Simulations of field emission of electrons from an electron gun are used to determine the angular distribution of the emitted electron beam and the percentage of charge transmitted through the grid. The simulations are a first step towards understanding the spherical aberration present after focusing the electron beam. The effect of offset of the cathode with respect to the grid and the separation between cathode and grid on the angular distributions of emitted electrons and transmission of the grid are explored

Costen, Nicholas P.

Getty, Stephanie A.

Glavin, Daniel P.

Hidrobo, Gregory B.

Southard, Adrian E.

NASA Technical Reports Server

Understanding the impact of field-emitter characteristics on electron beam 
focusing in the VAPoR Time-of-Flight Mass Spectrometer  
 
Adrian E. Southard  
University Space Research Agency and NASA Goddard Space Flight Center 
Greenbelt, U.S.A 
Adrian.e.southard@nasa.gov 
Stephanie A. Getty, Nicholas P. Costen, Gregory B. Hidrobo and Daniel P. Glavin 
NASA Goddard Space Flight Center 
Greenbelt, U.S.A. 
 
Abstract—Simulations of field emission of electrons from an 
electron gun are used to determine the angular distribution of the 
emitted electron beam and the percentage of charge transmitted 
through the grid.  The simulations are a first step towards 
understanding the spherical aberration present after focusing the 
electron beam.  The effect of offset of the cathode with respect to 
the grid and the separation between cathode and grid on the 
angular distributions of emitted electrons and transmission of the 
grid are explored.  
Keywords- Electron gun, mass spectroscopy, computer 
simulation 
I. INTRODUCTION  
  To maximize the mass resolution of the time-of-
flight mass spectrometer (TOFMS) being developed for the 
VAPoR instrument (Volatile Analysis by Pyrolysis of 
Regolith)[1], a simulation of field-emission from its electron 
gun is undertaken.  The electron gun cathode is composed of 
an array of carbon nanotube based pillars [4] pointed towards  
a hexagonal grid, which provides the extraction field to 
produce an electron beam.  Pillar height and alignment to the 
grid are still a challenging part of the electron fabrication to be 
reported on separately.  The focus of this study is to examine 
how the height of these pillars and their position relative  to 
the grid affect the angular distribution of electrons transmitted 
through the grid.  This distribution affects the electron beam 
spot size which determines the size of the ionization region 
and ultimately the ability of electrostatic lenses to spatially 
focus an ion packet at the detector[3]. In addition, the 
transmission efficiency of the grid will also be determined as 
this impacts the sensitivity of the TOFMS.   
In the TOFMS, the electron beam spot size In 
previous work, our electron gun featured a narrow aperture 
that reduced the electron beam acceptance angle, which had 
the interesting consequence of reducing contributions from 
spherical aberration at the ionization volume of the ion source.  
With recent improvements to the hardware to eliminate the 
narrow aperture and increase ionization efficiency, however, 
we have found that the resulting spherical aberration is now an 
important consideration in determining the smallest spot size 
attainable with the beam at the image focus [2].   
I. APPROACH 
https://ntrs.nasa.gov/search.jsp?R=20140011241 2019-08-31T19:43:16+00:00Z
The angular and kinetic energy distributions of 
emitted electrons depend on the pillar geometry and its 
alignment to the grid which varies from electron gun to 
electron gun and even within the array of ~ 100,000 pillars and 
grid elements used in our emitter array. A top-down view of a 
section of one of the fabricated pillar arrays is shown in Fig. 
1a. This particular emitter features square pillars and a 
hexagonal grid.  A schematic of the cross-section of this array, 
indicated by the red plane in Fig. 1a is shown in Fig. 1b.  
We explored the effects of pillar height and grid-
pillar misalignment on the performance of the electron gun.  A 
software package, SIMION, was used to determine trajectories 
of charged particles in the presence of electric and magnetic 
fields[5] for various emitter geometries.  The emitter was 
simulated using dimensions that closely match as-fabricated 
emitters.  The spacing between the surrounding substrate and 
the grid was held constant, as is the case in fabrication.    
Because major features in the emitter are on the one-micron 
scale, the model used a 0.25 μm/grid unit mesh.  The model 
contained a representative sub-array of 7 pillars, each with 5 
μm x 5 μm square cross section.  These pillars are positioned 
below a commensurate array of hexagonal grid holes, each 
with a 28 μm opening along the diagonal.  The pitch along the 
arm-chair direction of the lattice was 30 μm.  The grid 
thickness used was 20 μm and the gap between the cathode 
substrate surrounding the pillars and the grid was 52 μm.  
As shown in Figure 2, the seven pillars are arranged 
in a hexagonal geometry.  Although the electron emission was 
only simulated at the central pillar, the six pillar/grid elements 
on the perimeter were necessary to screen the effects of 
Neumann boundary conditions applied at the edge of the 
potential array. The model shown in Fig. 2 contains 13.5 µm-
high pillars positioned directly below the center of the holes, 
i.e. a 0 µm pillar array offset along both the x and y axis. The 
models used to simulate various pillar heights and offsets in 
pillar positions with respect to the grid were based on the 
model shown in Fig. 2. In simulations of the emitted electron 
trajectories, 16 electrons were emitted per grid point,  a total 
of 6561 electrons.  These electrons were birthed at locations 
uniformly distributed at the top of the central pillar with zero 
kinetic energy and allowed to move in the field between the 
pillar array, at 0 V, and the grid, at 200 V.  This potential 
difference is typical for electron gun operation. Because of the 
square pillar cross-section, the Fowler-Nordheim field 
enhancement factor is expected to vary across the top 
“surface” of the pillar.  The resulting variation of emission 
current across the top of the pillar was accounted for by 
invoking a charge weighting factor, which is a value 
normally used to allow one particle to represent a cluster of 
ions or electrons.  Here, it associates a weight to each 
simulated electron that can be chosen to be proportional to the 
Fowler-Nordheim emission current, IFN: 
 CWF=IFN=αF2exp(-β/F) (1) 
where F is the electric field in V/grid unit (denoted V/gu), α 
depends on the work function and area of the emitting surface 
and β depends on the work function of the pillar and field 
enhancement due to individual carbon nanotubes extending 
above the pillar surface.  Note that traditionally, β, accounts 
for any electric field enhancement beyond what is obtained 
with a parallel plate geometry; however, here field 
enhancement due to the pillar’s shape modifies the local value 
of β and further enhancement due to nanoscale effects, e.g. 
pillars that protrude above the pillar’s surface, are subsumed 
into the parameter β. For the sake of comparing various 
emitter geometries, α and β have been set equal to 1 V2/gu2 
and 1 V/gu, respectively. This value for  is representative of 
a pillar surface where individual carbon  nanotubes are 
 
