Novel statistical fluctuation of dopant concentration and its influence on scaled MOS device performance

Statistical fluctuation of both boron and phosphorus concentration at Si surface has been experimentally studied by monitoring the impurity concentration obtained by the substrate bias sensitivity of the threshold voltage of an individual n- and p-channel MOSFET of an 8 k MOSFET array with 0.7 mm² area. In this study, the vertical distribution from Si surface of the impurity concentration fluctuation can be measured by changing the substrate bias. It is found that both boron and phosphorus concentration within a unit volume systematically fluctuates with several ten nanometer correlation lengths at Si surface, whereas the standard deviation of the dopant number in a unit depletion volume can be explained by the usual square root law of the dopant number