On the Distribution of Single Defect Threshold Voltage Shifts in SiON Transistors

Abstract

To improve MOS transistors operating characteristics, such as the switching speed and power consumption, the dimensions of integrated devices are continuously decreased, amongst other advances. One of the main drawbacks of geometry scaling is the increased variability of the threshold voltage between nominally identical devices. The origin for this lies in defects located inside the oxide and at the interfacial layer between the oxide and the semiconductor. At the same time, the number of defects becomes a countable quantity in devices approaching the tens of nanometer scale. Furthermore, their impact on the device performance significantly increases, in a way that charge transitions from single defects can be observed directly from electrical measurements. To describe the degradation of the devices caused by single defects, one has to investigate the distribution of their impact on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {V_{\mathrm {th}}}$ </tex-math></inline-formula> shift. For SiON technologies, uni-modal exponential distributions of step heights of single defects have been reported in the literature. However, our results reveal that the step heights are more likely bi-modal exponential distributed. These findings are essential for the accurate evaluation of the tail of the distribution, i.e., the defects showing an enormous impact on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {\Delta V_{\mathrm {th}}}$ </tex-math></inline-formula> . Such defects can give rise to an immediate failure of devices and circuits. In this study, the statistical distributions of the effect of single defects are created and analyzed. We compare the results to values calculated using the commonly applied charge sheet approximation (CSA) and show that the CSA significantly underestimates the real impact of the defects for the studied technology. Finally, we use the obtained distributions and analyze their effect on the variability of measure-stress-measure simulations using our compact physical modeling framework.