Analytical model and simulation of the Schottky effect on a cryo-cooled bialkali photocathode

LOW ENERGY ACCELERATOR, RAY AND APPLICATIONS

Analytical model and simulation of the Schottky effect on a cryo-cooled bialkali photocathode

Hua-Mu Xie，

Er-Dong Wang，

Ke-Xin Liu

Nuclear Science and Techniques

Vol.29, No.5

Article number 71

Published in print 01 May 2018

Available online 31 Mar 2018

DOI：10.1007/s41365-018-0400-6

69200

A bialkali photocathode with the quantum efficiency(QE) in the range of a few percent was fabricated for the 704 MHz SRF gun at Brookhaven National Laboratory. The photoemission properties of the bialkali photocathode in the superconducting radio frequency (SRF) gun were measured for the first time, and a good beam experiment result was obtained. The performance of the bialkali photocathode was investigated during the commissioning process of the 704 MHz SRF gun. The effect of electric field on the QE of the cryo-cooled cathode was characterized by an analytical model and a code for the first time.

Schottky effectBialkali photocathodeSurface potentialSuperconducting radio frequency gun

Introduction:

Superconducting radio frequency (SRF) guns[1-4] were widely investigated in free electron lasers (FELs), energy-recovery linacs (ERLs), electron cooling, etc. The wavelength of a free electron laser is partially restricted by the emittance of the electron beam. Thus, many efforts were made to reduce the beam emittance. The gradient on the surface of the cathode in an SRF gun is very high, so the space charge effect-induced emittance can be very low. A bialkali photocathode[5] is chosen in many electron guns (DC, NCRF, and SRF guns) as the electron source owing to high QE (4–10%), low intrinsic emittance, weeks of lifetime in a reasonable vacuum (~2-5×10⁻⁸ Pa).

In SRF guns, a cathode is inserted into the superconducting cavity, and the electric field on the surface of the cathode is around 20 MV/m. The heat induced by the RF field on the stalk can be as high as hundreds of watts[6], so the stalk must be cooled to protect the cathode from degradation. In BNL’s 704 MHz SRF gun[4] and HZDR’s 1.3 GHz SRF gun[1], the cathodes are both cooled by liquid nitrogen. The final temperature of the cathode is stabilized at 80 K. During the cooling process, the QE of the cathode would drop to 20% of the original value in the 704 MHz SRF gun. The detailed description of the cooling effect of a bialkali photocathode can be found in the previous reference[6]. The incident photon energy (2.32 eV) is very close to the ionization energy of the K₂CsSb photocathode (~2.1 eV), and the ionization energy change from the cryo effect is in the range of 0–0.15 eV[6]. Therefore, the excess energy of emitted electrons is also near the threshold. An analytical model and a code are built to explain this effect. From the analytical model and the code, we predicted that if an electric field was applied to the cathode, the Schottky effect would lower the surface potential and hence would compensate the QE reduction caused by cooling. An experiment was designed to demonstrate this prediction.

Experimental Section:

There are a deposition chamber and a load lock chamber in the bialkali photocathode deposition system (Figure 1). The load lock chamber is baked every time a new photocathode is fabricated. A substrate is mounted in the transport cart, which is connected to the deposition chamber via the load lock chamber. The transport cart consists of long moving bellows, an ion pump, and a high-vacuum gate valve. The substrate can be inserted into the deposition chamber for the photocathode deposition. A heater is connected to the gas inlet tube at the end of the cart. The substrates are heated by hot flowing nitrogen gas. The gas channel can also be used to cool the substrate with flowing nitrogen gas or liquid nitrogen. Three sources, Cs, K, and Sb are assembled in three separate bellows, which are connected with the main chamber using ultrahigh-vacuum gate valves. During the thin-film deposition process, the valve is open and the source arm can be inserted into the chamber. The vacuum of the main chamber can reach 4×10⁻⁸ Pa with a sputtering ion pump and a non-evaporative gas (NEG) pump. A quartz crystal monitor is used to record the film thickness during the evaporation process. A residual gas analyzer (RGA) can give the residual gas partial pressure in the main chamber. The cathode is irradiated by a 0.5 mW green laser. An anode is equipped in the main chamber to collect electrons emitted from the cathode surface, and the photocurrent is monitored by a Keithley P6485 picoammeter.

Fig. 1.

(Color online) Bialkali photocathode deposition chamber for the 704 MHz SRF gun

We use Cu-breezed Cr as the substrate for the cathode deposition. The substrate is polished with diamond pastes, with diameters ranging from 10 nm to 1 nm. The roughness of the substrate after polishing is measured using an atomic force microscope (AFM) and can be found in Fig. 2. Laser cleaning^[5] is also introduced in the substrate processing to get higher QE.

