Molecular hydrogen diffusion in nanostructured amorphous silicon thin films

The use of hydrogenated amorphous silicon a-Si:H as the active layer in devices such as thin-film transistors and solar cells is possible, thanks to the defect passivation role of hydrogen H .1 However, H is also involved in the degradation of the electronic properties of a-Si:H when exposed to light.2,3 In contrast, polymorphous silicon pm-Si:H , a grade of nanostructured amorphous silicon, exhibits enhanced hole mobility4 and a lower density of metastable electronic defects after prolonged illumination.5,6 Despite the importance of H stability and evolution in a-Si:H and pm-Si:H, there is still a lot we do not know about it. Evolved gas analysis EGA experiments are extensively used to analyze H stability and evolution.7 Samples are usually heated at a constant rate in vacuum and the desorbing H2 molecules are detected by mass spectrometry. For devicequality a-Si:H thin films, a single peak is observed at high temperatures 500–700 °C .8 This is associated with H atoms that are dissolved in the Si-Si network, diffuse in atomic form and eventually reach the material’s external surface where they form the H2 molecule and evolve. For lowquality films, with an interconnected void network, a lowtemperature peak 300–400 °C Refs. 7 and 8 is also observed. This is attributable to the rupture of Si-H groups located on the surfaces of internal voids and the simultaneous formation of H2 molecules that evolve without any significant delay. We recently suggested, following EGA and DSC differential scanning calorimetry measurements,9,10 that the main dehydrogenation process in pm-Si:H has an intermediate character; it involves the formation of a H2 molecule that diffuses through the film. This process is due to Si-H groups presumably located at the interfaces between the amorphous matrix and the embedded nanocrystals. The EGA thermogram of Fig. 1 shows that this process has a characteristic two-peak structure: a sharp peak P1 followed, at a higher temperature, by a broader peak P2 . What is extremely puzzling is the fact that whereas peak P1 is associated with an exothermic peak of the DSC curve, there is no calorimetric counterpart associated with peak P2. This is the case despite the number of H atoms evolving with peak P2 the area below the EGA curve being much higher than the number evolving with peak P1 Fig. 1 . The absence of an exothermic peak P2 is even more obvious with a thicker layer9 inset of Fig. 1 . In this case, the results obtained at two heating rates make the common identification of peak P1 in the DSC and EGA thermograms clearer. Since the calorimetric signal is due to residual oxidation occurring during the breaking and rearranging of bonds,12 we suggest that the Si-H groups dissociate at peak P1 with simultaneous formation of H2 molecules and that most of these molecules evolve later at peak P2 due to diffusion. We would like to point out that this interpretation of peak P1 is strengthened by the fact that its thermal activation energy is very similar to that observed for other Si-H groups9 polymeric Si-H2 n and H on the surfaces of voids for which the simultaneous formation of H2 has been demonstrated by isotope-labeling experiments.8 Furthermore, other Si-H dissociation processes with simultaneous formation of H2 molecules have been identified in pm-Si:H and Si nanoparticles.9,13 In all cases, these processes lead to a peak in the DSC thermogram. Other authors have recently predicted that molecular diffusion is a significant process in amorphous silicon containing embedded nanocrystals such as in pm-Si:H ,14 and ab initio simulations15 have reported the formation of H2 molecules in a-Si:H. However, until now, experiments have only reported evidence of significant amounts of H2 molecules in a-Si:H Refs. 16 and 17 but not their diffusion.

The use of hydrogenated amorphous silicon ͑a-Si:H͒ as the active layer in devices such as thin-film transistors and solar cells is possible, thanks to the defect passivation role of hydrogen ͑H͒. 1 However, H is also involved in the degradation of the electronic properties of a-Si:H when exposed to light. 2,3In contrast, polymorphous silicon ͑pm-Si:H͒, a grade of nanostructured amorphous silicon, exhibits enhanced hole mobility 4 and a lower density of metastable electronic defects after prolonged illumination. 5,6Despite the importance of H stability and evolution in a-Si:H and pm-Si:H, there is still a lot we do not know about it.
