We report on a method of photoemissive film growth that controls stoichiometry in real time. We show that stoichiometry control using a feedback loop is possible because (a) photoemissive properties exhibit a distinct dependence on the stoichiometric composition and (b) stoichiometric composition strongly depends on the ratio of the incident fluxes. The reported results were obtained on Cs3Sb but are expected to be relevant to other alkali antimonides and tellurides.

Alkali antimonide photocathode films such as Cs3Sb and K2CsSb are likely candidates for the next generation electron sources with high beam brightness.1 However, while exciting results of material engineering have been accomplished in user-facilities,2–4 the state of the art for injector growth systems is represented by nanocrystalline films, whose physical and chemical roughness does not allow approaching the thermal limit of the mean transverse energy of emitted electrons.5 Significant progress is needed in the growth technology in order to fabricate near atomically smooth single crystalline alkali antimonide thin films, and this technology needs to be transferable to cathodes that can be used in injectors. The study presented in this Letter addresses the issue of stoichiometry control, a pre-requisite for elaborate growth techniques such as molecular beam epitaxy (MBE), and does not rely on expensive and/or time-consuming techniques involving Kelvin probe force microscopy (KPFM),5 scanning tunneling microscopy (STM),4 or synchrotrons2,3 to achieve it.

A strong effect of alkali antimonides' stoichiometry on the quantum efficiency (QE) was discovered more than 50 years ago in the context of the studies of polarity of conductivity, see Chap. VI in Ref. 6. It was established experimentally that maximum photoemission is attained not at 1:3 Sb-to-alkali atomic ratio but with a small (a few percent7,8) stoichiometric offset instead. The peak of photoemission was found to coincide with the stable state of the compound, the one that is achieved when a film with excess alkali content eventually loses it into vacuum.6 In this Letter, we will refer to such slightly off-stoichiometric composition that corresponds to maximum photoemission as optimum stoichiometry.

The studies mentioned above were conducted on the films obtained by the sequential deposition method when a film undergoes extremely wide changes in stoichiometry, starting with 100% antimony, then significantly alkali-rich, and finally arriving at the optimum.6,9 The significance of stoichiometry control is greatly amplified for the case of molecular beam deposition, when the goal is to slowly grow a uniform film that was also shown to be significantly smoother.2,10 To differentiate from sequential deposition, molecular beam deposition of alkali antimonides is often dubbed as co-deposition4,10,11 or co-evaporation.2 The fact that the ratio of incident fluxes has a strong effect on the QE of a growing alkali antimonide film has been reliably established experimentally.4,11–14 Thus, within a fairly wide range in the vicinity of optimum stoichiometry, the ratio of incident fluxes affects the stoichiometric composition; hence, dynamically adjusting the ratio creates a tool to control the stoichiometry.

Adjusting the ratio of incident fluxes during the growth is, indeed, a common practice in the field to achieve higher QE, with some reports claiming that QE maximization can actually be accomplished.4,13 Given the absence of details on the flux adjustment procedures, we are led to believe that those are manual and largely intuitive actions that are somewhat successful at attaining higher QE at the end of the growth, but are not truly maximizing instantaneous QE in real time. In fact, it would be impossible to implement a QE maximization scheme because QE of the film is also a function of its thickness.6,15 One could arguably normalize QE by the film's thickness first or attempt to maximize the rate of QE increase vs time. Although not impossible in principle, practical realization of such schemes would introduce another level of ambiguity and complexity, making it prone to lags and instabilities.

Sample to sample variation of alkali antimonide films QE is rarely mentioned. Whenever reported, it is very large4,13,14—a ratio of two or more between the best and the worst sample in a series, and so is the variation of stoichiometric composition14 and of the ratio of fluxes4,13—several tens of percent. It is, therefore, reasonable to consider poor stoichiometry control as a significant, if not dominant, factor in unsatisfactory reproducibility of alkali antimonide film growth experiments.

The study reported in this Letter was conducted in a UHV molecular beam deposition system.16 Stable and relatively agile pre-calibrated elemental sources were used to obtain the necessary accuracy of flux control (of the order of 1%). The fluxes were directed at about 15° with respect to sample substrate normal, with flux non-uniformity across 1 cm substrate estimated to be better than 10%. Laser diode modules attenuated to deliver ∼100 μW in a ∼1 mm2 spot were used for intermittent photo-excitation of the samples with a moderate sampling rate (∼0.1 Hz), synchronized with the photocurrent measurements. A bias of approximately 100 V was applied to an anode ring placed at 2–3 cm in front of the sample; collected photocurrent was measured by a picoammeter. Commercial Si substrates were cleaned at 600 °C in UHV for a few hours prior to depositions.

