Integrated photonics for low transverse emittance, ultrafast negative electron affinity GaAs photoemitters

In traditional negative electron affinity (NEA) GaAs photocathodes, a photon beam is shined on the GaAs surface, exciting carriers that travel to the surface and emit with sufficient energy.¹ However, the structure of this device imposes a coupling between photon energy, mean transverse energy (MTE), quantum efficiency, and response time, which limits electron emission performance. Specifically, as photon energy increases, response time and quantum efficiency benefit at the expense of large transverse energies. Critically, ultralow emittance emitters are highly desirable for future generation electron sources, with electron source emittance reduction directly proportional to both free electron laser cost and performance. Thus, the ability to minimize mean transverse energy, which is proportional to the square of emittance,⁶ without sacrificing response time and quantum efficiency, is an important challenge. Here, we propose the use of an optical waveguide to decouple the photon energy, response time, quantum efficiency, and mean transverse energy relationship. Specifically, by integrating an optical waveguide and negative affinity GaAs photocathode, we can thin the GaAs emission layer and utilize low photon energies while still absorbing the majority of incident photons.

The key focus of this work is to determine how an ultrathin layer of GaAs (e.g., 20 nm) could be efficiently excited with low-energy photons. The use of low energy, near band edge photons is well established as one route toward low emittance.^2,3 However, for standard free-space NEA GaAs emitters, this corresponds to unacceptably long response times due to the long photon absorption lengths. These long absorption lengths cause a significant fraction of photoexcited carriers to be generated far from the emitting surface, increasing the amount of time it takes for those carriers to travel to the surface and increasing the response time of the emitter.⁴ Solving this could be achieved by using a thin layer of GaAs excited by 1.4 eV photons, which would ensure that all photogenerated carriers are generated very near the emitting surface and minimize the response time. However, without any kind of optical strategy to enhance the absorption in the thin GaAs, the overall quantum efficiency would be extremely low, as only a small fraction of the incident light would be absorbed over the length of the thin GaAs. Thus, in this work, we show that this challenge can be overcome by using well established techniques developed for the silicon integrated photonics community, but applied to NEA GaAs emitters.

To explore the design space available with Cs-GaAs and integrated photonic devices, we simulate the behavior of waveguide integrated NEA GaAs photoemitters as a function of the thickness of the GaAs and excitation wavelength. To obtain these results, we use a coupled simulation that first determines temporal and spatial optical generation in the GaAs layer via 3-D finite difference time domain (FDTD) Maxwell's equation solver⁷ and then uses those results in a 2-D Monte Carlo Boltzmann transport equation (MC-BTE) solver.⁸ Using this approach, we first show that it is possible to reproduce published GaAs photoemission results. Calibrating our results to published results, we then simulate the behavior of the proposed structure. These simulations predict that the use of integrated photonic elements, such as waveguides, results in the decoupling of the photocathode response times, mean transverse energy, and quantum efficiency, making it possible to achieve fast response times at low photon energies without decreased quantum efficiency and increased transverse energy.

Most negative affinity GaAs photoemitters utilize free-space optical coupling to generate electron-hole pairs in the GaAs, either through front-side illumination, where light is incident on the emitting surface of the NEA GaAs, or back-side illumination, where the light is incident on the nonemitting surface of the wafer. For a front-side illuminated bulk emitter, the absorption profile is given by Beer's law type profile as shown in Fig. 1(b). Thus, the absorption length is simply a function of the absorption coefficient of GaAs for the excitation photon energy. In this bulk emitter, absorption lengths reach the order of 1 μm for 1.55 eV light as displayed in Fig. 1(b).⁸ Thus, in order to obtain sufficient absorption, the GaAs thickness should be on the order of 1 μm when 1.55 eV light is used. For photon energies of 1.4 eV, the absorption length becomes very long, requiring on the order of 100 μm of materials to absorb 90% of the incident photons. The choice to focus on 1.4 eV and 1.55 eV is, therefore, made to identify the effect of the GaAs absorption coefficient at the incident photon energy on the behavior of the integrated photonics cathode. The reflectance of GaAs is taken to be 0.3.⁸ Therefore, 70% of incident power is absorbed in the bulk GaAs device. Critically, as the absorption length increases, the time necessary for photoexcited carriers to arrive at the emitting surface of the NEA GaAs increases, dramatically increasing the response time. However, simultaneously, lower energy photons decrease the transverse energy component of the emitted electron beam, which is highly desirable. This has been established through both experimental and theoretical work in the past.^3,5,6 Thus, reducing the absorption depth for low-energy photons is key to breaking the mean transverse energy-response time tradeoff.