Fig. 2.

(Color online) Surface information of the Cr substrate after being polished with diamond nanoparticles. The four inserts are related to the surface topography of the sample, surface of the sample measured using the deflection mode, roughness of the sample along the line in the first insert measured using a constant force mode, and roughness measured using the deflection mode.

The deposition process of the bialkali photocathode was as follows:

1. The substrate was heated at 350 °C for 3 h to release the absorbed gas and then cooled to 90°C.

2. After the degassing procedure, a Sb source was moved to the front of the substrate. The heating current was 67 A, and the thickness of the film was monitored from the quartz crystal monitor.

3. The substrate temperature was then raised to 130 °C, and the K deposition process was started. During the deposition process, the cathode was irradiated with the 532 nm green laser, and the photocurrent was monitored with the picoammeter. When the photocurrent reached the plateau, the K evaporation stopped.

4. After degassing, the Cs activation process was started. The heating current of the Cs source was approximately 5.5–6 A. During the activation process, the photocurrent kept growing. When the photocurrent reached the plateau, the heating power was reduced and the substrate was cooled by the flowing nitrogen gas.

The substrate was then moved out, and the cart was disconnected from the main chamber. The transport cart was moved to the cave and connected to the SRF gun. Before the cathode was inserted into the gun, the alignment of the stalk and cavity needed to be performed first. The alignment accuracy was about 50 µm. During the baking process of the load lock chamber, the cathode was protected with a liquid nitrogen finger to avoid being polluted by the gas released from the valve between the cart and the load lock. The liquid nitrogen finger is a stainless steel part, which is cooled by liquid nitrogen and can be moved in and out of the cathode cart by moving the bellows. An in-situ QE measurement system was installed in the transport cart to measure the QE of the cathode during the transport process (Fig. 3).

Fig. 3.

(Color online) Transport cart connected to the 704 MHz SRF gun

After the cathode was inserted into the gun cavity, flowing liquid nitrogen was conducted in the channel to cool the cathode down to 80 K. The detail of the beam experiment can be found in reference^[4]. The parameters of one beam experiment are shown in Table 1.

Parameters in the beam experiment [4] of the 704 MHz SRF gun

Parameters	Values
Gun voltage (MV)	1.2
Pulse repetition rate (MHz)	9.38
Duty factor	0.3%
Bunch charge (pC)	50

The QE of the cathode inside of the gun was around 4% and reduced to 1% after RF conditioning and long beam running. The degradation was mainly caused by the multipacting between the cathode stalk and the high-gradient SRF cavity. During the beam experiment, the QE of the cathode dropped to 0.2 % owing to the cooling effect [6]. The peak gradient on the cathode was set to 11 MV/m. The laser distribution is truncated Gaussian. With the green laser (the wavelength was 532 nm) illuminating the cathode, emitted electrons were accelerated by a high electric field. The bunch charge was measured by Integrating Current Transformer (ICT). The QE of the cathode was calculated by the bunch charge and the laser pulse energy. Then we started the RF phase scan process; the QE changed with the RF phase during this experiment.

Results and Discussion:

The experimental result is shown in Figure 4. During the phase scan process, we could see that the QE of the cathode increased gradually. After 10°, the QE increased much slower. We assume that the space charge limit caused this phenomenon.

Fig. 4.

Experimental results, analytical model, and simulation results of the Schottky scan experiment. The black dots are the experimental results. The gray line is the calculation results of the space charge limit. The blue line is the analytical model calculation of the Schottky effect. The red line is the Monte-Carlo simulation of the Schottky effect on the bialkali photocathode. In both the analytical model and the code, the space charge limit is not included.

(1) Space charge limit calculation

Here, the photoemission of the cathode is "pancake photoemission", based on reference^[7]. The maximum surface charge $Q_{sat}$ can be expressed as

Q_{sat} = σ_{sat} π R^{2} ≅ ε_{0} E π R^{2} = ε_{0} E_{0} π R^{2} \sin θ,

(1)

where $σ_{sat}$ is the maximum surface charge density, $ε_{0}$ is the vacuum dielectric permittivity, $R$ is the laser beam size, E is the electric field on the surface of the cathode, and $θ$ is the RF phase. The effective QE, which relates to the photocurrent extracted and the incident photon energy, can be calculated as

Q E_{eff} = \frac{Q_{sat} \times f \times h v}{P \times e},

(2)

E_{0} = E_{p} Sinθ,

(3)

where f is the laser repetition rate, E_p is the peak electric field on the surface of the cathode, P is the laser power, $h v$ is the incident photon energy (here, we used the 532 nm green laser), d is the gap length between the anode and the cathode, and $θ$ is the RF phase. With Eqs. (1–3) and the parameters listed in Table 2, the effective QE can be calculated as shown in Figure 4.

