Graphene, being an atomically thin conducting sheet, is a candidate material for gate electrodes in vacuum electronic devices, as it may be traversed by low-energy electrons. The transparency of graphene to electrons with energies between 2 and 40 eV has been measured by using an optimized vacuum-triode setup. The measured graphene transparency equals ∼60% in most of this energy range. Based on these results, nano-patterned sheets of graphene or of related two-dimensional materials are proposed as gate electrodes for ambipolar vacuum devices.

With electronic devices becoming ever smaller, the need is growing for precise and miniature control of electric fields and electron paths. Whereas in vacuum devices, metal grids work well if biased with negative potentials, which repel electrons from the gate (see, e.g., Ref. 1), positive gate biases usually cause too high of gate current losses. Thus, gate materials that are conducting but highly electron-transparent are needed. Being ultrathin, two-dimensional materials are excellent candidates for such applications (see, e.g., Ref. 2). Graphene is one example of those. With its low electron density (n ∼ 1012/cm2, see, e.g., Ref. 3), graphene is expected to have a small scattering cross section for electrons traversing the sheet in perpendicular direction, which is small compared to that of thin films comprising heavier atoms. Its high mechanical strength4 and thermal robustness5,6 are further favorable properties for the application of graphene as a gate material.

Indeed, graphene has been thoroughly investigated for use as an electron-transparent material, for example, as a sample substrate in transmission electron microscopy,7,8 as a gate in metal-oxide-semiconductor field-effect transistors with vacuum channels,9 and as a gate in field-emission electron guns.10 For these applications, the transparency of graphene for electrons has been investigated. This is usually done by measuring the transmission coefficient T(E) = IT/I0, which is a function of the energy E of the incoming electrons. Here, IT and I0 are the electron currents impinging on the graphene and passing through it, respectively. Simulating propagating electron wave packets in real space and time, Yan et al.11 calculated the transmission and reflection coefficients of graphene for electrons with kinetic energies ranging from 20 to 200 eV and found the transmission coefficient to vary between ∼0.05 (20 eV) and ∼0.95 (200 eV). The transmission was also experimentally investigated. Longchamp et al.12 measured the transparency in a setup in which electrons emitted by a tungsten tip used as the point source were passed through a graphene sheet before reaching a microchannel detector plate. They determined the transmission of graphene for 66 eV electrons to be 0.73. Using point projection microscopy, Mutus et al. measured a transparency of ∼0.75 (100 eV).13 Srisonphan and coworkers studied the characteristics of junctions formed by graphene suspended on top of a void channel in a SiO2/Si substrate. According to their work, the transparency of graphene to electrons with kinetic energies <3 eV equals ∼99.9%.14 Kraus et al. explored the transmission factor in photoemission setups and found the transmission to increase with energy from 0.6 (300 eV) to ∼0.86 at 1400 eV.15 Li et al. found the transparencies to increase from 0.1 at 300 eV to ∼0.88 at 3 keV.10 All these measurements show graphene to be electron transparent, some of the differences in the data likely being caused by differences of the experimental setups and the preparation of the graphene. Unfortunately, no data are available for the energy range from 5 to 20 eV, which is relevant for many applications in vacuum electronics,1 including thermoelectronic energy converters.16 

For these reasons, we measured the graphene transparency Tg for low-energy electrons in a realistic device environment using a triode setup in which a monolayer graphene served as the gate, and thermionic emission took place from dispenser cathodes heated to 700 and 800 °C. As the graphene in these measurements is placed in vacuum next to a hot thermionic emitter, its transparency is lowered by adsorbates originating from the emitter and collector. As the adsorbates reduce the transparency, our data provide a lower bound to the transparency of ultraclean graphene for electrons between 2 and 40 eV.

