Concentration dependent and independent Si diffusion in ion-implanted GaAs T. Ahlgren,* J. Likonen, ² J. Slotte, J. Ra ¨ isa ¨ nen, M. Rajatora, and J. Keinonen Accelerator Laboratory, University of Helsinki, P.O. Box 43, FIN-00014 Helsinki, Finland Received 25 March 1997 The diffusion of silicon has been studied in  100 GaAs implanted with 1 10 16 40-keV 30 Si + ions/cm 2 . The Si concentration profiles were measured by secondary-ion mass spectrometry and nuclear resonance broadening techniques and the defect distributions by the Rutherford backscattering spectrometry channeling technique. The implanted samples were subjected to annealing in argon atmosphere in the temperature range 650 °C–850 °C. Two independent silicon diffusion mechanisms were observed. Concentration independent diffusion, observed as a broadening of the initial implanted distribution, is very slow and is assigned to Si atoms diffusing interstitially. Concentration dependent diffusion with low solubility and extending deep into the sample is quantitatively explained by diffusion via vacancies of Si atoms in the Ga and As sublattices. Diffusion coefficients together with carrier concentration as a function of Si concentration are given at different temperatures. The solid solubility of Si in GaAs has been determined and an exponential temperature depen- dence observed. An estimate of the amount of Si atoms residing on either Ga or As sites and the amount of Si Ga + -Si As - pairs is given. Finally, a fast method is presented for solving the diffusion equation numerically. S0163-18299703331-6 I. INTRODUCTION Silicon is the main n -type dopant used in GaAs, and it is usually incorporated into GaAs by ion implantation or by diffusion employing an external source. The diminishing size of the submicrometer devices calls for the use of ion implan- tation to control the depths and amounts of impurities. 1 Ion implantation is also the only convenient way of introducing impurities exceeding the solid solubility limit; however, ion implantation studies have earlier been done only for concen- trations under 10 17 atoms/cm 3 . 2,3 The diffusion of silicon in GaAs utilizing external diffusion sources has been exten- sively studied over the years. Both Vieland 4 and Antell 5 re- ported the effect of arsenic pressure on the diffusion rates. Greiner and Gibbons 6 and Kavanagh et al. 7 have shown that the diffusion is concentration dependent for high Si concen- trations. In the case of low Si concentrations, Schubert et al. 8 obtained diffusion coefficients that were concentration inde- pendent and two orders of magnitude smaller than those ob- tained for high Si concentrations by Greiner and Gibbons. 6 Deppe et al. 9,10 observed that Si diffusivity is strongly influ- enced by doping of the GaAs substrate. Three models have been proposed in the literature to de- scribe concentration dependent Si diffusion in GaAs. Greiner and Gibbons 6 suggested a model in which rapid diffusion takes place when two Si atoms are located on nearest- neighbor Ga and As sites making a neutral donor-acceptor Si Ga + -Si As - pair. This model is charge neutral and thus inde- pendent of the Fermi level; therefore, the diffusion profiles should not depend on the doping of GaAs. However, the experiments of Deppe et al. 10 clearly show that the doping species and concentrations have a significant effect on the diffusion profiles of Si atoms. 11 Kavanagh et al. 12 proposed a vacancy concentration gradient model. In this model, it is assumed that the vacancies diffuse from the capping layer and substrate interface into the substrate at a finite rate. Un- der such conditions a nonuniform vacancy distribution is cre- ated in the surface region. The impurity diffusion therefore becomes dependent on the local vacancy concentration. The third model is the Fermi-level effect model proposed by Yu, Go ¨ sele, and Tan, 13 which incorporates the experimental re- sult that Si is an amphoteric impurity. In this model, it is assumed that Si Ga + and Si As - diffuse via pairing with Ga and As vacancies, respectively, while the Si Ga + -Si As - pair does not diffuse. It should be noted that this assumption is just the opposite of that invoked in Greiner’s pair diffusion model. The purpose of this paper is to explain both high and low concentration Si diffusion in GaAs. The solid solubility of substitutional Si in GaAs as a function of temperature is given and the observed exponential behavior is explained qualitatively. The implantation dose used in this study is considerably higher than in earlier studies and the annealings also extend to lower temperatures. By ion implantation, we avoid complicated surface diffusion and the longer annealing times, compared to RTA rapid thermal annealing, ensure steady-state diffusion. We also present a fast method of cal- culating the diffusion profiles and use it to fit the theoretical model to the experiments. II. EXPERIMENT Commercially prepared samples of undoped,  100 - oriented single-crystal GaAs were implanted by using the 100-kV isotope separator at the University of Helsinki. The 40-keV room-temperature implantations to total fluences of 1 10 16 30 Si + atoms/cm 2 were performed in vacuum 10 -4 Pa, where the  100 crystal axis was tilted 7° off the beam direction. The annealings were carried out in a quartz-tube furnace in Ar atmosphere at a pressure of 660 torr. During the annealings, performed in steps of 50°C, in the temperature interval of 650 °C to 850 °C, the samples were encapsulated by GaAs wafers to minimize impurity buildup on the GaAs surface and the possible loss of arsenic. The annealing tem- PHYSICAL REVIEW B 15 AUGUST 1997-II VOLUME 56, NUMBER 8 56 0163-1829/97/568/45977/$10.00 4597 © 1997 The American Physical Society