Quantum efficiency, photoemission energy spectra, and mean transverse energy of ultrananocrystalline diamond photocathode

High-density bunched electron beams required for accelerators in X-ray Free Electron Lasers (XFELs),¹ Ultrafast Electron Diffraction and Microscopy experiments,² Inverse Compton Scattering X-ray sources,³ etc. are typically produced using photoinjectors. Photoinjectors essentially consist of a photoemissive material (photocathode) placed in a large accelerating field, which is typically in the range of 5–100 MV/m depending on the design of the photoinjector. The performance of a photocathode is usually characterized by the emitted charge or, equivalently, the quantum efficiency (QE). The cathode must also have a long lifetime, fast response time, and low intrinsic emittance. QE is defined as the number of electrons emitted per incident photon. High-QE photocathodes are desirable for applications that require high average current or high bunch charges and to mitigate the effects of non-linear photoemission.

The response time of a photocathode is given in terms of the extracted electron bunch length when compared to the incoming laser pulse. Photocathodes require a fast response time to temporally shape the initial electron distribution and maintain the beam quality during acceleration in the photoinjector. A fast response time implies that the electrons are emitted quickly after the absorption of incident photon energy. However, electrons excited deep within the cathode surface can take tens of pico-seconds to escape into the vacuum leading to undesirable temporal structure. A fast response time (⁠$<1$ ps) is desirable for various photoinjector applications.⁴ 

The intrinsic emittance of a photocathode is expressed in terms of rms laser spot size and mean transverse energy (MTE) of the emitted electrons and is given by the following equation:

where $εn,x$ is the normalized transverse emittance in the x–z plane, $σl,x$ is the rms laser spot size in the x-direction, $me$ is the mass of an electron, and $c$ is the speed of light. The MTE of the electrons depends on the cathode material, its surface morphology, and the laser photon energy and fluence used for excitation.⁵ For the case of metal photocathodes, the MTE of the emitted electrons follows the Dowell–Schmerge model, which says that the MTE of the electrons scales as one-third of the excess energy (difference between the photon energy and work function) and at the threshold is limited by the thermal limit.⁶ For example, the smallest MTE of 25 meV was demonstrated for antimony films when operated near the threshold at room temperature.⁷ For the semiconductor photocathode such as GaAs activated to negative electron affinity using Cs and NF$3$⁠, the observed value of MTE is 40 meV at room temperature.⁸ However, in most photoinjectors, the MTE extracted from photocathodes is in the range of 0.1–1 eV.⁵ 

Another parameter that determines the MTE of the emitted electron beam is the physical roughness and work function variation (also termed as chemical roughness) of a photocathode. Nano-scale physical roughness on the cathode results in an increase in MTE and this can be attributed to two effects. First is the “slope effect” where the electrons are emitted from the local surface normal of the photocathode as opposed to its global surface normal. The second, known as the “field effect,” arises due to the generation of a transverse local electric field due to the roughness on the photocathode surface. In general, the field effect dominates as compared to the slope effect and ergo the slope effect is usually ignored in the analysis. A detailed analysis of MTE increase due to physical roughness has been previously reported.^9–12 Assuming the sinusoidal variation in the surface roughness profile, the scaling of MTE to the first order is given by the following equation:

where E is the applied electric field, a is the amplitude, and $λ$ is the period of the physical roughness profile. As we can see, the contribution to MTE due to physical roughness increases with increasing accelerating field gradient. The chemical roughness arises due to lateral potential variations, which is the result of the varying work function. It has been shown that the effect of chemical roughness becomes less prominent with increasing accelerating field gradient.¹³ The combined effect of physical and chemical roughness has been calculated by Gevorkyan et al. by decomposition of electric field components close to the cathode surface and numerically tracking the trajectory of the emitted electron in the applied electric field.¹⁴ 

