Two-level systems and growth-induced metastability in hydrogenated amorphous silicon

Specific heat measurements from 2 to 300 K of hydrogenated amorphous silicon prepared by hot-wire chemical vapor deposition show a large excess specific heat at low temperature, significantly larger than the Debye specific heat calculated from the sound velocity. The as-prepared films have a Schottky anomaly that is associated with metastable hydrogen in the amorphous network, as well as large linear and excess cubic term commonly associated with tunneling two-level systems in amorphous solids. Annealing at 200 {\deg}C, a temperature that enables hydrogen mobility but not evaporation, irreversibly reduces the heat capacity, eliminating the Schottky anomaly and leaving a reduced linear heat capacity. A non-monotonic dependence on growth temperature and H content is observed in all effects, except for sound velocity, which suggests that the tunneling two-level systems and the Schottky anomaly are associated with atomic hydrogen and require low density regions to form, while sound velocity is associated with the silicon network and improves with increasing growth temperature.

made as thin films by vapor deposition, measurements of TLS require techniques sensitive to the low mass of a thin film, such as nanocalorimetry. In the present work, we investigate the specific heat of HWCVD a-Si:H films prepared at different growth temperatures yielding different H concentrations, and focus on the role hydrogen plays in the formation of TLS in a-Si:H and the deviations from the TLS model that we observe.

II. EXPERIMENTAL
Device quality a-Si:H thin films were prepared by HWCVD using pure silane, at growth rates between 1 to 3 nm/s, and substrate temperatures (T S ) of 300, 370, 430, and 470 • C [17].
Higher T S yields films with lower hydrogen content (from 9 to 3 at.% H). Films were grown on membrane-based nanocalorimeters [18] as well as other substrates for other characterizations.
Film thicknesses were measured with a KLA-Tencor Alpha-Step IQ profilometer with an uncertainty of 2%. Uncertainty in film thickness is the dominant source of error in the specific heat measurements. Films' atomic densities n at were determined by Rutherford backscattering (RBS) in combination with profilometry measurements. Oxygen resonant scattering was used to probe for oxygen in the films; the only oxygen detected was limited to a thin surface layer. Hydrogen forward scattering (HFS) was used to measure H content, and in particular to show that annealing did not remove hydrogen from the films. Longitudinal sound velocities were measured at room temperature by a picosecond ultrasonic pump-probe technique [19], with annealed states showing no significant change from their as-prepared counterparts. Internal friction Q −1 (T ) measurements were carried out on the sample grown at 370 • C, in both the as-prepared and annealed states; these showed a low temperature TLS plateau with Q −1 0 ≈ 10 −5 similar to previous measurements of a-Si:H, with no notable change upon annealing [20]. Room temperature thermal conductivity was measured using time-domain thermoreflectance and found to be comparable to previous HWCVD a-Si:H films [13] but lower than the single high conductivity film reported in Ref. 21.
Specific heat C P (T ) was measured from 2 to 300 K using a microfabricated thin-film nanocalorimeter [18]. Samples grown at 300, 370, and 430 • C were measured in their asprepared and annealed states. The anneals were done in-situ alternately to the specific heat measurements, in high vacuum for 10 4 seconds using the nanocalorimeter sample heater.
The sample grown at 470 • C was measured and kept in its as-prepared state to verify that samples were stable throughout the duration of the study. After the first measurement, all other samples were annealed at T A = 200 • C, then fast-cooled (quenched) at ∼ 10 4 K/s, measured, annealed again at the same T A , then slow-cooled at ∼ 5 K/min and re-measured.
This series was repeated for T A = 300 • C (for the samples grown at 370 and 430 • C). The fast cooling rate was achieved by turning off the sample heater power while keeping the thermal bath at 4.2 K; the slow cooling required software control to ensure a constant rate.
The quenching preserves the high T equilibrated state, including any electronic or bonding defects, while slow cooling allows for further mobility and quasi-equilibration of the system at lower temperatures [22]. ship v t = (0.56 ± 0.05)v l between the transverse and longitudinal sound velocities verified for many amorphous materials [23], including our own a-Si grown at different temperatures [9].