Parameters used for the calculation of the space charge limit

Parameters	Values
Permittivity, $ε_{0}$ (C²/N m²)	8.85 × 10⁻¹²
Electron charge, e (C)	1.6 × 10⁻¹⁹
Peak gradient, $E_{p}$ (MV/m)	11
Laser beam size, r_m (mm)	2
laser pulse length (ps)	10
Laser power, p (W)	0.15

(2) Schottky effect calculation

Schottky effect-induced surface potential change $Δ W$ [8]at the RF phase $θ$ can be calculated as

Δ W = \sqrt{\frac{e}{4 {π ε}_{0}} \frac{ε - ε_{0}}{ε + ε_{0}} E_{p} Sinθ},

(4)

where ε is the relative permittivity of a bialkali material. During the beam experiment, the scanned phase was around π/2, so the surface potential change is calculated to be approximately 0.11 eV.

(3) Analytical model:

In order to give a detailed description of the Schottky effect on the QE of the cooled bialkali photocathode, we used the same analytical model built to explain the cryogenic performance[6]. The model was based on Spicer’s[9] three-step model. The analytical model successfully explained the cooling effect in the previous literature[8]. In this model, only those electrons with energy higher than the ionization energy E_e can be emitted into the vacuum. E_e was expected to increase by 0.15 eV when the cathode was cooled to the temperature of liquid nitrogen based on Ref.[10]. Here, the Schottky scan effect would change the surface potential with a sine function, and the maximum change in the surface potential is calculated to be 0.11eV as shown in the last part. We added this surface potential change $Δ W$ into the analytical model[6], and the QE could be written as

Q E = C (1 - e^{- α (ћ ω) L}) (1 - \int_{0}^{E_{e} (0) + φ (T) - (ћ ω - σ) - Δ W} f (E, σ) d E),

(5)

where α(ћω) is the absorption coefficient of K₂CsSb at the photon energy ћω, $E_{e} (0)$ is the ionization energy at room temperature, which equals the sum of the bandgap energy E_g and the electron affinity E_a at room temperature. The temperature has an effect on the crystal lattice and its surface properties, and hence the energy bandgap or the electron affinity [11] is changed. φ(T) is the change in the ionization energy at temperature T, and φ(T) is set to zero at room temperature. σis the energy spread in the valence band. $f (E, σ)$ is the Maxwell–Boltzmann [12] probability distribution function of electrons in the valence band of the bialkali photocathode. C is a constant, which is determined by the cathode material and is fitted as illustrated in Ref.[6].

With $Δ W$ changing as a sine function of the RF phase, Equation 5 can be used to calculate the QE change at different RF phases. The result is shown in Fig. 4. The calculated result shows the same trend with the experimental result beyond the space charge limit.

(4) Code Simulation

In Ref.[6], a Python code was developed to simulate the photoemission process of the bialkali photocathode. The code starts from the initial distribution [13] of electrons in the valence band; after absorbing the photon energy, the excited electron would diffuse in the conduction band. Electron–electron scattering, electron–phonon scattering, and electron–hole scattering are included in the code. At the third step, the electron can emit into the vacuum if the electron energy after the second step is higher than the electron affinity and the transverse momentum is conserved.

This code is used to explain the Schottky effect of the bialkali photocathode. The Schottky effect is added to the code, and the surface potential is changed as illustrated in Eq. 3. The electron affinity of the bialkali photocathode at 77 K is 0.3 eV. The change in the electron affinity is set as a sine function of the RF phase. The maximum of the electron affinity change is calculated to be 0.11 eV. We run the code and get the RF phase dependence of the effective QE of the bialkali photocathode at 532 nm. The effective QE change with the laser phase is shown in Fig.4:

At the beginning of the RF scan, the effective QE is restricted by the space charge effect. The simulation starts from 10°, and no space charge effect was included. The simulation results agree well with the experimental results.

Conclusion:

A high-QE bialkali photocathode was fabricated with a mature deposition method. A Cr substrate was a laser cleaned before the cathode deposition. The cathode was cooled with liquid nitrogen during the beam experiment. The Schottky scan experiment was performed to explore the influence of electric field on the bialkali photocathode. The phase scan of the RF field changed the QE of the cathode dramatically. It could compensate the QE drop of the bialkali photocathode caused by the liquid nitrogen temperature. The analytical model and the code, which explained the cooling effect, is used for the first time in this paper to successfully describe the Schottky scan effect.

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