.
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FIG. 11. EPR signal of a SiriON/ SiNx passivated p-type silicon sample before and after a firing step at 700 ° C with subsequent illumination for 15 min. A clear shallow donor signal appears at g = 1.9998⫾ 0.0001. After firing, the signal transforms into an asymmetric line shape 共A ⬎ B兲.
changes its shape from the symmetric Lorentzian line shape to an asymmetric line shape with an asymmetry of A / B ⬇ 1.8. Generally, two conceivable scenarios for the existence of such an asymmetric line shape exist. First, a signal can be distorted if it results from a superposition of different resonances, which could for instance be caused by an anisotropic g-tensor or by a superposition of spin states with varying bond distance and bond angles 共strain兲. Second, the Dyson effect42 that accounts for the existence of conduction electrons may be responsible for the observed line-shape asymmetry, as the resonance shows the typical shape for a sample thickness in the order of the skin depth. This is further corroborated by the fact that even in a second-harmonic generation scheme no indication for any g-anisotropy or strain behavior is observed. Furthermore, the asymmetric line shape appears only after the firing step and seems to result from the same resonance as the symmetric signal detected for the same layer before the firing step. Therefore a conductivity-induced Dyson effect seems more likely. If conduction electrons are included in the detected signal, this should further affect the temperature dependence. In Fig. 12, the temperature dependence of the susceptibility for a fired double layer sample is plotted. The experiment shows a distinct deviation from Curie magnetism, which is pointed out by a fit of the temperature dependence with Curie’s law 关see formula 共14兲兴 in comparison to a fit with an additional constant summand for the Pauli susceptibility. Obviously, a superposition of Curie and Pauli magnetism nicely reproduces the experimental data. The results of the two fits with the calculated spin densities are summarized in Table IV. TABLE III. List of all detected EPR signals. Spin densities have been calculated by comparison with a galvinoxyl Curie spin standard.
Sample SiNx as deposited SiNx fired SiriON/ SiNx as deposited SiriON/ SiNx fired and illuminated
Line shape
g
⌬B 共mT兲
Ns 共⫻1011 cm−2兲
Lorentzian Lorentzian Lorentzian
1.9991 1.9991 1.9998
0.2 0.2 0.1
7.4 1.2 8.3
Dysonian
1.9997
0.1
FIG. 12. Normalized magnetic susceptibility of the fired and illuminated SiriON/ SiNx double layer sample at different measurement temperatures. The data points are fitted with Curie’s law 共solid line兲 and with a superposition for Curie and Pauli electrons 共dashed line兲.
The density of Pauli spins could not be calculated without additional knowledge about the Fermi level position in the resonant material. Using Eq. 共15兲 and assuming a Fermi energy of at least 10−1 eV the density could be estimated to NsPauli ↔ 1013 cm−2. However, not only the presence of delocalized electrons is sufficient to cause the Dysonian-like asymmetric line shape. Additionally, the thickness of the conductive sample has to exceed the characteristic skin depth to form an inhomogeneous microwave field, in which the paramagnetic delocalized electrons move. The sample investigated here consists of different materials: the silicon substrate and the surface passivation layer 共see Fig. 1兲. The silicon substrate can be excluded as a location for the paramagnetic conduction electrons, because for all samples the same substrate material was used and only for one does the asymmetric line shape appear. Hence for the location of the paramagnetic delocalized electrons only the interfaces and the passivation layers come into consideration. The inversion layer at the silicon surfaces will form the most conductive region of the sample at 20 K. However, inversion electrons presumably are not detectable with EPR because of surface scattering, leading to an excessively broad linewidth, which is expected to be at least ⌬B ⬎ 5 mT.45 To our best knowledge, this problem is only discussed for SiO2 in the literature but even if a surface is formed by the SiriON/ SiNx double layer passivation that reduces the scattering of inversion electrons, it seems unlikely that this could result in such a small linewidth as measured here 共⌬B = 0.1 mT兲. Therefore, it has to be assumed that the paramagnetic Pauli-electrons are located in the SiriON-layer. This means the formation of donor-like states in an order that shifts the Fermi-level up to the mobility edge in the amorphous layer. It is rather improbable that the resulting conductivity in the SiriON is sufficient to allow for a significant absorption of the microwave field to explain the asymmetric line shape. But it can be expected that the conductivity of the inversion layer supports the microwave absorption. The inversion layer, however, is very thin 共approximately 1 nm at T = 20 K, in total about 26 nm for the thirteen plates兲. For estimation of the skin depth for this conductivity, the mobility of the inversion electrons n at 20 K has to be known. In