III. RESULTS AND DISCUSSION
As previously observed [9] and here further confirmed, longitudinal sound velocity v l increases with growth temperature (see Table I). The low temperature (below 10 K) C P (T ) is significantly reduced after the first anneal, changes little with further annealing, and remains significantly larger than c D . The large change in C P (T ) on annealing, well below growth temperatures but where hydrogen is allowed to equilibrate and redistribute without leaving the sample (from 150 up to 400 • C) [24], along with the lack of change in sound velocity, is a strong indication that the change in C P (T ) is due to H rearrangement. No cooling rate dependence was observed, indicating that metastable states, if present after annealing, completely equilibrate even during fast cooling. The differences in C P (T ) between annealed states at different temperatures are negligible, so we focus our analysis on the differences between samples in the as-prepared and annealed (at 200 • C) states. which is only weakly dependent on growth temperature (300 to 470 • C) and is unchanged upon annealing. The line labeled T is for comparison to a linear temperature dependence. Figure 2 shows C P (T ) plotted as C P /T vs T 2 for the samples grown at 300, 370, and 430 • C. The specific heat signature for these samples is described by a large excess C P (T ) in the as-prepared state, which includes a sub-linear temperature dependence (down to 2 K) that disappears upon annealing. The excess C P (T ) in the as-prepared film must have a peak at or below 2 K, the lowest measured temperature, since C P → 0 as T → 0 in order to have a finite entropy at T = 0 K. The simplest physical explanation for such a peak is a Schottky anomaly associated with two-level systems (which may or may not be due to tunneling) with a specific energy splitting The specific heat C P (T ) of a distribution of two-level systems n(∆) is given by where ∆ = E/k B is the energy splitting of the two-level systems, n(∆) is the density of states for two-level systems with a particular ∆, k B is the Boltzmann constant, and T is temperature. Note that Eq. 1 is valid both for the tunneling two-level systems (TLS) and for any other type of two-level systems. In the standard tunneling model, n(∆) is taken as constant over a wide energy range due to the uniform distribution of tunnel barrier heights, so that n(∆) ∼ n 0 . Under these conditions, the solution for Eq. 1 yields the canonical linear specific heat term due to tunneling states [4,5]: where n 0 is the density of TLS per unit energy and unit volume (J −1 m −3 ), n at the total atomic density, and N A is Avogadro's number. If instead n(∆) is considered to be a delta function N δ(∆ 0 ) to represent N two-level systems, per mol of sample, with a specific energy splitting ∆ 0 , and assuming no degeneracy, from Eq. 1 we obtain the specific heat for a Schottky anomaly The data in Figures 1 and 2 are well described by where the cubic term coefficient c 3 is decomposed as c 3 = c D + c ex , where c D is the Debye specific heat due to phonons, calculated from the sound velocity, and c ex is an excess specific heat T 3 term that is comparable in magnitude to c D but not explained by the standard tunneling model and likely associated with localized non-propagating modes [8,25]. We have previously shown that in a-Si c ex is proportional to n 0 , which suggests a common structural origin [9].  The sound velocity was found to be unchanged on annealing at 200 • C, so changes in c 3 are entirely due to changes in c ex .
The values of n 0 and c ex from the fits for as-prepared and annealed states are shown in Table I, and plotted versus the growth temperature in Fig. 3      (for all H content) than those for a-Si grown at similar temperatures, despite low internalfriction-derived TLS densityP [20]. The dangling bond density n DB in HWCVD a-Si:H samples is ≤ 10 16 cm −3 [12], while for e-beam a-Si n DB ∼ 10 19 cm −3 [9]. Here we report values of n 0 for a-Si:H orders of magnitude higher than in a-Si samples grown at similar temperatures, thus showing no direct correlation between dangling bonds and TLS.
In a-Si we observed that increasing the growth temperature reduces the density of TLS, and we suggested this is because higher growth temperature enables Si adatoms to find more stable sites during growth, leading to a denser and more energetically stable structure, which in turn leads to low TLS due to the absence of "nearby" similar energy wells that enable tunneling states to form [9,16]. In a-Si:H, however, the overall C P (T ) [ Fig. 1(a)] as well as the extracted values in both the as-prepared and annealed states (shown in Table I), show a non-monotonic behavior versus the growth temperature, with a minimum around 370 • C (Fig. 3).
The Schottky peak amplitude also shows the same minimum with growth T, as seen most clearly in Fig. 2 and in Table I. When the separate fitting parameters N and ∆ 0 are plotted, the minimum is clear in the number of Schottky systems N , but the energy gap ∆ 0 becomes monotonically smaller as T S increases. This effect may be a result of the limits of the fit, which is over a limited temperature range and assumes a single gap ∆ 0 , or may be a real shift to lower ∆ 0 with higher T S . We considered all possible scenarios in which the parameters N and ∆ 0 were either constant or free; allowing them to vary from sample to sample yielded the best fitting results.
We next consider the structural motifs that give rise to the TLS in the a-Si:H films.
