Beam brightness from Cs–Te near the photoemission threshold

The demand for robust photocathodes has made Cs–Te a popular choice for driving free electron lasers (FELs), as it combines the high quantum efficiency (QE) of a semiconductor photocathode with durability that approaches that of some metals.^1–3 High QE is particularly important for high average current applications where the power demanded of the UV driving laser may be impractically large for metal photocathodes. At 260 nm (4.7 eV), where Cs–Te is commonly used, the QE is reliably in excess of 10% compared to $10−5$ − $10−4$ for copper.⁴ The durability of Cs–Te has been measured through its operational lifetime, which is routinely in the hundreds of hours in high charge RF photoinjectors.^5–7 Some Cs–Te photocathodes have been successfully used for over 100 days in a photoinjector with minimal degradation of the QE.⁸ In addition to traditional photocathode applications, these properties have caused thin films of Cs–Te to be investigated for activating GaAs photocathodes^9–12 as well as for use in superconducting RF photoinjectors.^13–15 

In spite of its success in terms of durability and QE, Cs–Te's modest mean transverse energy (MTE) in the UV can limit achievable photoinjector emittance. Most measurements place the MTE of Cs–Te at 260 nm (4.7 eV) between 150 meV and 300 meV.^3,15–17 While this MTE is acceptable for present high repetition rate, soft x-ray FEL injectors, planned upgrades to existing facilities such as LCLS-II HE have an emittance requirement as low as 100 nm at 100 pC bunch charge and may directly benefit from reduced intrinsic emittance.^18,19 Driving photocathodes near threshold is a well-known strategy in reducing their MTE at the cost of QE. Dowell and Schmerge²⁰ showed that the three step model predicts a linear rise in MTE with respect to photon energy for ideal photocathodes and the MTE for near-threshold photoemission has been shown to be limited by temperature in some cases (⁠$MTE=kBT$⁠).^21–23 This motivates the present measurement of the MTE of Cs–Te near threshold at both room and cryogenic temperatures.

Cs–Te photocathodes, for which the bulk of photoemission comes from Cs₂Te, often exhibit a “shoulder” in their spectral response that consists of low QE (⁠$<10−5$⁠) photoemission at visible wavelengths. Excess Cs was blamed for the shoulder throughout the 1960s based on photomultiplier tube measurements.^24–26 However, Fisher et al.²⁷ and later Powell et al.²⁸ contradicted this claim and argued that another phase of Cs_xTe other than Cs₂Te must be present in the cathode along with elemental Cs. They found that the shoulder vanished when adding Cs followed by heating and failed to decrease when Te was deposited along with more heating, which should have converted the excess Cs into Cs₂Te. Additional data from UV photoemission spectroscopy failed to line up with that of elemental Cs or elemental Te alone.²⁸ 

Direct confirmation of a second phase of Cs_xTe that coexists with Cs₂Te first came from x-ray diffraction data, which identified that phase as Cs₅Te₃.²⁹ However, a lack of photoemission measurements prevents confirmation that this phase is correlated with observed photoemission properties. Later work using Auger electron spectroscopy (AES) and x-ray photoemission spectroscopy (XPS) during the growth of Cs–Te photocathodes identified impurities of the form Cs_xTe with x = 1.2 and x = 0.9.^30,31 Recently, real time in situ x-ray characterization of Cs₂Te growth was also able to observe the production of a Cs_xTe in their photocathodes, but found that it could be eliminated in diffraction measurements by using a codeposition growth technique.³² However, x-ray fluorescence spectra of the codeposited samples indicated that the photocathode was not fully stoichiometric Cs₂Te.³² 

In this paper, we present measurements of the MTE of Cs–Te photocathodes for near-threshold photoemission. First, our growth technique is discussed and results of our measurements are presented for both room and cryogenic temperatures. We observe a sharp increase in MTE as the driving laser's wavelength approaches the photoemission threshold of pure Cs₂Te. Two models are posited, which help to explain this behavior as pollution of the photoemitted electron distribution by emission from low work function compounds present alongside Cs₂Te. Our results indicate the need for phase-pure Cs₂Te photocathodes in order to achieve the low near-threshold MTE desired for future accelerator physics applications.

Two Cs–Te photocathodes were grown with sequential deposition on commercial Si substrates: one that is expected to be representative of typical growth procedures (here, called “sample one” or “cesium rich” growth) and one where the growth was terminated early to reduce the level of cesium on the surface (“sample two” or “low cesium” growth). The substrates were both cleaned at 600 °C for 12 h under ultra-high vacuum and then held at $∼120$ °C while a 20 nm layer of tellurium was deposited (chosen to be a common thickness used in photoinjector facilities). The QE at 405 nm (3.0 eV) was monitored while cesium was evaporated into the chamber as in Fig. 1. For sample one, evaporation was terminated after the QE reached a second peak. For sample two, the deposition was stopped at the first peak in QE at 405 nm (3.0 eV). The reported “effective Cs thickness” is derived from a quartz crystal microbalance and may have varying accuracy with process parameters. It is used here only to illustrate the growth procedure.

