My colleagues Dr. Minliang Ren and Rahul Agarwal, have adapted SHG polarimetry and successfully demonstrated the capability of this technique on II-VI nanostructures (CdS, CdTe) to provide crystallographic information, using the set-up
shown in Figure 4.2. It must be noted that the χ(2)of these materials is well characterized
in bulk. These structures contain tetrahedral bonding between cations and anions, as in the case of diamond or Si. However, Si (or diamond) possesses an inversion symmetry center, which is the center of a Si-Si bond, whereas a similar position in II-VI materials has a group II element on one side, and a group VI on the other breaking the centrosymmetry. Hence these II-VI materials, which are non-ferroelectric, owing to the loss of centrosymmetry, give an SHG signal, which was analyzed by my colleagues to obtain crystallography sensitive information and compared with the TEM results. Here are some quick excerpts and lessons from their work:
Optical SHG on CdS nanowire system (wurtzite) reveals the nanowire
orientation: In order to validate the SHG characterization technique for nanostructures,
we started with the simple case of single crystalline wurtzite CdS (non-centrosymmetric) nanowires, which were first analyzed via TEM and later through optical SHG. For
generality, we studied CdS nanowires with three different growth orientations: c-axis
parallel to NW’s long-axis (c//NW, α0=0), perpendicular to NW’s long-axis (c NW,
α0=90°) and at an angle relative to NW’s long-axis (c NW, 0<α0<90⁰). In all the cases
of different growth axes, when the fundamental wave is polarized along the nanowire (transverse magnetic, TM) SHG is also polarized along the nanowire (TM). However, when the fundamental is polarized perpendicular to the nanowire (transverse electric,
! 92!
TE), regardless of the growth axis, the SHG signal always follows the c-axis of the nanowire- consistent with our mathematical analysis (Figure 4.3).
Figure 4.3: TEM data and SHG polarimetry results on CdS (wurtzite) nanowires. (A) Growth axis is along c-axis, (B) Growth axis is perpendicular to c-axis, (C) Growth axis at an angle to c-axis. Scale bars correspond to 100 nm.
Optical SHG on CdTe nanowire system is sensitive to the type of stacking twins
and the volume fraction of twin domains: CdTe nanostructures, in contrast to CdS
nanostructures, are typically synthesized in a zinc-blende structure in which twin domains
exist based on different stacking sequences along the [111] direction viz abcabc… (A
domain) or acbacb… (B domain) 6. Depending on the chirality of the anionic tetrahedra
centered with a cation of stacking sequence abcabc…(domain A), each domain can exist in A(+) or A(-) configurations, and their coexistence results in an APB along the (111) plane at the boundary. Twin boundaries between domains with cationic stacking sequences abcabc… (domain A) and acbacb… (domain B) may be classified as upright
if domain A(+) is obtained from domain B(+) via a rotation of 180o about [111] direction,
and inverted if a reflection operation transforms A(+) to B(-). The !tensor for each of
these four domains (A(+/-), B(+/-)) is different in a fixed lab frame of reference, and hence the contribution from different domains to the total SHG signal is different.
and in the lab frame can be obtained via suitable transformations from crystal
χ(2) (2) A χ ± (2) B χ ±
! 93!
frame, and it can be shown mathematically that SHG intensity as a function of SHG polarization angle θ and the fundamental wave polarization angle θ0, may be given as :
where f1 and f2 are known functions, and x is a fitting parameter which depends on the volume fractions (Vi) of individual domains at θ0=90o (TE polarized fundamental) as
Figure 4.4: Different response of TE-excited second harmonic generation (SHG) from different regions of a twinned CdTe nanobelt. (A) Bright field TEM micrograph of the twinned nanobelt. Dark field TEM micrograph (inset) exhibits a non-uniform domain pattern. Scale bar: 200 nm. (B) SAED pattern confirming the twinned structure of the nanobelt. (C-F) Polarization properties of TE-excited SHG signal (I2ω) from different excitation regions as marked in (A).
RA
RB =
VA(+)−VA(−)
VB(+)−VB(−) =( 2−x) ( 2+x) I2ω(θ,θ0)∝ f1(θ0)cosθ+ f2(θ0)xsinθ2
! 94!
Figure 4.4A is a bright field TEM micrograph (inset: dark field TEM micrograph) of one such twinned CdTe nanobelt displaying distinct twin domains, and different domain fractions in different regions. Twinning is also confirmed by the SAED pattern with superimposed diffraction spots from the two crystallographically distinct twin domains (A and B) (Figure 4.4B). The domains A and B are stacked alternatively along the [111] direction, forming the domain boundaries (or twin planes) perpendicular to [111]. In the SHG measurement, we measured the SHG signal under TE excitation (along
the long-axis, or perpendicular to [111]) at four different points on the nanobelt, Q1, Q2,
Q3, and Q4 (Figure 4.4C-F). We find at Q1 with x = – 0.36 and therefore
+A(or –A) seems to dominate over +B (or –B). Similarly, at Q2 with x =
0.92, showing that +B (or –B) dominates over +A (or –A). At Q3, and ,
leading to the equivalent fraction of +A (or –A) and +B (or –B). In contrast,
and at Q4, which indicates that domain +B (or –B) dominates over
domain –A (or +A). From the above analysis of the SHG signal, we can conclude that ±A and ±B exist in twinned CdTe nanobelts simultaneously but randomly, as commonly
observed in other materials7,8.
It is important to note that SHG polarimetry can easily distinguish the polarity of domains (+/-) and hence between inversion and upright twin boundaries, which diffraction contrast and phase contrast TEM cannot (unless analytically complicated convergent beam diffraction techniques are used). Hence SHG has been successfully developed on II-V1 nanostructures for gathering quantitative information about twin domains, and their polarity. With the success of these experiments serving as the
RA RB =1.68 RA RB =0.21 0 x≈ RA RB ≈1 3.57 x= RA RB =−0.43
! 95!
inspiration, we have decided to adapt the SHG polarimetry technique to a more complicated case of GeTe.
4.3. SHG polarimetry on single-crystalline <110> synthesized GeTe nanowires