Reduction of surface roughness emittance of Cs₃Sb photocathodes grown via codeposition on single crystal substrates

Semiconductor photocathodes, such as alkali antimonides, are the electron sources of choice for many accelerators, ranging from energy recovery linacs,¹ high repetition-rate free electron lasers,² and systems for ultrafast electron scattering.³ Among semiconductors, alkali antimonides have a high quantum efficiency in the visible spectrum, are relatively robust in high power beam delivery, and have been shown to be capable of low mean transverse energy (MTE) photoemission, where MTE characterizes the width of the initial transverse momentum distribution of photoemitted electrons.^1,4 The maximum normalized transverse beam brightness achievable by a linear accelerator B_n, a critical figure of merit for a great number of applications, depends on MTE,

where m_e is the electron mass, c the speed of light, I the beam current, and σ_x the rms beam size at the cathode.

MTE can be reduced by reducing the photon energy of the drive laser to match the material's work function at the cost of quantum efficiency.⁵ In this condition, the MTE of emission is typically limited by the thermal energy at the material temperature, which at room temperature is $MTE=kBT=25$ meV. Cooling both metallic and semiconductor photocathodes has yielded further reductions in MTE.⁶ Cs₃Sb was demonstrated to be capable of sub-room-temperature emission (⁠$MTE=22$ meV) when operated near the photoemission threshold (wavelength 690 nm) and at low temperature (90 K), while maintaining a QE of $∼10−4$ which is at least three orders of magnitude higher than metals operating in similar conditions.^4,6 High QE is critical to keep laser fluence low so as to not stimulate mulitphoton effects, which can increase MTE.⁷ 

Importantly, the minimum MTE of 22 meV measured from Cs₃Sb significantly exceeds the sample temperature (90 K) thermal energy (k_BT = 8 meV). The lowest measurable intrinsic emittance can also be limited by the surface inhomogeneities of photocathodes, such as physical surface roughness and work function variations (often termed “chemical roughness”), that can give rise to field-dependent MTE contributions of several tens of meV at realistic electric fields, even for the smoothest, most homogeneous photocathodes grown to date.^4,8–11 The effects of chemical roughness on MTE decrease with increasing extraction electric field, whereas those from physical roughness increase. As modern photoinjector designers seek to maximize photocathode electric field^12–14 to minimize the space charge effect, we focus on the effects of physical roughness in this work. Furthermore, we use MTE throughout this work (as opposed to intrinsic momentum spread) because the MTE contribution from physical roughness is directly proportional to the applied electric field.

The surface roughness of alkali antimonide photocathodes strongly depends on the growth procedure. The first synthesis method used for alkali antimonides in accelerators was sequential deposition: a Sb film is deposited first, and then it is exposed to alkali vapors, until the photocurrent is maximized.^1,15–18 More recently, studies have focused on growth by coevaporation of Sb and alkali metals, which has yielded much flatter photocathodes, but still with roughness-induced MTEs much higher than room temperature for the highest field electron sources.^9,11,19

We study the surface properties of Cs₃Sb photocathodes grown with elemental effusive sources on various single crystal substrates and transferred via UHV suitcase to a scanning tunneling microscope (STM) system. We investigate both lattice-matched (i.e., having in-plane lattice parameters close to the ones of the film) and lattice-mismatched substrates. Lattice-matched substrates promote heteroepitaxial growth that can potentially give single crystalline samples with reduced roughness and higher brightness.²⁰ 

Our results show that high efficiency Cs₃Sb photocathodes grown by codeposition have widely varying surface morphology as a function of substrate material. One lattice-matched substrate, 3C–SiC(100), yielded island sizes roughly 10 times the size of the other substrates, with reduced roughness. Using the STM data, we then compute the contribution to MTE from surface roughness for each sample and find that this MTE varies by a factor of 17 across all samples, with the lowest value, 0.24 meV per unit MV/m, lower than typical calculated values on alkali antimonide photocathodes.^9,11 Finally, we present results of dosing one of the measured samples with O₂ and show that oxidation has no discernable effect on the nanoscale morphological features. This suggests that alkali antimonide photocathodes can retain their surface topography despite incidental oxidation during transport or during use in an electron gun.

