characterization, modeling, and design of esd protection circuits

4.1. Calibration Procedure 105
past VCC and the drain voltage stepped at values around VCC , so prior calibration of the
drain current implies that the substrate characteristic should be fit only by adjusting the
∞
αn and λn coefficients (Eq. (3.28)). Similarly, the breakdown voltage, BVDSS , in Fig.
4.40e is dependent upon the drain-substrate junction profile, but calibration of BVDSS should concentrate on adjusting the ionization coefficients because the results of the drain
and gate calibrations suggest that the junction model is already accurate. Adjusting the
impact-ionization coefficients should not affect the drain, gate, and subthreshold
characteristics because relatively high electric fields are not involved. However,
introducing the II model to the drain-characteristic simulations does increase the drain
current in the 0.5µm-gate structure up to 10% for Vds = 6V (well above VCC ) because the
electric field is fairly high and the drain sinks most of the electrons generated by impact
ionization.
In MEDICI the default II coefficients are based on measurements of impact ionization in
bulk silicon [63], but as discussed in Section 3.1 impact-ionization rates in MOSFETs are
lower than in bulk silicon because II generation occurs near the surface, where the mean
free path is lower, i.e., where the critical electric field of Eq. (3.27) is higher. Therefore,
the final fitting values of the electron and hole mean free paths, λn and λp , are expected to
be lower than the MEDICI defaults. In keeping with the philosophy of manipulating as
few model coefficients as possible, only λn and λp were adjusted to calibrate the substrate
∞ ∞
and breakdown curves while the pre-exponential coefficients, αn and αp , were held
constant. This approach works for calibration of the standard MOSFET characteristics,
but it has a significant consequence on the snapback simulations that will be discussed in
the next subsection.
Calibration of the substrate curves was performed before that of the breakdown curves
because the substrate current depends only on the electron II coefficients while BVDSS depends upon the hole coefficients as well as the electron coefficients. In Fig. 4.40d, Ib consists of holes diffusing from the high-field region under the drain side of the gate
where they are generated by impact ionization (recall that Vds is around 3.3V during the
stress, so the electric field is relatively high in this area). Since the device current consists
almost entirely of electrons, only the electron II coefficients affect the level of substrate
current. An explanation of the shape of the Ib-Vgs characteristic is given in [42]. Basically,
the initial increase of Ib with Vgs is due to the deepening inversion layer which increases
the drain current and proportionately increases Ib . At a critical value of Vgs , however, the