A consistent model of P diffusion in Si is presented which accounts quantitatively for the existence of electrically inactive P, the "kink" and the tail regions of the P profile, and the emitter dip effect. In this model it is shown that three intrinsic P diffusion coefficients exist, each one associated with the diffusion of P with vacancies in three different charge states. In the so-called "anomalous" high concentration region of the profile (n ~ 10 2~ cm-a), it is shown that equilibrium concentration of P+V = pairs dominates P diffusion and P electrical activity. At lower electron concentrations when the Fermi level is ,~0.11 eV below the conduction band, the V = vacancy gives up an electron, and the 0.3 eV lower binding energy of the resulting P+V-pairs enhances the probability for pair dissociation by a factor of 10-35, depending on the temperature. This effect creates a steady-state excess concentration of Vvacancies which flow away from the point of pair dissociation. The concentration of excess V-vacancies created is proportional to the number of P +V = pairs created at the Si surface times the enhanced probability for pair dissociation. These vacancies in the V-charge state interact with P to create the enhanced tail diffusion. In a npn structure, the charge state of the excess vacancies becomes V + in the base region, thus enhancing the diffusivity of the base dopant and causing the emitter dip effect. The magnitude by which the P tail diffusivity and the base dopant diffusivity are enhanced is the same and may reach a factor of 135 for a 900~ diffusion.At high concentrations the diffusion of phosphorus (P) into silicon (St) produces an impurity atom distribution that differs considerably from the Gaussian or complementary error-function distributions (I-7). Numerous models have been proposed to explain this anomalous deviation from simple diffusion theory. Lawrence (8) suggested that the retardation of P diffusion was a result of the precipitation of P at moving dislocations. Dash and Joshi similarly postulated that the onset of anomalous P diffusion occurred simultaneously with the generation of dislocations in the Si lattice, at a critical integrated P concentration (9). However, the recent results of Sato et al. (10) disagree with this model, and Duffy et al. (11) found no evidence of dislocations or precipitation following the predeposition of prominently kinked P profiles. Significant numbers of dislocations and accompanying preCipitation occur only after the drive-in cycle (11).Other P diffusion models include the saturated lattice site model of Bakeman and Borrego (12), the thin surface barrier model of Makris et al. (13), impurity band effects on the electron activity coefficient (10, 14), the existence of a molten Si-P phase to explain the apparent flattened region of the P profile (15), and That's model of enhanced diffusion due to plastic deformation and subsequent generation of excess vacancies (16, 17). All of the above models have been criticized by Hu in a recent review (18), and so ad...
In order to characterize implanted-diffused As layers in Si and to develop general processing information, impurity profiles were determined by secondary ion mass spectrometry (SIMS) and differential conductivity measurements. An analysis of these profiles is given which has yielded information regarding the diffusion of AS and the electrical quality of these implanteddiffused layers. It is shown that implanted-diffused As profiles with Cwo ~ 1 • 10 .20 cm -8 can be described by a Chebyshev polynomial approximation to the diffusion equation with concentration-dependent diffusivity. The diffusion of As is not dependent upon the furnace ambient, but As pile-up within 200-400A of the Si surface does occur during diffusion in an oxidizing atmosphere. It is also shown that implanted-diffused As layers show higher electrical activity for diffusion temperatures below ll00~ than layers diffused from chemical sources. For implanted As layers in which the peak concentration is greater than the solubility limit, the fraction of electrically active As increases at a rate proportional to t 1/~.
In a previous paper, the diffusion of ion-implanted As in <100> Si was discussed as well as the electrical quality of implanted-diffused layers. It is the purpose of this paper to derive equations that describe the important characteristic profile parameters, and to support these equations with experimental data. A discussion of total As surface concentration, junction depth, and profile gradient will be presented, which will be followed by an analysis of the sheet resistance of implanted-diffused As layers and the surface concentration of the electrically active As. AnalysisTotal As surface concentration, CTO, and junction depth, xj.--It was shown previously (1) that the implanted-diffused total As profile shape is approximately described by the equationt is the diffusion time (sec), Di is the intrinsic As diffusivity (cm2/sec), n1 is the intrinsic electron concentration, and CTO is the As surface concentration (atom/cm 8) assumed to be greater than ,~1 X 1019 cm-~ Equation [1] is a Chebyshev polynomial approximation to the solution of the diffusion equation with a linear concentration-dependent diffusion coefficient and constant surface concentration, CT0. It is probable that the polynomial coefficients are time-dependent for the case of nonconstant CTO, such as the case of a redistributing impurity distribution. For the case of implanted As in St, CT0 decreases as t -~/~, and the con-
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