characterization, modeling, and design of esd protection circuits

80 Chapter 3. Simulation: Methods and Applications
∆T ss / K
2000
1500
1000
500
Eq. (3.35)
Eq. (3.36)
P´ ss /κ = 1.37X10 4 K
0
1 10
b / c
100
Fig. 3.31 The dependence of the steady-state change in peak temperature, ∆Tss , on
b ⁄ c (log scale) as described by Eq. (3.35) is approximated by Eq. (3.36).
rectangular semiconductor region with uniform doping, thermal boundary conditions of
applied on the perimeter of the structure, and electrical contacts placed along
two opposing sides. In each simulation the applied voltage is ramped up to its steady-state
value in 0.01ps to create a uniform, constant power source ( ) in the structure, and
the maximum temperature in the structure, Tmax , is then monitored vs. time from 0.01ps to
1 second. Since the thermal box model assumes heat generation, thermal conductivity, and
specific heat are independent of time and temperature, the temperature dependences of κ,
Cp , and the band-gap energy are removed in the simulation models and a high doping
level of 10 18 cm -3 T0 = 300K
V
is used to reduce the effect of temperature on carrier concentration, i.e.,
to keep the resistance constant. Fig. 3.32a shows simulated curves of vs. time,
where ∆T = , for a constant applied power and varying ratios. Note from
any of the Pf equations that plotting vs. time for constant power yields the same
curve as plotting power vs. time for constant ∆T. The 2D curves are similar to the 3D
Pf vs. tf curve of Fig. 2.12 except that there are only two clearly defined regions. For times
less than tc (which in Fig. 3.32 is 140ps for and 9.0ns for ),
2 ⁄ R
1 ⁄ ∆T
Tmax – T0 b ⁄ c
1 ⁄ ∆T
c = 0.25µm
c =
2.0µm