Monolayer graphene samples were grown on a 25 μm thick copper (Cu) foil catalyst surface in a 4 in. Aixtron BM chemical vapor deposition (CVD) reactor. The Cu foil was annealed prior to the graphene growth for 15 min at 1000 °C using a mixture of argon and hydrogen in order to reduce the native Cu oxide and to increase the grain size. The graphene was grown at 1000 °C for 10 min using a mixture of methane and hydrogen (1:4) with argon as carrier gas. After the growth, the system was cooled to room temperature in a hydrogen and argon atmosphere. The graphene was transferred onto gold nets covered by perforated amorphous carbon foils by a wet transfer using FeCl3 as the etchant.

A sketch of the measurement setup is shown in Fig. 1. This setup was designed to allow calibration by reference measurements. For electron emitters, we used BaO:W dispenser cathodes.17 The electrons pass through graphene sheets mounted on perforated amorphous carbon carrier foils fixed onto gold substrates (Fig. 1(b), center)18 or through one of the two reference apertures (Fig. 1(b), left and right). One reference aperture was fitted with a gold substrate and a perforated amorphous carbon grid devoid of graphene (Fig. 1(b), left). The second reference aperture was a plain hole without a gold substrate (Fig. 1(b), right). The aperture diameters equaled 3 mm, the holes in the gold grid measured 60 μm, and the perforated holes in the amorphous carbon grid were 2.6 μm in diameter. The geometrical transparency, i.e., the ratio of the open area to the total area, of the perforated amorphous carbon foils mounted on the gold substrates equaled ∼11% (Fig. 1(c)). A stainless steel block was used as collector. The emitter-gate distance deg equaled ∼300 μm and the gate-collector distance dgc was ∼500 μm (Fig. 1(a)). To allow for the reference measurements, the emitter was moved in situ between the different apertures, while keeping d = deg + dgc nominally constant. The setup was operated in a vacuum chamber with a base pressure of ∼1 × 10−8 mbar. The emitter was electrically connected to ground; the grid and collector were biased relative to the emitter. The low energy of the electrons absorbed in the collector and the positive bias of the collector with respect to all surrounding conductors prevented the flow of secondary electrons from the collector.

FIG. 1.

(a) Sketch of the measurement setup with the BaO:W emitter (top, red), three different gate configurations (center, green and black), and the collector (bottom, blue). The arrows that refer to current flow indicate the flow of electrons. Panel (b) Top view of the geometry shown in (a). Panel (c) Optical microscope image of the gate grid with gold support (yellow) and a perforated amorphous carbon foil (light blue). The carbon foil is covered by a graphene sheet not visible in this image.

FIG. 1.

(a) Sketch of the measurement setup with the BaO:W emitter (top, red), three different gate configurations (center, green and black), and the collector (bottom, blue). The arrows that refer to current flow indicate the flow of electrons. Panel (b) Top view of the geometry shown in (a). Panel (c) Optical microscope image of the gate grid with gold support (yellow) and a perforated amorphous carbon foil (light blue). The carbon foil is covered by a graphene sheet not visible in this image.

Close modal

Accurate measurements with large signal-to-noise ratios were possible for collector voltages exceeding ∼5 V. The threshold for emitter–collector currents was approximately 2 eV as determined by the difference between the work function of the stainless steel collector (∼4.4 eV) and that of the BaO:W emitter (∼2.7 eV). A positive collector potential is therefore needed to align the vacuum levels between the emitter and collector. Thus, electrons approaching the collector do not encounter an energy barrier and sizeable collector currents flow. The graphene shields the collector field. This screening is a function of the gate-voltage dependent carrier density of the graphene. The kinetic energy of the electrons at the grid is therefore determined by the grid potential, the thermal energy of the electrons, and the not perfectly screened part of the collector field. Typical emission currents were in the range of 0.3–0.7 mA.

To elucidate whether the graphene remained intact on the aperture during exposure to the nearby hot emitter and to search for chemical modification of the graphene, Raman spectroscopy was performed at several positions of the graphene grids prior to and after the experiment. Both Raman spectra match well and show no formation of a D peak around 1350 cm−1 (Fig. 2(a)). The Raman data therefore showed no sign of any damage to the graphene sheet. The broad shoulder between 1250 and 1500 cm−1 is assigned to the amorphous carbon foil. Depending on how much laser light is scattered by the surrounding gold foil, the background luminescence of the Raman spectrum varies slightly between different positions of the measurement. Scanning electron microscopy imaging performed after the experiment confirmed the presence of the graphene (Fig. 2(b)). The measured fraction of holes not covered by graphene was used as input to calculate the graphene transparency.