Evolved gas analysis ͑EGA͒ experiments are extensively used to analyze H stability and evolution. 7Samples are usually heated at a constant rate in vacuum and the desorbing H 2 molecules are detected by mass spectrometry.For devicequality a-Si:H thin films, a single peak is observed at high temperatures ͑500-700 °C͒. 8This is associated with H atoms that are dissolved in the Si-Si network, diffuse in atomic form and eventually reach the material's external surface where they form the H 2 molecule and evolve.For lowquality films, with an interconnected void network, a lowtemperature peak ͑300-400 °C͒ ͑Refs.7 and 8͒ is also observed.This is attributable to the rupture of Si-H groups located on the surfaces of internal voids and the simultaneous formation of H 2 molecules that evolve without any significant delay.
We recently suggested, following EGA and DSC ͑differential scanning calorimetry͒ measurements, 9,10 that the main dehydrogenation process in pm-Si:H has an intermediate character; it involves the formation of a H 2 molecule that diffuses through the film.This process is due to Si-H groups presumably located at the interfaces between the amorphous matrix and the embedded nanocrystals.
The EGA thermogram of Fig. 1 shows that this process has a characteristic two-peak structure: a sharp peak ͑P1͒ followed, at a higher temperature, by a broader peak ͑P2͒.What is extremely puzzling is the fact that whereas peak P1 is associated with an exothermic peak of the DSC curve, there is no calorimetric counterpart associated with peak P2.This is the case despite the number of H atoms evolving with peak P2 ͑the area below the EGA curve͒ being much higher than the number evolving with peak P1 ͑Fig.1͒.The absence of an exothermic peak P2 is even more obvious with a thicker layer 9 ͑inset of Fig. 1͒.In this case, the results ob-tained at two heating rates make the common identification of peak P1 in the DSC and EGA thermograms clearer.Since the calorimetric signal is due to residual oxidation occurring during the breaking and rearranging of bonds, 12 we suggest that the Si-H groups dissociate at peak P1 with simultaneous formation of H 2 molecules and that most of these molecules evolve later ͑at peak P2͒ due to diffusion.We would like to point out that this interpretation of peak P1 is strengthened by the fact that its thermal activation energy is very similar to that observed for other Si-H groups 9 ͓polymeric ͑Si-H 2 ͒ n and H on the surfaces of voids͔ for which the simultaneous formation of H 2 has been demonstrated by isotope-labeling experiments. 8Furthermore, other Si-H dissociation processes with simultaneous formation of H 2 molecules have been identified in pm-Si:H and Si nanoparticles. 9,13In all cases, these processes lead to a peak in the DSC thermogram.Other authors have recently predicted that molecular diffusion is a significant process in amorphous silicon containing embedded nanocrystals ͑such as in pm-Si:H͒, 14 and ab initio simulations 15 have reported the formation of H 2 molecules in a-Si:H.However, until now, experiments have only reported evidence of significant amounts of H 2 molecules in a-Si:H ͑Refs.16 and 17͒ but not their diffusion.In this paper, we report on systematic EGA experiments on a series of device-quality pm-Si:H films of varying thicknesses, grown with the aim of demonstrating H 2 molecular diffusion.The films were deposited on a glass substrate by plasma-enhanced chemical vapor deposition from a silane plasma highly diluted with hydrogen ͑ϳ6% in volume͒ at temperatures ranging from 175 to 225 °C.The EGA measurements were taken in vacuum ͑ϳ10 −6 mbar͒ with an MKS Spectra quadrupole ͑Micro Vision Plus͒.Samples were wrapped in platinum foil in contact with a thermocouple and placed inside a fused silica tube.DSC experiments were carried out with a Mettler Toledo calorimeter ͑DSC822e͒.
