Sticking coefficients of selenium and tellurium

Renewed interest in the growth of chalcogenide based thin films is fueled by two remarkable properties in this material family.^1–5 First, many chalcogenide phases containing the chalcogen elements (X) sulfur, selenium, or tellurium, such as transition metal (M) mono- and dichalcogenides MX and MX₂, as well as post-transition metal (P) sesqui-chalcogenides P₂X₃ form layered structures due to a large bond anisotropy present in these materials. Strong bonds within each layer ensure structural rigidity and long-range crystalline order, while a somewhat weaker interlayer interaction eases the epitaxial constraint thus allowing to combine layers with different chemistries, and thus different physical properties. The ability to grow these individual layers by molecular beam epitaxy provides a bottom-up approach to access a multidimensional material design space, in which properties can be tailored at the atomic scale by combining different layers and engineering their coupling strengths. This allows a paradigmatic shift in which otherwise mutually exclusive material properties can be combined due to the weaker interlayer interaction, which mitigates structural constraints on the atomic arrangement, thus enabling a much larger nanostructured material design space in which “structure follows properties.”

Second, the strong spin–orbit coupling strength present in chalcogen compounds made from high Z number elements can invert the conventional bulk band structure, giving rise to electronic phases with nontrivial topologies, such as topological insulators, Dirac or Weyl semimetals.^6–10 On demand design of quantum materials offers unprecedented access to new phenomena enabling novel functionalities and devices that are beyond the more conventional application space of traditional IV-VI and II-VI chalcogenide materials, such as (Si,Ge,Sn,Pb)(S,Se,Te) and (Zn,Cd,Hg)(S,Se,Te) for thermoelectrics and photovoltaics, as well as material building blocks for diode lasers and detectors operating from the mid-infrared range all the way into the visible spectrum.^11–21 

The growth of binary chalcogenide compounds can be achieved using a single thermal effusion cell heated to a temperature that allows for a congruent sublimation of the targeted compound.²² This approach is suitable only if the volatilities of the different elements are comparable, limiting it to compounds with cations matching the relatively high volatilities of chalcogen elements, such as CdTe, ZnTe, CdSe, and ZnSe.²³ More generally, i.e., for binary compounds made from elements with large volatility differences, as well as for the growth of ternary and quaternary compounds, molecular beams of the respective elements have to be supplied from different effusion cells. This approach requires a careful adjustment of the individual fluxes to ensure that a phase pure film with the targeted composition, stoichiometry, and a low unintentional defect concentration is formed. Here, a favorable surface reaction kinetics can ease the flux control requirement. If the sticking coefficients, i.e., the ratio of atoms incorporated into the film versus supplied to the growth surface, are different, the more volatile species can be oversupplied since the excess amount accumulated on the growth front easily desorbs. This favorable growth kinetics has been first identified for the growth of GaAs using modulated beam mass spectrometry, where Ga was found to have a near unity sticking coefficient at sufficiently low temperatures, while the sticking coefficient of the more volatile As species was zero except excess Ga was present at the growth front.^24–27 Therefore, determining the temperature dependent sticking coefficient of the more volatile element is key to understand the kinetic processes occurring during film growth. Specifically, in the case of chalcogenide films, the sticking coefficient of the chalcogen elements selenium and tellurium is expected to be low due to their high volatilities.

Surprisingly, only a few reports determining sticking coefficients for chalcogenide films are available. While modulated beam mass spectrometry, which has been instrumental to investigate and understand the growth kinetics of GaAs films, has not been commonly employed for the MBE growth of chalcogenide films,¹⁷ other indirect determination of sticking coefficients using film growth rates has been employed instead.^28–33 Individual fluxes used for the growth were first calibrated at low temperatures at which sticking coefficients were near unity, to then determine film growth rate and film stoichiometry as a function of deposition temperature and flux ratio to extract the temperature dependent sticking coefficient. These experiments are complicated by the fact that the sticking coefficient not only depends on temperature, but also on the chemical state of the surface. Even small amounts of group II elements affected the sticking coefficient of chalcogens, and the assumption that group II elements had a sticking coefficient close to unity even at lower growth temperatures were found to be incorrect.³² 

