Modeling the Stress Evolution of Ion Beam Synthesized Nanocrystals
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Modeling the Stress Evolution of Ion Beam Synthesized Nanocrystals D. O. Yi1,3 , I. D. Sharp2,3 , Q. Xu2,3 , C. Y. Liao2,3 , J. W. Ager III3 , J. W. Beeman3 , Z. Liliental-Weber3 , K. M. Yu3 , D. Zakharov3 , E. E. Haller2,3 , and D. C. Chrzan2,3 1 Applied Science and Technology Group, Univ. of Calif., Berkeley, CA 94720, U.S.A. 2 Dept. of Materials Science and Engineering, Univ. of Calif., Berkeley, CA 94720, U.S.A. 3 Materials Sciences Division, Lawrence Berkeley Nat. Lab, Berkeley, CA 94720, U.S.A. ABSTRACT Under certain conditions, nucleation and growth can lead to substantial stresses in nanocrystals embedded in a host matrix. These stresses may be relaxed through subsequent annealing treatments. A model is presented for the relaxation of these stresses via diffusive processes within the matrix. The model reflects the effects of surface tension, potential phase transformations at or near the processing temperature, and differential thermal expansion. It is demonstrated that the model describes well the stress relaxation of ion beam synthesized Ge nanocrystals embedded in a silica matrix. INTRODUCTION In the past decade, a number of techniques have been developed to create nanometer-sized crystalline semiconductors embedded in a host matrix. These nanocrystals are potential building blocks for photonic and opto-electronic applications and their properties must be well understood. One interesting property that is not yet understood quantitatively is the stress state of ion beam synthesized (IBS) nanocrystals. These nanocrystals are typically found to be under compressive stresses of a few GPa[1–3]. After thermal annealing, however, these stresses may decrease. Several reports have described qualitatively the existence of the compressive stresses and the subsequent relaxation of stress after thermal processing[1–3]. Here, a quantitative model of the relaxation process is presented. BACKGROUND The experiments under consideration[4] involve the implantation of multi-energy Ge ions into a thin film (500 nm) of silicon dioxide (figure 1). The implanted samples are annealed at 900◦C for one hour to produce Ge nanocrystals. The resulting ‘as-grown’ nanocrystals are, on average, 5 nm in diameter. The stress state of the nanocrystals is characterized using Raman spectroscopy. The effects of phonon confinement produce a red shift of the peak frequency from the bulk value of the characteristic wavenumber, as measured by Raman spectroscopy at room temperature. However, Raman measurements performed on the embedded, as-grown, Ge nanocrystals show a blue shift from the bulk value. This blue shift is attributed to the presence of compressive stress on the nanocrystal[5]. When additional Raman
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Figure 1: (1)Ge ions are implanted into silica. (2) Nucleation and growth at 900◦ C results in nanocrystals under pressure. (3)Annealing at 800◦ C relaxes as-grown pressure. measurements are performed on nanocrystals that have been liberated from their host matrix[6], the expected red sh
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