The samples were grown on single crystalline substrates with different in-plane lattice parameters: Al₂O₃(⁠$101¯0$⁠) (⁠$a1=0.4758$ nm, $a2=1.299$ nm), rutile TiO₂(001) (⁠$aTiO2=0.4594$ nm), cubic SiC (3C–SiC)(100) (⁠$a3C=0.4397$ nm), all with $90°$ angle between the in-plane lattice parameters. Our target compound, Cs₃Sb, has a cubic structure with lattice parameter a = 0.9147 nm, close to twice the in-plane lattice parameter of TiO₂(001) and 3C–SiC(100). The surface finish of the epitaxy ready substrates is characterized by a roughness average $Ra<0.5$ nm for TiO₂(001) (MTI) and Al₂O₃ (⁠$101¯0$⁠) (Crystech), and $Ra<1$ nm for the 3C–SiC(100) (MTI).

All substrates were sonicated for 15 min in acetone and methanol, thoroughly rinsed in DI water and degassed at $∼550 °$C in vacuo for about 6h. Samples were grown at substrate temperature of $70 °$C, molecular fluxes of $0.9–1.3×1013$ atoms/cm²/s for Cs, and $2–3×1012$ atoms/cm²/s for Sb, with a total deposited Sb thickness of $∼15$ nm. The Sb flux was tuned during the growth to maximize the QE at 530 nm. After the growth, the samples were loaded in a UHV suitcase and transferred to a UHV XPS-STM chamber. Typical QE of the as-grown samples was 3%–7% at 530 nm; after the transfer the QE decreased to $∼2%$ (see the supplementary material). Details on growth, QE measurements, and transfer procedure are reported in Refs. 21 and 22. A sample grown on H-terminated Si(100)²² at $90 °$C was used for controlled oxidation experiments.

STM measurements were performed in constant current mode with an Omicron variable-temperature STM at room temperature, using electrochemically etched W tips. In constant current mode, the tip is raster scanned on the sample surface (x, y) while a feedback loop controls the tip-sample distance to maintain a constant tunneling current. The height profile is mapped as a function of the raster scan area, and finally, the best-fit plane is subtracted from the raw data. The resulting $z0(x,y)$ is a convolution of the surface topography and the local density of states. Given the spatial scale of the measured tip displacements, we interpret them as arising entirely from surface topography.

In Figs. 1(a1)–1(d2), we show the STM images of 4 samples grown on different substrates (on Al₂O₃, TiO₂, and SiC). In these images, the surface morphologies are displayed in a pseudo-shadowed format which emphasizes edges by mimicking the shadowing observed in glancing incidence illumination, allowing the representation of both subtle and large-scale morphological changes in one image (see the supplementary material).²³ Conversely, the height histograms in Figs. 1(a3)–1(d3) represent the actual tip height data z₀.

The samples grown on Al₂O₃ and on TiO₂ [Figs. 1(a) and 1(b)] show surface features that we can interpret as grains of the order of 10 nm in horizontal size and a height histogram which is symmetric about the mean, which is broader for the TiO₂ sample. This grain size is consistent with morphologies that have been measured by other groups.^9,11

A very different sample morphology is measured on the samples grown on SiC, which show $∼10$ times larger islands. The height histograms in Figs. 1(c3) and 1(d3) are characterized by a narrower peak with longer tails. This distribution is driven by predominantly flat islands surrounded by comparatively rarer trenches and protrusions. Surface features of this size have not been observed previously in alkali antimonide growths.^9,11 A typical metric used to quantify the surface quality of a photocathode is the root mean square (rms) roughness σ_r. The σ_r for the various samples is reported in Table I. We also report the rms value of the slope σ_s defined as²⁴ 

