characterization, modeling, and design of esd protection circuits

5.1. Methodology 145
reaches its peak. This is justified because less than 4% of the pulse energy is contained in
the time before the pulse reaches its peak value. Substituting Eq. (5.44) into Eq. (5.42),
HBM
Efail Ipk
2 RHBMCHBM = RDUT---------------------------- . (5.45)
2
Equating Eq. (5.45) to Eq. (5.43), we see that for equivalent energies the TLP pulse width
must be 75ns for the same peak current (ITLP = Ipk = VHBM /RHBM ).
To determine the validity of the assumed adiabatic boundary conditions, we need to
reexamine the three-dimensional thermal-failure model presented in Section 2.2.2. Recall
that in this “thermal-box” model for an MOS transistor a uniform Joule heating due to a
constant-current stress is assumed to occur in a rectangular parallelepiped whose
dimensions are defined by the transistor width, the drain junction depth, and, roughly, the
gate length. Failure is assumed to occur when the peak temperature at the center of the box
reaches a critical value. The ballast resistances of the non-silicided source and drain
regions create additional potential drops and heat sources which affect the boundary
conditions. Nonetheless, we still expect the model to serve as a first-order description of
device failure.
Using this model the power to failure (Pf ) is calculated vs. stress time (tf ), with four
regions of the Pf vs. tf curve bounded by three time constants which are determined by the
box dimensions (Fig. 2.12). Each time constant is defined as
t i
=
i 2
⁄
( 4πD)
(5.46)
where D is the thermal diffusivity and i takes on specific values of a, b, or c, which for our
technology are assumed to be 50µm for the transistor width (a), 0.5µm for the gate length
(b), and 0.2µm for the junction depth (c). Using D = 0.13cm 2 /s (based on the calculations
from [23]), these result in values of ta = 15µs, tb = 1.5ns, and tc = 0.24ns.
The model allows us to determine that the power to failure, normalized by the transistor
width (Pf / a), is inversely proportional to stress time for times less than tc (Eq. (2.6)).
Since the product of the power to failure and the time to failure is constant in this region, a
constant energy is needed to induce failure, i.e., this is the adiabatic region. The time