Calorimetry of dehydrogenation and dangling-bond recombination in several hydrogenated amorphous silicon materials

P. Roura,1 J. Farjas,1 Chandana Rath,1,2 J. Serra-Miralles,1 E. Bertran,3 and P. Roca i Cabarrocas4 1GRMT, Department of Physics, University of Girona, Campus Montilivi, Edif.PII, E17071-Girona, Catalonia, Spain 2School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi, India 3FEMAN, Departament de Física Aplicada i Optica, Universitat de Barcelona, E08028, Barcelona, Catalonia, Spain 4LPICM (UMR 7647 CNRS) Ecole Polytechnique, 91128 Palaiseau Cedex, France Received 8 July 2005; published 13 February 2006


I. INTRODUCTION
Hydrogen plays a crucial role in the quality of amorphous silicon materials.It reduces the density of dangling bonds and the internal stress of the silicon network, which results in a narrowing of the band tails.These facts improve the electronic and optical properties of hydrogenated amorphous silicon ͑a-Si: H͒ with respect to pure amorphous material. 1 number of hydrogen states are known to exist at room temperature and are characterized both by the kind of bonding with the Si atoms and by their atomic environment: i.e., the monohydride ͑wSiH͒ may be isolated, clustered at the surfaces of internal voids, or form platelets in bulk.The most useful technique for the identification of the particular hydrogen states is infrared ͑IR͒ absorption spectroscopy. 2From their characteristic stretching and bending modes, the isolated monohydride ͑wSiH͒, the clustered monohydride ͓͑wSiH͒ n ͔, and the dihydride ͑vSiH 2 ͒ can be distinguished. 3,4Recently, a new vibrational mode has been identified and associated with H atoms located at the interfaces between silicon clusters or nanocrystals and the surrounding amorphous matrix. 5,6For the sake of completeness, we must say that molecular hydrogen located in internal voids 7 or individually trapped in bulk 8 has been detected by nuclear magnetic resonance.
0][11][12] When the material is heated at a constant rate, dehydrogenation peaks ͑proportional to the hydrogen desorption rate͒ appear at characteristic temperatures.From these experiments and provided that dehydrogenation is not diffusion controlled, the activation energy of Siu H bond breaking can be obtained.The most complete work devoted to this objective is that of Khait et al. 13 In their paper, the thermal activation of a lowtemperature peak ͑below 400 °C͒, characteristic of lowquality material, is analyzed.They obtain an activation energy of 1.9 eV, consistent with independent experiments on the desorption of hydrogen from the surface of monocrystalline silicon 14 and with theoretical calculations. 15This energy corresponds to the breaking of two neighboring SiH groups and the simultaneous formation of an H molecule.From this and other experimental evidence, it is known that this lowtemperature dehydrogenation process is usually associated with clustered SiH groups on the surface of internal voids. 16hen dehydrogenation is diffusion controlled, desorption experiments have proven useful for the analysis of the diffusion mechanisms of hydrogen in a-Si: H. 17,18 The results are of special interest when done on device-quality material, where most hydrogen is in the isolated monohydride or clustered states in bulk.In this case, there is broad agreement that hydrogen diffuses in atomic form 16,19 until it reaches the external surface where it is desorpted as molecular hydrogen.
During dehydrogenation, extensive bond breaking and new bond formation occur, resulting in a thermal signal from the heat evolved from the material.In contrast with hydrogen desorption experiments ͑where the signal is detected when the atoms leave the external surface of the material͒, in calorimetric experiments no delay exists between bond breaking and the thermal signal.So the kinetics of Siu H bond breaking and subsequent dangling-bond recombination can be studied directly.On the other hand, the enthalpy of the processes can be calculated from the heat exchanged and the total energy of the H states and dangling bonds can be deduced. 202][23][24] They were reviewed in Ref. 20.In that paper, we studied the dehydrogenation process occurring at the lowest temperature in a-Si: H nanoparticles and compared its kinetics with the results obtained from the desorption experiments reported for a-Si: H thin films by Khait et al. 13 Dangling-bond formation energy of 1.05 eV was obtained and the enthalpy of dehydrogenation was around 50 meV/͑H atoms͒ ͑exothermic͒.
The purpose of this paper is to extend our previous work 20 to thin films and to analyze all the dehydrogenation processes detected both by calorimetry and by desorption experiments.In addition to amorphous silicon nanoparticles, two kinds of device-quality films have been studied: a conventional amorphous silicon material and a so-called polymorphous silicon material.The interest in polymorphous silicon lies in its improved transport properties 25 and the lowest density of defects ever obtained in any amorphous silicon material, 26 allowing the fabrication of p-i-n photodiodes with very low dark-current densities. 27Even after light soaking, the density of defects remains lower than in conventional amorphous silicon, 25 which can produce enhanced photovoltaic conversion efficiency. 28The microstructure of polymorphous silicon consists of silicon clusters or nanocrystals embedded in an amorphous matrix 29 and is similar to other kinds of a-Si: H materials grown "on the edge of crystallinity." 30 Consequently, it can be considered as an intermediate state between silicon nanoparticles and conventional amorphous silicon.In fact, it shares the main SiH groups encountered in nanoparticles and those found in amorphous silicon. 31omparison of the three materials has allowed us to identify three particular SiH groups in addition to the main H state in the bulk of the amorphous Si network.Their bondbreaking kinetics has been characterized, and the enthalpy of all the dehydrogenation processes, the Siu H dissociation, and dangling-bond formation energies have been quantified.Finally, the dangling-bond recombination, which occurs after or during dehydrogenation, has been analyzed.