A more direct way to determine the sticking coefficient is to use a heated quartz crystal microbalance (QCM). Early experiments using this approach were reported to determine the evaporation rates of ZnSe, CdSe, ZnTe, and CdTe films as well as the flux rates needed to grow stoichiometric films.²³ Here, we report the direct measurement of the temperature dependent sticking coefficient for the elements selenium and tellurium. Molecular beams supplied from thermal effusion cells were directed onto a heated quartz crystal microbalance. Within a narrow temperature range of about 20 and 30 °C, both sticking coefficients were found to sharply drop from over 0.8 down to about 0.2 at temperatures around 35 °C for selenium and 115 °C for tellurium. While the tellurium sticking coefficient reached zero at temperatures of 150 °C and above, the selenium sticking coefficient remained about 0.2 up to a temperature of 60 °C, suggesting that selenium was supplied in different chemical forms with different adsorption and desorption kinetics.

All experiments were carried out in a R450 molecular beam epitaxy reactor from DCA Instruments. The system was equipped with a heated quartz crystal microbalance (Colnatec) that could be moved into the sample position using a linear motion, as shown schematically in Fig. 1(a). A heating filament and air-cooling system integrated into the QCM head allowed to heat and stabilize the quartz crystal temperature, measured indirectly by a thermocouple (TC) installed in the QCM sensor housing behind the crystal, see Fig. 1(b). An infrared (IR) thermal camera system Xi80 from “Optris” mounted behind an IR transparent ZnSe viewport pointed on the quartz crystal was used to thermally image the quartz crystal surface and to directly monitor its temperature.

The entire quartz crystal microbalance head assembly can be retracted behind a gate valve allowing to replace the quartz crystal without breaking vacuum in the MBE chamber. Pure silicon dioxide monocrystals (RC-cut) were used as oscillating quartz crystals with “Inficon” patterned gold electrodes deposited on the chromium underlayer (PhillipTech). Electrode surfaces had a nominal rms roughness of 7 μm. Quartz crystals were operated at 5.989 MHz.

Prior to each experiment, a previously unused quartz crystal was loaded to avoid deposition history effects. Typical MBE chamber pressure during the experiments was about 5 × 10⁻⁹ Torr. Low temperature, single filament Knudsen effusion cells were used to supply selenium and tellurium fluxes to the QCM. Typical effusion cell temperatures were 165 and 225 °C for selenium and tellurium, which resulted in atomic fluxes of 1.79 × 10¹⁴ Se atoms/(cm²× s) and 8.44 × 10¹³ Te atoms/(cm²× s) and thus deposition rates of 0.49 and 0.29 Å/s, respectively. These fluxes were kept constant throughout the present work. The tooling factor for the QCM measurements of both fluxes was determined by physical thickness measurements of Se and Te films. For Se, x-ray reflectivity measurements were used to extract the thickness of Se cap grown on Bi₂Se₃ films at room temperature. A Te film was deposited on a sapphire sample and physical thickness measurements were obtained using secondary electron microscopy images of the sample's cross section.

Quartz crystal microbalances (QCMs) are commonly employed to determine the deposition rate in physical vapor deposition systems.³² An electric AC signal applied to metal electrodes of the piezoelectric quartz element generates bulk acoustic waves, and the shift of resonant frequency induced by depositing additional mass is detected. However, frequency shifts can also occur due to changes of the quartz’ stress state, which can be mitigated using SC-cut (stress-compensated) quartz.³⁴ Unintentional temperature increase or the presence of thermal gradients due to radiant heat exposure from effusion cells or e-beam evaporator can originate these stress induced frequency artifacts. The choice of RC-cut quartz crystals over more conventional AC-cut quartz offers advantages of increased sensitivity and higher stability against temperature fluctuations.³⁵ Since any frequency shift detected by the control electronics is interpreted as a change in the oscillating mass, temperature and stress induced changes in the piezoelectric properties of RC-cut crystals will give rise to a “deposition rate” as well.

In order to distinguish temperature induced effects from actual film deposition rates, a QCM temperature calibration was initially performed. The results of the temperature baseline measurements are shown in Fig. 2. A new quartz crystal was mounted, and the frequency shift detected in the absence of any deposition was recorded. Rather than using a PID controller to maintain a fixed QCM temperature, a constant current was applied to the QCM heater (constant power mode). Different QCM heater power settings ranged from 10% to 30%. Temperature curves measured by the thermocouple element inside the QCM head and quartz crystal surface temperatures detected by the IR camera along with the deposition rate signals during QCM heating are shown in Figs. 2(a) and 2(b). After the maximum temperature was reached, the QCM heater power was set to zero to cool down the QCM head. Temperature curves and rate signals during QCM cool down are shown in Figs. 2(c) and 2(d).

