characterization, modeling, and design of esd protection circuits

3.6. Extraction of MOSFET Pf vs. tf Curve 83
log 10(P f / (a ⋅ κ ⋅ ∆T))
6
4
2
0
−14
2D, Eq. (3.37)
3D, Eq. (2.3)
a = 50µm
b = 0.5µm
c = 0.2µm
−12 −10 −8 −6 −4 −2 0
log10 (time / sec)
Fig. 3.33 Power to failure, normalized by a, κ, and ∆T, is plotted vs. time to failure
for the 2D and 3D implementations of the thermal box model. The time
constants for the given box dimensions are t a = 5.6µs, t b = 560ps, and
t c = 90ps.
this time region (less than 100ps for a leading-edge MOS technology) is of little interest
because measurements are not possible and parasitics in any circuit render an ESD pulse
of such a short duration impossible. In the region of interest for ESD, say 10ns to 1µs, the
power to failure predicted by 2D simulation is too high by about an order of magnitude.
From Eq. (3.36) and Eq. (2.9), the ratio of the 2D to 3D predicted steady-state power to
failure is
P′ f, ss
P′ f, ss
( 2D)
4b
--------------------------- =
⎛
-----
⎞
for , (3.38)
( 3D)
⎝πc⎠ ( ln ( a ⁄ b)
+ 2)
b» c
which is always greater than unity since a > b> c.
Eq. (3.38) states that regardless of the
value of critical temperature chosen, the power needed to reach this temperature in steady
state is greater in the 2D model than in the 3D model, i.e., the 2D model predicts a more