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The approach to equilibrium of the grain structure and electrical properties has been studied in high-resistivity, As-implanted polycrystalline silicon films on thermally oxidized silicon wafers. Thermal annealing parameters are found to be critical in determining the film sheet resistance. Results from spreading resistance analysis, secondary ion mass spectroscopy, and transmission electron microscopy indicate that As diffusion down the grain boundaries into the film leads to a large fraction of the As being left in inactive grain boundary sites. Reactivation of the As is negligible when processing temperatures are 900 °C or lower. A relatively simple diffusion model has been developed that can fit the As concentration profile over the entire film thickness. This makes the model applicable to normal integrated circuit processing conditions where film thickness effects and nonequilibrium dopant distributions are important.

I. INTRODUCTION Lightly doped polycrystalline silicon is very useful for fabricating small area, high-value resistors in integrated circuits because the resistivity can be varied over many orders of magnitude. Considerable work has been done in determining the mechanisms underlying this property.1"5 Generally, carrier trapping models can explain the strong resistivity variations with dopant density without invoking dopant segregation effects. Electrostatic barriers build up at the grain boundaries due to charge trapping at grain boundary defects arising from the lattice mismatch in these regions. To preserve charge neutrality, the trapped charge is screened by ionized dopant atoms in the depletion regions surrounding the grain boundary. This leads to the following expression for the zero bias barrier height2:

ho ~ -^-f f ' Nt (E) [f (E,Ef) -AE,Elb) ]dEY, (1) where (f>b0 is the band bending at zero bias, Ef and Efb are, respectively, the equilibrium and neutral Fermi levels in the boundary, TV, is the trap density, Nd is the donor density, and Ev and Ec are the valence and conduction band edge energies. Clearly one can affect the barrier height through either Nt or Nd. In lightly doped materials the barriers are high and wide enough that conduction across them is by thermionic emission. The equation below gives the current across a single grain boundary5:

X 1 - exp

"(£)])•

(2)

J. Mater. Res. 1 (2), Mar/Apr 1986 http://journals.cambridge.org

where/is the current density, Fis the applied bias, A *is an effective Richardson constant, c is the capture coefficient for electrons being trapped and reemitted at the grain boundary, T is the absolute temperature, and f is the separation of the bulk Fermi level and the conduction band. The exponential dependence of the current on the barrier height leads to a strong dependence on Nd and N, through Eq. (1). The above discussion has assumed uniform dopant density and stabilized grain structures. The relationships between the donor density, the barrier height, and the carrier trapping process are complex even under such ideal conditions. However, in norm