We identify two different structural regions: (i) high structural order regions, or network, containing very few H atoms, and (ii) lower structural order regions that give rise to defects and low density structures, including dangling bonds and nanovoids, where H atoms may cluster [26]. We propose, consistent with previous discussions of TLS in a-Si:H films, that TLS occur in the lower structural order regions, while sound waves are predominantly carried by the network. With increasing T S , the sound velocity v l linearly increases ( Table I), suggesting that the network becomes more ordered with a stronger dependence on T S than for hydrogen free a-Si [9]. The atomic density n at is non-monotonic in growth temperature, with a maximum close to the crystal silicon density (5.0 x 10 22 atoms cm −3 ) at 370 • C, and a strong reduction at both higher and lower T S , despite the monotonic trend of sound velocity, indicating an increased amount of low density regions at both low and high T S .
That increase in turn leads to a higher amount of TLS (n 0 and c ex due to a distribution of ∆) and two-level systems (c Sch due to a single ∆ 0 ). We suggest that lower density regions contain underconstrained Si atoms and H, which lead to TLS and Schottky anomaly. Most strikingly, as seen in Figure 3, the presence of H causes high n 0 and c ex , relative to a-Si, but these excess heat capacities are not proportional to the at.% H (Table I), and instead depend on the presence of both H and low density regions. Annealing leaves the sound velocity and atomic density unchanged but eliminates c Sch , reduces n 0 and increases c ex , although still leaving these larger than in a-Si. All of these effects are explained by the atomic mobility of H at the annealing temperature.
The details of the local hydrogen environment in similar HWCVD a-Si:H has been obtained from proton nuclear magnetic resonance (NMR). These measurements have shown that hydrogen is primarily found as bonded Si-H, and secondarily as molecular H 2 , in both cases either clustered or isolated [26][27][28]. The NMR spectra change irreversibly upon annealing at T A comparable to that used here, which is notably below T S and show that the as-prepared state is metastable [29]. At these temperatures, above the H mobility threshold T > 100 • C [22], hydrogen diffuses away from clustered Si-H regions and increases the fraction of isolated Si-H bonds, where it is trapped via a mechanism of reconstructing Si-H bonds [30]. The trapped states that occur when H diffuses to a locally deep potential well originate either from a weak Si-Si bond that forms a dangling bond plus a Si-H bond [31], or a dangling bond that then forms a Si-H bond [32]. Hydrogen atoms may also combine with other H to produce H 2 [20].
Hydrogen molecules can lead to a Schottky anomaly below 5 K attributed to the freezing of the rotational motion of ortho-H 2 trapped in the film [24]. In the present study, annealing either increases the molecular H 2 concentration or leaves it unchanged but we find that annealing removes the Schottky anomaly. Furthermore, we do not see any sign of the H 2 melting point in C P (T ), unlike that observed in Ref. 24, nor in Q −1 (T ) measurements of these samples [20], implying that clusters of H 2 are not large enough to be detected by these means. These observations show that molecular hydrogen is likely present as isolated H 2 and is not the source of the Schottky anomaly. We instead suggest that the Schottky anomaly is associated with distinct H sites with slightly different energies near metastable weak Si-Si bonds, such as would be found in low density, disordered regions of the film. In support of this idea, we note that in these samples the number of systems N (in %) with energy spitting ∆ 0 is comparable to but smaller than the at.% H (Table I).
To understand the n 0 and c ex dependence on growth temperature, we first consider the films' atomic density n at , shown in Table I, since previous work on a-Si showed n 0 and c ex have a strong correlation with n at [9]. Here in a-Si:H, n at shows the same dependence with growth temperature as n 0 , c ex and c Sch , suggesting a similar dependence of TLS density on atomic density, although for any given atomic density n at , the TLS density n 0 is at least 2 orders of magnitude larger in a-Si:H than in a-Si, an effect we attribute to the presence of H and the inherent differences between the growth techniques used. This optimum growth temperature behavior, resulting in the lowest n 0 , c ex , c Sch , and highest n at values, is notably replicated by Urbach edge and n DB measurements on device quality HWCVD a-Si:H [17], techniques traditionally used to establish the film quality. It is similarly notable that the reduction in n DB in device quality a-Si:H requires H, but is not proportional to its content.
