# Presentation: 071072

## 

**

**Characterizing the Order in 2D Block Copolymer Single Crystals  **
**Edward J. Kramer, University of California-Santa Barbara, DMR 0307233**

- 2D single crystal monolayers of block copolymer spheres are of interest to pattern arrays with nanoscale
- periodicity. Theoretically the order in such crystals is limited by thermal excitation of long wavelength
- phonons, the severity of this limitation depending inversely on the 2D shear modulus of the crystal. To
- test these ideas we have templated the formation of highly oriented single crystals in arrays of 12 m wide
- hexagonal wells, 30 nm deep, that span the entire area of 5 cm diameter silicon wafers.  The structure of the
- aligned 2D crystals was determined by grazing incidence small angle X-ray scattering (GISAXS), resulting
- in single crystal diffraction patterns. From line shape analysis of the diffraction peaks, we found that the
- translational order decays with distance from a given sphere as a power law with a decay exponent of -0.2,
- consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young theory for a 2D crystal with a 2D shear
- modulus of 2  10-4 N/m. This value is equivalent to a 3D shear modulus of 9.2 kPa and is in good agreement
- with predictions from self-consistent mean field simulations.
-                          G.E. Stein. E.J. Kramer, X. Li. J. Wang  Phys. Rev. Lett. **98**, 086101 (2007)

- Array of hexagonal wells on silicon
- used to template 2D block copolymer
- single crystals

- GISAXS geometry.  Diffraction data are
- obtained as the hexagonal well array is
- rotated in increments of ***  *as small as 0.1°

- Single crystal diffraction pattern from
- block copolymer in a set of 12 m wide
-  wells.  Intensity scale is logarithmic.

## Broader Aspects of Research Accomplishments

**Broader Aspects of Research Accomplishments**

- New graduate students joined this project in January 2007.
- Pictured below is **Adetunji Onikoyi**, who is a first year
- graduate student in Chemical Engineering at UCSB.  He
- comes to us from the University of Houston (ChE) where he
- did undergraduate research with Professor Ramanan
- Krishnamoorti.  “Tunji” will construct still smaller wells on
- silicon surfaces using electron beam lithography in order to
- more closely confine the block copolymers laterally.  We
- expect this closer confinement to decrease the decay exponent
- and improve the translational order in the wells. We are in
- discussions with Joy Cheng and Ho-Cheol Kim from
- IBM-Almaden for Tunji to have access also to some of their
- advanced optical lithography facilities for producing
- templating structures in silicon.

*“**Tunji” Onikoyi resealing one of our high vacuum annealing ovens*

*Gila Stein checking the alignment of her 2D block copolymer*
*single crystal at beam line XOR-8 of the Advanced Photon*
*Source at Argonne National Lab where she carried out her*
*GISAXS experiments.*

**Gila Stein** won a prestigious NRC Postdoctoral
- Fellowship at NIST where she is working with
- Alex Liddle at the Center for Nanoscale Science and
- Technology. She defended her outstanding PhD thesis at the
- end of October 2006 and will be interviewing for faculty
- positions in Chemical Engineering over the coming year
- with the idea of starting her career in academia in Fall of
- 2008 or Spring 2009.  Her research achievements mark her
- as one of the most promising polymer scientists and
- engineers of her generation.

**E. J. Kramer, University of California-Santa Barbara, DMR 0307233**