Stability of low-carrier-density topological-insulator Bi$_2$Se$_3$ thin films and effect of capping layers

Although over the past number of years there have been many advances in the materials aspects of topological insulators (TI), one of the ongoing challenges with these materials is the protection of them against aging. In particular, the recent development of low-carrier-density bulk-insulating Bi$_2$Se$_3$ thin films and their sensitivity to air demands reliable capping layers to stabilize their electronic properties. Here, we study the stability of the low-carrier-density Bi$_2$Se$_3$ thin films in air with and without various capping layers using DC and THz probes. Without any capping layers, the carrier density increases by ~150% over a week and by ~280% over 9 months. In situ-deposited Se and ex situ-deposited Poly(methyl methacrylate) (PMMA) suppresses the aging effect to ~27% and ~88% respectively over 9 months. The combination of effective capping layers and low-carrier-density TI films will open up new opportunities in topological insulators.

Topological insulators (TIs) are new class of electronic materials which are insulating in the bulk, but metallic on the surfaces with linear Dirac-like surface states, which are robust against any defects and disorders as long as the time reversal symmetry is preserved [1][2][3] . Bi2Se3, an archetypal 3D topological insulator 4,5 , has garnered a lot of attention over the past number of years. However, degradation and aging in air over time limit the realization of Bi2Se3-based devices. There have been transport and spectroscopic studies on how the properties of Bi2Se3 evolve when it is exposed to atmospheric gases [6][7][8] . In regular Bi2Se3 thin films grown on different substrates including sapphire 9 , silicon 10 , and amorphous silicon oxide 11 , the surface Fermi level generally resides above the bottom of bulk conduction band and their sheet carrier densities are generally much higher than ~1 × 10 13 cm -2 with the bulk state of the samples metallic. Due to the initial high carrier densities, the carrier densities remain relatively stable in air with the change in carrier densities limited only to a few tens of percent 7,12 . The relative stability of these high-carrier-density samples has helped attaining numerous consistent results across different probing techniques even without any special care to protect the surface layers 9,13 .
In contrast, recently developed low-carrier-density bulk-insulating Bi2Se3 films 14,15 exhibit quite significant aging effect in air. The as-grown sheet carrier densities of these samples are about an order of magnitude lower than the previous generation samples. This order of magnitude decrease in carrier density implies that the few tens of percent change in carrier density of the previous generation films in air would amount to a few hundreds of percent in these new films, if we assume that similar absolute level of aging effect occurs for both types of samples. Moreover, as we discussed earlier, in order to ensure the bulk insulating character of these low-carrier-density samples, it is critical to keep the sheet carrier densities substantially below 1 × 10 13 cm -2 and maintain upward (instead of downward) band bending near the surfaces 16 . Below, we show that in order to stabilize the low-carrier-density Bi2Se3 films, it is essential to use proper capping layers. Among the three capping layers we studied, in situ-deposited In2Se3, in situdeposited Se and ex situ-deposited PMMA, only Se and PMMA exhibited good stabilization effect.

