(a) characteristics of Cu∕thermally grown capacitors and (b) Al∕thermally grown capacitors after stressing under at .
as a function of the BTS time and temperature for thermally grown capacitors stressed at the electric field of after subtracting the for Al gate capacitors from that of Cu gate capacitors. Solid dots indicate measured value of by measurement after BTS and the lines indicate numerically calculated value of with different maximum solid solubility (Cs) of Cu at each temperature.
The numerically calculated flatband voltage shift as a function of BTS time (a) with the different value of Cu diffusivity at the constant maximum solid solubility of Cu in ; (b) with the different values of maximum solid solubility (Cs) at the constant Cu diffusivity of . Solid dots indicate measured value of after BTS at the temperature of and the electric field of .
Evolution of the Cu concentration in as a function of the BTS time with the different value of maximum solid solubility of Cu at a constant diffusivity of . The electric field is and the temperature is . As the depth of increases, the concentration profile initially decreases rapidly and shows a nearly constant value while it decreases sharply again. The initial decrease of Cu concentration profile results from the sharp decrease of electric field by the previously migrated Cu ions in . (Ref. 3).
(a) The increasing rate of with BTS time as a function of the temperature obtained from the slope of linear fitting lines for measured in Fig. 2. (b) as a function of the Cu diffusivity obtained by numerical calculation.
Cu diffusivity as a function of temperature in thermally grown extracted by comparing of measured and calculated value with the BTS time.
Summary of previously reported Cu diffusivities in 4% PSG, SiN:H, and thermally grown . Cu diffusivities in thermally grown , PECVD , PECVD oxynitride, and methyl-doped extracted using the presented method are also depicted. The diffusivities in PECVD dielectrics and methyl-doped were extracted by the present method using the as a function of the BTS time reported by Loke et al. (Ref. 9) and Cui et al. (Ref. 10).
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