Another factor that determines the choice of a photocathode in a photoinjector is its lifetime/robustness. Many emerging applications such as Free Electron Lasers (FELs), Linear Accelerators (LINACs), and Relativistic Heavy Ion Collider (RHIC) experiments require high peak current along with high-quality electron beams.¹⁵ High-brightness photocathodes such as GaAs, which have low MTE and high QE, tend to have a longer lifetime when operated at low peak currents. However, it degrades very quickly when operated at high peak currents.^16,17 For high peak current applications, one requires a photoemissive material with high conductivity. A wide-bandgap semiconductor such as diamond is a promising candidate for such applications because of its mechanical, thermal, and electrical stability along with an intrinsically fast response time (⁠$∼100$ fs).^18,19 Moreover, its vacuum robustness allows it to work under harsh conditions and, thus, makes it a promising candidate for photoinjector applications. A comparison between the emission properties of single-, micro-, nano-, and graphite-like nano-crystalline diamond films suggests that graphite-like nano-crystalline diamond has a better performance compared to the others. The QE of graphite-like nano-crystalline diamond was reported to be $10−4$ at 200 nm.²⁰ However, none of these films showed a good performance above 200 nm.

One way to improve the performance of diamond at wavelengths $>200$ nm is to take advantage of the negative electron affinity (NEA) of the diamond. A way to do so would be by n-doping of the diamond films and surface treatment in a hydrogen environment.²¹ Recently, n-doping of micro, nano, and ultrananocrystalline diamond (UNCD) films using nitrogen has been performed by many groups.^22–24 It has been shown that the addition of nitrogen to UNCD films increased its electrical conductivity up to 1854 S cm$−1$ and the maximum current density to 8 mA cm$−2$⁠.²⁵ This is advantageous for high peak current photoinjector applications. Such films with nitrogen incorporation are termed as nitrogen-incorporated ultrananocrystalline diamond (N)UNCD. (N)UNCD typically consists of sp$2$ as well as sp$3$ bonded carbon atoms. The sp$2$ bonded carbon phase, also known as the graphitic phase, resides in the grain boundary region of sp$3$ bonded carbon phase, also known as the diamond phase. It has been reported that the photoemission of electrons from such materials originates from the sub-nm scale grain boundaries, which are predominantly composed of sp$2$ bonded carbon atoms.²⁶ In addition, the NEA can be introduced in (N)UNCD after synthesis via surface hydrogenation treatment leading to the surface C–H dipole formation. Such cathodes are known as hydrogen-terminated nitrogen-incorporated ultrananocrystalline diamond [(N)UNCD:H].

The QE of (N)UNCD:H as well as (N)UNCD has been reported by many groups. It was observed that the QE of (N)UNCD:H was two orders of magnitude higher than the QE of (N)UNCD, which was $∼10−5$ at 254 nm.²⁷ However, not many experimental measurements of the MTE of (N)UNCD have been reported. A recent experimental measurement of MTE of (N)UNCD:H by Chen et al. using solenoid scan technique at the electric field of 0.45 MV/m suggests that the MTE of (N)UNCD:H is constant at 266 meV with decreasing photon energy.²⁸ Another experimental measurement of MTE of an (N)UNCD was performed in an RF gun environment at the electric field of 30 MV/m. The normally incident 262 nm laser had a Gaussian longitudinal distribution with a full width at half maximum pulse length of 300 fs. The measured MTE was reported to be $∼1000$ meV.²⁹ 

In this work, we report proof-of-concept QE, photoemission spectra, and MTE measurements for the (N)UNCD photocathode grown on a molybdenum substrate. The measurements were carried out in the near UV range of 200–300 nm, standard for many photocathode applications. Further, the measurements were performed for (N)UNCD photocathode prior to bakeout and after the bakeout of the sample. The bakeout was performed at $120°$C for 24 h. The QE of the baked sample was higher than the QE of the unbaked sample by an order of magnitude for the same range of photon energies. In the photoemission energy distribution spectra, the sum of work function and kinetic energy corresponding to the maxima in the emission spectra does not match the excitation energy. This indicates that the scattering of electrons influences the emission. The measured MTE approximately scales as one-sixth of the excess energy. It is proposed that this trend in MTE is due to the relaxation of electrons possibly via phonon scatterings in the conduction band before emission. The MTE of $∼70$ meV close to the threshold is attributed to the physical and chemical roughness of the (N)UNCD photocathode.