FIG. 2.

(a) Raman spectra of the monolayer graphene covering the holes of the grid structure taken before and after the transmission experiments. (b) Scanning electron microscope image of the graphene layer spread across the holes of the perforated amorphous carbon foil. The image was acquired at 5 keV electron energy using a Zeiss Merlin inlens detector. This graphene sheet shows a rupture on one of the holes (bottom of image).

FIG. 2.

(a) Raman spectra of the monolayer graphene covering the holes of the grid structure taken before and after the transmission experiments. (b) Scanning electron microscope image of the graphene layer spread across the holes of the perforated amorphous carbon foil. The image was acquired at 5 keV electron energy using a Zeiss Merlin inlens detector. This graphene sheet shows a rupture on one of the holes (bottom of image).

Close modal

Figure 3 compares the transparency of the graphene-covered grids with the ones covered only with the graphene-free perforated amorphous carbon, both measured as a function of collector voltage. Considering the transparency of the graphene-covered grid stack to be given by the transparency of the stack times the transparency of the graphene, the graphene transparency is obtained (Fig. 3). The graphene transparency is found to be approximately constant above ∼11 V. The transparency increases when Vc is decreased below this value, as will be discussed below. Electrons thermionically emitted are accelerated towards the grid and reach the graphene with an energy of Ekine(Vg − ΔΦ), as the thermal energy is kTeeVg. Here, ΔΦ is the work function difference between the emitter and the gate stack. According to the literature, Φ ∼ 4.8 eV for gold and ∼4.5 eV for graphene.19,20 The measured work function for the BaO:W emitter equals ∼2.7 eV. This suggests ΔΦ ∼ 2 eV. This value represents an upper limit for the work function of the electrode materials used in the experiment because Ba/BaO is evaporated from the emitter and deposited on the grid, reducing its work function (see below). We therefore measured ΔΦ from the onset of the collector current Ic in the Ic(Vg) characteristic. As this measurement yielded ΔΦ ∼1 eV, we used this value to obtain the graphene transparency as a function of Ekin controlled by Vg. The results are shown in Fig. 4. In the energy range from 10 to 20 eV, the transparency of the graphene in the measurement setup is Tg ∼ 0.6 with no significant energy dependence. The steep increase at energies below 10 eV is likely due to space charge effects. As emitter and grid are at similar potentials in this range, space charge builds up between them, inhibiting the emission of electrons from the emitter surface.16 This effect is stronger for the graphene-covered grid that more effectively shields the collector field. The effect should decrease with smaller emitter-gate distances deg, which are not possible with the current setup and are therefore beyond the scope of this publication. The data were quantitatively reproduced with a different graphene gate. The Raman spectra and scanning electron images show the graphene to be clean, uniform, and flat. We point out that the measured transparency of the graphene refers to graphene operated in an ultra-high vacuum (UHV) chamber under the conditions described. The transparency values we measure are bracketed by the literature values taken at lower or higher electron energies, as discussed above.

FIG. 3.

Graphene transparency calculated by dividing the electron transmissions of the graphene-covered and bare grid stacks. The data of curves a, b, c show three independent measurements taken on the same grid over a period of 48 h, illustrating the reproducibility of the measurements. The dashed curve (multiplied by a factor of 32 for clarity) shows the absolute transmission of a graphene-covered stack. After an onset around 2 V, a drastic increase of Ic/Ie at small Vc is observed. The data were taken with Vg = 6 V and Te ∼ 800 °C.

FIG. 3.

Graphene transparency calculated by dividing the electron transmissions of the graphene-covered and bare grid stacks. The data of curves a, b, c show three independent measurements taken on the same grid over a period of 48 h, illustrating the reproducibility of the measurements. The dashed curve (multiplied by a factor of 32 for clarity) shows the absolute transmission of a graphene-covered stack. After an onset around 2 V, a drastic increase of Ic/Ie at small Vc is observed. The data were taken with Vg = 6 V and Te ∼ 800 °C.