Figure 1(a) Contrast enhanced optical image of a section of one e-gun showing square carbon nanotube pillars below a hexagonal grid (top down 
view) with a red plane indicating the cross section shown in (b). 
 
Figure 2 A three dimensional SIMION model of a section of the pillar-
emitting without screening one another and exhibit field 
enhancement factors of ~19,000.  Note that field enhancement 
factors of individual multiwall carbon  nanotubes up to 30,000 
have been reported[6].  It must be noted, then, that the values 
produced in this study must be treated qualitatively; we will 
focus only on comparisons between model geometries, rather 
than making quantitative predictions of experimental field 
emission currents.  The fine granularity in field emission 
properties due to the fact that the pillars comprise ~ 1000 
individual carbon nanotubes is outside of the scope of this 
study.  It is therefore assumed that the field computed here 
averages over nanoscale variations in the field due to field 
enhancement at the tips of carbon nanotubes. 
 
II. PREPARE YOUR PAPER BEFORE STYLING 
Within the geometry of the TOFMS, the ionization volume is 
described by the intersection of the electron beam and the ion 
acceptance into the instrument.  Therefore, the width of the 
electron beam along the ion path has a direct influence on 
mass resolution.  Since ions formed after electron ionization 
are extracted parallel to the y-axis, electrons emitted at small 
values of θ, the elevation angle, are ideal (Fig. 2).  Thus, the 
following discussion will focus on how the pillar-grid 
geometry affects elevation angle distributions. A narrow 
electron distribution centered about θ = 0 degrees is desirable 
for optimized TOFMS performance. 
  In Fig. 3, the y-axis is proportional to the amount of 
charge transmitted through elevation angles of 2 degrees, 
regardless of azimuthal angle φ, normalized by the total charge 
emitted, and plotted as a function of elevation angle.     
An offset in position along the x-axis, denoted X 
offset in Fig. 3a leads to an almost symmetric distribution 
whose peak height is reduced almost uniformly as offset is 
increased.  A slight asymmetry in the elevation distribution 
with no X nor Y offset is due to limitations in the potential 
refinement at the edges and corners of the pillars. Note that 
even with no offset, a small number of electrons are able to 
pass through all six of the grid holes surrounding the central 
one and this leads to small peaks in the spectrum at -12 and 14 
degree
s. A Y 
offset 
leads 
to a 
strongl
y 
asymm
etric 
distrib
ution 
(Fig. 
3b), 
redistributing emission at 0 degrees to emission at 3 degrees.  
The case of a Y offset of 10 µm results from the beam exiting 
through four different grid holes.  
As pillar height is decreased, the elevation angle 
distribution becomes more sharply peaked, as shown in Figure 
4.  This is caused by a smaller variation of the field at and 
around the pillar surface. This is explainable due to the fact 
that a shorter pillar gives an electric field that approaches that 
of the constant field between two parallel plates.     
In Table 1, a comparison of the amount of charge 
emitted and transmitted is given for each configuration 
simulated.  Recall that the simulations are not sophisticated 
enough to predict the actual amount of charge physically 
emitted and that only comparisons between the different 
geometries can be made.  The amount of charge transmitted is 
higher when X and Y offsets are zero or in the case of the 
shortest pillar.  The amount of charge emitted is largest when 
the electric field is largest which for a constant applied voltage 
is when the gap between the pillar and grid is smallest.   
 