The diamond deposition process for the synthesis of (N)UNCD films was performed by Advanced Diamond Technologies. Details of different steps for the preparation of (N)UNCD are reported elsewhere.³⁰ Typically, it has 1 $μ$m layer of conductive (N)UNCD films, followed by a layer of 15 $μ$m microcrystalline diamond. A diamond film is brazed to a polished Mo substrate using the brazing material TiCuSil. Figure 1 shows the Raman spectrum of an (N)UNCD sample measured using a custom built Raman spectrometer in a $180°$ geometry. The sample was excited using a 150 mW Coherent Sapphire SF laser with a 532 nm laser wavelength. The laser power was controlled using a neutral density filters wheel and an initial laser power of 100 mW. The laser was focused onto the sample using a 50X super long working distance plane APO Mitutoyo objective with a numerical aperture of 0.42. The signal was discriminated from the laser excitation using an Ondax®SureBlock™ ultranarrow-band notch filter combined with two optigrate notch filters. The broad peaks at 1350 and 1550 cm$−1$ correspond to the D and G bands of diamond and graphite, respectively.

QE, photoemission spectra, and MTE measurements of the (N)UNCD sample were performed using a photoemission electron microscope (PEEM).³¹ The base pressure of the PEEM chamber was in the low $10−10$ Torr range during the measurements.

QE measurements were performed using a 500 kHz repetition rate femtosecond pulsed laser with a pulse length of 150 fs from a pulsed Optical Parametric Amplifier (Light Conversion Orpheus pumped by Light Conversion Pharos). The LASER was made incident onto the sample at $65°$ angle of incidence with respect to the normal of the sample surface and was focused by a lens down to the spot size of $100×250μm2$⁠. One millimeter real space field of view (significantly larger than the LASER spot size) was selected to image all the emitted photo-electrons using a double micro channel plate (MCP) detector at the end of the PEEM column. The photoelectron current was determined by recording counts/second on the MCP detector and using a predetermined calibration factor to convert it into photocurrent at each wavelength.

The photoemission spectra were obtained by using the imaging energy filter (IEF) capability of the PEEM. The IEF unit is placed after the PEEM column and before the imaging unit of the microscope. It consists of two pre-retardation lens and two retardation grids that form the retarding field analyzer (RFA). The retarding field acts as the high pass energy filter that allows for energy filtered imaging. Background subtracted energy filtered images were obtained for the (N)UNCD sample using RFA of the PEEM with sub 65 meV energy resolution. The contrast aperture (CA) of diameter 1750 $μ$m placed in the backfocal plane of the objective lens in the PEEM column was selected to ensure transmission of all the emitted electrons from the sample surface. After acquiring the energy filtered images, a numerical differentiation of high pass spectrum of the RFA was performed and the normalized counts were plotted against the kinetic energy of emitted electrons for each photon energy for both baked and unbaked samples.

MTE measurements were performed by operating PEEM in k-space mode with a sub 8-mÅ$−1$ k-space resolution. A 35$±5$ $μ$m region of the sample was selected by the adjustable iris aperture that was placed in the first intermediate image plane of the PEEM column while imaging in the real space mode. After limiting the area under investigation in the real space mode by adjustable iris aperture, its counterpart in the k-space mode was imaged by changing the projective settings of the PEEM. Figure 2 shows k-space images taken at 240 nm with FOV of 1.9 and 3.9 Å$−1$ and the Gaussian fit applied to the $kx$ and $ky$ distributions obtained from 1.9 Å$−1$ FOV. The MTE was then calculated using the second moment obtained from the Gaussian fit applied to the measured k-space distribution of the emitted electrons using the following equation:

Here, $ℏ$ is the reduced Planck’s constant, $m$ is the mass of an emitted electron, and $σ=σkx2+σky2$⁠, where $σkx$ and $σky$ are the second moments obtained from the Gaussian fit applied to k$x$ and k$y$ distributions of the emitted electrons as shown in Figs. 2(c) and 2(d).