Close modal
FIG. 4.

Graphene transparency measured as a function of gate voltage (upper horizontal scale) and electron kinetic energy (lower scale). In deriving the kinetic energy of the electrons at the graphene, full screening of the collector potential by the graphene was assumed. The kinetic energy axis is offset by ∼1 eV (translating the raw data to lower energies) to compensate for the work function difference between the emitter and the grid stack. The collector voltage Vc was 15 V. Curves a and b show measurements taken on two different grids in independent measurement runs. Grid c was subject to excessive Ba exposure induced by long-term operation next to the Ba dispenser emitter heated to 800 °C.

FIG. 4.

Graphene transparency measured as a function of gate voltage (upper horizontal scale) and electron kinetic energy (lower scale). In deriving the kinetic energy of the electrons at the graphene, full screening of the collector potential by the graphene was assumed. The kinetic energy axis is offset by ∼1 eV (translating the raw data to lower energies) to compensate for the work function difference between the emitter and the grid stack. The collector voltage Vc was 15 V. Curves a and b show measurements taken on two different grids in independent measurement runs. Grid c was subject to excessive Ba exposure induced by long-term operation next to the Ba dispenser emitter heated to 800 °C.

Close modal

Since the graphene is in close proximity to the hot Ba dispenser emitter, the possibility exists for Ba or BaO to be deposited onto the graphene. Indeed, energy-dispersive X-ray (EDX) measurements showed the presence of Ba on grids that had been operated at high temperatures for extended periods of time. Barium may alter the work function of the grid, reduce its transparency, and lead to electron emission from the grid. Barium deposition on the grid offers a natural explanation for the apparent increase of the graphene transparency shown in Fig. 3 at Vc < 10 V. As Ba condenses on the graphene, the Ic vs. Vc curves of both grid configurations shift with respect to each other on the voltage axis. The altered threshold voltage provokes the apparent increase of the transparency, which is the ratio of the two. Furthermore, on a graphene gate that had been subjected to excessive Ba exposure, a significantly reduced transparency was observed (Fig. 4).

Our data show that graphene operated in a vacuum environment next to a hot dispenser cathode is semi-transparent for electrons with energies between 2 and 40 eV. The measured transparency of 60% provides a lower bound to the transparency of adsorbate-free graphene. As graphene is thermally resilient and has a sufficient mechanical strength to be patterned with holes (see, e.g., Ref. 21), its geometrical transparency can be enhanced by perforation to optimize its electron transparency. As electron-transparent gate material, graphene, therefore, opens new possibilities for vacuum-based or gas-based microelectronic devices. For such applications, possible excitations of the graphene, for example, plasmons, and interband excitations22 caused by the traversing electrons would constitute an unwanted energy loss channel. Patterning of the graphene reduces these losses accordingly. We therefore envision the use of patterned graphene sheets in micro-sized vacuum tubes that utilize ambipolar gate voltages. Another application of such patterned graphene sheets is gates in thermoelectronic power generators.16 In all cases, graphene-compatible cathodes have to be utilized to avoid depositing detrimental, electronically active adsorbates. It also seems worthwhile to explore the suitability of other two-dimensional materials for such uses.

We gratefully acknowledge helpful discussions with T. Geballe and S. Meir, as well as support by I. Hagel, P. Kopold, K. Lazarus, M. Schmid, V. Srot, and W. Winter. J.H.S. acknowledges financial support from the graphene flagship and the graphene priority programme (DFG).