Note a significant temperature difference between the quartz crystal surface measured by the IR camera and the thermocouple reading inside the QCM housing. In the temperature interval used for the experiments, a linear relationship between thermocouple reading T_TC and quartz crystal surface temperature T_IR was found, see Fig. S1 of the supplementary material.⁴¹ 

The rate signal approached zero as soon as the QCM temperature stabilized. The time to reach a stable QCM temperature was dependent on the output power. While negligible rates for an output power setting of 10% were obtained after about 20 min, higher output power settings needed to achieve a higher QCM temperature resulted in longer rate stabilization times. Irrespective of heating or cooling cycle and output power levels used QCM temperature stabilization and a vanishing rate signal were achieved after about 2 h. Rate signal deviations from the actual rate were found to be proportional to the temperature ramp rate, which was highest during the initial time after turning the QCM heater on or off. Specifically, in the first 25 min of a heating process with 30% power a high temperature ramp rate of ∼5 °C/min was recorded, while at a power level of 10%, the temperature ramp rate was only ∼0.4 °C/min. The steeper temperature ramp rate at 30% heater power led to a significant frequency shift and thus to a larger deviation from the nominal rate of 0.0 Å/s. Typical peak values of the rate signal during QCM heating ranged from just over 0.5 Å/s (10% output power) to close to 7.0 Å/s (30% output power) and typically occurred within the first ten minutes of the QCM temperature ramp-up. For the highest power settings used here the positive ramp rate was followed by a negative ramp rate, which reached values of about −1 Å/s (25% output power) and −2 Å/s (30% output power). The temperature and rate signal behavior suggested that temperature gradients across the quartz crystal affected the rate signal. An increase in temperature gradient resulted in a positive deviation from the nominal rate signal, while a decrease of the temperature gradient gave rise to a negative deviation from the nominal rate signal. These effects were more pronounced during QCM cool down. Rate deviations up to 50 Å/s were detected right after turning off the power due to a current spike to the heater. The sudden rate signal increase was followed by a negative rate signal, which returned to the actual rate of zero within 90 min. Temperature and rate signal cycles were found to be very reproducible for different heater power levels, see Fig. S2 of the supplementary material.⁴¹ 

Knowing the temperature induced rate deviation characteristics of the QCM allowed measuring the temperature dependent sticking coefficient of selenium and tellurium directly. Since sticking coefficients are strongly affected by the surface chemical state a chalcogen film was deposited on the QCM first. This deposition was performed without heating the QCM and was used to calibrate the chalcogen supply rate from the Knudsen effusion cells. An effusion cell temperature of 16 and 225 °C was used for selenium and tellurium, which resulted in a deposition rate of 0.49 and 0.29 Å/s, respectively. It was further assumed that this deposition rate reflected the ideal sticking coefficient of unity. Note that the thermocouple of the QCM assembly was reading room temperature, while the quartz crystal surface measured by the IR camera was 4 °C. The temperature discrepancy was attributed to a remote cooling effect of the quartz crystal surface being directly exposed to the cryoshroud of the MBE reactor being at liquid nitrogen temperature. In contrast, the QCM thermocouple was shielded by the QCM housing which caused the pronounced difference in the two temperature readings. Taking into account the ratio of vapor pressures for selenium and tellurium at these quartz crystal surface temperatures and the respective effusion cell temperatures the desorption rates normalized to the incident flux were estimated to be about six (seven) orders of magnitude smaller for selenium (tellurium),^36,37 sufficient to assume a sticking coefficient of one.

Following the flux calibration with the QCM, the effusion cell temperature was kept constant using a PID controller and the QCM was heated up to the initial temperature step. During temperature ramp-up, the QCM was continuously exposed to an atomic flux to compensate for unintentional loss of the initial chalcogenide layer thus ensuring that the QCM surface remained completely covered by the chalcogenide element of interest.

After QCM rate stabilization in the presence of an atomic flux, the shutter was closed to confirm that the actual rate signal was constant. The following shutter sequence was performed at a fixed QCM temperature: open shutter initially for about 30 min, then twice for about 10 min, separated by about 10 min of closed shutter. After finalizing the shutter sequence at a fixed temperature, the constant power level of the QCM heater was increased and the shutter was opened again until the QCM temperature stabilized at a higher temperature. The sequence employed is schematically shown in Fig. 3.