We performed a series of EGA experiments at different heating rates and film thicknesses to analyze desorption and diffusion processes.The results are plotted in Fig. 2. All the curves show the characteristic two-peak structure ͑P1-P2͒ already found for the thicker films ͑Fig.1͒.In addition to the direct proof that P1 coincides with an exothermic peak in the DSC thermogram for the 2 m film, we can provide an indirect proof for the thinner films of the series where DSC experiments are much more difficult to perform.The lowtemperature desorption processes in a-Si:H are described by first-order reaction kinetics 8,9,13,18 with rate constant, K, thermally activated according to where ⌬S is the activation entropy, E A is the activation enthalpy, and h and k are the Planck and Boltzmann constants, respectively.We determined ⌬S and E A of peak P1 by means of the Kissinger plot described in Ref. 9 and drawn in the upper part of Fig. 3.The activation values of the five films were then compared with the values obtained by DSC experiments on thick pm-Si:H samples and a-Si:H nanoparticles 9 and EGA experiments on a-Si:H thin films 18 ͑lower part of Fig. 3͒.A particular dehydrogenation process is related to an H state and is characterized by a linear relationship between its activation entropy and enthalpy that constitutes its signature. 18We see in Fig. 3 that, as expected from Fig. 1, the P1 points are close to the signature of Si-H groups "at interfaces" determined by DSC. 9 We can thus conclude that the EGA peak P1 is related to an exothermic process that takes place at the same temperature.
The experimental thermograms were fitted to a simple diffusion model.We consider that all Si-H groups at interfaces are dissociated during the temperature interval of peak P1, and that the concentration of the diffusing species ͑H 2 molecules͒, c͑x , t͒, increases throughout the whole of the film volume.Consequently, c͑x , t͒ will be given by the diffusion equation where the formation of the H 2 molecules is simulated by a Gaussian distribution, g͑t͒, centered at peak P1, and D m ͑t͒ is the diffusion coefficient of molecular H, where E m is the activation energy and D m,0 is the preexponential term and T͑t͒ = T 0 + ␤t ͑T 0 is the initial temperature and ␤ is the constant heating rate͒.Equation ͑2͒ is i.e., there is no hydrogen flow from the layer to the glass substrate ͑at x =0͒ and the hydrogen concentration at the free surface is negligible ͑at x = d͒.The latter condition is based on the extremely small sticking coefficient of molecular hydrogen in Si surfaces. 20,21This assumption is reinforced by the fact that there is not a significant delay between the heat released and the H 2 desorption at peak P1.Once solved, the hydrogen evolution rate is given by In addition, to account for the smaller peak P3 appearing at a higher temperature, which is due to the H diffusion in atomic form, 8 the analytical solution given for this process in Ref.
22 has been added, where c 0 is the initial concentration of Si-H groups in the bulk of the film and D a ͑t͒ = D a,0 exp͓−E a / kT͑t͔͒ is the diffusion coefficient related to peak P3 with activation energy E a and pre-exponential term D a,0 .According to our model, the internal structure of EGA thermograms consists of the superposition of two independent desorption processes ͑dashed curves at the bottom of Fig. 2͒.The first process is due to the main Si-H group present in pm-Si:H films ͑Si-H at interfaces͒ and has the characteristic two-peak structure.Although all Si-H groups that dissociate at peak P1 form H 2 molecules, only those located near the free surface contribute almost instantaneously to the EGA signal at peak P1 whereas the rest of them contribute at the diffusion-delayed peak P2.Note that, due to their common origin, no free parameter can be used to fit the relative intensity of peaks P1 and P2.The second process is described by a single peak ͑P3͒ because, for this process, there is not a characteristic "dissociation temperature" that triggers the atomic diffusion of H. Instead, H diffuses at any temperature in a trapping and releasing process that determines the concentration of mobile H atoms with respect to those trapped. 7,23he fitting process is quite simple.The parameters of the Gaussian function, g͑t͒, position and width, are approximately those of peak P1.An initial estimation of the molecular and atomic diffusion coefficients, D m and D a , is obtained from the position of peaks P2 and P3, respectively.The diffusion coefficients are then fine tuned to obtain the best fit.From Fig. 2 it is apparent that this simple diffusion model provides a good description of the complete desorption process.From the fitting of the EGA thermograms we obtained the activation energy for peaks P2 and P3; for peak P3 this was E a = 1.57Ϯ 0.1 eV.Note that all fittings deliver practically the same activation energy.This value is in agreement with the approximate value of ϳ1.5 eV determined experimentally 22,[24][25][26][27] for the atomic diffusion in undoped a-Si:H, and confirms that peak P3 is due to atomic diffusion.For peak P2 the value we obtained for molecular diffusion was E m = 0.99Ϯ 0.1 eV.This value is consistent with nuclear-magnetic-resonance ͑NMR͒ experiments. 16Indeed, it has been observed that molecular H is located in the amorphous equivalent of tetragonal T sites and that the jumps from T site to T site require an activation energy of approximately 1 eV.This activation energy is slightly higher than that observed in crystalline silicon ͑0.78-0.91 eV͒. 28,29ith regard to the pre-exponential term D m,0 , this varies over 1 order of magnitude.We attribute this dispersion to the fact that, in pm-Si:H films, the sudden formation of a large amount of H 2 molecules ͑peak P1͒ results in cracking. 30In Fig. 4 one can observe the formation of these cracks in a 0.98 m thick film after dehydrogenation.As a consequence of the cracking, the diffusion length is not equal to film thickness and an "effective diffusion length," related to the average distance between cracks, is more appropriate to describe the results.The existence of a nearly common effective diffusion length for all the films is reinforced by the fact that the peak temperature of P3 ͑without any doubt controlled by diffusion͒ is independent of the film thickness.