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TABLE IV. Fit results for the two fits of the temperature dependence of the detected asymmetric EPR signal are calculated from measured at the SiriON/ SiNx double layer 共see Fig. 12兲. The densities of Curie spins NCurie S the respective fit parameters using Eq. 共14兲. The density of Pauli spins NPauli can not be calculated from Eq. 共15兲 S without additional knowledge about the Fermi energy E f = kBT f in the investigated material. However, it can be . estimated to be two or three orders of magnitude higher than NCurie S
Formula
norm共T兲 = C / T norm共T兲 = C / T + P
Normalized 2 16.2 1.3
C
P 共K−1兲
12.5⫾ 0.2 ¯ 6.6⫾ 0.7 0.38⫾ 0.04
Ref. 46 the carrier mobility for inversion electrons under thermally grown SiO2 at low temperatures was investigated experimentally. If these results are transferred to the SiriON/ SiNx sample, an order of magnitude for the mobility can be estimated to be n ⬇ 104 cm2 / V s. This is a rather vague estimation, as not only the surface passivation differs, but also the strong magnetic field can influence the mobility. With this value and an inversion electron density of 1012 cm−2, in about 1 nm a skin depth of about 10 m results. This is three orders of magnitude larger than the sum of all inversion layers in the sample measured normal to the surface. Consequently the asymmetric line shape could not be explained straightforwardly. Beside the uncertain value for the mobility, two other effects can lead to a more effective microwave absorption than estimated. First the conductivity in the silicon substrate could support the absorption if charge carriers are not frozen in completely. This then would be the case for every measured sample but only if the resonant electrons are delocalized will the line shape be affected significantly. Second, it has to be taken into account that the sample plates are positioned upright in the cylindrical resonator. This means that the inversion layers are aligned parallel to the propagation direction of the microwave. An efficient absorption of the microwave could thus happen along the conductive interfaces, but more work is needed for a detailed investigation of such influences. Even if the asymmetric line shape could not be explained in detail, it could be concluded for the final discussion that delocalized electrons in shallow donor states are created in the SiriON layer after firing. V. DISCUSSION
It has been presented that a PECVD double layer of 30 nm silicon-rich silicon oxynitride 共SiriON兲 capped with 70 nm silicon nitride 共SiNx兲 yields an excellent thermally stable surface passivation layer system for crystalline silicon. The surface passivation is activated by a high temperature step and can be further upgraded by intense illumination. SPV and CV measurements show a very high fixed charge density 共Q fix ⬎ 1.3⫻ 1013 cm−2兲 while the space charge density stays comparatively low 关Qsc = 共4.1⫾ 0.1兲 ⫻ 1011 cm−2兴. Thus in equilibrium the main part of the positive charges is balanced by interface trapped electrons. Paramagnetic electrons in shallow donor states could be detected using EPR with a Pauli-electron contribution, which could be estimated in the same order of magnitude as the measured fixed charge
NCurie S 共⫻1011 cm−2兲
NPauli S 共⫻1011 cm−2兲
4.2 2.2
¯ 1.5⫻ 102 eV−1 ⫻ E f ⬇ 102 – 103
density. This leads to the hypothesis, that those shallow donor states can be responsible for the detected positive fixed charge density by emitting their electrons. In thermal equilibrium most of the shallow donors are in the neutral state, leading to the comparatively low charge density concluded from the SPV and to the asymmetric paramagnetic resonance. The delocalized character of the electrons shows that an emission into the silicon will be easily possible. This emission is directly enforced by an applied negative voltage as it is used in the CV-measurement and activates the huge charge density detected here. Such states will most likely be formed by overcoordinated oxygen or nitrogen atoms in the amorphous silicon network of the SiriON. If fourfold nitrogen atoms 共N04兲 cause the paramagnetic resonance, a clear hyperfine interaction has to be detected, as the nitrogen nucleus 14N is paramagnetically active. Such a splitting has been previously confirmed, for example, at N04 centers in crystalline silicon.47 Therefore, if we suggest overcoordinated atoms as the origin of the observed states, the oxygen atoms have to be taken into consideration. It is assumed that oxygen impurities can act as donors in amorphous silicon,48,49 but the doping efficiency of oxygen is rather low. Recalling the huge number of fixed charges 共Q fix ⬎ 1.3⫻ 1013 cm−2兲 in the 30 nm SiriON layer, a density of overcoordinated oxygen atoms of 关O+3 兴 ⬎ 4 ⫻ 1018 cm−3 has to be achieved. As the concentration of oxygen and nitrogen atoms is approximately in the 10% region, an interaction between the nitrogen and the oxygen atoms in the amorphous network has to be taken into account. As is known from Czochralski grown silicon, oxygen–nitrogen complexes 共ONCs兲 can form shallow donor states.50 In the silicon crystal, an interstitial nitrogen 共Ni兲 and an interstitial oxygen atom 共Oi兲 can force a neighboring interstitial oxygen atom into a trivalent bonded configuration,51 see Fig. 13. A similar effect is calculated for
FIG. 13. Structure of the Ni – O2i-complex as described in Ref. 51 in the neutral state. In the positively charged state, the central silicon atom creates a bond with an oxygen atom.