Both samples were transferred into the MTE meter described in Ref. 33 and their QE was measured at room temperature and 80 K, using liquid nitrogen, as shown in Fig. 2. MTE was measured as a function of wavelength using the voltage scan technique with a cathode voltage that ranged from −3 kV to −10 kV. Uncertainty in the measurements is shown as the vertical bars in the plot or, when not visible, is smaller than the data points shown. Both measurements were made with the cathodes illuminated by a monochromated arc-lamp based light source. At long wavelengths, measurement of the MTE was hindered by the low QE of the photocathodes and the low power of the light source used.

To better investigate the non-monotonic behavior of the photocathodes at visible wavelengths, another set of samples was grown using the typical procedure (“sample three”) and early termination (“sample four”). MTE and QE were measured using an NKT Photonics SuperK Extreme monochromated supercontinuum light source, with comparatively greater power. These data are plotted in Fig. 3. Additional points at short wavelengths were collected using the arc-lamp based light source, the third harmonic of an Amplitude Systems Tangerine fiber laser (343 nm or 3.6 eV), and a set of UV LEDs. The low energy nature of the voltage scan measurements and the pulsed output of the supercontinuum light source make these data susceptible to the effects of space charge. Additionally, high intensity illumination on the cathode may cause multiphoton photoemission, which affects the MTE.³⁴ We confirm that these sources of error are avoided by checking for agreement with measurements at select wavelengths using low intensity (but similar average power to the supercontinuum light source) CW diode lasers (plotted in Fig. 3).

The non-monotonic behavior of Cs–Te's MTE suggests that multiple compounds contribute to photoemission for wavelengths below the threshold of Cs₂Te. Because the MTE is the variance of the momentum distribution of the electrons off the cathode, the MTE of a combined distribution (here, from multiple photoemitting materials) will be a weighted sum of individual MTEs, where the weights are determined by the QE and abundance of each source. We express this as

where the index i runs over all of the components of the photocathode and the weights w_i account for the prevalence of each component. For a two (or more) compound system where the QE is dominated by the higher work function material at high photon energies, the MTE will be set by the lower threshold material at low photon energies and by the higher threshold material at high energies. This may lead to non-monotonic behavior even when the MTE of each individual compound only rises with excess energy. A schematic of how this can happen is shown in Fig. 4.

For simplicity, we consider emission from multiple compounds (and crystalline orientations) with an assumed step function electron occupation, where their MTE and QE are given by the analytical expression due to Dowell and Schmerge.²⁰ The QE in the absence of reflectivity and scattering is given by

and the MTE is

where E_f is the Fermi energy, $ℏω$ is the photon energy, and $ϕ$ is the work function. The free parameters are the workfunctions of each component at each temperature [$ϕi$ (80 K) and $ϕi$ (300 K)], the component's Fermi energies (⁠$Ef,i$⁠), and the relative contribution of each component to the total photoemission. The work function is assumed to encompass an ∼15 meV shift in the photocathode's threshold due to Schottky lowering in the instrument's 0.1–1 MV/m extraction field. The temperature dependence in this model is dealt with by a change in the work function of each material as a function of temperature, which is known to occur from expansion of the crystal lattice³⁵ or from a surface dipole due to adsorption of molecules on the cooled surface.

A minimum of three components is needed to reproduce the experimental data. These can be attributed either to different compounds or to different crystalline orientations, since the work function of a material may also depend on the particular crystal face. Our parameters of best fit are listed in Table I and the predicted MTE as a function of temperature and photon energy is shown along with the underlying data in Fig. 3. In sample two, we only fit data at high temperature below a photon energy of 2.95 eV (418 nm) because the sudden drop in MTE observed there is likely due to the onset of photoemission from another compound, which we do not consider here, or possibly from the Cs₂Te itself, which has a bandgap energy of the same value.²⁸ We do not place great physical significance on the Fermi energies returned by the fitting procedures, which are large in some cases. In the context of the Dowell–Schmerge (DS) formulas, the Fermi energy only shows up in the expression for QE and only affects a small change in the MTE of the multiple components model. Additionally, we are fitting a model designed principally for metals to a sample that may include semiconductors where the QE will also depend on band structure parameters.