II. EXPERIMENT
A number of a-Si: H materials were grown by plasmaenhanced chemical vapor-deposition ͑PECVD͒.Amorphous silicon nanoparticles ͑np-Si: H͒ were obtained at room temperature from decomposition of pure silane.The usual growing conditions and structure are described elsewhere. 32Typical particle diameters are much smaller than 100 nm.They have a high hydrogen concentration ͑Ͼ30% ͒ and a residual amount of oxygen that is incorporated when the reaction chamber is opened to the air.The IR spectra in the bending region contain the 2000-2090 doublet 33 which is usually attributed to isolated monohydride ͑2000 cm −1 ͒ and vSiH 2 groups or ͑wSiu H͒ n on surfaces ͑2090 cm −1 ͒.The intense absorption band in the wagging region of the spectrum ͑845-910 cm −1 ͒ ͑Ref.33͒ indicates the existence of polymeric chains ͓͑SiH 2 ͒ n ͔.
In addition to the nanoparticles, two films were grown at 250 °C.One corresponds to a device-quality standard material ͑a-Si: H in the rest of the paper͒, while the other one is a special grade known as polymorphous silicon ͑pm-Si: H͒.The standard material contains most of the H atoms as isolated or clustered monohydride in bulk ͑wSiu H͒ whereas in pm-Si: H a detailed analysis of the IR stretching region reveals three states of hydrogen: 5 isolated and clustered monohydride in bulk ͑2000 cm −1 ͒, hydrogen on surfaces or vSiH 2 groups ͑2080 cm −1 ͒, and hydrogen on interfaces ͑2030 cm −1 ͒.The existence of this special state of hydrogen on interfaces results from the particular growing conditions of pm-Si: H.In this material, silicon clusters or nanoparticles are deposited together with SiH x radicals. 34Both films were deposited onto the walls of the reaction chamber for a very long time ͑deposition time Ϸ10 h͒.The thick deposit of about 10 m was then scratched from the walls and enough material ͑around 100 mg͒ was obtained for the experiments of calorimetry.
The chemical composition of all the samples is detailed in  details͒.Calorimetric experiments were carried out in a differential scanning calorimeter ͑DSC822e of Mettler Toledo͒ in an inert atmosphere of argon ͑impurities content Ͻ5 ppm͒.These experiments were programmed at various heating rates ͑10, 20, 40, and 80 K / min͒ up to 700 °C.The sample was then kept at a high temperature to ensure that, during a second heating ramp under the same conditions, no additional structural transformations would occur.This second thermogram was subtracted from the first one in order to correct it for the apparatus baseline.Due to the sensitivity of nanoparticles to low-temperature oxidation, 35 the sample mass was measured before and after the experiment.If after correction by the mass loss due to dehydrogenation a significant mass gain due to oxidation was detected, the thermogram was rejected.Despite this precaution, the contribution of any residual oxidation to the thermal signal cannot be discarded.Finally, in addition to the standard temperature calibration, the temperature axes have been corrected by the time delay of the apparatus related to the generation of the thermal signal ͑3 s͒.
The desorption experiments, henceforth referred to as "evolved gas analysis" ͑EGA͒, were performed in a vacuum furnace pumped down to 10 −6 Torr by a turbomolecular pump.The evolved hydrogen molecules were detected by a mass spectrometer whose signal was considered, as usual, 16 to be proportional to the evolution rate.The heating rate was kept constant at 10 or 40 K / min.

A. Evolved gas analysis
The EGA thermograms obtained at 10 K / min ͑Fig.1͒ show several dehydrogenation processes whose relative intensities depend on the material.All thermograms measured up to now on nanoparticles 20,32 contain a two-peak structure ͑A and B͒ with maxima below 500 °C ͑around 380 and 480 °C, respectively͒, the peak at the lowest temperature ͑A͒ always being more intense.For the standard material ͑a -Si: H͒, the thermogram is dominated by a high-temperature process centered at 580 °C ͑peak C͒ and a very weak process at 400 °C ͑AЈ͒ unlike those in the nanoparticles.͑At this point, this is a tentative asignment based on comparison with the thermogram of pm-Si: H.However, it will become clearer in Sec.IV A, notably with the diagram of Fig. 9.͒ In polymorphous silicon, the four processes detected in nanoparticles or in a-Si: H ͑A, AЈ, B, and C͒ make a contribution.In the corresponding thermogram, the first peak ͑A͒ is closed in brackets because, as opposed to the other processes, we do not have any independent proof for this assignation.When the experiments are done at 40 K / min, the minor contributions of the A, AЈ, and B processes are also detected for the a-Si: H sample ͑Fig.2͒.That is, all the dehydrogenation processes detected in pm-Si: H are also present in the standard material, although they are much less intense.The deconvolution of these EGA thermograms gives the amount of hydrogen atoms released by the material for each process which does not depend significantly on the heating rate ͑40 or 10 K / min͒.The mean values are detailed in Table I.

B. Differential scanning calorimetry
The shape of the DSC thermograms ͑Fig.3͒ is much more complex because, in addition to dehydrogenation, other structural transformations contribute to the thermal signal.In all samples, the DSC thermograms consist of several peaks superimposed on a continuous signal.In the whole temperature range, this signal is always exothermic.A similar continuous heat release was also detected in silicon materials amorphized by ionic implantation, 36 where it was interpreted as due to structural relaxation.Although the exact microscopic processes have not yet been clarified, 37 structural relaxation means that the progressive changes in the covalent network of silicon atoms lead to a more relaxed, less energetic, structure.From Fig. 3 it is clear that these relaxation processes are much more active in pm-Si: H than in a -Si: H below 500 °C.
Concerning the dehydrogenation of nanoparticles, the two-peak structure detected by EGA in the nanoparticles has its counterpart in the DSC thermogram.The main difference is that the DSC peaks appear at a lower temperature.This means that there is a significant delay between the processes of Siu H bond breaking and the rearrangement of bonds ͑responsible for the thermal signal͒ and the evolution of the hydrogen molecules at the outer surfaces of the sample ͑the EGA signal͒.
For polymorphous silicon, a very pronounced exothermic peak corresponding to the B-dehydrogenation process is detected.A weaker peak, related to the AЈ process, is less evident and can be identified because it appears at a very similar temperature in the DSC curve of the standard a-Si: H ͑Fig. 3͒.This coincidence is even clearer in the experiments done at 80 K / min ͑Fig.4͒.All these DSC peaks are "advanced" compared to their EGA counterparts.Concerning the hightemperature desorption process C, it makes a very low contribution to the DSC thermogram of polymorphous silicon that can only be identified after comparison with the a -Si: H thermogram.
For the standard material, peaks AЈ and B have been detected ͑Figs. 3 and 4͒.However, the most relevant feature in its DSC thermogram at 10 K / min is the high intense exothermic band beginning at 480 °C ͑Fig.3͒.This threshold is similar to that of the EGA signal, indicating that it is due to process C and that, for this particular process, no delay exists between hydrogen desorption and its thermal signal.
The heat released per gram of sample during each dehydrogenation process ͑Q i ͒ has been quantified from the peak areas and has been normalized ͑E i ͒ to the number of hydrogen atoms obtained from the EGA experiments.The results are summarized in Table I, where the values quoted are the average of the enthalpies obtained at several heating rates.The enthalpy of dehydrogenation per hydrogen atom is very low ͑Ͻ50 meV͒ for nanoparticles and polymorphous silicon, but much higher for the standard material.In fact, a-Si: H, E A Ј has an unrealistic value of about 5 eV.
In order to analyze the kinetics of dehydrogenation, DSC thermograms have been recorded at ␤ = 10, 20, 40, and 80 K / min.The peak temperatures ͑T M ͒ have been extracted after subtraction of the continuous signal due to structural relaxation.Typical results are shown in Fig. 5 ͑peak B of pm-Si: H͒ and Fig. 6 ͑peak B of np-Si: H͒.The dependence of peak temperatures on heating rate is collected in the Kissinger plots of Figs. 7 and 8 where the Y axis ͑␤ / T M 3 ͒ is chosen for further analysis ͑Sec.IV A͒.
For the A, AЈ, and B peaks, the relative variations of enthalpy among different heating rates can be as high as 50% of the maximum value ͑Fig.5͒.It is worth noting that, at the heating rates given in Fig. 5, the peaks are very reproducible and their areas can be quantified with an error bar of ±5%.So the differences among the enthalpies obtained at several heating rates and for different samples ͑Table I͒ are significant.
For completeness, we can say that no thermal signal corresponding to process A has been detected in the films and that the threshold appearing at 680 °C corresponds to crystallization. 31