Here, we aim to address this issue by changing the direction of illumination. Instead of directly illuminating a bulk emitter through either front-side or back-side illumination, we show that a waveguide structure, which allows evanescent coupling into an ultrathin emitter, can be used as an alternative illumination option. In Figs. 1(c) and 1(d), the schematic of a III-V NEA GaAs photocathode integrated waveguide is shown. The GaAs emission layer resides on the surface of the Al₂O₃ optical waveguide. Unlike a bulk emitter, where the photon absorption and electron emission occur in the same direction, the waveguide integrated approach decouples the electron emission and photon absorption directions. We simulate Al₂O₃ for the waveguide material, chosen for its low optical loss properties and its emergence as a low-loss waveguide for integrated photonic applications;^14,15 however silicon nitride waveguides could also be used for the photon energies explored here. Importantly, the structures here are very similar to III-V lasers, which are integrated with silicon integrated photonics through epitaxial transfer and wafer bonding approaches. Therefore, while the device proposed here is nontrivial to fabricate, the general process has already been demonstrated by many groups, however in the context of III-V lasers, not photoemitters. The dimensions and optical mode of the waveguide/GaAs heterostructure will determine the absorption per unit length and the absorption profile. In this case, a single Bragg mirror at the end of the device structure is used to provide a double path interaction between photons and the emission layer. Figure 1(e) shows the carrier generation profile orthogonal to the waveguide in 20 nm thick GaAs. Critically, we see that the vertical absorption profile in the electron emission direction is similar for both 1.55 and 1.4 eV photons. In this case, the major change occurs in the absorption length of the photons and consequently the absorption time.

In order to better understand the absorption in waveguide integrated photoemitters, we have plotted the 2-D absorption profiles for waveguide integrated GaAs along the direction of the waveguide and orthogonal to the surface of the waveguide. Figures 2(a) and 2(b) show the absorption profile in GaAs for 1.55 eV photons injected into a waveguide with a GaAs emitter length of 5 μm, a thickness of 20 nm, and a width of 600 nm. The simulated structure included an Al₂O₃ waveguide below the GaAs of 600 nm in width, 200 nm in thickness, and 5 μm in length. This structure was chosen to allow for single mode operation, but it should be noted that the precise details of the waveguide structure will mainly change the length over which photons of a specific energy will be absorbed by modulating the mode overlap between the GaAs emitter and the optical mode in the waveguide. The simulated waveguide has a Bragg reflector designed at the end of the 5 μm GaAs emitter. The black arrow in the cartoon schematic in Fig. 2(a) shows the direction along which the absorption is being plotted. In Fig. 2(a), the x-axis in the absorption profile is along the black arrow in the cartoon schematic while the z-axis is into the page with respect to the cartoon schematic. In Fig. 2(b), the y-axis is along the black arrow in the cartoon schematic. The absorption profile is shown for photons injected into the waveguide from the left and reflected off the Bragg reflector on the right of the emitter. For this device, we see that three features exist. First, an exponential decay, which occurs due to the absorption of the photons in the waveguide by the GaAs. Next, we see two large “lobes” which occur due to the mode of the mixed GaAs/Al₂O₃ structure, and, finally, we see the fine features which occur due to the coherent nature of the injected photons. It should be noted that these “lobes” occur because of the reflected wave which back-propagates due to the Bragg reflector at the end of the waveguide. Without this reflector, there would not be these larger features in the absorption profile. This is important as it allows us to potentially shape the output electron beam without needing to create a high quality factor optical cavity. Figure 2(b) shows the absorption profile in the direction indicated by the black arrow in the cartoon schematic. Here, we see that the absorption follows the general shape of the mode in the waveguide structure, but the absorption decays from the waveguide/GaAs surface toward the emitting surface.