As we will show in the following, σ_r alone cannot describe the surface roughness contribution to MTE. While it is possible to use higher statistical moments of the height distribution,²⁵ a more complete description can be obtained by the Fourier decomposition of the images. The surface height data are expanded in real-valued 2D Fourier components $ϕm,ni$⁠,

with

where a is the lateral size of the image, $ϕ1i=0$ for i = 1, 2 and $ϕ1i=−π/2$ for i = 2, 3. Similarly $ϕ2i=0$ for even i and $ϕ2i=−π/2$ for odd i. Since the grain structure is not ordered, the Fourier amplitudes $Am,ni$ only depend on $m2+n2$⁠. In Fig. 2, we report the radial average of $|Am,ni|$ for the samples of Fig. 1 vs the spatial frequency modulus. We observe that the Fourier amplitudes of the SiC#1 sample decay faster than the ones of the SiC#2 sample, despite the former having a larger σ_r.

Under the assumption of very small kinetic energy of photoemitted electrons, valid for near-threshold photoemission, the growth of intrinsic emittance from a rough surface is due to the distortion of the surface electric fields. These fields steer emitted electrons, causing them to acquire a transverse velocity v_fx. Following Ref. 9, the growth in the MTE due to roughness-induced surface fields is given by

where E₀ is the electric gradient, e is the electron charge, and the $Cm,ni$ are fit coefficients in a series solution of the Laplace equation for the electrostatic potential $U(x,y,z)$⁠, generated by a surface described by Eq. (3), as described in Ref. 24.

For $σs≪1$⁠, one can show that $Cn,mi≈E0An,mi$⁠. Thus, the Fourier amplitudes shown in Fig. 2 provide a reasonable figure of merit for comparing roughness emittance. Additionally, this shows that Δ_MTE scales linearly with the applied field, and so $ΔMTE/E0$ is used as a figure of merit throughout.

The roughness-induced MTE, Δ_MTE, is reported in Table II, together with the RMS error on $U(x,y,z)$⁠, which we label $ΔU$⁠. Details on the convergence of the calculations are reported in the supplementary material.

The samples grown on SiC, characterized by larger islands, are calculated to provide a much smaller contribution to intrinsic emittance due to roughness. Similar RMS roughness values do not result in similar Δ_MTE. It is interesting to note that for samples having similar RMS roughness, the sample with lower RMS slope achieves lower Δ_MTE.

The STM chamber also houses an x-ray photoelectron spectroscopy (XPS) system. In a previous work, we performed a detailed XPS analysis of these samples as transferred and as a function of oxygen dose. From this analysis, we determined that the transferred photocathodes were chemically similar and were exposed to an oxygen dose on the order of 1 L during transfer via vacuum suitcase, where 1 L = $1.33×10−6$ mbar $·$ s.²² In order to assess the effect of O₂ exposure on the surface morphology of these photocathodes, we performed a controlled oxidation experiment while continuously scanning the surface of a sample. We sequentially dosed 1, 10, and 100 L of O₂. Measurements beyond 100 L exposure were prevented by a sudden change of the imaging conditions.

In Figs. 3(a) and 3(b), we report the STM images acquired on a control sample grown on Si (100) in similar conditions as the samples of Fig. 1, as grown and while dosing 100 L of O₂, respectively. The height histograms in Fig. 3(c) also show similar height distribution to the ones of Figs. 1(a) and 1(b). The small observed changes in the surface features and in the height histogram are due to a lateral drift of the sample position. These results indicate that an oxygen dose up to 100 L does not affect the measured morphology of the samples on the scale of the measured height variations, confirming that they are representative of the as-grown samples.