A. Identification of the dehydrogenation processes
Up to now, the labels we have assigned to the dehydrogenation bands on the EGA and DSC thermograms ͑A, AЈ, B, and C͒ are tentative.In fact, this assignation relies on the order in which they appear as the temperature is raised.However, if their position does not coincide for different samples, one may wonder if the dehydrogenation processes are really the same.This is the case, for instance, for peak B in the DSC thermograms of nanoparticles and polymorphous silicon ͑Fig.3͒.On the other hand, in view of the similarity between these two thermograms below 500 °C, one might think that, in fact, peak AЈ in pm-Si: H should be labeled A, as in nanoparticles.Another important question is the correspondence of the processes we have detected with those already reported in the literature.In view that apart from the enthalpies obtained for the standard material ͑Table I͒ all the enthalpies are very similar, peak identification will rely on their thermal activation.In other words, in principle the position in one single thermogram ͑DSC or EGA͒ is not sufficient for the purpose of peak identification.One must measure, instead, how the peak shifts to higher temperature when the heating rate is increased.
If we compare the signal of the dehydrogenation processes measured at the same heating rate ͑10 K / min͒ by DSC ͑Fig.3͒ and EGA ͑Fig.1͒, we realize that, apart from process C, the peak positions are always shifted to higher temperatures in the EGA thermograms.For all peaks, the shift is larger than 50 °C.The thermal signal is measured at the time where the Siu H bond breaking and bond rearrangement occur whereas the hydrogen molecules are detected ͑EGA signal͒ when they reach the mass spectrometer.Consequently, the delay of the EGA signal with respect to the DSC signal indicates that once the Siu H bond is broken, the hydrogen atoms or molecules diffuse for a long while before they reach the external surfaces of the sample.In other words, the EGA thermograms measured in our experiments are diffusion controlled and their thermal activation cannot be used to extract the activation parameters of the Siu H bond-breaking processes.For this purpose, the DSC signal must be used instead.Peak identification will rely on the activation parameters thus deduced.
We take as reference the low-temperature desorption process already analyzed in a-Si: H films, 13,16 and we consider a first-order reaction kinetics where n i is the number of H atoms in a particular SiH group ͑i = A , AЈ , B͒ and K i is the rate constant.K i is thermally acti- vated with activation energy ⌬E i and a prefactor ͑K i ЈT͒, pro- portional to the thermal frequency 0 = kT / h, where h and k are the Planck and Boltzmann constants, respectively.That is, where ⌬S i is the activation entropy.⌬S i and ⌬E i can be obtained from the shift of the peaks to higher temperatures as the heating rate ␤ is increased.It can be shown that the peak temperature T M is related to the heating rate ␤ according to the formula ͑see the Appendix͒ ln ␤ which is more accurate than the formula used for the analysis of gas desorption from surfaces 38 because it takes into account that 0 depends on T.
The Kissinger plots of Figs. 7 and 8 allow determination of the ⌬S i and ⌬E i values, which have been collected in Table II.It is apparent that, for the same hydrogen state ͑A, AЈ, or B͒, ⌬E and ⌬S change considerably from sample to sample.According to Refs. 13 and 39, the barrier ⌬E can diminish by the transfer of energy from charge carriers located in the vicinity of the SiH group or by short-lived large energy fluctuations of single atoms 40 ͑kinetic compensation effect͒.These contributions result in variations of the entropic barrier.So a particular dehydrogenation process is not characterized by a single value of ⌬E, but by a set of ͑⌬E, ⌬S͒ values that must follow a linear relationship. 13In Fig. 9 we see that there is excellent agreement between our experimental points and theory.This constitutes a proof that the A peak corresponds to the same H state in all nanoparticles and that the B peak is the same state in all the samples.
Additionally, in Fig. 9 the activation parameters of the low-temperature process analyzed by Khait et al. 13 are plotted for a number of thin films.These films were deposited at low temperature, which resulted in a high density of interconnected voids.For this particular low-temperature process and films, Khait et al. 13 demonstrated that the EGA signal was not diffusion controlled so that their deduced activation parameters correspond to the reaction kinetics of Eq. ͑1͒ and their signature can be directly compared with those of peaks  41 analyzed the desorption peak in nanoparticles where the EGA signal was not diffusion controlled and the activation parameters could be obtained from the same procedure as Khait et al.The corresponding point ͑error bars smaller than the point itself͒ has been included in Fig. 9, and it perfectly agrees with the straight line that fits our results on nanoparticles.
Concerning the AЈ peak, only two points ͑one per thin film͒ can be plotted in Fig. 9. Their associated straight segments are, in fact, very elongated rhombs which are the loci of the ͑⌬E, ⌬S͒ values corresponding to an uncertainty of  ±1 °C in the peak temperature.In this particular Fig. 9 the usual representation of the error bars for the X and Y values is not correct because, according to the Appendix ͓Eq.͑A5͔͒ the constant term of the linear fitting depends on both ⌬E and ⌬S ͑through KЈ͒.The points of peak AЈ for the two thin films are closer to the signature of Khait et al. than that of peak A. So we think that peak AЈ in our films corresponds to the same H state and, consequently, that it is different from the A process detected in nanoparticles.This assignment is reinforced by the existence of the peak detected at the lowest temperature in our films ͑EGA thermograms of Figs. 1 and 2͒ which would correspond to peak A in nanoparticles.Unfortunately, the activation parameters of this process cannot be deduced because the corresponding thermal signal has not been detected and, consequently, the bond-breaking kinetics cannot be characterized.
Once it has been established that four different SiH groups are responsible for the peaks appearing in the EGA and DSC thermograms, one should try to identify their microscopic origin.Peak C has been extensively studied in the literature because it corresponds to the main SiH group in device-quality material.It comes from desorption of the isolated or clustered monohydride in bulk. 17,18The signature of peak AЈ ͑Fig.9͒ had been previously established, 13 because in the low-quality films studied by Beyer 16 the EGA signal was not diffusion controlled.According to Beyer, peak AЈ corresponds to SiH groups located on the surface of internal voids.In contrast with peaks AЈ and C, the kinetics of the dehydrogenation processes A and B has not been previously characterized.The main reason is that they are dominant in nanoparticles and polymorphous silicon, respectively, whereas they are almost absent in conventional films.The IR absorption spectra of nanoparticles contain a pronounced doublet at 840 and 910 cm −1 ͑Ref.42͒ related to polymeric ͑SiH 2 ͒ n groups. 43The high hydrogen fraction in this state is confirmed by the appearance of a 2140-cm −1 component in the stretching mode attributed to uSiH 3 groups, 44,45 which would terminate the polymer chains.So peak A corresponds to polymer chains.This assignation could not be previously stated 20 because, at that time, we were not able to obtain the characteristic signature for this process ͑Fig.9͒.Finally, peak B is the dominant process in pm-Si: H and it is characteristic of nanoparticles, too.This coincidence is not surprising in view of the particular nanostructure of polymorphous silicon which contains nanoparticles embedded in the amorphous matrix.Additionally, it gives a significant contribution to the EGA thermograms of hydrogenated nanocrystalline silicon. 5,46Other authors recorded EGA thermograms similar to that of the polymorphous sample in a-Si: H films deposited "on the edge of crystallinity" 6 which contain nanocrystals within the amorphous matrix, too.Although it is not possible to extract the kinetic parameters from their single EGA thermogram, its shape indicates that most of the hydrogen desorpted at low temperature is due to process B. Mahan et al. 6 concluded that "the vast majority of hydrogen is bonded on the surfaces of small crystallites."This assignation is further supported by molecular-dynamics simulations of hydrogen evolution from nanocrystalline silicon 47 which predict a low-temperature evolution peak at 250-400 °C ͑peak B͒ in addition to the usual peak of hydrogen in bulk ͑peak C͒.We conclude, then, that peak B corresponds to SiH groups at the interfaces between nanocrystals or silicon clusters and the surrounding amorphous matrix.
Before leaving this section, we should stress that the signatures of peaks A and B are similar to that of peak AЈ ͑the series of points from Khait et al. in Fig. 9͒.In fact, the signature of peak AЈ lies between the other two.So the mechanism of Siu H bond breaking should also be similar.In addition, Beyer demonstrated through isotope-labeling experiments 13 that the low-temperature desorption process in thin films proceeds with the simultaneous formation of a H 2 molecule during the dissociation of two neighboring SiH groups.We can thus assert that hydrogen molecules are formed during the dissociation of any of the low-temperature processes ͑A, AЈ, and B͒.This conclusion is reinforced by the values of the dehydrogenation enthalpy ͑see next section͒ and will be a key point for further analyses.

