Photon Factory Activity Report 2004 #22 Part B (2005)
Electronic Structure of Condensed Matter

NE1A1/2002G025/2004G022

Three-dimensional electron momentum density in Si
Hidefumi UCHIYAMA1, Sunji KISHIMOTO2, Masayoshi
ITOU3, Hiroshi SAKURAI4,
2
Hiroshi KAWATA
1
Graduate University
forAdvanced
Studies, Tsukuba, Ibaraki 305-0801, Japan
2
KEK-PF,
Tsukuba,
Ibaraki 305-0801, Japan
3
Spring-8,4Kouto, Mikazuki-cho, Sayo-gun,Hyogo 679-5198 Japan
Gunma Univ., Kiryu, Gunma 376-8515, JapanObserved electron momentum density
Figure 2 shows the observed ρ (p) on the (110) plane.
In a region of ± 0.5 a.u. anisotropic momentum densitywith two-fold symmetry is clearly observed. Figure 3(a)shows the section along the [100] axis and 3(b) shows thesection along the [111] axis. The full line represents

110

Users' Report

References[1] Y. Kubo, private communication.
[100] or [111]∼ 100 nmSi

SiO2(200 nm)

Sisubstrate∼ φ 5mmFig. 1 Schematic drawing of a cross-section of a SOI
wafer and a thin foil Si single crystal.

Fig. 2 Observed electron momentum density in Si on the(110) plane.pz is in the [001] direction and px is in the[110] direction.
Experimental result
FLAPW theory

Experiment
FLAPW theory1ρ(p) [electrons/a. u.3]

Preparation of thin foil of single crystal Si
The spectrometer measures the direction and energy of
the recoiled electrons by a time of-flight method and thedirection of Compton scattered photons in coincidence
mode. Therefore, a sample should be thin enough for therecoiled electrons to come out without being additionally
scattered in the sample. In the present experimental
conditions the incident photons have an energy of 115.6
keV, the center of the energy spectrum of the recoiledelectrons is 34.6 keV and that of the Compton scatteredphotons is 81.0 keV. We estimated the mean free path ofan electron of 34.5 keV to be 43 nm using the total crosssection for elastic scattering given by the Wentzel model.
Therefore, the thickness of the sample should be less than
100 nm. To prepare a 100 nm thick sample we utilize
commercially available silicon-on insulator (SOI) wafers.
A cross-section of the SOI is schematically shown in Fig.
1. We paste the 100 nm Si side to a sapphire plate by wax
and mask the Si substrate side also with wax but leaving
an unmasked area of about 5 mm in diameter, thenchemically etch the Si substrate and SiO2 layer. Finally
we dissolve the wax to retrieve the 100 nm Si foil
supported by the SOI wafer. In the following we present
results obtained by using a single crystal foil whose plane
normal is [100].

theoretical results obtained by Kubo [1] using theFLAPW method. The theoretical curve is convoluted withthe present experimental resolution. The experiment isnormalized to the theory at p=0. Overall shape of theexperimental momentum density is well reproduced by
the theory. However, noticeable discrepancy between
theory and experiment is found in the tail part where theexperimental curve is higher than the theoretical curve.
We speculate one of the causes of the discrepancy to be
multiple scattering of the recoiled electrons in the sample.

ρ(p) [electrons/a. u.3]

Introduction
Compton profile measurements have been extensively
used to study electronic structure of materials. Compton
profile usually denoted as J(pz), pz being taken along thephoton scattering vector, is electron momentum densityρ (p) integrated over two momentum components px andpy. To explore electronic structure in greater detail,however, it is best to obtain ρ (p) directly fromexperiment. For this purpose we have developed an (XeX) spectrometer which can directly observe ρ (p). The
details of the spectrometer are described in the preceding
report. In this report we present some of the results onelectron momentum density in Si observed by thisspectrometer.

0.80.60.4
0.2
0-3-2-1
012
p on [100] axis [a. u.]

3

1

0.5

0-3-2-101
2
p on [111] axis [a. u.]

3Fig. 3 Electron momentum density on the [100] axis (a)and on the [111] axis (b).