Scanning Electron Microscopy and X-Ray Microanalysis

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5

found in wires, electronics, or electrical engineering. Beam

current at the sample surface is a measure of the number of

electrons per second that impact the specimen. It is usually

measured in fractions of an ampere, such as microamperes

(μA), nanoamperes (nA), or picoamperes (pA). A typical

SEM beam current is about 1 nA, which corresponds to 6.25

× 10^9 electrons per second, or approximately one electron

striking the sample every 160 ps. The usual symbol used to

represent beam current is I, or i, or a subscripted variant such

as Iprobe, Ibeam, Ip, or Ib.

5.2.4 Beam Current Density

Similar to the beam current, the concept of current density is

relatively easy to understand and corresponds directly with

the same concept in electrical engineering or electrical

design. Current density in an electron beam is defined as the

beam current per unit area, and it is usually represented by

the symbol J, or Jbeam. In standard units this quantity is

expressed in A/m^2 , but there are also derived units better

suited to the SEM such as nA/nm^2 or similar. The most

important thing to understand about current density is that

it is an areal measure, not an absolute measure; this means

the current depends directly on and varies linearly with the

area of the region through which the stated current density

passes.

To make this concrete, let’s consider an example calcula-

tion of the current density in an electron beam.. Figure 5.2

shows a circular beam with a diameter of 5 nm; and the total

current inside the circular beam spot is 1 nA. The area of the

beam is

Ar

d

circle

nm

== nm









 =











ππ π  =

2

22

2

2

5

2

19 6.

(5.1)

and therefore the current density in the round beam is

J

I

circle A

circle

circle

nA

nm

nA

nm

= = = = pA nm

1

19 6

22 0 0509 50 9^2

.

../

(5.2)

. Figure 5.2b shows the situation if you decrease the diame-
ter of the beam by half, from 5  nm to 2.5  nm, yet keep the
same total current in the beam. Now the area has gotten
smaller, yet the current is unchanged, so the current density
has increased. The new current density is

J

I

A

circle

circle

circle

nA

nm

nA

nm

= = = = pA nm

1

491

22 0 204^2042

.

./

(5.3)

Since focusing the electron beam in an SEM changes the

diameter of the beam but does not change the beam current,

the current density must change. As can be seen in. Fig. 5.2,

shrinking the beam width by a factor of two results in a four-

fold increase in beam current density.

5.2.5 Beam Convergence Angle, α

One of the fundamental characteristics of the electron beam

found in all SEM instruments is that the shape of the beam as

seen from the side is not a parallel-sided cylinder like a pen-

cil, but rather a cone. The beam is wide where it exits the final

aperture of the objective lens, and narrows steadily until (if

the sample is in focus) it converges to a very small spot when

it enters the specimen. A schematic of this cone is shown in

. Fig. 5.3. The point where the beam lands on the sample is
denoted S at the bottom of the cone, and the beam-defining
aperture is shown in perspective as a circle at the top of the
cone, with line segment AB equal to the diameter of that
aperture, dapt. The vertical dashed line represents the optical
axis of the SEM column, which ideally passes through the
center of the final aperture, is perpendicular to the plane of
that aperture, and extends down through the chamber into
the sample and beyond. The sides of the cone are defined by
the “edge” of the electron beam. As mentioned above in the
definition of the beam diameter, this notion of a hard-edged

1 nA

5 nm

1 nA

2.5 nm

a

b

Current density = 50.9 pA/nm^2

density = 204 pA/nm^2

. Fig 5.2 a Current density in a circular electron beam; b current
density if the beam diameter is reduced by a factor of two with the
same current

S S

ABAB

dapt dapt

2α WWα

ab

. Fig. 5.3 a Definition of beam cone opening angle 2α; b definition
of beam convergence (half ) angle α

Chapter 5 · Scanning Electron Microscope (SEM) Instrumentation