Collision cascade DisorderCollision cascade Disorder
Chapter 4 Experimental Techniques and sample preparation
4.2.1 MEIS Introduction and basic principles
4.2.1.5 Dose and concentration calculations
It is possible in principle to calculate the number of target atoms per unit area. The scattering yield Y is given by
QNt d
d Q
Y= d = σ ΩΩ (4.5)
where dσ/dΩ is the scattering cross section which describes a probability for scattering, described in more detail in section 2.2.1, Qd is the number of detected particles, Q is the
number of incident particles, Ω is the acceptance solid angle of the detector and Nt is the areal density. The differential scattering cross section can be calculated from the interaction potential V(r). For M1<<M2.
(
1 2)
2 2 2 1 g ,M ,M E 4 e Z Z F d dσ ⋅ θ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⋅ = Ω (4.6)For interactions at the energies used in MEIS the nuclear events occur at distances of the order of the screening length, so the scattering is not purely Coulombic and a screening factor F, has to be applied. Screening functions are described in more detail in section 2.2. For MEIS it is generally accepted that a function derived from the Molière potential (26) is best (1, 2). Then F is given by,
E Z Z 042 . 0 1 F 3 4 2 1 − = (4.7)
for M1<<M2. The screening term lies typically in the range 0.85 ≤ F ≤ 1 (1). For a 100
keV He beam there is a 3% deviation in the potential from the case of the purely repulsive Coulombic Rutherford scattering. The implications are small and only have a minor affect with the MEIS scattering yield. The function g(θ, M1, M2) is a
transformation factor from the centre of mass to the lab frame of reference, for M1<<M2
given by:
(
,M ,M)
1 2(
M /M)
sin(
/2)
g 2 4 2 1 2 1 θ θ ≈ − − (4.8)Equations 4.5 and 4.6 have important implications for the choice of experimental parameters and the ability of MEIS to detect different elements. Since dσ/dΩ is a function of Z12 then the scattering yield is four times higher for He+ than H+ and
similarly as dσ/dΩ is a function of Z22 then there is a considerably higher scattering
yield from heavier elements, eg As, compared to light elements, eg B. Using a lower energy beam gives a higher scattering yield. A smaller scattering angle gives a rapid rise in the scattering yield because of the sin-4(θ/2) dependence. The requirements for the experimental set up are discussed more in section 4.2.2.2.
Returning to the calculation of implantation dose, in practice equations 4.5, 4.6 and 4.7 are not used since the acceptance angle of the detector and the detection efficiency are not normally known with sufficient accuracy (1). The yield will also be varied by the neutral fraction. Instead results obtained are compared with the result from a randomly oriented (amorphous) sample or an ion implanted sample with a well known amount of a heavy dopant (4). Data was frequently taken from amorphous Si samples therefore the random level was the preferred concentration reference. It is expected that doses can be calculated to within 5% using this method (1). The density of an amorphous Si sample is known to within 5%, and therefore the number of Si atoms represented by each backscattering count can be determined. This value can be converted for dopant ions by accounting for the difference in scattering cross sections between Si and the dopant ion. The number of atoms per count has to be multiplied by (ZSi/Zatom)2. It is largely justifiable to ignore the differences in the screening function as
they are small compared to the differences due to the scattering cross sections. With the random yield typically 375 counts, representing a concentration of 5 × 1022cm-3 Si atoms, then displaced Si can be detected down to ~ 1 × 1020 cm-3 and As to 1×1019 cm-3. A correction has to be applied to account for the different energy widths that peaks of the different elements have on the energy scale. The heavier the element, the greater energy range that equates to a fixed depth. Stated differently ∆E/∆z is larger for higher masses and hence energies. The variation is usually less than 10% but needs to be accounted for (4). It can be most convenient to calculate the number of dopant atoms on the basis of the depth scale.
The effect of neutralisation should be considered when using an electrostatic analyser, as neutrals cannot be detected (1). Analysis of data taken at the MEIS facility at the FOM institute (NL), carried out at Daresbury Laboratory, would suggest that there was little variation in neutral fraction for different elements at the energies used in MEIS (48), which was contrary to other findings (44). The measured results showed that the neutral fraction varied with the velocity of the ion leaving the sample, being lower at lower energies. The amount of variation was small over the energy range of a MEIS spectrum (48). The implications for the dose calculation would therefore appear to be not particularly significant. This is supported by a comparison of the results of MEIS dose calibration with results of RBS measurements carried out at the University of Salford, using a surface barrier detector, which detects neutrals. Good agreement to within 3% was obtained.
4.2.1.6 Crystallography – Channelling, shadowing, blocking and dechannelling