1.
Vacuum Electronics
, edited by
J. A.
Eichmeier
and
M.
Thumm
(
Springer
,
Berlin, Heidelberg
,
2008
).
2.
M. C.
Lemme
,
L.-J.
Li
,
T.
Palacios
, and
F.
Schwierz
,
MRS Bull.
39
,
711
(
2014
).
3.
K. S.
Novoselov
,
A. K.
Geim
,
S. V.
Morozov
,
D.
Jiang
,
Y.
Zhang
,
S. V.
Dubonos
,
I. V.
Grigorieva
, and
A. A.
Firsov
,
Science
306
,
666
(
2004
).
4.
C.
Lee
,
X.
Wei
,
J. W.
Kysar
, and
J.
Hone
,
Science
321
,
385
(
2008
).
5.
K.
Kim
,
W.
Regan
,
B.
Geng
,
B.
Alemn
,
B. M.
Kessler
,
F.
Wang
,
M. F.
Crommie
, and
A.
Zettl
,
Phys. Status Solidi RRL
4
,
302
(
2010
).
6.
A. A.
Balandin
,
Nat. Mater.
10
,
569
(
2011
).
7.
J. C.
Meyer
,
C. O.
Girit
,
M. F.
Crommie
, and
A.
Zettl
,
Nature
454
,
319
(
2008
).
8.
Z.
Lee
,
K.-J.
Jeon
,
A.
Dato
,
R.
Erni
,
T. J.
Richardson
,
M.
Frenklach
, and
V.
Radmilovic
,
Nano Lett.
9
,
3365
(
2009
).
9.
S.
Srisonphan
,
Y. S.
Jung
, and
H. K.
Kim
,
Nat. Nanotechnol.
7
,
504
(
2012
).
10.
C.
Li
,
M. T.
Cole
,
W.
Lei
,
K.
Qu
,
K.
Ying
,
Y.
Zhang
,
A. R.
Robertson
,
J. H.
Warner
,
S.
Ding
,
X.
Zhang
 et al,
Adv. Funct. Mater.
24
,
1218
(
2014
).
11.
J.-A.
Yan
,
J. A.
Driscoll
,
B. K.
Wyatt
,
K.
Varga
, and
S. T.
Pantelides
,
Phys. Rev. B
84
,
224117
(
2011
).
12.
J.-N.
Longchamp
,
T.
Latychevskaia
,
C.
Escher
, and
H.-W.
Fink
,
Appl. Phys. Lett.
101
,
113117
(
2012
).
13.
J. Y.
Mutus
,
L.
Livadaru
,
J. T.
Robinson
,
R.
Urban
,
M. H.
Salomons
,
M.
Cloutier
, and
R. A.
Wolkow
,
New J. Phys.
13
,
063011
(
2011
).
14.
S.
Srisonphan
,
M.
Kim
, and
H. K.
Kim
,
Sci. Rep.
4
,
3764
(
2014
).
15.
J.
Kraus
,
R.
Reichelt
,
S.
Gunther
,
L.
Gregoratti
,
M.
Amati
,
M.
Kiskinova
,
A.
Yulaev
,
I.
Vlassiouk
, and
A.
Kolmakov
,
Nanoscale
6
,
14394
(
2014
).
16.
S.
Meir
,
C.
Stephanos
,
T. H.
Geballe
, and
J.
Mannhart
,
J. Renewable Sustainable Energy
5
,
043127
(
2013
).
17.

Purchased from HeatWave Labs, Inc., www.heatwavelabs.com.

18.

Purchased from Graphenea, www.graphenea.com.

19.
H.
Hibino
,
H.
Kageshima
,
M.
Kotsugi
,
F.
Maeda
,
F.-Z.
Guo
, and
Y.
Watanabe
,
Phys. Rev. B
79
,
125437
(
2009
).
20.
S.-J.
Liang
and
L. K.
Ang
,
Phys. Rev. Appl.
3
,
014002
(
2015
).
21.
J.
Ding
,
K.
Du
,
I.
Wathuthanthri
,
C.-H.
Choi
,
F. T.
Fisher
, and
E.-H.
Yang
,
J. Vac. Sci. Technol. B
32
,
06FF01
(
2014
).
22.
F. J.
Nelson
,
J.-C.
Idrobo
,
J. D.
Fite
,
Z. L.
Mišković
,
S. J.
Pennycook
,
S. T.
Pantelides
,
J. U.
Lee
, and
A. C.
Diebold
,
Nano Lett.
14
,
3827
(
2014
).