B. Enthalpy of dehydrogenation of the low-temperature processes
Although DSC is the most suitable technique for measuring the enthalpy of structural transformations in amorphous silicon, it has been applied to a very limited extent and, concerning dehydrogenation, the results have been very poor.According to the experiments of Battezzati et al., 21 the sensitivity of the DSC measuring cell can be greatly perturbed during dehydrogenation due to the high thermal conductivity of the evolved H 2 .This effect, which would explain the erroneous endothermic signals initially detected on a-Si: H films, 24,48 depends on the physical construction of the DSC and has been shown to be negligible in our apparatus. 20An additional verification has been done with the polymorphous sample, which was measured in another laboratory and gave identical results. 49n Table I, the averaged values of the dehydrogenation enthalpies are collected.It is clear that dehydrogenation in amorphous silicon materials is an exothermic process.In fact, apart from the conventional thin film, the enthalpy is very low ͓Ͻ50 meV/͑H atoms͔͒ and it should be said that dehydrogenation is an isenthalpic process; i.e., the enthalpies of the initial and final states almost coincide.
Our results can be compared with several theoretical calculations of the energetics of various SiH groups 15,50 from which the dehydrogenation energy can be obtained if one assumes complete dangling-bond recombination and that hydrogen atoms recombine into a molecule.From the calculations of Allan et al. 15 on a-Si: H, slight endothermic energies of −͑0.10-0.14͒eV/͑H atoms͒ for the dehydrogenation of monohydride, dihydride, and neighboring SiH groups are obtained.From those of Fedders, 50 we obtain −0.21 eV/͑H at-oms͒ for weakly bonded hydrogen in clusters ͑from the analysis of Sec.IV F, it can be shown that the dehydrogenation energies at 0 K are almost equal to the corresponding enthalpies at the dehydrogenation temperature͒.These theoretical values agree with our results in the sense that they are close to zero too, when compared with the large energies needed for breaking and forming the individual bonds ͓for instance, 2.26 eV/͑H atoms͒ for a H 2 molecule͔.We should emphasize, however, that whereas experiments prove that dehydrogenation is exothermic for any of the processes detected, calculations predict endothermic enthalpies.The absolute discrepancies of around 0.2 eV would indicate the reliability of the present theoretical models for predicting the individual energies involved in dehydrogenation.
From this comparison with theoretical predictions ͑in particular, from the approximate agreement of the enthalpy values and from the fact that the experimental enthalpy is even more exothermic than expected͒, we can conclude that, after dehydrogenation, a high percentage of the dangling bonds left behind by hydrogen atoms recombine.This conclusion agrees with the measurement of post-hydrogenation levels of dangling bonds. 12,51The highest level reported is two orders of magnitude lower than the initial concentration of hydrogen. 51Our results give additional evidence of a high level of dangling-bond recombination.If a significant fraction of them survived, then one would expect dependence of the enthalpy on the material microstructure or on the particular SiH groups being dissociated.The very small absolute differences in the enthalpies of several tens of meV among samples ͑except for a-Si: H͒ and among dehydrogenation processes ͑Table I͒ exclude this possibility.
Within this context, the variations of enthalpy from sample to sample for the same SiH group should be analyzed.In the case of nanoparticles, one possible explanation could be the contribution of the low-temperature oxidation process previously reported. 35Although special care has been taken, a minor oxidation level could affect the measured enthalpy, owing to its highly exothermic character ͓9.32 eV/͑Si atoms͒ ͑Ref.52͔͒.However, this explanation can be excluded for the enthalpy variations observed in pm -Si: H at different heating rates ͑Fig.5͒ because, due to their compact microstructure, oxygen atoms cannot react with the dangling bonds that hydrogen atoms leave behind, far from the external surfaces of the sample ͑sample thickness around 10 m͒.The enthalpy difference of 31 meV between the B peaks measured at 10 and 40 K / min in pm-Si: H ͑Fig. 5͒ could be accounted for by a small difference of around 3% in the level of dangling-bond recombination ͓we take a dangling-bond recombination energy of 1.05 eV ͑Ref.20͔͒.However, another explanation is possible.The high level of dangling-bond recombination deduced from the value of the enthalpy requires that these defects move through the silicon covalent network.On their way, a degree of bond rearrangement is possible, leading to a diminution of the elastic energy stored in the strained bonds.In other words, dangling-bond recombination will promote a ͑limited͒ degree of lattice relaxation, which would release less than 30 meV/͑H atoms͒.
In summary, we can say that, from the values of the dehydrogenation enthalpy of peaks A, AЈ, and B, the state after the bond-breaking and rearrangement processes responsible for the thermal signal ͑i.e., the state just after the DSC peak͒ is a H 2 molecule and a reconstructed silicon network with most dangling bonds recombined and with lower elastic energy.Thus, the measured enthalpy is the result of a number of contributions: where E͑H u H͒ T is the dissociation enthalpy of hydrogen, E i ͑Siu H͒ T is the dissociation enthalpy of the Siu H bond, and E͑DB͒ is the dangling-bond recombination energy.All these quantities are positive and are given at the temperature T of the DSC peak.E relax is a minor contribution due to lattice relaxation, and from the analysis, it is clear that coefficient is close to 1.
Before passing to the next section, we should emphasize that in a-Si: H materials most dangling bonds recombine after Siu H bond breaking.This is in contrast with the hydrogen desorption process from the surfaces of crystalline silicon, where the dangling bonds survive. 53This difference is not currently appreciated and has led to the consideration that dehydrogenation in amorphous silicon is also an endothermic process. 48The eventual measurement of exothermic peaks would be related to the "relaxation" ͑including dangling-bond recombination͒ of the silicon network after dehydrogenation.Given that extensive and rapid ͑see Sec.V G͒ dangling-bond recombination occurs after Siu H bond breaking, we consider that it is more adequate to say that dehydrogenation in amorphous silicon is a slightly exothermic process.