Figure 4 shows the deposition rates measured for selenium at six different film surface temperatures ranging from 17 to 60 °C. Spikes in the rate measurements exceeding the maximum supplied rate were observed after about 20 min in Fig. 4(b), upon initial shutter opening in Fig. 4(c), and after 30 min in Fig. 4(d), which were found to be unrelated to QCM temperature or heater output power changes and therefore attributed to flux instabilities of the effusion cell. Their origin is unclear. These flux instabilities were found to be not relevant for the extraction of sticking coefficient since the measured rate always stabilized at the initial value and identical rate-time dependence of a shutter opening/closing sequence were found in three consecutive, measurements at each temperature step.

At the lowest temperature (power level 10%, film surface temperature 17 °C), QCM rates were constant for open and closed shutters, see Fig. 4(a). While the rate for a closed shutter was near zero, the deposition rate did not quite reach the initial value of 0.49 Å/s, but was reduced to an average value of 0.44 Å/s. Similar rate behavior was found at a film surface temperature of 27 °C [power level 12%, see Fig. 4(b)], while for 35 °C (power level 14%) two new features emerged, shown in Fig. 4(c). Upon opening the shutter (M), a high initial deposition rate peaked to about 0.4 Å/s, which quickly reduced to values a little over 0.2 Å/s. More remarkably, upon closing the shutter (N), the measured rate took small negative values which indicated a net loss of selenium. The rate transients right after shutter operation suggested the presence of a physisorbed (precursor) state with a time delay between adsorption and desorption events.^33,38 Selenium adsorbed on the surface did not immediately evaporate, but rather stayed physisorbed for some time. These physisorption sites were empty prior to shutter opening, which upon starting Se supply to the surface gave rise to a large increase in the deposition rates due to an enhanced adsorption into these physisorption sites without immediate desorption. Over time adsorption into the physisorbed sites saturated and delayed desorption from these sites set in. A steady state was reached resulting in a constant but overall reduced selenium adsorption rate. A similar time delay to “empty” these physisorption sites was observed when the shutter was closed. Here, the deposition rate peaked to negative values due to the delayed, yet still ongoing desorption of selenium from these physisorption sites.

At slightly higher film surface temperatures [power level 15%, Fig. 4(d)], this transient behavior was somewhat reduced, but still present. Upon shutter closing, the negative rate was comparably smaller. While the physisorption sites were still present, although less in number, the average time to desorb off the surface from the physisorbed sites may have shortened and thus could not be resolved in these experiments. Alternatively, physisorbed selenium was more effectively incorporated into the film. For the latter case, one would expect a higher deposition rate compared to the previous temperature, however a much stronger reduction of the sticking coefficient of other, more volatile selenium species at the higher temperature potentially overcompensated for this, resulting in the recorded overall reduction of rate signal when the shutter was open. A slightly negative deposition rate was found throughout the entire shutter sequence when shutters were closed. Since the film surface temperature was constant throughout the entire shutter sequence, this behavior was attributed to a small but constant desorption of the film accumulated on the QCM surface.

Further increasing the temperature [power level 16%, see Fig. 4(e)] enhanced both trends. The rate transient upon shutter opening was further reduced, an even smaller steady state rate was found when exposing the film surface on the QCM to a selenium flux, and a more pronounced deviation toward negative deposition rates was recorded during shutter closed times. Finally, at the highest film surface temperature of 60 °C a rate transient was found that closely resembled the features of the rate profile found at the lowest temperature [Fig. 4(a)]. The rate transient vanished, the rate change upon shutter operation was immediate and a rate difference of about 0.13 Å/s was found. Remarkably, the QCM rate for the open shutter state was about −0.27 Å/s, suggesting that even in the presence of a selenium flux the film desorbed from the QCM surface.

The temperature dependent QCM rate signals suggested that the Se flux supplied from a thermal effusion cell contained more than one chemical form of selenium with different adsorption and desorption kinetics. Measuring the sticking coefficient at higher temperatures was not further pursued because the high net desorption rate even upon exposure of the QCM with Se fluxes could have resulted in a complete desorption of the Se film, altering the sticking coefficient measurements in an uncontrolled manner.