We are motivated to consider the particular impurities Cs₅Te₃ and Cs from the direct evidence of their presence with Cs₂Te from diffraction data and AES/XPS data. We consider their photoemission properties in the context of the three step model. The electronic band structures of Cs and Cs₅Te₃ were calculated numerically using the density-functional theory (DFT) code JDFTx,³⁶ Garrity-Bennett-Rabe-Vanderbilt (GBRV) ultrasoft pseudopotentials,³⁷ and the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA) functional.³⁸ The calculations used a plane wave cutoff of 544 eV and a Brillouin zone sample mesh of 6 × 6 × 6. The lattice of Cs₅Te₃ was taken from powder x-ray diffraction data³⁹ and structural relaxation was performed before the electronic calculations. An optimal value of the lattice constants for the monoclinic crystal was found to be a = 4.03 nm, b = 1.35 nm, c = 2.85 nm, and $β=135.0°$⁠. For both compounds, a set of maximally localized Wannier functions⁴⁰ (five for Cs and 41 for Cs₅Te₃) was used to capture the band structure in a region ∼6 eV wide surrounding the Fermi energy using the Wannier interpolation method.⁴¹ 

Given the numerical band structure, a surface orientation, and work function, the probabilities of the three step model and, therefore, the desired photoemission properties may be calculated using the method described in Ref. 42. The rate of direct transitions between states in the band structure is given by Fermi's golden rule weighted by the probability of the initial state being occupied and the final state being unoccupied. For the sake of simplicity, the Cs₅Te₃ is assumed to be undoped with the Fermi level in the middle of the bandgap. For a crystalline orientation whose surface has the normal vector $r→s$⁠, we require electrons excited to a final state with crystal momentum $k→f$ to satisfy the condition

if they will be transmitted to the surface in the absence of scattering. The electrons will escape from the crystal as long as their final state energy is large enough to satisfy the condition

where $T⊥$ represents the kinetic energy of an electron in a direction perpendicular to the surface once in vacuum. A weighted average of the escape probability and transverse energy of escaping electrons is computed for all direct transitions in the first Brillouin zone using a Monte Carlo integrator to obtain the QE and MTE.

The weights of compounds, weights of crystal orientations, bandgap temperature dependence of Cs₅Te₃, and workfunctions of each compound were fit to the photoemission data using derivative-free global optimization.⁴³ The parameters of best fit for both samples are reported in Table II and the best fit curves are shown in Fig. 3. The sign of the work function's temperature dependence points to adsorption as a likely cause. The failure of the model to match the qualitative behavior of the low temperature data in sample four could be due to us not accounting for all orientations of the compounds that are present. The Cs₅Te₃ could also be severely disordered, or other impurities may be present.

In this Letter, we have reported measurements of the MTE of Cs–Te for near-threshold photoemission and at cryogenic and room temperatures. Our analysis of the measurements has shown that the near-threshold behavior of the photocathodes may be explained by emission from multiple compounds that emit below the threshold of pure Cs₂Te. Historical measurements suggest that the likely identity of the low work function compounds in Cs–Te is metallic Cs and the semiconductor Cs₅Te₃, which is known to show up in samples with a similar ratio of Cs and Te to what is used for photocathode growth. We were able to model the below threshold behavior of the photocathodes by assuming that multiple compounds contribute to emission, each of which is well described by the Dowell–Schmerge expressions for MTE and QE. Taking the compounds to be Cs and Cs₅Te₃ and computing their photoemission properties numerically, we were able to achieve good subjective agreement with the data in almost all cases.

Photoemission from the additional compounds may also help explain the measurement of two-photon photoemission at 800 nm (1.5 eV) reported in Ref. 44. In that study, photocurrent was measured as a function of pulse energy under illumination with an ultrafast 800 nm (1.5 eV) light source. It was observed that emission scaled quadratically with pulse energy instead of the expected cubic dependence if the sample was pure Cs₂Te and had a threshold in the UV. The anomalous two photon photoemission may be explained if the electrons were being emitted from the low work function compounds observed here rather than the pure Cs₂Te assumed in the paper.

Low threshold compounds that are present alongside a high work function photocathode may present a barrier to achieving low MTE even when those compounds are present in trace amounts. These compounds may show up as a shoulder in the cathode's spectral response. Indeed, there are other alkali tellurides that have low level photoemission at long wavelengths similar to what we see in Cs–Te.^24,45 The use of this family of photocathodes will likely require research into methods of growing phase pure samples. Some promising results are already coming from this area with reports that codeposition growth of Cs–Te is able to produce a more pure photocathode than the sequential deposition growth studied in this work.³² Further studies on the near-threshold MTE of photocathodes grown with this procedure and of other alkali metal photocathodes with a photoemission shoulder may be warranted.

The authors wish to thank Kevin Nangoi and Tomás Arias for valuable discussions. This work was supported by the U.S. National Science Foundation under Award No. PHY-1549132, the Center for Bright Beams.