C. H 2 trapped in conventional a-Si: H and the real values of n HA Ј and n HB
The analysis of the previous section is valid for the lowtemperature desorption processes ͑A, AЈ, and B͒ in all samples except for the conventional material.In the a-Si: H sample, an unrealistic enthalpy of 5 eV is obtained for peak AЈ and a high value of 760 meV is deduced for peak B ͑Table I͒.In fact, the heat exchanged per unit mass ͑Q i ͒ is quite low and high enthalpies result because the amount of H atoms detected by EGA for the AЈ and B processes are very low ͑n H / n Si =10 −4 and 10 −3 , respectively͒.
The simplest explanation of this discrepancy is that most of the H 2 molecules resulting from the AЈ and B processes remain trapped in internal voids and cannot escape to ͑or be detected at͒ the external sample's surface.In other words, the values of n A Ј and n B for the a-Si: H sample quoted in Table I underestimate the real concentration of these H states in the material and, consequently, the deduced enthalpy per H atom results in being unusually large.According to this interpretation, it is possible to obtain the real concentration of the AЈ and B SiH groups in the conventional material by simply taking the enthalpy of peaks AЈ and B of the polymorphous sample as reference ͑E A Ј Ϸ E B Ϸ 50 meV͒.The result is n H / n Si =1ϫ 10 −2 and 1.5ϫ 10 −2 for the AЈ and B peaks, respectively.Although this concentration is small compared with the total hydrogen content of the conventional sample ͑12ϫ 10 −2 ͒, it indicates that a significant fraction ͑around 20%͒ of the hydrogen atoms reside on the surface of internal voids and on interfaces.Finally, note that the real values of n A Ј and n B are much larger than those reported in Table I ͑obtained from EGA͒, which reveals that around 99% and 95% of the atoms released after dissociation of the AЈ and B SiH groups remain trapped in the a-Si: H sample, respectively.
The presence of hydrogen molecules in the internal voids of amorphous silicon can be detected by NMR. 7 Their concentration was measured after isothermal annealing, and it was shown to increase at the temperatures where the main SiH groups began to dissociate. 54However, one cannot say properly that, in those experiments, the H 2 molecules were effectively trapped.Their detection could simply indicate the delay between SiH dissociation and hydrogen evolution which is evident in our experiments from the delay between the DSC and EGA peaks.
In contrast with the conventional material, the similarity between the value of the enthalpy of peak B and those obtained in nanoparticles indicate that in polymorphous silicon the H 2 molecules do not become trapped.So in its microstructure there are paths for the easy transport of molecular hydrogen to the external surface.

D. State of hydrogen after SiA H bond breaking: Diffusion of H 2 molecules
Up to now, we have assumed that, for the low-temperature desorption peaks, the bond-breaking and rearranging processes leading to the thermal signal result in the formation of a H 2 molecule ͓Eq.͑4͔͒.The main evidence comes from the similarity between the ͑⌬E , ⌬S͒ signatures of the A and B peaks with that of the thin films characterized by Khait et al. 13 ͑Fig.9 and Sec.IV A͒.Additionally, the experimental enthalpies have been compared with theoretical predictions by assuming that, just after the DSC peak, the energy of H 2 is that of the molecule in vacuum ͑Sec.IV B͒.Of course, this is always the energy of hydrogen once outside the material; however, a long time ͑several minutes͒ elapses between the SiH dissociation ͑DSC peaks͒ and the detection of the H 2 molecules ͑EGA peaks͒.So one may wonder whether the energy of the H 2 molecule inside the sample is similar or not to that of H 2 in vacuum ͓i.e., if E͑H u H͒ T in Eq. ͑4͒ is the dissociation energy with all species in vacuum͔.In fact, the high dielectric constant of silicon would raise the energy of a H 2 molecule with respect to vacuum.First-principles calculations give an increment of 0.39 eV per H atom for crystalline silicon. 55If in our experiments the H 2 molecules had this energy before leaving the sample, then heat would be released at the moment where the molecules leave the sample ͑just when they are detected͒.So an additional highly exothermic peak should be detected with a peak shape similar to that of the EGA signal ͑dashed curve in Fig. 5͒.This signal would be around 10 times higher than the DSC peak actually detected during SiH dissociation and would mask it.From the actual shape of the DSC thermograms, it is clear that the energy of the H 2 molecule does not change significantly when it evolves from the sample's external surface.
An independent proof can be obtained from previous experiments on Si nanoparticles. 20In that case, no delay was observed between the DSC and EGA signals for peak A and, consequently, the hydrogen state after the DSC peak is the H 2 molecule in vacuum.So one would expect that the difference in the energies between the H 2 molecule in vacuum and any intermediate state would increase the measured enthalpy with respect to the values reported in Table I.This is not the case: a similar enthalpy of 50 meV was obtained.We can thus conclude that there is not an intermediate state of the H 2 molecule before it leaves the sample.The hydrogen formed after dissociation of the A, AЈ, and B SiH groups diffuses towards the sample surface in a molecular form that cannot be distinguished from that in a vacuum.It is transported along diffusion paths that are open in silicon nanoparticles and polymorphous silicon but are not open in the conventional device-quality material.The dehydrogenation experiments done on films deposited "on the edge of crystallinity" 6 lead one to propound that H 2 out-diffusion to the sample surface ͑peak B͒ could proceed along grain boundaries created by an incipient low-temperature grain growth of the nanocrystallites.Although appealing, this explanation should be carefully complemented by independent crystallization experiments.However, our own experiments on pm-Si: H indicate that, at the usual heating rates of the EGA thermograms ͑Ͼ10 K / min͒, its crystallization kinetics is identical to that of conventional a-Si: H films 31,56 and no incipient crystallization related to the nanocrystals of its structure is detected.
As far as we know, our results constitute the first experimental evidence of a dominating diffusion mechanism of H in molecular form through the bulk of a device-quality amorphous silicon material ͑such as polymorphous silicon͒.Previous evidence of transport of H 2 in amorphous silicon was reported for low-quality thin-film materials, 16 where the microstructure contained a large amount of interconnected voids.In contrast, polymorphous silicon is a much denser material with a void volume fraction lower than 1%. 57

E. SiA H dissociation energy
In Sec.IV B it has become clear which are the initial and final states before and after the bond-breaking and rearranging processes and which are the individual contributions to the enthalpy of dehydrogenation ͓Eq.͑14͔͒.Apart from the minor contribution of the relaxation processes ͓E relax Ͻ 30 meV/͑H atoms͒, Sec.IV B͔, Eq. ͑4͒ contains two unknowns: the dangling-bond formation energy ͓E͑DB͔͒ and the dissociation energy of the Siu H bond ͓E i ͑Siu H͔͒.We need, thus, an independent equation to determine these energies.E i ͑Siu H͒ can be obtained from the analysis of the dehydrogenation kinetics.
Although in the past some doubts have arisen concerning the mechanism of dehydrogenation from surfaces of crystalline silicon ͑c-Si͒, 53 nowadays it is commonly agreed that it proceeds through the simultaneous formation of a H 2 molecule when two neighboring Siu H groups dissociate: where Si• means a dangling bond.Recent quantum-chemistry calculations have analyzed the desorption processes from Si͑100͒ surfaces and predicted energy barriers ͑Ϸ2.6 eV͒ as well as reaction orders that agree with experiment. 58The interpretation of the energy barrier is simply the energy balance of step 1-that is,

