Categorization of PBTI Mechanisms on 4H-SiC MOSFETs by the Stress Gate Voltage and Channel Plane Orientation (2023)

To analyze the mechanism of the positive bias temperature instability (PBTI) of 4H-SiC MOSFETs based on existing models and predict the practical PBTI lifetime in low stress operation, its possible models were classified by the magnitude of the stress gate voltage <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(V_{GS\_{}stress})$ </tex-math></inline-formula> under high-temperature gate-bias (HTGB) stress and channel plane orientations: Si-face (0001), C-face (000-1), and a-face (11-20). The test samples were vertical MOSFETs with planar surface channels on the Si- or C-face and trench-sidewall channels on the a-face. The measurement-stress-measurement cycles that alternately repeat the HTGB stress and the conventional drain current - gate voltage <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(I_{D}-V_{GS})$ </tex-math></inline-formula> sweep derived the gate threshold voltage shifts <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({\Delta }V_{TH}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{s}, sweep$ </tex-math></inline-formula> )) measured after both the stress time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t_{s})$ </tex-math></inline-formula> and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{TH}$ </tex-math></inline-formula> -shift-recovery with the sweep process. These were more conspicuous on higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{GS\_{}stress}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt;$ </tex-math></inline-formula> approximately 35, 25, and 30 V for the Si-, C-, and a-faces, respectively) at stress temperature <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(T_{stress})\,\,=$ </tex-math></inline-formula> 448 K, identified as components trapped in the gate oxide bulk of the Fowler-Nordheim tunneling electrons. For lower <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{GS\_{}stress}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$ </tex-math></inline-formula> 15 V), we measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }V_{TH} (t_{s}, t_{r})$ </tex-math></inline-formula> as a function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{s}$ </tex-math></inline-formula> followed by the relaxation time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t_{r})$ </tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{stress}\,\,=$ </tex-math></inline-formula> 293, 448, and 573 K. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }V_{TH} (t_{s}, t_{r})$ </tex-math></inline-formula> was analyzed by the capture/emission time (CET) mapping suitable to evaluate the barrier energy beyond which channel electron carriers are (de-)trapped on the MOS interface states. The CET map successfully illustrated the dependence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }V_{TH} (t_{s}, t_{r})$ </tex-math></inline-formula> on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{stress}$ </tex-math></inline-formula> , demonstrating negative or positive correlation owing to shallower or deeper traps, early in the relaxation phase or after long-term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{s}$ </tex-math></inline-formula> , respectively. This also enabled to estimate the lifetime for a defined allowable limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }V_{TH} (t_{s}, t_{r})$ </tex-math></inline-formula> . When the lifetime is set to about 30 years, the reaching <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }V_{TH}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{s}, sweep$ </tex-math></inline-formula> ) was calculated to be approximately 70, 150, 350 mV for the Si-, C-, and a-faces, respectively, after <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{s}\,\,=$ </tex-math></inline-formula> 1E9 s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\approx 30$ </tex-math></inline-formula> years) at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{stress}\,\,=$ </tex-math></inline-formula> 448 K on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{GS\_{}stress}\,\,=$ </tex-math></inline-formula> 15 V.