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The low-carrier-density Bi2Se3 films used for this study were grown on (Bi1-xInx)2Se3 buffer layers on sapphire substrate using a custom-designed molecular beam epitaxy (MBE) system by SVT Associates; details will be published elsewhere 15 . As for capping layers, 100 nm amorphous Se and 50 nm amorphous In2Se3 were deposited in situ at room temperature, whereas ~200 nm PMMA was spin-coated ex situ, followed by baking process at different temperatures. Both capped and uncapped films were measured for over 280 days. Standard Hall effect measurements were carried out at room temperature in air in magnetic field up to 0.6 T with the standard van der Pauw geometry, which uses indium wires pressed on the four corners of the square sample as contact leads. Sheet carrier density (nsheet) is extracted from ℎ = (e dR Hall dB ⁄ ) -1 where e is the electronic charge and dR Hall dB ⁄ is the slope of Hall resistance as a function of magnetic field B. Mobility is calculated using = ( ℎ ℎ ) −1 at zero magnetic field. In order to study the evolution of the transport properties over time, nsheet and μ were measured continuously for more than 36 hours immediately after the sample was taken out of the MBE chamber. After that, they were measured almost every day for 7 days, and then intermittently at couple-of-day intervals for the following ~9 months.
The continuous measurement of 30 QL (1QL ≈ 1 nm) uncapped sample for 40 hours ( Fig. 1(a)) shows a telling decrease in nsheet (~30% drop from the initial value) and a simultaneous increase in μ at around hour 16, which is also observable in other uncapped samples. Similar short-time decrease in carrier density was observed in our previous study of high-carrier-density Bi2Se3 samples 7 . The trigger point of this decrease depends on ambient conditions, such as relative humidity and temperature. This shows that there are competing processes such that there is a short-time window in which the sample properties improve, and after that it gets worse rapidly until the carrier density reaches twice the initial value after a day. This drastic degradation necessitates an effective capping layer for stabilizing the properties of these thin films. Clearly, the uncapped sample shows a rapid degradation for ~80 days with 280% increase in nsheet.
However after that, film properties recover to some extent presumably because the charge exchange process between the film and air balances out. This recovery happens for all capping layers at some point, except that for the uncapped sample it is more noticeable since it recovers after a huge change in nsheet. Another comparison in Fig. 1(c) shows the change in μ for all the capping layers along with the uncapped sample.
It is clear that the mobility of the uncapped sample has a sharp drop in short time, and it gets slowly recovered after ~100 days. This is also true for capped samples, but the change in uncapped sample is more conspicuous.
In2Se3-capping layer makes the electrical properties of the film significantly worse immediately (Figs. 1(b) and 1(c)). The In2Se3-capped sample has initially almost two times higher nsheet compared to the uncapped sample. For depositing In2Se3 on Bi2Se3, selenium shutter was open for a few seconds prior to opening indium shutter to ensure Se rich environment in the vicinity of the substrate surface before indium atoms arrive; we tried various other schemes of depositing In2Se3 but all resulted in similarly degraded transport properties of Bi2Se3 films. One possible explanation for this drastic degradation is that indium tends to bond with selenium from the Bi2Se3 rather than the surrounding selenium, hence this mechanism leaves behind more selenium vacancies in the film. The result from In2Se3-capping layer shows that although superficially this capping layer may seem compatible with Bi2Se3 because of its similar structure, it does not function as an effective capping layer.
PMMA-capping, helps to suppress the drastic aging effect. Moreover, the coating and removing of this commonly used polymer is straight forward. Due to ex situ deposition, the transport results before and after PMMA coating could be compared. The films were exposed to air less than 10 minutes prior to PMMA-capping. Figure 2 summarizes nsheet and μ for different temperatures of PMMA baking. The initial values before PMMA-capping are also marked in the plots. There is a sudden increase in nsheet right after PMMA coating compared to the value before capping, which might be due to the delay in capping and/or curing of the PMMA layer. However sometime after coating ( Fig. 2(a)), there is always a decreasing trend in nsheet until it reaches a minimum close to the original nsheet. This is probably due to the fact that the solvent in the PMMA dries out over time. The inset graph in Fig. 2(a) shows the percentage change in nsheet right after PMMA-capping for each baking temperature compared to the original value before capping. This shows that for higher temperature baking, the amount of sudden change in the value of nsheet is lower, and this is probably due to the fact that harder baking reduces residual solvent and the density of pores in the PMMA-capping. Although compared to the uncapped sample, PMMA-capping makes the aging much slower, PMMA-capped sample goes through degradation before recovering again. This degradation is likely due to ambient species eventually reaching the film through PMMA layer, or due to change in PMMA properties over time. The start and peak of degradation process ( Fig. 2(a)) depends on PMMA baking temperature, which presumably corresponds to the amount of leftover solvent in PMMA. For the case of change in μ, the mechanism is more complicated but it is clear that the mobility of the sample measured right after PMMA coating is always lower than the value before capping, which might be due to delay in PMMA-capping or heat from the baking process. The mobility values eventually recover after a decreasing trend, which is consistent with our previous discussion.
Among the capping layers, selenium gives the best result in terms of stability of nsheet for both short and long-time compared to the uncapped sample. Our comprehensive study on Se-capped sample for more than 280 days using DC transport measurements demonstrates the remarkable effectiveness of this capping.
It should be noted that the in situ deposition of this capping guarantees no direct exposure of the film's surface to air. Figure 1(a) shows that the change in nsheet is less than 27% over the course of 280 days, compared to uncapped sample, which confirms that the Se-capping efficiently protects the sample against environmental doping. Figure 1 shown in the inset of Fig. 1(d)  University on samples grown at Rutgers University. The uncapped samples were measured a day (after one-day shipping) and a week after the growth day. A sharp change in the real conductance as a function of THz frequency (Fig. 3(a)) is noticeable in this short time. The real conductance for PMMA-and Secapped samples was measured a day, a month and two months after the growth day (Figs. 3(b) and 3(c), respectively). The small change in the real conductance spectra for 20 nm Se-capping after 2 months aging confirms the effectiveness of this capping layer in stabilizing the sample's properties.
The carrier density of each topological surface state (TSS) can be calculated based on nsheet = kF 2 /4π.
An effective transport mass m*=ℏkF/vF can still be defined for massless Dirac fermions where the Fermi velocity is determined by = /ℏ . In our analysis, we will consider up to quadratic dispersion for surface states (EF=AkF+BkF 2 , where A = 2.02 eVÅ and B = 10.44 eVÅ 2 ) and model the top and bottom surface states as identical with the same carrier density as done previously 18,19 . Considering the TSS dispersion for surface states up to quadratic correction, the Drude spectral weight 2 (proportional to total areal under real conductance at zero field GD1) can be expressed in terms of Fermi wave-vector kF.
, where o is the free-space permittivity, e is the electronic charge and d is the film thickness.

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In Drude-Lorentz fit, the conductance spectra can be well fit by an oscillator model with a Drude term describing free electron-like motion, a Drude-Lorentz term modeling the phonon, and a lattice polarizability ∞ term that originates from absorptions outside the spectral range.
, where ωpD and ΓD are Drude plasma frequency and scattering rate. ωpDL, ωDL, and ΓDL are, respectively, the plasma and center frequencies, and scattering rate of optical phonons. DL stands for Drude-Lorentz.
The fit provides Drude plasma frequency ωpD (which gives the spectral weight 2 ) and scattering rate ΓD. By using the spectral weight and equation (1) ) not only for the free-electron spectrum toward the low frequencies but also for the phonon peak. It is also worth noting that with higher thickness for Se-capping and higher baking temperature for PMMA-capping, the stability would have been even better.