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FIG. 14. Sketch of a possible band diagram of the SiriON/ SiNx double layer on p-type silicon. It is assumed that positive charges in the SiriON are not dangling bonds as in SiNx but originate in shallow donor states formed by oxygen-nitrogen-complexes 共ON兲. 52
nitrogen incorporated at a SiO2 / c-Si interface. Here the nitrogen atom enhances an oxygen atom in a threefold coordination, creating a state near the c-Si conduction band as well. The donors in Czochralski grown silicon can be detected by EPR, whereas because of the anisotropic situation, the crystal orientation has to be considered. Resonances for these Ni – O2i–complexes in different crystal orientations are determined in Ref. 50; g具100典 = 1.999 89, g具011典 = 1.999 52, and g具011¯ 典 = 1.997 98. These values cannot be compared precisely with the resonance detected here. To define the value of such a complex in an amorphous environment, an integration over the resonance spectra for the different orientations has to be performed. Moreover, the totally different atomic composition in the SiriON could shift the resonance field. The determined value g = 1.9998⫾ 0.0003 for the amorphous layer however, is in the range of the anisotropic values. Regarding the interactions between nitrogen and oxygen in c-Si and at the SiO2 / c-Si interface and the similar resonance field, it seems quite reasonable to assume similar ONCs in the SiriON. The SiriON therefore can be considered as a highly n-doped amorphous semiconducting layer. This situation is sketched in Fig. 14. The high density of donor states will lift the Fermi energy perhaps even to the mobility edge ECSiriON, and thus delocalized electrons can appear as detected with EPR. Mobile electrons will very easily be pushed in the silicon while applying a negative voltage. This will lead to the huge number of fixed positive charges measured by CV while without this voltage most of these electrons will stay in the SiriON, and the space charge will be comparatively low as calculated from the SPV. In this model, the behavior of the illuminated samples could be explained as well. In the equilibrium state, a comparatively low number of charges is activated in the SiriON, but inversion is still given.40 Only a very small density of holes is present at the surface. By illuminating the sample to high injection, a great number of holes will reach the surface. As most of the interface states will be filled with electrons from the SiriON, holes will very likely be trapped. Now there are two possibilities, as illustrated in Fig. 15; the hole
FIG. 15. Sketch of the interface situation under illumination. An interface captured hole can recombine with an electron from the SiriON 共a兲 or from the silicon 共b兲.