In order to establish true stoichiometry control, one first needs to find a parameter that (i) is fundamentally related to stoichiometry, (ii) can be measured in situ as the film is growing, and (iii) is film thickness-independent.12 We provide here an experimental demonstration that such parameter can be identified, owing to the fact that not only QE of an alkali antimonide film strongly depends on the stoichiometry in a wide range of wavelengths, but the shape of the spectral response curve also changes, see Fig. 1. We chose to track the ratio of QEs measured well above the photoemission threshold (at 405 nm, QE405 nm) and slightly above the threshold (at 532 nm, QE532 nm). It is likely that the change of the ratio is related to the shift of photoemission threshold of a few tens of meV,12 but because of uncertainty in the determination of the threshold value, further studies are required to make a stronger statement. The growth (Fig. 1) is started in the Cs-rich mode, and then as the Cs flux is slowly ramped down, the optimum growth condition is achieved at some point with subsequent transition into the Sb-rich mode. Because of a relatively high substrate temperature (roughly estimated at 80 °C17) and slow growth rate (about 0.03 Å/s), the excess Cs atoms are expected to have enough time to diffuse through the bulk of the film toward the top; hence, during the experiment, largely the whole film undergoes transition from slightly Cs-rich to slightly Sb-rich, not just its top layer. Nonetheless, in a dynamic equilibrium, some non-uniformity remains; therefore, the dependence in Fig. 1 should be interpreted semi-quantitatively as follows. Because the ratio of fluxes changes approximately linearly vs time, time axis effectively represents stoichiometry (note that we limited ourselves to defining the fluxes ratio in arbitrary units because of calibration uncertainties; however, the atomic ratio is, indeed, close to 3:1, indicating that the effective rejection rate for Cs is low). Thus, a well-defined dependence with an asymmetric minimum of QE405 nm/QE532 nm vs stoichiometric composition exists (Fig. 1), making QE405 nm/QE532 nm a parameter that satisfies all three requirements mentioned above. In light of the dependence of the photoemissive properties on the stoichiometric compositions (Fig. 1), pronounced oscillations of the QEs and QE405 nm/QE532 nm observed in response to a modulated Cs/Sb flux ratio in Ref. 12 can be largely attributed to the periodic variations of the film's stoichiometry, while in the Cs-rich growth mode; the fact that the oscillations of the QEs are essentially in phase with each other but out of phase with respect to the QE405 nm/QE532 nm oscillations suggests that the position of the minimum of QE405 nm/QE532 nm is close to the optimum stoichiometry in terms of maximum photoemission (dominated by QE well above the threshold) in Sommer's experiments, Chap. VI in Ref. 6. The ratio of QEs QE405 nm/QE532 nm can enable real-time control of alkali antimonide stoichiometric composition if used as an optimization parameter in a feedback loop. In an ideal situation, one would probably want to target the very minimum value of the parameter. Practically, we have to deal with the limitations of our instrumentation, so we chose to confine ourselves within the Cs-rich range of stoichiometry (to the left from the minimum in Fig. 1). Within that range, the correlation between QE405 nm/QE532 nm and fluxes ratio is very strong and always positive, making it possible to employ simple yet robust feedback loop, such as proportional–integral–derivative (PID) controller. Targeting the values of QE405 nm/QE532 nm of about 2 should result in production of a few percent Cs-rich film. Coincidentally, producing a slightly Cs-rich rather than a slightly Sb-rich film is likely beneficial since excess alkali metal will be naturally removed from the film after the growth.6 

FIG. 1.

Response of the Cs3Sb film photoemission to a gradual change of incident fluxes ratio.

FIG. 1.

Response of the Cs3Sb film photoemission to a gradual change of incident fluxes ratio.

Close modal

An example of Cs3Sb growth controlled by a PID loop targeting the value of optimization parameter QE405 nm/QE532 nm of 2.2 by adjusting the Sb flux is shown in Fig. 2. Prior to the experiment, the PID gains for an approach with some overshoot were found using the Ziegler–Nichols method. The values of PID gains are highly system-dependent, therefore without universal significance. Tuning the PID loop differently would certainly affect the approach to target, as would a different algorithm type. We confirmed that an extremum seeking algorithm18 set to minimize the value of QE405nmQE532nmTarget can be used instead of a PID controller. After the initial settling process, the algorithm locks on the target at about 3000 s. Overall, the evolution of QEs proceeds as expected for a uniform film—approximately linear growth in the beginning of the cycle followed by saturation. Noticeable dips on QE405 nm and, especially, QE532 nm dependences between approximately 1500 and 2500 s are, indeed, due to deviation from stoichiometry, which, in turn, comes from the non-ideal settling process (overshoot). It is a technicality that can be mitigated by better algorithm tuning, using slower growth rates until the target is reached, using more accurate estimates for starting fluxes, and eliminating the measurements artifacts (abnormally high values of QE405 nm/QE532 nm in the beginning of the growth are due to slightly photoemissive chamber walls generating additional photocurrent from scattered laser light). QEs in the experiment in Fig. 2 saturate at values that are approximately a factor of 2 lower than expected for Cs3Sb;6,9,11 an accidental contamination of the Cs source has been confirmed as the cause; the film attains full QE if left in UHV for a few days after the deposition. It is possible that the presence of an undesired contaminant in Cs3+xSb is distorting the photoemissive properties, namely, the value of the QE ratio, as compared to a pure material. We believe that such distortion is not very significant because our earlier experiments conducted with pure Cs (see, e.g., Ref. 12) are in good agreement with the QE ratio dependence (Fig. 1), in terms of existence of an asymmetric minimum of QE405 nm/QE532 nm (steep on Cs-rich side, almost flat on Sb-rich side), whose value is not more than 1.7.

