Page 235 - Electrical Properties of Materials

Microelectro-mechanical systems (MEMS) 217

The solution is to attach, at least to a certain fraction of the molecules,
a charge. How? We ionize them. There are actually many ways to do that.
∗
We shall mention only one of them: electron impact ionization. Either the ∗ This is a good method when the analyte
electrons are produced by thermionic emission (Section 6.5) or they are field- (the substance to be analysed) is a gas.
induced (Section 6.7), and then they are accelerated to acquire the right amount
of energy. As it happens, the right energy can be found by a very simple argu-
ment. The average bond length of the molecules of interest is about 0.15 nm. If
we want electrons to break those bonds then it makes good sense to choose an
accelerating voltage which leads to a de Broglie wavelength of the same length.
Luckily, we have already looked at this calculation when working out the ac-
celerating voltage for the experiments of Davisson and Germer (Section 2.1).
We got a de Broglie wavelength of 0.1 nm using a voltage of 150 V. Hence, to
obtain 0.15 nm we need about half of that voltage (remember, the de Broglie
wavelength is inversely proportional to the square root of the applied voltage),
and indeed the voltage usually employed is 70 V. The accelerated electrons are
then injected into an ionization region, where they encounter the analyte.
Next we need to filter the ionized molecules according to their mass. The
most obvious way of doing that is to introduce the ions into a homogeneous
magnetic field, where they will be deflected (remember eqn (1.46)) by a force
perpendicular both to the applied magnetic field and to the electron velocity.
This type of filtering works very well indeed. Mass spectrometers based on it
were developed originally by the fathers of mass spectroscopy, Thomson, As-
ton, and Bainbridge, some hundred years ago. Nowadays it is less fashionable. Francis William Aston, Nobel
The way which is in the ascendancy is quadrupole filtering. It needs four paral- Prize in Chemistry, 1922.
lel electrodes, which can produce the right electric field distribution. Between
the electrodes there is a channel, into which the ions are injected. What do we
want to achieve? That most of the ions fall by the wayside (bump into elec-
trodes) but those with the right mass sail through unharmed. It turns out that
static electric fields on their own cannot be used for this purpose. On the other
hand, if they are aided and abetted by a time-varying voltage in the lower MHz
range and, in addition, the electrodes are shaped so as to produce a hyperbolic
∗
potential distribution, then the aim can be achieved. For a specific ratio of the ∗ Ideally, electrodes of hyperbolic shape
d.c. and a.c. voltages, ions with a particular mass have bounded trajectories are needed but it is not easy to pro-
duce them. It turns out, however, that
and transit without discharging. Tuning of the filter is done by varying the d.c. the required potential distribution can
and r.f. voltages but keeping their ratio constant. It is an ingenious solution. be well approximated by electrodes of
The inventor, Wolfgang Paul, got a Nobel Prize for it in 1989. cylindrical shape.
Having got the right ions through the channel, we need to detect them. That
is relatively easy. Ions may be detected on a separate electrode, where they dis-
charge to become molecules, leaving the charge to be converted into a voltage
by a low-noise amplifier.
So we have got everything we need: an ion source, a mass filter, and a
detector. But, you may say, what happens if there are two different kinds of
molecules with identical mass? Can we distinguish them? Yes, we can, but not
on the basis we have described so far. We have not told the full truth. When
the molecules are ionized they may fragment into daughter ions. Instead of
just one type of ion, each molecule generates a distribution of ions, a kind of
signature that can be recognized.
Finally, let’s see how a quadrupole can be constructed. A relatively simple
way is to etch down crystal planes of silicon in a particular direction. The
◦
(111) planes lie at 54 to the surface of (100) oriented wafers, and are resistant