For all the measurements, the fluence of the laser pulses incident on the sample was kept small enough to ensure linear electron counts and avoid effects of space charge and non-linear photoemission. The QE was measured at the extraction field of 0.005 MV/m and the photoemission spectra and MTE were measured at the extraction field of 0.5 MV/m. For the case of semiconductor, according to Stratton,³² the Schottky work function lowering is given by the following equation:

where $α$ is the fine structure constant, $e$ is the electron charge, and $Ks$ is the dielectric constant. Assuming $Ks=5.7$⁠, typical for diamond,³³ and the maximum extraction field of 0.5 MV/m on the (N)UNCD photocathode surface in the PEEM, Eq. (4) results in a Schottky work function lowering effect of only 22.47 meV that is comparable to the thermal energy at the room temperature. QE, photoemission spectra, and MTE measurements were performed in the near UV range of 200–300 nm standard for many photocathode applications.

According to the Dowell–Schmerge model,⁶ for photoemission near threshold, the quantum efficiency is given by the following equation:

where $ℏω$ is the photon energy and $Φ$ is the work function of a photocathode. Hence, on plotting the square root of QE vs photon energy, the x-intercept gives the work function of a photocathode sample. Figure 3 shows experimentally determined square root of QE values for the (N)UNCD sample. There are four main features in Fig. 3. First, the QE of the baked sample is higher than the QE of the unbaked sample for the same range of photon energies. This enhancement in QE can be attributed to the desorption of contaminant layers from the (N)UNCD surface during the bake-out. Second, the QE of the unbaked (N)UNCD sample is of the order of $10−8$ and that of the baked sample is of the order of $10−7$ at 4.9 eV photon energy. These values are comparable to the previously reported values.²⁷ Third, the photoemission threshold for both unbaked and baked samples is observed at the photon energy of $4.4±0.1$ eV. This is comparable to the previously reported values.^28,29 Last, there is a significant rise in QE beyond 5.4 eV photon energy. Since the bandgap of diamond is 5.4 eV,³⁴ this increase in QE can be attributed to a higher number of electrons being excited in the conduction band when the photon energy is greater than the bandgap of diamond.

Figure 4 shows experimentally determined photoemission spectra for the (N)UNCD sample before and after the bakeout of the sample. For a given photon energy, the energy spectra appear identical for both baked and unbaked samples. For both baked and unbaked samples, the photoemission spectra broaden in kinetic energy with increasing photon energy. The top x-axis in Fig. 4 shows the sum of kinetic energy (E$k$⁠) of the emitted electrons and the work function (⁠$Φ$⁠) of the (N)UNCD photocathode. Considering the work function of the (N)UNCD to be $∼4.4$ eV, as obtained from the QE spectral response in Fig. 3, the sum of the maximum kinetic energy of the emitted electrons and the work function approximately equal to the photon energy. Also, from the top x-axis in Fig. 4, we can see that the sum of the work function and the kinetic energy corresponding to the maximum of the energy distribution curves does not coincide with that of the photon energy. This indicates that the electrons are scattered possibly by phonons before being emitted from the (N)UNCD sample. A similar electron scattering mechanism is observed for nitrogen-doped diamond films³⁵ and other semiconductor photocathodes.³⁶ In the case of an unbaked sample, at 4.13 eV photon energy, the emission spectrum is broadened due to non-linear photoemission. This non-linear photoemission is also reflected in the MTE plot shown in Fig. 5, which results in an increase in MTE at 4.13 eV photon energy.³⁷ 

