EELS Measurement of Hafnium
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Table 2402a. Main edges of Hf used in EELS analysis.

Edge(s)
Edge onsets (eV)
N4,5 213
M4,5 1660

In order to record the signals of Hf together with other elements in a single EEL spectrum, a proper edge of Hf should be selected. For instance, Table 2402b lists some application examples of Hf edges used in the particular cases.

Table 2402b.Application examples of the Hf edges used in particular cases.
Materials
Analyzing elements
Hf-edge (eV)
Other elements and their edge(eV)
Reference
HfSiO, SiO2 & HfO2 layers Hf & Si M4,5: 1660 Si K: 1840  
C-HfO2 Hf, C, O N4,5: 213 C K: 283; O K: 533 Figure 2402a

Figure 2402a shows an EELS experimental spectrum recorded from an HfO2 material. It is clear that the two Hf edges (N4,5) are very weak.

EELS experimental spectrum recorded from an HfO2 material

Figure 2402a. EELS experimental spectrum recorded from an HfO2 material. Adapted from [1]

Band gap can be determined based on Bethe’s theory. In this case, the SSD (single scattering distribution) spectrum is described to be proportional to the product of the joint density of states (JDOS). Here, the JDOS is given by,
        Schematic illustration of Si and Ge SSD spectra in the low-energy range for a direct band gap, ------------- [2402a]
and,
        Schematic illustration of Si and Ge SSD spectra in the low-energy range for an indirect band gap ------------- [2402b]
where,
        I0 and c -- The constants.
        E -- The energy loss.

Therefore, Eg can be extracted by fitting the single scattering spectrum using Equations [2402a] and [2402b]. Figure 2402b shows the band gap determination of the HfO2 layer in a Si/SiO2/HfO2/poly-Ge stack by using Equation 2402a (direct band gap [Eg = 5.26 eV] for HfO2).

Schematic illustration of Si and Ge SSD spectra in the low-energy range

Figure 2402b. Band gap determination of the HfO2 layer in a Si/SiO2/HfO2/poly-Ge stack. Adapted from [1]


 

 

 

[1] Marie C. Cheynet, Simone Pokrant, Frans D. Tichelaar, and Jean-Luc Rouvière, Crystal structure and band gap determination of HfO2 thin films, Journal of Applied Physics 101, 054101 (2007).

 

 

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