Thermal desorption spectra from cavities in helium-implanted silicon G. F. Cerofolini * STMicroelectronics, Stradale Primosole 50, 95100 Catania CT, Italy G. Calzolari, F. Corni, S. Frabboni, C. Nobili, G. Ottaviani, and R. Tonini Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica, Universita` di Modena, 41100 Modena MO, Italy ~Received 14 June 1999; revised manuscript received 5 August 1999! Thermal desorption spectra at constant ramp rate have been determined after helium implantation into bare silicon prepared for a large set of experimental conditions. The spectra can phenomenologically be classified as composed by two peaks: the a peak, centered on a temperature of 750–800°C with a shoulder extending to lower temperature ~down to 550°C), and the b peak, centered on a lower temperature depending on the implantation-annealing conditions. The a peak is attributed to the emission from cavities, while the b peak is attributed to the emission from vacancylike defects. A detailed theory describing helium effusion from stable cavities as controlled by the interatomic helium-helium potential is proposed and found to reproduce accurately most of the a peaks. The postimplantation of hydrogen into samples displaying a pure b emission results in an a peak which can be described by the same model as above provided that the cavities are unstable and shrink during desorption in such a way as to maintain constant the concentration of contained helium. I. INTRODUCTION Helium desorption from helium-implanted solids occurs in general at temperatures much higher than those expected from helium diffusivity. This behavior may be explained by assuming that helium is captured in the vacancylike defects produced by the implantation itself, and the outdiffusion re- quires the dissolution of the gas embedded in vacancylike defects into the solid. Helium-implanted silicon runs in this situation. The most detailed information on the state of helium in silicon comes from extended computational studies. Ab initio molecular dynamics calculations 1 show that helium is dis- solved in silicon in T d interstitial sites, the solution enthalpy D H ² being positive, D H ² 5(0.8260.06) eV ~in this work we assume the energy of the free atom in a vacuum as zero energy level!. Helium diffusion ~i.e., its motion from one interstitial site to another! occurs via a zigzag path passing through hexagonal sites, the activation energy of this process being e ²² * 5(0.9660.13) eV. The diffusion coefficient at temperature T is given by D ² 5D ²,0 exp~ 2e ²² * / k B T ! , ~1! where D ²,0 5n ² l ²² 2 , n ² is the helium vibration frequency in an interstitial site ( n ² 52 310 13 s 21 ), l ²² is the separation between adjacent T d sites measured along the zigzag-shaped path connecting them ( l ²² 51.62 Å!, and k B is the Boltz- mann constant. The values of solution enthalpy and migra- tion energy calculated by ab initio molecular dynamics are in excellent agreement with those obtained from permeation 2,3 and diffusion experiments. 4 Interstitial helium shows a ten- dency toward clustering, the enthalpy required to bring in solution one helium from a cluster with two atoms being 0.08 eV. The calculations also show that a helium atom lo- cated initially in a vacancy diffuses out to an interstitial site, so that ‘‘a single vacancy does not act as a trapping center for He atoms.’’ 1 In spite of this conclusion, implanted helium is, however, expected to segregate in vacancy clusters result- ing from the implantation, transforming them in more or less stable cavities. The desorption kinetics from helium-implanted silicon are expected to contain rich, though difficult to extract, informa- tion on the interaction between helium and vacancylike de- fects. Isothermal data do indeed provide information on these phenomena, but in a restricted energy domain ~of the width of a few k B T ) around a certain energy. 5 Though nonisother- mal methods, like thermal programed desorption ~TPD!, are by far less sensistive than isothermal methods to the energy landscape of the system, they, however, overcome the above difficulty bringing in the laboratory time scale phenomena which in isothermal conditions would otherwise be inacces- sible. The matter of this work is the experimental determina- tion and theoretical understanding of TPD spectra from helium-implanted silicon as a function of the implantation conditions and subsequent thermal treatments. II. EXPERIMENT The TPD spectra presented in this work are part of an extended characterization involving elastic recoil detection analysis ~ERDA!, Rutherford backscattering in channeling conditions ~RBS!, multiple-crystal x-ray diffraction ~XRD!, positron annihilation spectroscopy ~PAS!, and transmission electron microscopy ~TEM!. The experimental details as well as the interpretation of major results of those combined characterizations are described in Refs. 6–11. In discussing the TPD spectra we shall recall the results of those charac- terizations as follows: Ref. # ~NAME! will denote an evi- dence reported in Ref. # obtained by means of the technique NAME. A. Materials and methods The samples were prepared implanting 4 He 1 into Czochralski-grown, single-crystalline, ~100!-oriented, p-type silicon, with resistivity in the interval 1.7–2.5 V cm. PHYSICAL REVIEW B 15 APRIL 2000-I VOLUME 61, NUMBER 15 PRB 61 0163-1829/2000/61~15!/10183~11!/$15.00 10 183 ©2000 The American Physical Society