Si:B
doping measurement by dark‐field electron holography
Authors: Boureau Victor , Benoit Daniel , Hartmann Jean‐Michel , Hÿtch Martin , Claverie Alain 
Published: December 2016

In modern MOS devices, sources and drains are of nanometric dimensions and highly doped (dopant concentration typically > 10
20
at.cm
−3
). Measuring such dopant concentrations and visualizing their spatial extensions in silicon, although mandatory for the development of the technology, is elusive in practice. Several TEM techniques such as EELS and EDX seem suitable to map dopant concentrations with the required resolution but while they are accurate to measure impurities concentrations, they cannot assess whether these impurities are on interstitial or substitutional sites, what is essential to define doping levels. Moreover, the detection of boron suffers from other physical limitations. Finally, bright‐field electron holography has been reported to be suited for such measurements but transforming the electrostatic fields which are measured into doping concentrations is far from straightforward.

In this work, we have explored the possibility to extract boron concentrations from the measurement of changes of the silicon lattice parameter induced by the substitution of boron atoms. For this we use dark‐field electron holography (DFEH) on specifically designed samples.

In a first part, we will present the DFEH principle [1]. This is an interferometry technique able to map strain with a precision of the order of 10
−4
and a few nanometers spatial resolution over micrometer fields of view. Two diffracted beams, one passing through an unstrained region of the lattice and acting as a reference, the other one passing through the region where strain has to be measured, are forced to interfere by using an electrostatic biprism and thus create an interference pattern (see figure 1). A phase map is extracted from the pattern by Fourier transform and converted into an atomic displacement field. By using two non‐collinear diffraction vectors, all the components of the strain tensor in the observation plane can be obtained.

For our experiment, a sample consisting of five 50 nm‐thick doped layers of increasing boron concentrations ranging from 3E
18
at.cm
−3
to 8.5E
19
at.cm
−3
was grown by RP‐CVD, under conditions insuring both extremely low concentrations of impurities and the full activation of boron [2]. The sample was further checked by SIMS and ECVP measurements, demonstrating that 100 % of boron atoms are on substitutional sites in all the doped layers. DFEH was used to measure the deformation of the doped layers. We could thus deduce the silicon lattice expansion coefficient (β) resulting from the adding of boron atoms in the crystalline silicon network, from these measurements, as explained below.

The boron atoms being on substitutional sites, the Si:B doped layers can be seen as solid solutions as confirmed by the homogeneity of the deformations imaged by DFEH. These layers are pseudomorphic on the pure silicon lattice as confirmed by the mapping of the in‐plane strain by DFEH. Thus, the change of the lattice parameter resulting from the incorporation of boron atoms is solely supported by the out‐of‐plane strain, through the Poisson's reaction of the material (figure 2). From the modeling of this sample by FEM and taking into account the relaxation affecting the thin lamella used for DFEH, we are able to retrieve the values of the relaxed Si:B lattice parameter as a function of the substitutional boron concentration. As expected for a solid solution, we find a linear relation between these two parameters. Knowing the boron concentration and the Si:B lattice parameter profiles, we are able to deduce that β coefficient equals ‐6.5E
−24
cm
3
(figure 3). Figure 4 compares the results we have obtained with those found in the literature, often measured by XRD.

Finally, β, the coefficient relating the boron concentration to the lattice parameter, allows us to transform a strain map obtained by DFEH into a “substitutional boron concentration” map with a precision of 3E
19
at.cm
−3
and a spatial resolution of 5 nm. We will illustrate the DFEH effectiveness to measure and image dopant concentrations in “real samples” through few examples, and will discuss the complementarity of the information obtained by this method and by bright‐field electron holography.