Mass calibration

For a particle of mass m and energy E we have

$E=\frac{1}{2}mv^2;\Rightarrow;v=\sqrt{\frac{2E}{m}}$

so if the detection path length is L

$t=\frac{L}{v}=L\sqrt{\frac{m}{2E}}$

if the energy E=q∙U for the charge q and the voltage U.

$m=\frac{2qU}{L^2}t^2$

For the case of ToF-SIMS, we define a variable sf as follow:

$sf=\frac{L}{\sqrt{2qU}}$

k0 is a time delay and the mass can be retrieved by:

$m=\left(\frac{t-k0}{sf}\right)^2$

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