͑5͒
where E͑Siu H͒ 0 and E͑H u H͒ 0 correspond to the transitions between the lowest-energy states of the initial and final species involved in the bond-breaking processes ͑i.e., they are the dissociation energies at 0 K͒ and accounts for any additional energy barrier between the activated state and the H 2 molecule ͑Fig.10͒.From the formation enthalpy of a H atom at room temperature and the enthalpy variations down to 0 K, 52 the value of E͑H u H͒ 0 can be obtained ͑4.476 eV͒.Consequently, the activation energy of hydrogen desorption, E ͑step 1͒, allows the quantification of E͑Siu H͒ 0 .
For dehydrogenation of SiH groups located at the surfaces of internal voids in amorphous silicon thin films ͑process AЈ͒, the same mechanism was proposed. 16In this case, the lower activation energy of 1.90 eV was tentatively explained as arising from dihydride groups.This proposal agrees with theoretical calculations 15 indicating a lowering of the energy barrier when the H 2 molecule is formed.Within this model, the dissociation energy of the SiH group of process AЈ was determined from EGA experiments. 13,16An additional complication that arises when dealing with a-Si: H materials is the fact that the energy barrier cannot be directly identified with the activation energy of the thermograms.As we have already commented in Sec.IV A and illustrated in Fig. 9, every SiH desorption process is characterized by a straight line relating the activation energies ͑⌬E͒ with the activation entropies ͑⌬S͒ measured for several samples.According to the interpretation given for process AЈ, 13 the energy barrier corresponds to the activation energy when ⌬S = 0, because, in this particular situation, no extra energy is provided by carriers to help in the bond-breaking process.This condition delivers E͑step 1͒ = 1.91 eV for process AЈ.The similar relationship between ⌬E and ⌬S observed for processes A and B ͑Fig. 9͒ leads us to conclude that the same mechanism of dehydrogenation applies and the values E͑step 1͒ = 1.80 eV and 2.09 eV are obtained for processes A and B, respectively.Finally, application of Eq. ͑5͒ with E͑H u H͒ 0 = 4.476 eV allows determination of the various Siu H dissociation energies: E͑Siu H͒ 0 = 3.14 eV ͑process A͒, 3.19 eV ͑AЈ͒, and 3.28 eV ͑B͒ ͑Table III͒ which must be considered as upper bounds to the actual values because the additional barrier has been neglected.
Since the mechanism of dehydrogenation involves the simultaneous formation of a H 2 molecule, E͑Siu H͒ 0 is, in fact, half the energy needed to dissociate a pair of neighboring SiH groups.The first-principles calculations of Allan et al. 15 on a-Si: H ͑Table IV͒ reveal that the dissociation energy of the first hydrogen atom is considerably higher than that of the second atom ͑Fig.11͒.Their average of 3.27 eV is very close to our experimental values, which would indicate that is small compared to the activation energy E ͑step 1͒.To confirm that this approximation is correct, theoretical calculations of the reaction paths leading to Siu H bond breaking and H 2 formation would be necessary.These kinds of analyses are very computationally intensive, which explains why, at present, theoretical predictions of are not available.Finally, our dissociation energies are also similar to the energy needed to break the first two Siu H bonds of a silane molecule, 3.27 eV per bond ͑see Fig. 11͒. 59efore finishing this section, we must say that moleculardynamics simulations of the dehydrogenation process from nanocrystalline silicon ͑process B͒ ͑Ref.47͒ predict the formation of H 2 molecules.However, they do not make clear whether the molecules are formed simultaneously with the breaking of the Siu H groups. From the characteristic signature of Fig. 9 we conclude that this is clearly the case.