 
III. SUMMARY 
In simulated field emission from CNT pillars, 
enhanced electron emission at the vertices and edges of flat-
top pillars produced a flatter elevation angle distribution and 
less overall charge transmission than would be the case if field 
this enhancement were ignored and the density of emitted 
Work sponsored by the NASA Astrobiology Science and Technology for 
Instrument Development Program (07-ASTID07-0020). 
-20 -15 -10 -5 0 5 10 15 20
-1
0
1
2
3
4
5
6
7
8
9
10
C
ha
rg
e 
tra
ns
m
itt
ed
(%
)
Elevation angle(degrees)
 10 um
 5 um
 0 um
Angle binsize= 2 degrees Y offset=0
X offset
-20 -15 -10 -5 0 5 10 15 20
-1
0
1
2
3
4
5
6
7
8
9
10
C
ha
rg
e 
tra
ns
m
itt
ed
(%
)
Elevation angle(degrees)
 0 um
 5 um
 10 um
Angle binsize= 2 degrees X offset=0
Y offset
 
Figure 3 Impact of pillar array offset along the (a)  x-axis and (b) y-axis on the elevation angle distribution. 
Table 1 Effect of pillar array offset on the percentage of
charge transmitted given a fixed pillar height of 13.5 µm
	





	



	



	



	


	
    	

   
 	

   	 		
   
 	
   
 	
    
    

 
electrons was independent of position along the pillar top.  
These edge and vertice effects would become more significant 
if field enhancement due to the large aspect ration of isolated 
carbon nanotubes was reduced by screening and would 
correspond to values of β>1.      
The silicon beams making up the hexagonal grid are 
not thick enough to block emission through neighboring grid 
holes.  This is especially evident when Y offsets are non-zero.  
A larger pitch with thicker beams could reduce this effect but 
at the cost of lower transmission of electrons through the grid.  
The effect of X offsets is to reduce the angular breadth of the 
beam at the expense of the percentage of charge transmitted.  
This effect is a result of the shape of the hexagonal holes 
making up the grid and would not present with a square grid.  
The shortest pillar height, 6.75 µm, showed a more 
pronounced peak in the elevation angle distribution and 
increased transmission of charge of ~5%; however, this 
corresponded to a reduction in emitted charge of more than 
50% compared to the 13.5 µm pillar.  In experiment, a larger 
bias voltage between the cathode and grid can compensate for 
reduced emission from a short pillar; however, this also 
increases power consumption due to both  the emission current 
and any leakage currents between the cathode and emitter.  
The larger bias voltage may also necessitate the use of 
electronics especially rated for high voltages. 
In conclusion, both pillar height and offset lead to a 
tradeoff between mass resolution and sensitivity. Determining 
the optimal geometry of the electron-gun will require  
examination of the impact of spherical aberration on the 
ability of electrostatic lenses to reduce the beam spot size.  
 
IV. ACKNOWLEDGMENT  
Thanks to David Manura for SIMION support and examples 
and Michael Collier for fruitful discussions.   
REFERENCES 
 
[1]  D. P. Glavin, C. Malespin, L. Inge, S. A. Getty, V. E. 
Holmes, E. Mumm, H. B. Franz, M. Noreiga, N. Dobson, A. 
E. Southard, and others, “Volatile Analysis by Pyrolysis of 
Regolith for Planetary Resource Exploration.” 
[2]  M. Szilagyi, “Optimum design of electrostatic 
lenses,” Journal of Vacuum Science & Technology B: 
Microelectronics and Nanometer Structures, vol. 6, no. 3, p. 
953, May 1988. 
[3]  R. J. Cotter, Time-of-flight mass spectrometry. Wiley 
Online Library, 1994. 
[4]  S. A. Getty, T. T. King, R. A. Bis, H. H. Jones, F. 
Herrero, B. A. Lynch, P. Roman, and P. Mahaffy, 
“Performance of a carbon nanotube field emission electron 
gun,” in Proc. of SPIE Vol, vol. 6556, p. 655618–1. 
[5]  Dahl D.A., “simion for the personal computer in 
reflection,” International Journal of Mass Spectrometry, vol. 
200, no. 1, pp. 3–25, 2000. 
[6]  J. L. Silan, D. L. Niemann, B. P. Ribaya, M. 
Rahman, M. Meyyappan, and C. V. Nguyen, “Carbon 
nanotube pillar arrays for achieving high emission current 
densities,” Applied Physics Letters, vol. 95, no. 13, p. 133111–
133111–3, Sep. 2009. 
[7]  M. Fransen, T. L. Van Rooy, and P. Kruit, “Field 
emission energy distributions from individual multiwalled 
carbon nanotubes,” Applied surface science, vol. 146, no. 1–4, 
pp. 312–327, 1999. 
 
-20 -15 -10 -5 0 5 10 15 20
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
C
ha
rg
e 
tra
ns
m
itt
ed
(%
)
Elevation angle(degrees)
 13.5 um
 27 um
 6.75 um
Angle binsize= 2 degrees
Pillar height
 
Figure 4 Impact of pillar height on the elevation angle distribution 


Understanding the Impact of Field-Emitter Characteristics on Electron Beam Focusing in the VAPoR Time-of-Fight Mass Spectrometer

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server