For the case of 1.55 eV photons, a 5 μm long GaAs emitter is sufficient to absorb a majority of the incident photons. However, for 1.4 eV photons, the GaAs emitter length needs to be increased to 220 μm due to the much weaker absorption. As shown in Fig. 1(e), this does not affect the absorption profile in the direction of electron emission. However, the reduced absorption coefficient at 1.4 eV dramatically increases the average length in the waveguide that a photon must travel before absorption. This increases the time needed to absorb photons by the travel length divided by the speed of light in the waveguide. Figure 2(c) shows the absorption as a function of time for a 5 μm long GaAs emitter excited with 1.55 eV photons and a 220 μm long GaAs emitter excited with 1.4 μm photons. For the shorter emitter, absorption occurs within the first <100 fs, however, for the longer emitter, we see that even at 1.4 ns, the absorption has not saturated. This is directly a result of the speed of light in the waveguide and the absorption time.

In order to carry out the electronic simulations, we used a Monte Carlo Boltzmann Transport Equation Solver based on the software Archimedes, with modifications to model photon absorption and electron emitting boundary conditions. In this software, the Boltzmann Transport equation is solved self-consistently with the Poisson equation. The initial photoexcited electron energy distribution is computed by considering transitions from the light hole, heavy hole, and split off bands to the conduction band gamma-valley. For each band, a parabolic approximation with the appropriate effective mass is used. The number of excited carriers at each position is proportional to light intensity and it is assumed that carrier generation is the only significant absorption process.⁸ 

The semiclassical Boltzmann transport equation Solver saves the position and crystal momentum of each carrier in the simulation and updates these values as time iterates. Scattering mechanisms and corresponding scattering rates, calculated using Fermi's Golden rule, are given in Fig. S3 in the supplementary material. Implementation details of polar phonon scattering, optical phonon scattering, acoustic phonon scattering, and impurity scattering are given in Ref. 13, and these scattering mechanisms are implemented in Archimedes.⁸ Implementation details of electron-hole scattering are given in Ref. 12. Scattering events update the participant electrons' crystal momentum. Electron position is updated by considering the group velocity of the electron

Electrons drift in a potential, given in Fig. S1 in the supplementary material, arising from surface Fermi level pinning with band bending calculations provided in Refs. 3 and 9. Crystal momentum is updated in the band bending region according to

Electron emission probability is calculated by propagating the electron wavefunction across a Fisher barrier with no external electric field applied as shown in Fig. S2 in the supplementary material. This is done with the matrix propagation method as detailed in Ref. 11. The Fisher barrier models the thin potential barrier that exists at the surface of the caesiated negative electron affinity (NEA) GaAs. Simulations of the integrated photoemitter couple time dependent absorption data from Lumerical FDTD simulations into the electronic simulation, taking the place of the Beer-Lambert absorption profile.

To ensure our MC-BTE solver is consistent with those in literature, we simulate the results from Karkare et al in Ref. 3. Specifically, we simulate a negative electron affinity front illuminated bulk GaAs photocathode. After simulating the structure, we extract quantum efficiency, or the number of emitted electrons divided by the number of absorbed photons, and mean transverse energy (MTE), which is the average magnitude of the emitted photon energy in the direction transverse to the electron emission direction. Figure 3(a) shows the quantum efficiency results for the simulation carried out in Ref. 3 and using our solver. Importantly, we see nearly identical results overall, with a small discrepancy at the lower photon energies. Next, we look at the MTEs for the devices as simulated in Ref. 3 and our work. Two sets of MTEs are reported for the structure. First, intrinsic MTE for an atomically flat emitter surface is simulated. These show values on the order of ∼10 meV, with little increase with photon energy. Importantly, we again see that our simulations match those of literature. We also show MTE assuming surface scattering, which is close to what is observed experimentally from NEA GaAs emitters. This surface scattering occurs due to the surface roughness which is naturally induced on the surface of the GaAs wafer during the caesiation to create the NEA surface. The surface scattering model that we use randomizes the azimuthal angle upon emission. We compute quantum efficiency and mean transverse energy for various incident photon energies. These results match simulations and experimental data generated by Karkare et al.³ 

After comparing our simulation with that of literature, we simulated the waveguide integrated structure described in Fig. 1(d). As shown in Fig. 1(e), the absorption profile in the electron emission direction is relatively flat, with the excitation essentially being back-side illumination due to the evanescent coupling of photons from the waveguide into the GaAs. Assuming the ability to control optical absorption with a waveguide, we fixed the absorption length at 10 nm and illuminated the device from the back assuming Beer-Lambert absorption. In this way, we were able to rapidly investigate the electronic response to various device thicknesses and photon energies. Simulation results are displayed in Fig. 4.

