Measurement of the tradeoff between intrinsic emittance and quantum efficiency from a NaKSb photocathode near threshold

Next generation continuous duty and pulsed photoinjectors for high brightness light sources such as energy recovery linacs^1,2 and free electron lasers^3,4 have demonstrated beam brightnesses directly limited by the brightness of the source.^5,6 Aside from increasing the gradient of the electron source to increase the extractable charge density,^7,8 the only other route to higher source transverse brightness is the reduction of the photoemitted electron transverse energy spread. This energy spread is commonly characterized by one of two quantities, the mean transverse energy (MTE), or the intrinsic emittance of the photoemission process, $ϵi,x$⁠. The two are related via

where σ_x is the initial rms size of the beam along a transverse Cartesian coordinate x and $mc2$ is the electron rest energy. MTE is analogous to the temperature of the photoemitted electrons.

The MTE and quantum efficiency (QE) of multialkali and bialkali cathodes have been shown to have comparable emittance performance to that of negative electron affinity (NEA) semiconductor photocathodes such as GaAs when driven with green light.^9–12 Furthermore, for the production of unpolarized electrons in high current photoinjectors, they routinely have significantly longer liftetimes than that of NEA photocathodes.^13,14 For photon energies much larger than the work function, $hν≫ϕ$⁠, which for NaKSb is approximately $ϕ=2$ eV,^11,15 the MTE is well approximated by a simple model assuming a constant density of states in the portion of the conduction band accessible by a photon of a given energy: $MTE=(hν−ϕ)/3$⁠.^11,12

However, for photon energies near the work function, it was known as early as 1958 (Ref. 15) that nonzero photoemission can be obtained from impurity states within the band gap. The yield from these states was shown to be strongly suppressed with decreasing photon energy and was further suppressed by reducing the cathode temperature to 77 K. Recent work¹⁶ has shown that for CsKSb not only the QE but also the MTE from photoemission from these states is similar to what one would expect from photoemission at the tail of the Fermi-Dirac distribution in a metal. For a free-electron gas (e.g., a metal), it can be shown that the MTE of photoemission near threshold is given by¹⁷ 

where here $Lin$ is the polylogarithm function of order n, $hν$ is the photon energy, $ϕ$ is the work function, and T is the temperature of the material. As $hν→ϕ$⁠, this expression approaches $kT$⁠. For CsKSb, a semiconductor, it was shown that the MTE also approaches $kT$⁠. Furthermore, reduction of the CsKSb temperature was shown to reduce the MTE. This work was performed at a single wavelength, $hν=1.8$ eV, and so the behavior of the MTE at intermediate wavelengths was not determined.

In the present work, we characterize the MTE and QE of a NaKSb photocathode, for 3 wavelengths near threshold, with photon energies from 1.8 eV to 1.9 eV, as well as in the green (532 nm) in order to map the tradeoff between MTE and QE with decreasing photon energy. NaKSb is chosen here as it has been shown previously to display lower MTE at 520 nm than other alkali-based photocathodes,^10,11 and thus we wish to determine whether this low emittance performance might extend into the near threshold regime.

These measurements are performed on a high voltage dc gun, where the extraction field was varied from 1.4 to 4.4 MV/m. This corresponds varying the gun voltage from 125 to 400 kV, using a 50 mm cathode-anode gap. The gun has been described in detail elsewhere.¹⁸ The use of electrostatic accelerating fields in the dc gun allows for in-situ characterization of the intrinsic transverse emittance using inexpensive continuous-duty (as opposed to pulsed) diode lasers, which are used throughout in this work.