F. Dangling-bond formation energy
Once the Siu H dissociation energy has been obtained, Eq. ͑4͒ allows us to determine the energy released when a pair of dangling bonds recombines ͓2E͑DB͔͒.This process is  just the inverse of the dangling-bond creation.So 2E͑DB͒ can be interpreted as the energy needed for the creation of a pair of dangling bonds.If we neglect the contribution of the Si network relaxation ͑E relax ͒ and consider that all dangling bonds created after the dissociation of the SiH groups recombine ͑ =1͒ ͑Sec.IV B͒ the calculation through application of Eq. ͑4͒ is straightforward.
For the dehydrogenation enthalpy we take the average value of all samples, excluding the conventional a-Si: H film.The dissociation enthalpies of the SiH groups and H 2 molecule at the dehydrogenation temperature can be calculated from their values at 0 K plus the contribution of "thermal" energies ͑vibrational and kinetic͒.Up to 800 K, the H 2 dissociation enthalpy is given within an accuracy of 1 meV ͑Ref.52͒ by the formula where 3 2 kT is of the order of 80-100 meV in the temperature range of interest ͑300-500 °C͒.Concerning the Siu H bond, its dissociation enthalpy at finite temperature increases with respect to the 0 K value, too, because the vibrational energy of the Siu H bond, ⌬U͑vib͒ T , is lower than the enthalpy increment of the H atom ͑ 5 2 kT ͒ : The vibrational energy is given by the Einstein theory of specific heat: 60 where the summation extends over the vibrational modes of frequencies with degeneracy g .Since no significant differences exist among different SiH groups, 55 the calculation of ⌬U͑vib͒ T will be done for the SiH group on a Si͑111͒ surface.It has a nondegenerate stretching mode at 2080 cm −1 and a doubly degenerate wagging mode at 630 cm −1 .The overall "thermal" contribution to the Siu H dissociation enthalpy is also 80-100 meV, in the temperature range of interest.Now, the introduction of the dissociation and dehydrogenation enthalpies in Eq. ͑4͒ delivers E͑DB͒ = 0.97, 1.05, and 1.12 eV for the dangling bonds created during processes A, AЈ, and B, respectively ͑Table III͒.͓Our previous determination for peak A in nanoparticles of ͑1.04 eV͒ ͑Ref.20͒ was  less accurate because, at that time, we were not able to build the signature of this particular process for nanoparticles and considered that it was the same as the AЈ process in thin films.͔Similarly to the case of the SiH energy ͑Sec.IV E͒, the actual value of E͑DB͒ is, in fact, lower by / 2 than the quoted values.However, in the absence of any theoretical or experimental estimation of , we consider it to be negligible.
Let us pay attention to the dependence of E͑DB͒ on the particular SiH group.The hydrogen in polymeric chains ͑peak A͒ corresponds to a less-confined state than hydrogen on the surfaces of internal voids ͑peak AЈ͒.Presumably, the degree of confinement is even higher for peak B because its kinetics has always been found to be diffusion controlled. 20,41Our results indicate, thus, that the danglingbond energy is higher when it becomes more confined.This means that one would expect a formation energy for an isolated dangling bond in bulk ͑peak C͒ higher than 1.10 eV.This conclusion is useful because calculations 15,61,62 try to simulate this particular dangling-bond defect.In addition, this is the kind of dangling bond that presumably accounts for the defect density in device-quality materials. 63 number of theoretical works devoted to predicting the formation energy of a dangling bond have been published ͑Table IV͒.They provide a very disperse set of values ranging from 0.6 to 1.2 eV.The first attempt was made by Allan et al., 15 whose values of 0.9 and 1.0 eV for neighboring dangling bonds and 1.2 eV for isolated dangling bonds agree reasonably well with our experimental results ͑0.97-1.12 and Ͼ1.10 eV, respectively͒.Furthermore, they provide additional support for the dependence of the dangling-bond energy with the degree of confinement.In contrast, a much smaller value of 0.6 eV was obtained by Kelires and Tersoff 62 for the three coordinated atoms that form in a-Si after rapid quenching from the liquid state.In this case, the reliability can be judged from the fact that the same authors obtained an energy of 1.1 eV when using an alternative interaction potential. 62On the other hand, the calculations of van de Walle 55 for crystalline silicon delivered 1.38 and 1.46 eV for the isolated dangling bond in bulk or on a Si͑111͒ surface, respectively.Following the author's opinion, 61 these values are unphysically large for a-Si and would be incompatible with results of hydrogen diffusion.Although our values do diminish, they are not as low as expected, 61 thus providing an additional constraint to the current models of hydrogen diffusion.
From other theoretical calculations we can extract straightforward predictions of the dangling-bond energy in bulk.First, a number of authors have calculated the formation energy of a vacancy in crystalline silicon 64,65 and obtained values ranging from 3.6 to 5.0 eV, which correspond to 0.9-1.25 eV per DB of the vacancy.Second, from realistic a-Si: H supercells, Fedders 50 has obtained E͑Siu H͒ 0 = 3.30 and 3.58 eV/͑H atoms͒ for isolated and strongly bonded clustered Siu H groups in bulk.Application of Eq. ͑4͒ with a dehydrogenation enthalpy ͑exothermic͒ of 40 meV/͑H atoms͒ ͑see Sec.IV H͒ delivers E͑DB͒Ϸ1.10 and 1.37 eV, respectively ͑Table IV͒.
From the experimental point of view, the only estimation of the dangling-bond formation energy comes from the analysis of the density of dangling bonds in a-Si: H. 63 In the classic paper by Smith and Wagner, 63 the authors use a value of 0.85 eV to fit the density of defects.Our prediction for the isolated dangling bond is clearly higher ͑Ͼ1.10 eV͒.We think that our value is more reliable for several reasons.First, the predicted defect density in equilibrium at the growth temperature depends critically on the particular microscopic model of defect reaction with hydrogen atoms leading to dangling-bond creation and annihilation. 66So the particular model used by Smith and Wagner may not be the main one.Second, in their particular analysis, they identify the formation energy of a dangling bond with the energy needed to promote an electron from the valence band to the empty acceptor level.This identification is clearly an approximation because it neglects the effect that a change of the charge state has on the energy of the core electrons of the threefoldcoordinated silicon atom.
Finally, the values we have obtained should be compared to the energy of formation of monatomic Si gas ͓1.16 eV/͑Si atoms͔͒. 52

G. High-temperature dehydrogenation of SiH groups in bulk
In both pm-Si: H and a-Si: H samples, a dehydrogenation process occurs above 500 °C ͑process C, Fig. 1͒.It corresponds to SiH groups in the bulk of the silicon network, and its kinetics is controlled by H diffusion.In fact, for thin enough samples 17 the activation energy of the EGA peak is just that of the H diffusivity.Following the most widely accepted model of H diffusion in a-Si: H, 4,67 H atoms are transported between lattice sites where they become trapped and released.This means that SiH groups in bulk are continuously created and dissociated until the H atoms reach the sample's surface where H 2 molecules are formed by a surface desorption process similar to those occurring at lower temperature.This picture implies that, in contrast with the low-temperature processes, for process C there is not a single SiH dissociation step and, consequently, the method used in Sec.IV E for determining the Siu H dissociation energy from the DSC curve cannot be applied.Unfortunately, our measurements do not allow us to determine this quantity.
The rest of this section will be devoted to analyzing the values of the enthalpy ͑E C in Table I͒.For the polymorphous sample E C ͓Ϸ40 meV/͑H atoms͔͒ is similar to the enthalpies of the low-temperature processes.However, this value is much higher ͓E C Ϸ 700 meV/͑H atoms͔͒ for the conventional amorphous sample.This apparent discrepancy can be explained by a structural relaxation.
The contribution of relaxation phenomena to the enthalpy of the low-temperature processes has been already discussed in Sec.IV B. We argued there that for those particular SiH groups, the corresponding term, E relax in Eq. ͑4͒, was small and that it could explain the variations of several tens of meV from sample to sample and for different heating rates.Additionally, we can say that, after Siu H bond breaking, little relaxation occurs due to the transport of molecular hydrogen because, as discussed in Sec.IV D, the interaction of the H 2 molecule with the silicon network is negligible.The situation is very different for peak C because hydrogen diffuses in atomic form.In his way, Siu H bonds are continu-ously broken and created, thus favoring relaxation phenomena such as anihilation of strained Siu Si bonds.
Within this framework, the amount of energy released per unit time due to relaxation will depend on ͑a͒ the random walk displacements of the H atoms through the Si network and ͑b͒ the particular state of the Si network at the beginning of process C. Thus, the random walk of H atoms has two effects: a release of energy and the diffusion of H atoms to the surface.This fact explains why the thermal and EGA signals of peak C are detected at the same temperature range ͑compare the curves of a-Si in Figs. 1 and 3͒.On the other hand, the state of the silicon network explains why process C is much more exothermic in conventional material than in polymorphous Si.Two facts can justify a higher relaxation in the conventional material: ͑1͒ structural analyses have revealed that, in the as-grown state, polymorphous silicon is a more relaxed material 29 and ͑2͒ from the DSC thermograms of Fig. 3, it is clear that the pm-Si: H sample has experienced a higher relaxation during the heating ramp up to 500 °C.Consequently, the a-Si: H sample reaches the onset of hightemperature dehydrogenation with a higher amount of energy stored in the Si network.We consider, then, that the enthalpy obtained from the polymorphous sample is close to the energy of the SiH groups in bulk whereas the difference with the enthalpy of the a-Si: H sample ͓Ϸ650 meV/͑H atoms͔͒ is due to lattice relaxation.This interpretation is reinforced by the fact that at a heating rate of 40 K / min the pronounced exothermic band in a-Si: H disappears. 31 In other words, the difference observed in Fig. 3 between pm-Si: H and a-Si: H is not due to different SiH groups in bulk but to the contribution of relaxation processes.
The heat released in a-Si: H during process C gives strong evidence that extensive relaxation occurs due to the movement of H atoms.This relationship was deduced in a more indirect way from the evolution of the H diffusivity 68 or material density 69 during long annealing times.Comparison of our EGA and DSC curves for a-Si: H sample ͑Figs. 1 and 3͒ indicates that relaxation occurs simultaneously with the dehydrogenation process C. It does not require long periods of thermal annealing.
Finally, let us note that the heat released per H atom is very high: 700 meV/͑H atoms͒ is more than one-half of the dangling-bond formation energy.When H transport proceeds, the network topology changes and evolves towards a less-strained configuration.In particular, a significant diminution of the density of weak Siu Si bonds will occur and, after release of the H atoms trapped in the deeper levels, recombination of isolated dangling bonds is expected.Both weak bonds and dangling bonds act as traps for H. 4 Given our results, it is doubtful to assume that the density of traps remains unchanged during H diffusion. 18,67 In fact, the assumption of constant trap density relies on very particular experiments 4 where samples were annealed ͑and thus re-laxed͒ before post-hydrogenation experiments.Under these conditions the Si network is presumably much more stable than in most diffusion experiments carried out on as-grown films. 17,18,70 CONCLUSIONS Application of differential scanning calorimetry to the analysis of dehydrogenation processes in amorphous silicon materials affords new information ͑the thermal signal͒ that cannot be obtained by the vast number of techniques that are currently used to elucidate the microscopic processes involved ͑a summary of the main numerical results is given in Table III which can be compared with the theoretical predictions collected in Table IV͒.In addition to the direct quantification of the enthalpy, the heat exchanged, as well as its thermal activation, allows determination of the energies related to elementary bond-breaking ͑Siu H dissociation͒ and rearranging processes ͑dangling-bond recombination͒.Secondary effects induced by dehydrogenation such as lattice relaxation can also be easily detected on time scales much shorter than the experiments already reported in the literature.The lack of any delay between bond breaking and the thermal signal makes it possible to identify the various dehydrogenation processes and their correspondence among different materials.This correspondence has usually remained doubtful when based on the temperature of the H-evolution bands detected by mass spectrometry.
These possibilities have been extensively explored in the present paper, which constitutes a very complete calorimetric study of hydrogenated amorphous silicon.We hope that our contribution will promote future applications of calorimetry to the analysis of other structural transformations in this material.
Note added in proof.Recent experiments of dehydrogenation at room temperature induced by light soaking 71 reinforce the interpretation of molecular diffusion in pm-Si: H and even in a-Si: H after the bond breaking of the A, AЈ, and B Siu H groups. Once the light is turned off, hydrogen continues to evolve from the sample during a long period of time ͑several tens of minutes͒.If hydrogen diffused in atomic form, without photons no energy would be available to break its bond to the Si atoms and it would remain trapped inside the sample.Furthermore, the diffusivity at room temperature ͑Ͼ5 ϫ 10 −14 cm 2 /s͒ is, at least, five orders of magnitude higher than the upper bound of the atomic diffusivity values, 4 indicating that the transport mechanism is different.

