Sensitivity of subthreshold current to profile variations in long-channel MOSFETs

The sensitivity of MOSFET behavior to small variations in doping profiles increases as the devices become smaller. This increased sensitivity raises new issues regarding the accuracy needed in manufacturing, modeling and measurement of small devices. A formalism has been developed to determine the maximum profile variations consistent with any prescribed allowable variation in gate bias δV _GS/V_GS. This formalism has been developed for arbitrary profiles, and has been applied to retrograde box profiles (that is, profiles with a low surface level of doping out to some box depth, followed by a more heavily doped region at greater depths). The results show that profile sensitivity can vary dramatically from one device to another in a family of devices designed to operate with similar threshold voltages. As box depth increases, sensitivity to box depth and to surface doping also increases (the allowed tolerances decrease), while sensitivity to the bulk doping value Is reduced (tolerance increases). The worst-case scenario (smallest tolerance) for variations in the box depth d occurs for depths where the depletion layer width w_I is least i.e. for cases near the onset of the condition w_I≈d. It is known that this condition results in devices with the best short channel immunity. It is found for a typical 1/4 μm device with an oxide thickness of 5 nm and a threshold voltage of 355 mV, a change in the depth of a box profile by ≈3 nm, or a change in the surface doping level of δN_s≈≈7×10¹⁶/cm³ is sufficient to require a compensating change in gate bias of 35 mV. Consequently, any profile measurement or process model that aims to predict 1/4 μm-MOSFET thresholds to within ±30 mV will have to locate dopant ions within ±30 mV will have to locate dopant concentrations to better than a few 10¹⁶/cm³