Electron holography characterization of the electrostatic potential of thin high-κ
dielectric film embedded in gate stack
Y. Yao(姚湲)1,a), Y. Yang(杨阳)1, X. F. Duan(段晓峰)1, Y. G. Wang(王岩国)1, R. C. Yu(禹日成)1,
Q. X. Xu(徐秋霞)2
1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,
Chinese Academy of Sciences, Beijing 100190, China
2. Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
Supplemental Material
1. Potential retrieved from the wedge-shape sample
Fig. S1 Schematic diagram of the interference between objective wave and reference wave
transmitting the wedge-shape sample.
Assuming that the thickness of the sample changes linearly in the wedge-shape sample, i.e.
t  kx  d , where the x-axis is along [001]Si axis, the objective phase and reference phase
superimposing at position A in Fig. S1 (as same as Fig. 1 in the paper) should be
obj  CEVobj (kx  d '') (from A'') and ref  CEVSi (kx  d ') (from A'), respectively. So in the
a)
Author to whom correspondence should be addressed; electronic mail: yaoyuan@iphy.ac.cn
phase objective approximation the phase difference reconstructed from the hologram is
  obj  ref  CE (Vobj  VSi )(kx  d '')  CEVSi (d '' d ')
(S1)
Eq. S1 also indicates that for the Si substrate covered in the view field its phase profile
Si  CEVSi (d '' d ') is an invariable. The experimental data shown in Fig. 4 in the paper
confirm this expectation. Therefore, the objective potential can be derived from the simplified Eq.
S1
Vobj 
   Si
 VSi
CE (kx  d '')
(S2)
where Vsi could be considered as the mean inner potential value of Si because the substrate is a
field-free area.
2. Phase reconstruction
(a)
(b)
(c)
(d)
(e)
Fig. S2 (a) The hologram of vacuum (b) The hologram of the high-κ stack with electron
passing through Si substrate as the reference wave. (c) The reconstructed amplitude
image and (d) the phase image. (e) The contrast profile of (a). Scale bar is 2 nm.
Fig. S2(a) is the hologram taken at the vacuum where biprism bias at 180 V. Its contrast
profile is shown in Fig. S2(e) and the fringe contrast is 20%. The side band of the Fourier
transform indicates the carrier frequency qc is 6.15 nm-1, so the mask radii qres is set at qc/3 ≈ 2
nm-1 for phase reconstruction, corresponding the lateral resolution 0.5 nm.
3. Measurement error
The standard deviation of the phase value of each point in Fig. 4 in the paper is 0.12, which is
calculated from 800×12=9600 data. The average thickness t of high-κ dielectric is about 52 nm
and the thickness error t is about 1.4 nm, thus the voltage resolution at the high-κ dielectric
should be
Vobj 
   Si
 VSi
CE t
  Vobj 

2    Si

t
CE t
CE t 2
2  0.12
1.6

1.4
0.0073  52 0.0073  52 2
0.7 (V)
4. Potential measurement of the FIB sample
(a)
(b)
Fig. S3 (a) Unwrapped phase image of the FIB cutting sample. Inset is the phase
change from Si substrate to Al cap. (b) Phase-shift of Si substrate, HfLaON insulator
and Al cap relative to vacuum, drawn along the arrow in (a).
Fig. S3(a) shows the reconstructed phase image in which high-κ and TiN film peaks can be
identified. The phase-shifts relative to vacuum of the Si substrate, high-κ film and Al cap are
drawn in Fig. S3(b). Assuming that the mean inner potential is the only contribution to the phase
shift, calculation declares the thickness of Si and Al are 117.6 nm and 135.0 nm (VAl =12.4 V1,),
respectively. The calculated maximum potential is 15.5 V in high-κ insulator film using average
thickness 126.3 nm.
Reference
S1. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials
Science, 2nd ed. (Springer Science + Business Media, LLC, 233 Spring Street, New York,
USA, 2009)