can recombine with a delocalized electron from the SiriON, resulting in a further positively charged shallow donor state in the SiriON, or it can recombine with an electron from the silicon, resulting in common surface recombination. A prolonged high injection condition at the surface will therefore lead to a charge piling in the SiriON, which means a decreasing probability for holes to reach the surface at all. It is not to assume that the total possible charge density of more than 1.3⫻ 1013 cm−2 will be activated by this process but depending on the defect density and the mobility in the SiriON layer and at the interface, a significant amount could be expected. The discharging has to appear by electrons penetrating from the silicon into the SiriON. It seems reasonable to assume an interface barrier for electrons between the silicon and the SiriON, as already included in Fig. 14. This barrier, in addition to the mobility of charge carriers in the SiriON, will be the limiting factors for the charge pile up and for the stability of the charges in the SiriON. The mobility is expected to be mainly influenced by the defect density in the SiriON and will be responsible for the probability of electron emission from the SiriON in the silicon. It can be assumed that, especially for the firing at 850 ° C, the defect density is increased because of hydrogen effusion or by breaking chemical bonds. This fits to the fact that these samples exhibit a higher surface recombination and no light induced improvement could be observed. The additional annealing could reduce the defect density, and therefore, a charge trapping effect could be possible, enhancing the field effect passivation, as is indicated by the lifetime measurement. The decrease in the effective lifetime after annealing the n-type sample could not be explained. Perhaps a discharging is enhanced here by an additional temperature step. Further work will be necessary to understand the particular annealing and illumination processes. So far this work tries to understand the passivation mechanism of the SiriON/ SiNx double-layer passivation by means of a field effect, which can explain the characteristic behavior caused by prolonged illumination. It is to be expected that the achieved high level of surface passivation is additionally caused by a chemical passivation of surface defects by hydrogen, as the SiriON layer is deposited with a
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high SiH4 gas fraction and therefore should exhibit a significant hydrogen content. This, however, shall be investigated in future work. VI. SUMMARY
A new excellent PECVD surface passivation layer system for crystalline silicon substrates has been introduced, consisting of an amorphous hydrogenated silicon nitride 共SiNx兲 and an amorphous hydrogenated SiriON. The passivation shows a salient thermal stability against a high temperature RTP adjusted on a contact firing process for silicon solar cells. It could be demonstrated that the surface passivation is based strongly on positive charges in the layer. The results from SPV, CV, and EPR measurement could be satisfactorily explained in a model including the creation of trivalent oxygen atoms in the layer, which can emit electrons in the silicon and therefore build up positive charges. ACKNOWLEDGMENTS
The authors gratefully acknowledge Dr. Lars Korte at the Helmholtz-Zentrum 共Berlin, Germany兲 for providing the SPV measurements and Tatiana Dimitrova at 4Dimensions 共Hayward, CA, USA兲 for the CV measurements. Their knowledge and availability allowed precise measurements on the samples presented in this work. J. Schmidt and A. G. Aberle, J. Appl. Phys. 85, 3626 共1999兲. J. Schmidt and M. Kerr, Sol. Energy Mater. Sol. Cells 65, 585 共2001兲. 3 S. De Wolf, G. Agostinelli, G. Beaucarne, and P. Vitanov, J. Appl. Phys. 97, 063303 共2005兲. 4 S. Dauwe, J. Schmidt, and R. Hezel, Proceedings of the 29th IEEE Photovoltaics Specialists Conference, New Orleans, Louisiana, USA, 20–24 May 2002, pp. 1246–1249. 5 I. Martín, M. Vetter, A. Orpella, J. Puigdollers, A. Cuevas, and R. Alcubilla, Appl. Phys. Lett. 79, 2199 共2001兲. 6 I. Martín, M. Vetter, A. Orpella, C. Voz, J. Puigdollers, and R. Alcubilla, Appl. Phys. Lett. 81, 4461 共2002兲. 7 M. Hofmann, C. Schmidt, N. Kohn, J. Rentsch, S. Glunz, and R. Preu, Prog. Photovoltaics 16, 509 共2008兲. 8 S. Gatz, H. Plagwitz, P. Altermatt, B. Terheiden, and R. Brendel, Appl. Phys. Lett. 93, 173502 共2008兲. 9 J. Seiffe, D. Suwito, L. Korte, M. Hofmann, S. Janz, J. Rentsch, and R. Preu, Proceedings of the 24th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, Germany, 21–25 Sept. 2009, pp. 1562– 1568. 10 G. Agostinelli, P. Choulat, H. F. W. Dekkers, E. Vermariën, and G. Beaucarne, Proceedings of the 4th World Conference on Photovoltaic Energy Conversion, Waikoloa, Hawaii, USA, 7–12 May 2006, pp. 1004–1008. 11 B. Hoex, J. J. H. Gielis, M. C. M. van de Sanden, and W. M. M. Kessels, J. Appl. Phys. 104, 113703 共2008兲. 12 P. Saint-Cast, D. Kania, M. Hofmann, J. Benick, J. Rentsch, and R. Preu, Appl. Phys. Lett. 95, 151502 共2009兲. 13 J. Seiffe, L. Weiss, M. Hofmann, L. Gautero, and J. Rentsch, Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, Spain, 1–5 Sept. 2008, pp. 1700–1703. 14 W. Mönch, Semiconductor Surfaces and Interfaces 共Springer-Verlag, Berlin Heidelberg, 2001兲. 15 J. G. Simmons and G. W. Taylor, Phys. Rev. B 4, 502 共1971兲. 16 W. Shockley and W. T. J. Read, Phys. Rev. 87, 835 共1952兲. 17 A. G. Aberle, Crystalline Silicon Solar Cells: Advanced Surface Passivation and Analysis of Crystalline Silicon Solar Cells 共University of New 1 2
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