FIG. 2.

Algorithm-controlled growth of the Cs3Sb film. The Cs flux is kept approximately constant. Target for QE405 nm/QE532 nm is set at 2.2.

FIG. 2.

Algorithm-controlled growth of the Cs3Sb film. The Cs flux is kept approximately constant. Target for QE405 nm/QE532 nm is set at 2.2.

Close modal

To demonstrate the accuracy and robustness of the stoichiometry control, we conducted a variable growth rate experiment, see Fig. 3. Right after the settling of the PID controller on the target of 2.0 for QE405 nm/QE532 nm, the Cs flux was programmed to follow a distinct asymmetric V-shaped pattern vs time. As evident from Fig. 3, the algorithm driving the Sb flux was largely able to keep up with the change of the Cs flux. The ratio of the maximum to minimum flux is about 2.5 for both Cs and Sb based on the calibrations, with the corresponding growth rates between approximately 0.05 and 0.02 Å/s. Note the lag of Sb heater voltage of about 500 s and deviations of the QE405 nm/QE532 nm from the target value during the process; these are inevitable effects of the algorithm operation. Both effects can be mitigated with better instrumentation and by choosing slower growth rates. Sb heater voltage steps are due to the resolution of the power supply. Dependence of Sb flux on the heater voltage is very non-linear; each voltage step corresponds to approximately 3.7%–4.0% change of flux. Judging by the amount of the overall distortion of the Sb heater voltage pattern, the accuracy of the stoichiometry control in this experiment can be estimated at a few percent level, also in agreement with the variation of QE405 nm/QE532 nm between approximately 1.75 and 2.25, see Fig. 1. It is important to note that experiments similar to the one represented by Fig. 3 can serve as a very efficient tool of finding the starting values of flux-setting parameters for fixed growth rate experiments (Fig. 2).

FIG. 3.

Variable growth rate experiment. The Sb flux is controlled by PID loop. Target for QE405 nm/QE532 nm is set at 2.0. Thickness is approximate, estimated with a quartz crystal microbalance. See text for details.

FIG. 3.

Variable growth rate experiment. The Sb flux is controlled by PID loop. Target for QE405 nm/QE532 nm is set at 2.0. Thickness is approximate, estimated with a quartz crystal microbalance. See text for details.

Close modal

We believe that the principles of the growth scheme demonstrated in this Letter could be immediately applied to some other mono-alkali antimonides as well as related compounds such as Cs2Te. Whether or not, and how effectively, the principles can be applied to bi- and multi-alkalis, depends on a particular relationship between the photoemissive properties and stoichiometry, now described by more than one parameter. For example, for K2CsSb, a version of dependence in Fig. 1 would become a three-dimentional plot (surface), where the ratio of QEs is a function of both K and Cs contents (normalized by Sb content). A global minimum likely exists on the surface, whose position is close to the optimum stoichiometry. If there are sufficiently smooth, large, and steep areas around the minimum, then the stoichiometry control can be accomplished using an algorithm that natively supports multiple control parameters.18 

In conclusion, we showed that stoichiometric composition of Cs3Sb has a strong effect on its photoemissive properties for low temperature growth conditions. We characterized the effect experimentally, by observing the change of QE405 nm/QE532 nm parameter. Relying on the strong correlation between QE405 nm/QE532 nm and stoichiometry for slightly Cs-rich films, we developed an automated growth control scheme where one of the fluxes is controlled by an algorithm. Effectively, the scheme maintains QE405 nm/QE532 nm at a target value around 2 that, in turn, defines a small offset from optimum stoichiometry. Several experiments were conducted with the targets for QE405 nm/QE532 nm ranging from 1.8 to 3.0; assuming reasonable starting conditions, the scheme always worked. We showed that the scheme is robust and can be used within a wide range of growth rates. Stoichiometry control is a capability that is critical for the development of future alkali antimonide growth recipes, such as the ones for MBE. At this point, we do not understand, even qualitatively, the physics behind the effect of stoichiometry on photoemissive properties (Fig. 1). We encourage photoemission model developers to explicitly consider the case of slightly non-stoichiometric alkali antimonides; we would be happy to support such efforts by conducting tailored validating experiments and sharing the data.

The authors wish to thank Fangze Liu and Anju Poudel for technical support. V.P. thanks Dimitre Dimitrov and Enrique Batista for fruitful conversations, and John Lewellen for thorough reading of the manuscript and valuable comments. The authors gratefully acknowledge the support of Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development (LDRD) program, Project Nos. 20190536ECR, 20210595DR, and 20220058ER. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is managed by Triad National Security, LLC for the U.S. Department of Energy's NNSA, under Contract No. 89233218CNA000001. This work was also supported by the Office of Science, Office of Basic Energy Sciences of the U.S. Department of Energy under Contract No. DE-SC0013190.

The authors have no conflicts to disclose.

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

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