In conclusion, we have reported on a series of systematic experiments designed to demonstrate that hydrogen diffuses in pm-Si:H mainly in molecular form.Several relevant results from the analysis of EGA measurements on samples with different thickness point out to the same conclusion, namely: ͑i͒ the signature of peak P1 confirms that it is related to Si-H bond breaking and it corresponds to a particular H state of pm-Si ͑Ref.9͒.Since this signature is close to that of Si-H on the surface of voids, 18 the bond-breaking process must be very similar ͑i.e., it entails simultaneous formation of a H 2 molecule͒; ͑ii͒ on the contrary, peak P2 is much broader than expected for the simple reaction kinetics governing the low-temperature dehydrogenation processes in a-Si:H ͑usually first-order kinetics͒.Its full width at half maximum would deliver an unrealistic activation energy of 0.5 eV; ͑iii͒ the complete EGA spectrum with three peaks can be fitted to a simple diffusion model where it is assumed that only two species diffuse, molecular and atomic hydro-gen.The characteristic two-peak structure for the molecular process with its sharp low-temperature peak is unveiled; ͑iv͒ the diffusion model would not lead to two distinct EGA peaks if one single species was diffusing.So, detection of P1 and P2 peaks indicates that two different species diffuse; ͑v͒ from the model fitting, the activation energies for molecular and atomic hydrogen diffusion are obtained.The first activation energy agrees with NMR experiments while the second one coincides with the well-known value of the activation energy of atomic hydrogen diffusion.
Molecular diffusion involves breaking Si-H groups that are presumably located at the interfaces between nanocrystallites and the amorphous matrix of pm-Si:H.Consequently, if active, this mechanism would be of secondary importance in monophasic a-Si:H.However, we think that it could be the main diffusion mechanism in microcrystalline silicon ͑c-Si: H͒.In fact, EGA thermograms of this material exhibit the two-peak structure analyzed here. 30is work was partially funded by the Spanish Ministerio de Educacin y Ciencia ͑MAT2006-11144 Project and SB2006-0062 postdoctoral Contract͒ and by the Generalitat de Catalunya ͑Contract No. 2005SGR-00666͒.The authors are indebted to J. Arbiol from the Serveis Científico-Tècnics ͑University of Barcelona͒ for the TEM micrograph.*fatiha.kail@udg.cat

FIG. 1 .
FIG. 1. DSC and EGA thermograms for a 2 m thick pm-Si:H thin film heated at 40 K/min.The inset shows DSC and EGA thermograms from Ref. 9 for a 5 m thick pm-Si:H film heated at 10 and 40 K/min ͑Ref.11͒.

FIG. 2 .
FIG.2.͑Color online͒ EGA thermograms obtained at different heating rates and film thicknesses ͑symbols͒ and fitted numerical solution of the diffusion equation ͑solid lines͒.The decomposition of the thermograms in two independent processes ͑one responsible for peaks P1 and P2 and a second responsible for peak P3͒ is indicated by the red dashed curves.

FIG. 3 .
FIG. 3. Upper plot: Kissinger plot of peak P1 ͑Fig.2͒ from which activation entropies and enthalpies were obtained.Lower plot: the activation entropy and enthalpy values of the films are plotted together with the characteristic signatures of several Si-H groups determined from diverse hydrogenated silicon amorphous materials ͑Refs.9, 18, and 19͒.