Beams with room-temperature transverse momentum spread (MTE = 25 meV) and sub-millimeter rms sizes have normalized emittances in the tens of nm. To verify the measurement of such small emittances, we use two different emittance measurement methods. The first method is a solenoid scan, in which a solenoid magnet (shown in Figure 1) just downstream of the gun is varied and the resulting rms beam sizes are measured with a fluorescent viewscreen (BeO) and a CCD camera. If one calculates the linear transfer matrix which propagates the beam transverse phase space coordinates $(x,px)$ from the cathode to the measurement screen, one can fit the resultant beam sizes as a function of solenoid current for the beam emittance and the initial spot size on the cathode. This method has been well documented and successfully employed to measure down to 30 meV in GaAs near threshold.¹² 

The second measurement uses what is called the emittance measurement system (EMS), also shown in Figure 1. The system is composed of two retractable horizontal slits, and two sets of fast vertical kicker magnets. The first slit and magnet system selects a small vertical slice of the beam's density distribution, and the second slit and magnet select a small slice in the vertical momentum of the beam's phase space distribution. Measuring the transmitted current through the slits with a downstream Faraday cup as a function of the kicker magnet setpoints, one can map the full 2-D vertical phase space density of the beam. The EMS has been described in detail elsewhere.¹⁹ 

To determine the MTE from these measurements of emittance, one must also know the laser spot size on the photocathode. In general, for both methods and for all applied fields, we use 3 laser apertures (0.7, 1, and 1.75 mm diameter) to determine the linear relationship between emittance and spot size, the slope of which determines the MTE. In the case of the solenoid scan, the spot size on the cathode is fit alongside the emittance. Thus, the only significant uncertainties associated with the measurement of emittance are the error in the solenoid scan fit, as well as the error in the determination of the spot size on the screen. In general, for an accurate model of the fields, the error in the fitting can be negligible, as it is in all cases in this work. However, the error in the calibration of the image size of fluorescent viewscreen on the CCD camera is more significant. We estimate it to correspond to a 5% relative error in all spot size measurements. This error is propagated through to the calculation of the MTE, yielding on average an error of ±3 meV for the MTEs measured here.

The systematic uncertainty in the EMS measurement is larger in general. The field integral of each kicker magnet is calibrated by measuring its deflection of a beam on a viewscreen, and thus each of the calibrations of the magnets depends on the viewscreen uncertainty. Furthermore, this measurement relies on the profiling of the laser distribution at a “virtual cathode” plane the same distance away from the shaping aperture as the actual photocathode. Our estimates of error in the MTE determined by the EMS system include both the uncertainty in determining the laser rms size and the uncertainty in the magnet calibrations. Given the larger total uncertainty (roughly ±10 meV near threshold) in the EMS measurements, they are considered as secondary check for the primary measurements performed with the solenoid scan.

The quantum efficiency is measured by retracting the slits and measuring the full beam current on the Faraday cup using a picoammeter, as well as measuring the laser power upstream of the laser's entrance into the vacuum chamber. For all measurements, the dc current density at the photocathode was on the scale of 0.5 μA/mm² or less, and so the force of space charge is negligible here.

The NaKSb cathode was grown via sequential deposition from pure metal alkali sources onto a polished stainless steel substrate, according to the specific procedure described in Ref. 11. All substrate temperatures, element deposition thicknesses, and the order of the element deposition were repeated closely. After growth, the photocathode was then first moved into the chamber of another dc gun,⁵ where the QE at 532 nm was measured to be 5.5%, with an absolute QE uniformity of 0.5% over the central 100 mm² area. This photocathode was used for a series of low average current (μA), high bunch charge measurements in the full Cornell photoinjector,⁵ and was then moved to the gun testing lab for these measurements. Due to multiple cathode transfers, as well as its use for beam measurements, the QE at 532 nm at the start of these measurements had decreased to 3.1%.

To check the agreement between the two emittance methods, the MTE at 532 nm and 4.4 MV/m (400 kV beam energy) was measured with the solenoid scan and the EMS. The measured values were 134 meV and 129 meV, indicating good agreement, as the uncertainty in the solenoid scan method here was approximately ±10 meV.

The measurement of MTE of NaKSb at 635 nm, 650 nm, and 690 nm is shown in Figure 2. There are several features of note. First, there is good quantitative agreement between the measured values from both the solenoid scan and the EMS method within the experimental uncertainty. Second, the value of the MTE is near the room-temperature limit for the longest wavelength used.