The origin of the dramatic, substrate-dependent morphological variations in the Cs₃Sb films is unclear. In general, the morphology of vacuum-deposited films is determined by a complex interplay of energetic and kinetic effects.²⁶ On the energetic side, strong substrate–film interactions promote surface wetting and smooth growth, whereas incommensurability (i.e., epitaxial strain) promotes rougher growth and defect formation. The fact that much smoother films were grown on a substrate with –4% epitaxial strain [i.e., 3C–SiC(100)] than on one with 0.4% strain [i.e., TiO₂(001)] suggests that epitaxial strain may not be the dominant factor. The small number of substrates studied limits our ability to draw chemical inferences. We note, for example, that films of comparable roughness were produced on both oxide (Al₂O₃, TiO₂) and non-oxide (Si) substrates. In terms of kinetics, the density of nucleation sites can influence grain density and, thus, morphology; however, nucleation kinetics are dependent on many variables, including the rate of surface diffusion and the characteristic defect–defect (e.g., step–step) distance.²⁶ Two of the substrates that produced rough films are susceptible to faceting transitions under certain conditions [Al₂O₃ $(101¯0)$⁠,²⁷ TiO₂ (001)²⁸] however, the third substrate that produced rough films, Si(100), is near-atomically smooth under our preparation conditions.²⁹ For TiO₂(001), in particular, faceting would change the (001) surface termination,³⁰ thus disrupting the favorable lattice match with Cs₃Sb. In situ measurements of the crystalline orientation of films grown on different substrates are needed to clarify this aspect.

These results have significant implications for both low and high gradient photoelectron sources. The samples grown on TiO₂ and Al₂O₃ have predicted MTEs which will be comparable to room-temperature scale at the modest electric field of DC electron sources, which have maximum fields of roughly 10 MV/m.³¹ In contrast, for the SiC#1 sample, the MTE only becomes comparable to room-temperature scale at $∼100$ MV/m, which is among the highest available electron source gradients today.³² 

The observed wide range of morphological variation, and the sensitivity of the roughness-induced MTE on those variations, suggests that the use of in situ probes of the surface morphology during growth, such as reflection high energy electron diffraction, would be highly desirable in order to accelerate the synthesis of low MTE photocathodes.

Despite the dramatic changes in surface chemical composition detected by XPS during controlled oxidation experiments,²² our STM measurements do not detect any morphological changes after dosing up to 100 L of O₂. Indeed, the length scale probed by XPS measurements at the Sb 3d energy, of the order of $λ≈1.5$ nm, is small compared to the measured height variations observed on all samples, including the ones grown on SiC (⁠$∼10$ nm). Consequently, the roughness contribution to the intrinsic emittance is unaffected by non-ideal transfer conditions, and by extension, to oxidation which may occur in electron sources with imperfect vacuum conditions. The change of surface composition with oxygen exposure, affecting the surface chemical potential,²² could, instead, be relevant in determining the emittance at the cathode at low applied electric fields.¹⁰ To confirm these conclusions, measurements of MTE on pristine and superficially oxidized Cs₃Sb samples grown on SiC are required and under development.

In this work, we have studied the surface morphology of high efficiency Cs₃Sb photocathodes grown via codeposition on different single crystalline substrates. In particular, we show that samples grown on 3C–SiC(100) substrates show 10 times larger island size than samples grown on other substrates under the same conditions, which is promising for the anticipated future production of epitaxially smooth and ordered alkali antimonides.

We estimated the contribution to the MTE of photoemitted electrons induced by surface roughness. Our results indicate that the surface morphology of the samples grown on SiC is effective in reducing the roughness contribution to MTE up to a factor of 17. This work provides a critical step forward in the direction of achieving epitaxial order in Cs-based semiconductor photocathodes, which may generate electron beam brightness well beyond the current state of the art when coupled with very high gradient accelerating structures.

See the supplementary material for spectral response of the as-grown and suitcase-transferred samples, STM image processing and electrostatic potential and Δ_MTE calculations.

This research was supported by the U.S. National Science Foundation under Award No. PHY-1549132, the Center for Bright Beams.