Figure 5 shows experimentally determined MTE values for the (N)UNCD samples. There are three main features in Fig. 5. First, the MTE of the (N)UNCD decreases with a decrease in excess energy and shows a flat trend close to the threshold, which is observed at a photon energy $∼4.4$ eV. This is in contrast to the constant MTE of 266 meV for (N)UNCD:H reported by Chen et al.²⁸ for a similar spectral range. Also, the MTE at 260 nm (4.76 eV photon energy) was observed to be $∼100$ meV. This is an order of magnitude smaller when compared to the MTE observed by Ref. 29 at 262 nm and 30 MV/m electric field gradient on the surface of the cathode. Second, the scaling of MTE with excess energy is not in accordance with the Dowell–Schmerge model.⁶ This behavior can be attributed to the relaxation of electrons possibly with phonon scattering in the conduction band before emission. A similar behavior is observed for other semiconductor photocathodes.³⁶ Last, the MTE at the threshold does not reach 25 meV (thermal limit) but flattens at $∼70$ meV. This is attributed to the physical and chemical roughness of (N)UNCD photocathodes and is discussed in detail in Sec. III C 2.

A detailed discussion of the effect of physical and chemical roughness of the photocathode on the MTE of the emitted electrons is done in Sec. I. The effect of physical roughness on the MTE due to the applied electric field is given by Eq. (2). In the case of UNCDs, the amplitude of physical roughness varies between 5 and 10 nm^38–40 and the period of the roughness corresponds to the grain size which is generally reported to be in the range of 5–15 nm.^41–43 The contribution of MTE$field$ as a function of surface roughness is plotted for different periods typical of UNCD photocathodes in Fig. 6. The MTE$field$ was plotted for two values of the electric field. First, 30 MV/m, which was the field gradient at the surface of the (N)UNCD reported in Ref. 29. Second, 0.5 MV/m (the inset of Fig. 6), which was the field gradient at the surface of the (N)UNCD films during our measurements of MTE. The MTE$field$ obtained at 30 MV/m is larger than the thermal limit (⁠$∼25$ meV) and is comparable to the previously reported value.²⁹ In addition, the contribution of MTE$field$ at 0.5 MV/m shown in the inset of Fig. 6 is $∼25$ meV for $a=10$ nm and $λ=10$ nm.

As discussed in Sec. I, another source of increase in MTE is the chemical roughness of the photocathode. From Fig. 1, there are two phases present in the (N)UNCD sample. First, the diamond phase and second, the graphite phase. These two phases can have work function difference of several 100s meV. If we consider $∼1$ nm graphite regions between $∼10$ nm diamond grains, the variation of several 100s meV in surface potential can have an additional contribution to the MTE at 0.5 MV/m electric field.^13,14

In general, for practical photocathodes with physical and chemical roughness, the MTE of the emitted electrons is given by

where MTE$kT$ is the contribution due to thermal limit which is $∼25$ meV at room temperature. Assuming $a=10$ nm and $λ=10$ nm, which is typical for UNCDs, the contribution of MTE$field$ at 0.5 MV/m is $∼25$ meV. Lastly, MTE$WF$ is the contribution due to the chemical roughness arising from several 100s meV variation in surface potential due to the presence of graphite phase and diamond phase in the (N)UNCD sample. Hence, the total MTE which is the sum of MTE$kT$⁠, MTE$field$⁠, and MTE$WF$ is $∼70$ meV at the threshold for the (N)UNCD photocathodes which is in agreement with what is shown in Fig. 5.