The significant variation in atomic density with growth temperature cannot be explained solely in terms of network distortion, nor dangling bonds, but instead requires the presence of nanovoids or loosely bonded regions. Even a few at.% H is sufficient to remove dangling bonds and therefore yield device quality a-Si:H, but nonetheless leaves a lower density structure with more low density disordered regions where H concentrates. As previously discussed by Street [33], both high and low T S thus result in a more disordered structure; here we show that this disorder correlates with lower atomic and higher TLS densities. We note the strong and monotonic increase of sound velocity with T S showing that the network becomes more ordered, and it is only the low density regions where disorder increases. Notably, there is no change in n at or H content upon annealing, despite a reduction in n 0 and a vanishing c Sch , showing that these excess specific heat terms are related to H in the low density regions, not to the presence of low density regions alone. At these relatively low annealing temperatures, annealing is known to result in H mobility, relocation and rebonding [28][29][30][31] that affects n 0 and c Sch , as well as c ex , which will be discussed below.
It is known that hydrogen lowers the energy barrier for breaking weak Si-Si bonds [34].
We suggest that these lowered barriers increase the tunneling probability and thereby increase the TLS density n 0 . The TLS density is associated with tunneling states created by these sites in conjunction with slight rearrangements of neighboring Si atoms that lead to the breadth of tunneling-split energy states of the TLS model. Upon annealing, H diffuses to locally deep potential wells increasing the isolated Si-H bonds fraction, and perhaps the H 2 concentration. These results suggest that both the Schottky anomaly and the large n 0 in the as-prepared state are associated with clustered Si-H in lower density regions. The concentration of clustered H, and thus the values for n 0 and c Sch , are reduced upon annealing.
The lack of correlation of at.% H with TLS density, despite the necessity of H to produce the large TLS, is similar to the effects seen with elimination of dangling bonds in a-Si:H, where H is essential to creating device quality electronic materials, but the necessary at.% ranges from 1 to 20%, depending on preparation details, and is uncorrelated with the reduction in n DB .
After annealing, the a-Si:H samples presented in this work show a decoupling between n 0 and c ex not observed in a-Si, despite the strong correlation in the as-prepared state. The TLS density n 0 decreases upon annealing (solid to dashed black lines in Fig. 3), while the excess specific heat T 3 term c ex increases (solid to dashed red lines in Fig. 3). This brings into question the simple explanation of c ex as being directly due to the structures that give rise to TLS. Instead, we propose that c ex is caused by low density regions, which give rise to the vibrational states detailed by Nakhmanson and Drabold [8,35]. In these models, low energy vibrational states are found to occur in lower structural order regions that would accommodate TLS, but are only coincidental. Annealing causes H to diffuse away from clustered regions and into deep potential wells, creating more stable bonds due to atomic rearrangement, such as isolated Si-H and H 2 . This process decreases the TLS themselves, but does not eliminate the underlying structural defects that caused them (nanovoids or concomitant strained regions), thereby still allowing for the modes responsible for c ex . The increase in c ex upon annealing is likely also associated with the same H diffusion process, causing a softening of the local modes that lead to c ex , which are localized in lower structural order regions.

IV. CONCLUSIONS
In summary, a large excess specific heat is seen at low temperatures in as-prepared films of a-Si:H that show a Schottky anomaly in addition to the linear and cubic terms that are commonly seen in amorphous materials and attributed to tunneling two-level systems. The Schottky anomaly as well as the large value of n 0 decrease upon annealing at modest temperatures (200 • C), well below the growth temperature, with the former vanishing entirely.
These annealing conditions are known to cause hydrogen to diffuse from a clustered Si-H to a more uniform distribution of isolated Si-H bonds.
The specific heat observations are suggested to be due to clustered atomic H in low density regions, which leads to both the two-level systems that produce the Schottky anomaly (H near weak Si-Si bonds) and, via depressed energy barriers, a greater probability of atomic rearrangements of Si structures that produce TLS. A strong correlation of n 0 , c ex , and c Sch with atomic density, which is not monotonic in growth temperature, and the lack of correlation with at.% H, despite the critical role that H plays in creating these specific heat effects, demonstrates that low density regions are essential to producing these effects, as was seen in pure a-Si. Atomic H thus greatly enhances the TLS compared to that seen in pure a-Si by lowering energy barriers, but the effects are not proportional to at.% H, similar to the lack of proportionality between dangling bond density and at.% H in device quality a-Si:H. The sound velocity's monotonic increase with growth temperature also suggests that TLS originate in low density regions, and not in the network.
The nature of the cubic c ex term is not yet understood, but the correlation in the asprepared state with n 0 implies that the structures responsible for its existence are related to those that produce the TLS density n 0 . Nevertheless, the different effect of annealing on n 0 and c ex points to an intriguing conclusion; atomic H is essential for n 0 and not for c ex .