APPENDIX: THERMAL ACTIVATION OF THE PEAK TEMPERATURE FOR FIRST-ORDER KINETICS
Consider that the kinetic constant K is thermally activated with an activation energy ⌬E and proportional to the absolute temperature T through the attempt frequency kT / h: where KЈ is temperature independent.For first-order kinetics, the transformation rate will be given by r͑t͒ ϵ where n is the untransformed fraction.During a heating ramp at constant rate ␤ ϵ dT / dt, the transformation rate will pass through a maximum value at the peak temperature T M .Derivation of r allows the determination of T M : which allows determination of the activation energy ⌬E and the temperature-independent preexponential constant KЈ from a Kissinger plot ͓ln͑␤ / T 3 ͒ vs 1000/ T͔.

FIG. 1 .
FIG.1.Gas-evolved analysis ͑EGA͒ thermograms measured at 10 K / min for the two films and one of the nanoparticles.

FIG. 3 .
FIG. 3. Differential scanning calorimetry ͑DSC͒ thermograms measured at 10 K / min for the two films and one of the nanoparticles.

FIG. 6 .
FIG. 6. Thermal activation of the DSC band related to process B in one of the nanoparticles.

A
and B. From Fig. 9 it is clear that the signature of the points of Khait et al. is different.One could think that the shift of the points of Khait et al. with respect, for instance, to the signature of peak A is due to the different fitting methods used to obtain ⌬E and ⌬S ͑Khait et al. obtained them from the shape of the EGA peak͒.We can discard this objection because Costa et al.

FIG. 9 .
FIG. 9. Signature relating the activation entropies ͑⌬S͒ and enthalpies ͑⌬E͒ for the low-temperature dehydrogenation processes obtained from the thermal activation of the DSC peaks ͑Figs.7 and 8͒.The straight segments around points AЈ of our thin films represent the uncertainty in their value.The procedure followed to obtain ͑⌬S, ⌬E͒ for the points of Costa et al. and Khait et al. was different ͑see text͒.Note the change of axes used to represent the highest points.

FIG. 10 .
FIG. 10.Energy diagram showing the two-step reaction kinetics used to interpret the dehydrogenation processes at low temperature.From the activation energy E ͑step 1͒ ͑deduced from the signature of Fig. 9͒ and the enthalpy of the particular process, E i ͑area of the DSC peak͒, it is possible to obtain the dangling-bond formation energy ͓E͑DB͔͒.

FIG. 11 .
FIG. 11. ͑a͒ Dissociation energies of several SiH groups in a -Si: H obtained from semiempirical calculations ͑Ref.15͒.͑b͒ Dissociation energy of the first two H atoms in a silane molecule obtained by Walsh ͑Ref.59͒ from experimental standard enthalpies of formation ͑in brackets, values corrected to 0 K͒.

Table I .
It has been determined by elementary analysis experiments combined with thermogravimetry ͑see Ref. 31 for

TABLE I .
Chemical composition of the samples studied, hydrogen content n i / n Si of the SiH groups determined by EGA, and enthalpy of the corresponding DSC bands per unit mass ͑Q i ͒ and per H atom ͑E i ͒ ͑all processes are exothermic͒.SampleComposition n HA / n Si n HA Ј / n Si n HB / n Si n HC / n Si a The real values of these quantities for the a-Si: H sample are discussed in the text.

TABLE II .
Thermal activation parameters of the low-temperature dehydrogenation processes ͑activation entropy ⌬S and enthalpy ⌬E͒.

TABLE IV .
Theoretical predictions that have been compared with our experimental results of Table III throughout the paper ͑enthalpies E are endothermic͒.Notes: Except those of Allan et al., all values have been corrected by the zero-point energy.From that paper, it is not clear whether their reported values have been corrected or not.E͑Siu H͒ 0 theoretical values and our dehydrogenation enthalpy ͑exothermic͒ of 40 meV/͑H atoms͒ ͑process C: see text͒.
b Obtained from Fedders' . ͑A3͒ Substitution of Eqs.͑A1͒ and ͑A2͒ into Eq.͑A3͒ leads to the exact relationship e −⌬E/kT M = ␤ Now, in most cases kT / ⌬E Ӷ 1 and the term closed in brackets can be approximated by e kT/⌬E .This approximation leads, after a little algebra, to the desired result ln ␤ ͑A4͒