We measured the QE, photoemission spectra, and MTE of a (N)UNCD photocathode in the UV range of 200–300 nm for unbaked and baked samples. The QE was measured to be $∼10−7$ for a baked sample and $∼10−8$ for an unbaked sample at 250 nm. From the photoemission spectra, we observed that the sum of work function and kinetic energy corresponding to the maxima in the emission spectrum does not match the excitation energy. This indicates that the scattering of electrons influences the emission. The MTE decreased with the decrease in excess energy and showed a flat trend near the threshold. This behavior is in contrast to the constant MTE of 266 meV reported for an (N)UNCD:H for a similar spectral range.²⁸ The MTE at 260 nm (4.76 eV photon energy) was observed to be $∼100$ meV. This is an order of magnitude smaller than the MTE reported by Ref. 29. We attribute this difference to the physical roughness of the (N)UNCD photocathode. The scaling of MTE with excess energy is not in accordance with the Dowell–Schmerge model.⁶ This observed trend in MTE is attributed to the relaxation of electrons possibly with phonon scattering in the conduction band before emission.³⁶ This scattering of electrons before emission is also evident in the photoemission spectra shown in Fig. 4. Furthermore, the MTE at the threshold does not go to 25 meV (thermal limit) but flattens at $∼70$ meV. This is attributed to the physical roughness due to the fabrication process and chemical roughness, which is a result of the work function variation due to the presence of graphite phase and diamond phase in the (N)UNCD sample.^13,14 The work function of the (N)UNCD obtained from the spectral response of QE and MTE was $4.4±0.1$ eV. This is in agreement with the previously reported values.^28,29

In summary, we have reported the spectral responses of QE, photoemission spectra and MTE of the (N)UNCD photocathode. With the QE comparable to that of metal photocathodes and MTE of 70 meV at the threshold, (N)UNCD photocathodes are suitable for various high peak current photoinjector applications. However, the use of these photocathodes at high electric field gradients can significantly increase the MTE of the emitted electrons owing to their surface roughness. Consequently, it can lead to a decrease in brightness of the emitted electron beams. Even at low electric fields, the contribution to MTE due to physical and chemical roughness is significant enough to increase MTE beyond the thermal limit at the threshold. One way to reduce MTE and consequently increase the brightness of (N)UNCD photocathodes is by optimizing the growth techniques to produce a smoother film. One way to do this would involve growing (N)UNCD films via tungsten interlayers.⁴⁴ As a result, future work would involve growing (N)UNCD films with reduced surface roughness and additional fundamental understanding of their emission mechanism.

This work is supported by the National Science Foundation Center for Bright Beams under Award No. PHY-1549132, the (U.S.) Department of Energy under Grant No. DE-SC0021092, and the Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development (LDRD) Program. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. 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 National Nuclear Security Administration, under Contract No. 89233218CNA000001.

The authors have no conflicts to disclose.

A. Kachwala: Conceptualization (Supporting); Data Curation (Lead); Formal Analysis (Lead); Investigation (Equal); Methodology (Equal); Project Administration (Supporting); Resources (Equal); Software (Equal); Validation (Lead); Visualization (Lead); Original Draft (Lead); Reviewing and Editing (Supporting) O. Chubenko: Conceptualization (Supporting); Data Curation (Supporting); Formal Analysis (Supporting); Investigation (Equal); Methodology (Equal); Project Administration (Supporting); Resources (Equal); Software (Equal); Validation (Supporting); Visualization (Supporting); Reviewing and Editing (Supporting) D. Kim: Conceptualization (Supporting); Data Curation (Supporting); Formal Analysis (Supporting); Investigation (Equal); Methodology (Equal); Project Administration (Supporting); Resources (Equal); Software (Equal); Validation (Supporting); Visualization (Supporting); Reviewing and Editing (Supporting) E.I. Simakov: Conceptualization (Supporting); Data Curation (Supporting); Formal Analysis (Supporting); Funding Acquisition (Supporting); Investigation (Equal); Methodology (Equal); Project Administration (Supporting); Resources (Equal); Software (Equal); Supervision (Supporting); Validation (Supporting); Visualization (Supporting); Reviewing and Editing (Supporting) S. Karkare: Conceptualization (Lead); Data Curation (Supporting); Formal Analysis (Supporting); Funding Acquisition (Lead); Investigation (Equal); Methodology (Equal); Project Administration (Lead); Resources (Equal); Software (Equal); Supervision (Lead); Validation (Supporting); Visualization (Supporting); Reviewing and Editing (Lead)

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