To account for the much lower volatility of tellurium, the QCM initially coated with a tellurium film was heated up to an initial power setting of 20% (film surface temperature T_IR= 88 °C). For subsequent increase of film surface temperatures on the QCM, the heater power level was increased in increments of 2% up to a maximum power level of 30% (T_IR= 165 °C). The QCM rates measured at all temperatures for tellurium are shown in Fig. 5. For the lowest two film surface temperatures of 88 °C [Fig. 5(a)] and 101 °C [Fig. 5(b)], constant deposition rates were found throughout the shutter opening time, which decreased with increasing temperature. The oscillatory behavior of the flux measured during the opening times was due to the PID settings of the tellurium effusion cell. At higher film surface temperatures of 115 °C [Fig. 5(c)] and 129 °C [Fig. 5(d)], the steady deposition rate further decreased considerably, while the transient behavior right after shutter operation emerged. The QCM rate for closed shutter was zero. Further increasing the film surface temperature to 149 °C [Fig. 5(e)] and 165 °C [Fig. 5(f)] suppressed the transient behavior and further reduced the steady deposition rate until at the highest temperature the deposition rate was near zero for open and closed shutter. At these high temperatures, the tellurium desorption rate during closed shutter times was negligible. At the highest temperature, a small negative rate was recorded, indicating the onset of tellurium film desorption to coincide with the temperature at which a near zero deposition rate was recorded.

The overall behavior of the temperature dependent adsorption and desorption behavior for selenium and tellurium are therefore quite different. While the kinetics of two different selenium species could be distinguished, thermally evaporated tellurium only contained a single type.

From the temperature dependent deposition rate sequences, the sticking coefficients of selenium and tellurium on the respective surfaces were extracted. Deposition rates measured about one minute right before and after shutter operation were averaged and the deposition rate change upon shutter operation was extracted. All six deposition rate changes extracted for a specific film surface temperature T_IR were averaged and are plotted in Fig. 6 for selenium and tellurium. Note that this extraction method determined the total sticking coefficient including the physisorbed states exhibiting the pronounced transient behavior. The reason for the relatively large error for sticking coefficient values around 0.5 was attributed to the different deposition rate changes from the transient state upon shutter opening and shutter closing.

The sticking coefficient of tellurium on tellurium started to drop at a film surface temperature of around 90 °C and sharply decreased at temperatures higher than 100 °C. Tellurium sticking coefficients for temperatures higher than 150 °C were zero within the error of the measurement. For selenium, a similar sharp drop of the sticking coefficient was obtained, albeit at much lower temperatures around 30 °C. Rather than approaching a zero-sticking coefficient at considerably higher temperature it remained slightly above 0.2. These results suggest that at least two selenium species with different sticking coefficients were supplied. Earlier work on the composition of Se species in the atomic flux of thermally evaporated solid source Se material by simple single filament effusion cells and cracker cells supports this conclusion.^39,40 It is speculated that the majority of species (∼80%) in the molecular beam generated by thermal evaporation of selenium had a very low sticking coefficient, which was near zero already at temperatures around 50 °C, while a minority of selenium species (∼20%) did not show a considerable reduction of sticking coefficients at these temperatures.

In summary, deposition rate measurements taken by quartz crystal microbalance at different temperatures allowed for the direct determination of temperature dependent sticking coefficients of the volatile chalcogen elements selenium and tellurium. Sensitivity to mass gain and robustness toward higher temperature RC-cut quartz crystals used as a microbalance were found to be ideally suited for this experiment. Pronounced reduction of the sticking coefficients by about a factor of 4 in narrow temperature ranges of 20 and 30 °C were determined for selenium and tellurium at 35 and 115 °C, respectively. While the sticking coefficient of tellurium reached zero at temperatures above 150 °C, the sticking coefficient of selenium remained about 0.2 up to a temperature of 60 °C, suggesting that selenium was present in different chemical forms with different sticking coefficients. The direct determination of sticking coefficients provides important insights into the growth kinetics of chalcogenide-based films pointing toward the need of a precise temperature control during chalcogenide film growth. Further experiments are needed to elucidate the different chemical forms of selenium and a comparison how selenium supplied from a cracker cell affects the amount and type of Se species.

The present work was supported by the Pennsylvania State University Two-Dimensional Crystal Consortium—Materials Innovation Platform (2DCC-MIP). 2DCC-MIP is supported by the National Science Foundation (NSF) Cooperative Agreement No. DMR-1539916.

The data that support the findings of this study are available from the corresponding author upon reasonable request.