Next, we note that there is only a small slope in the MTE as a function of the applied field. This behavior is also seen in Eq. (2) near threshold. The change in the MTE from Eq. (2) due to the change in applied fields used here (via the Schottky effect, see Figure 4 below) results in a MTE change of <10 meV at 635 nm. The longer wavelengths are expected to have even smaller MTE changes at these fields. The difference in the slopes in MTE from solenoid and EMS measurements may be due to the fact that the ultimate resolution of the EMS also depends slightly on the orientation of the phase space at the slit, which is a function of both solenoid current and the gun voltage. Coupling this with the larger uncertainty, it is difficult to draw conclusions from the slope of the EMS data; however, the overall quantitative agreement with the solenoid scan measurement in this field range lends confidence to the small measured values of MTE.

The quantum efficiency at these wavelengths is shown in Figure 3. We note that the quantum efficiency near threshold is a stronger function of the applied field than the MTE, with the QE for each wavelength increasing by at least a factor of 1.5 when the field is increased from 1.6 MV/m to 4.5 MV/m. Again, this is similar behavior to a metal emitting near threshold, in that for a metal, a small change in energy in the tail of the Fermi-Dirac distribution can have a large impact on the number of electrons at that energy. We note that while the QE has decreased sharply with decreasing photon energy, the lowest QE measured is larger than the QE of typical metal photocathodes (⁠$10−5$⁠).²⁰ 

To compare the behavior of the MTE of NaKSb to the metallic model given in Eq. (2), we replot the solenoid scan data as a function of excess energy, defined as the difference between the photon energy and the Schottky lowered work function: $Eex=hν−(ϕ−eeE/4πϵ0)$⁠. This data is plotted against Eq. (2) (also including the Schottky work function lowering) in Fig. 4. The model of the metallic emission applied to NaKSb neglects a host of differentiating effects (varying density of states, phonon scattering, among many others^20,21) and so does not capture the specific MTE values, but it does indicate that the photoemission MTE is well parameterized by the excess energy.

Reducing the intrinsic emittance of photocathodes is the most direct route to increasing the brightness of emittance-compensated beams. Emission at 690 nm from NaKSb yields near room temperature electrons (35 meV) for a room temperature cathode, giving an intrinsic emittance approximately a factor of two less than at 532 nm. Though the response time of NaKSb photoemission near threshold was not characterized in this work, it is expected to be ps-scale or smaller. This expectation is due to both the small thickness of the photocathode film (10's of nm), as well as the use of multialkali photocathodes in streak cameras with sub-ps resolution in this wavelength range.²² 

The lowest temperature electron beam sources to date, cold atom electron sources for ultrafast electron diffraction (UED), have demonstrated MTEs between $∼1$ and $∼20$ meV,^{23,24,26–28} with the smallest MTE limited directly by disorder induced heating.²⁵ However, both the electron bunch charge and beam density are directly constrained by the density of the cold atom cloud, which can make sufficient charge production challenging.^23,26

Assuming a prompt temporal response, NaKSb photocathodes operating at threshold are shown here to be a low-emittance alternative to cold atom sources for UED or ultrafast electron microscopy²⁹ having much more relaxed limits on the beam density and bunch charge extractable. Furthermore, the QE at 690 nm is comparable to that of a metal, and so such photocathodes could be driven near threshold for next-generation high brightness photoinjectors. For instance, a 1 MHz high brightness photoinjector, delivering 100 pC bunch charges from NaKSb using 690 nm light would require $≤1$ μJ per pulse, or only 1 W of average power at the photocathode.

In this letter, we have characterized the long wavelength photoemission behavior of a NaKSb photocathode installed in a high voltage dc gun. We found that increasing the wavelength from 532 nm to 690 nm decreases the MTE from ∼134 meV to ∼35 meV, with a corresponding QE drop from $∼3×10−2$ to $∼2×10−4$ for various applied fields of several MV/m. We also use the comparison to metallic emission near threshold to explain the qualitative behavior of the photoemission properties as a function of wavelength and applied field. We find that operation of a NaKSb photocathode near threshold results in a dramatic decrease in intrinsic transverse emittance, offering a feasible route to emittance reduction in high brightness, emittance-compensated beams.

This work was supported by the National Science Foundation (Grant Nos. PHY-1416318 and DGE-0707428), as well as the Department of Energy (Grant No. DE-SC00039650).