Temperature Coefficient of Threshold Voltage in High-$k$ Metal Gate Transistors with Various TiN and Capping Layer Thicknesses

The temperature coefficient of $V_{\text{th}}$ ($=dV_{\text{th}}/dT$), which is commonly utilized for circuit design, was systematically obtained against various TiN and capping layer thicknesses in high-$k$/metal gate field-effect transistors (FETs). It is known that the magnitude of $|dV_{\text{th}}/dT|$ for such FETs is larger than that of polycrystalline silicon (poly-Si) gate FETs. The origins of the $dV_{\text{th}}/dT$ difference among high-$k$/metal gate FETs were attributed to differences in the temperature coefficient of flat band voltage ($=dV_{\text{FB}}/dT$) and the equivalent gate oxide thickness (EOT). Thicker TiN layers reduced $dV_{\text{FB}}/dT$, which enlarged the magnitude of $|dV_{\text{th}}/dT|$. The EOT increased as the TiN metal layer or Al 2 O 3 capping layer increased in thickness. The large EOT led to an increase in $|dV_{\text{th}}/dT|$, since $dV_{\text{th}}/dT$ is a function of the inverse of gate capacitance. In contrast, La 2 O 3 capping hardly affected $dV_{\text{th}}/dT$. This is because La 2 O 3 capping did not affect EOT differently from Al 2 O 3 capping. The relationship between $dV_{\text{th}}/dT$ and EOT implies that EOT scaling relieves the issue of large $|dV_{\text{th}}/dT|$ for high-$k$/metal gate FETs.