As shown in Fig. 4(a), quantum efficiency increases as the device thickness decreases until the device thickness becomes comparable to the band bending width, in which case electrons are not able to gain sufficient energy from the field present in the band bending region in order to emit. Within the band bending region, transitions between the valence band and conduction band place electrons at lower energies. Figures 4(b) and 4(c) show that, for 1.7 eV light, as the device thickness increases, electrons excited near the back of the device have more room to relax to the conduction band minimum. These electrons travel to the surface and gain energy from the electric field in the direction normal to the surface. Thus, upon reaching the surface, emitted electrons have lower transverse energies as the device thickness, normal to the emission surface, increases. The Fisher barrier stands ∼0.3 eV above the bulk GaAs conduction band minimum,^9,10 and the bandgap of GaAs is ∼1.4 eV.⁸ Therefore, electrons gain the ability to traverse the barrier, without additional energy from the electric field, when 1.7 eV light is used. In the case of 1.4 eV and 1.55 eV light, as device thickness increases, the number of electrons that reach the surface with the ability to emit decreases significantly. Thicker devices select for electrons that have unusually high energies. Thus, for these photon energies, as the device thickness increases, the mean transverse energy increases. As the bandgap of GaAs is ∼1.4 eV, electrons generated with 1.4 and 1.55 eV light do not lose a significant amount of energy as they relax to the conduction band minimum. Figure 4(d) shows that with a thin GaAs emission layer, the response time increases dramatically, reaching ∼0.1 ps with 1.7 eV light. As the device thickness is reduced to 20 nm, electrons are generated closer to the surface and are thus able to reach the surface more rapidly. Additionally, as photons are absorbed evanescently, absorption does not suffer greatly as the device thickness is reduced.

Figure 4 demonstrates that with a device thickness of ∼20 nm and photon energy of 1.55 eV, large quantum efficiency, low mean transverse energy, and ultrafast response time is achieved. It is important to note that even with surface scattering considered [Fig. 4(c)], mean transverse energy is acceptable, ∼37 meV, with 1.55 eV light and 20 nm emitter thickness. A comparison with Fig. 3(b) shows that with the bulk photocathode, a comparable mean transverse energy is only obtained with the lowest photon energies which yield unacceptably low quantum efficiencies [Fig. 3(a)].

From Fig. 4, it was determined that the optimal thickness of the integrated photocathode emission layer is 20 nm and the optimal photon energies lie below 1.7 eV. Thus, optical simulations were carried out with 1.4 eV and 1.55 eV light to determine spatial and temporal absorption profiles (Fig. 2). This absorption data were then coupled into the Boltzmann Transport Equation solver. Results for 1.4 eV and 1.55 eV light, with the device thickness fixed at 20 nm, are displayed in Table I.

An improvement in response time of about an order of magnitude from 1.4 eV to 1.55 eV light is shown. For 1.55 eV light, a 0.15 ps response time is predicted, where conventional bulk photocathodes often exhibit response times of several orders of magnitude larger. Furthermore, ∼3% quantum efficiency and ∼40 meV mean transverse energy, with surface scattering, is predicted. These values are comparable to the best quantum efficiencies and transverse energies that can be obtained with bulk photocathodes. Furthermore, these results demonstrate that all of these exceptional values can be achieved at once in this integrated photocathode, without sacrificing one for another.

These simulations indicate that a photocathode structure utilizing evanescent optical coupling and a thin emission layer allows for a significant reduction in response time while enabling high quantum efficiency and low transverse energy. Utilizing negative electron affinity technology, which facilitates excellent control over electronic behavior, and an optical waveguide, which enables control over optical behavior, the constraint between photon energy, quantum efficiency, transverse energy, and response time that plagues conventional photocathodes is lifted. This work demonstrates the viability of an improved electron source technology especially useful for applications requiring high temporal precision. Future work will include fabrication using techniques well established within the III-V laser community, as well as quantum efficiency, transverse emittance, and response time measurements as performed in Refs. 3 and 16.

See the supplementary material for Figs. S1–S3. Figure S1 shows the band diagram of the negative electron affinity caesiated GaAs. Figure S2 demonstrates a wavefunction and shows transmission coefficients as a function of electron energy across the Fisher barrier. Figure S3 shows scattering rates as a function of energy with respect to the gamma-valley, L-valley, and X-valley.

This work was supported by ASFOSR (Grant No. FA9550-16-1-0306).