A Systematic Study of Temperature, Polarity, Thickness, and Ramp Rate Dependencies of Ramp-Voltage Stress for SiO₂ and its Comparison with 2D Gate Dielectrics

A systematic study of ramped <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathbf{RVS})$</tex> compared to constant (CVS) voltage stress over a wide range of temperature (-50 °C to 280 °C), ramp rate (10 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{V}/\mathbf{s}$</tex> to 0.0002 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{V}/\mathrm{s})$</tex>, thickness - <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{diel}$</tex>, (~2.0 nm to 12 nm), and polarity dependence for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{SiO}_{2}$</tex> breakdown (BD) is conducted. We report three important new findings: 1) a new relation explaining the large difference between activation energies <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta H_{TBD}(\sim 0.7\text{eV})$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta H_{VBD}(\sim 0.01\text{eV})$</tex> using a power-law model; 2) a thickness-dependence of Weibull slopes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\beta)$</tex> of voltage-to-breakdown <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(V_{BD})$</tex>; and 3) a universal thickness-dependence of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{V}_{\boldsymbol{BD}}$</tex> spanning a wide range of thickness regardless of stress polarities and modes. We demonstrate that all BD parameters, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{n}, \boldsymbol{\beta}$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\Delta} \boldsymbol{H}$</tex> collected using slow CVS tests can be equally obtained using fast RVS tests. An equivalent reliability projection methodology using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{V}_{\boldsymbol{BD}}$</tex> data instead of time-to-breakdown <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\boldsymbol{T}_{BD})$</tex> to calculate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{V}_{max}$</tex> is presented. Finally, we compare <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{SiO}_{2} \boldsymbol{V}_{\boldsymbol{BD}}$</tex> data to those of two-dimensional (2D) gate dielectrics showing the use of dielectric-strength <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(B_{BD}=V_{BD}/t_{diel})$</tex> can have misleading conclusions.