Model Verification

In this section, it will be demonstrated that the proposed compact model well represents:

1) Vt1(VGS)

2) Vt1(Nf, wf)

3) Non-uniform turn-on of the MOSFET fingers

3.4.1 Gate Bias Effect

Figure 3.8(a) shows the measured and simulated TLP I-V curves measured at different values of VGS. Figure 3.8(b) shows the extracted Vt1 as a function of VGS. Simulation accurately represents the I-V curves and Vt1 as functions of gate bias, except in the case that only one finger of the device is triggered on, which is elaborated on in the following sections. VGS modulates the impact ionization generated body current which, in turn, provides the base current for the parasitic LNPN [13],[57]; snapback occurs when the LNPN turns on. Accurate modeling of VGS(Vt1) is critical for designing gate-coupled MOSFET protection circuits and active rail clamp protection circuits [63].

3.4.2 Trigger Voltage Vt1

The trigger voltage, Vt1, depends on the body resistance seen by the finger that first turns on. This first finger is most likely to reside at the center of the multi-finger structure because it is farthest away from the body pick-up ring at the periphery. Figure 3.9 shows the Vt1 values extracted from both measurement and simulation for GGNMOS with a varying numbers of fingers (Nf) and finger width (wf). Although the measured Vt1 varies by about 0.1V from pulse to pulse or sample to sample, the simulated Vt1 values match the measurement results reasonably well, indicating that the distributed MOSFET model captures the dependency of Vt1 on layout parameters.

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3.4.3 Non-uniform Turn-on of Fingers

Figure 3.10 compares the measured IDUT-VDUT curve of Figure 3.6 with that from simulation. Simulation correctly predicts non-uniform triggering of the gate fingers and confirms that it is the central two fingers which turn on at the lowest current, because the central fingers see a larger effective body resistance. The on-state resistance (RON) of each branch of the IDUT-VDUT curve is accurately represented in simulation.

Because the distributed model in Figure 3.2 is constructed based on the symmetric layout in Figure 3.1, the model is also symmetric and thus cannot represent conduction by an odd number of fingers. Therefore, it will not reproduce the IDUT-VDUT branch labeled as “1-finger” in Figure 3.6. However, this branch can be forced to appear in simulation by disabling all fingers except a central one or by introducing a small asymmetry into the model. The dashed line in Figure 3.10 shows the 1-finger simulation result; it matches up well against the measurement data, confirming that this branch of the curve is indeed due to conduction by just 1 finger.

Figure 3.11 shows the simulated IB-IDUT curve. The discontinuities and the slope changes evident in the measurement data are replicated in the simulation; these occur each time a new finger or pair of fingers is triggered on, as will be demonstrated next. At any given point on the curve, the total body current IB is the sum of the individual fingers’ body currents as indicated in (3.7).

𝐼𝐵= ∑ 𝐼𝐵[𝑖] 𝑜𝑛

, 𝑖 ∈ [1, 𝑁] (3.7)

where IB[i] is the body current contributed by the ith finger of a N-finger device; note that the sum in (3.7) is taken over only the fingers that are triggered on. IB jumps, i.e. IB(IDUT) is discontinuous, whenever a new finger is triggered on and the number of current sources in the sum changes. This will be illustrated for the specific case of the 6-finger GGNMOS shown in Figure 3.2. Define 𝐼̂𝐷𝑈𝑇 as the minimum current for which 4 fingers are triggered on; for 𝐼𝐷𝑈𝑇< 𝐼̂𝐷𝑈𝑇, only the center 2 fingers will be on. The body potential for each of the triggered on fingers is expressed in (3.8).

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𝑉𝐵[𝑖] = 𝑉𝐵𝐸,𝑜𝑛+ 𝐼𝑆[𝑖] ∙ 𝑅𝑆 (3.8)

where IS[i] is the current flowing in the source of the ith finger and RS is its source-side series resistance; RS is the same for each finger. Once a finger is triggered, the potential drop across its LNPN’s base- emitter junction is roughly pinned at VBE,on. In the case that 𝐼𝐷𝑈𝑇< 𝐼̂𝐷𝑈𝑇 (“case (a)”), the current divides equally between the center two fingers, i.e., 𝐼𝑆[1] = 𝐼𝑆[2] =

1

2(𝐼𝐷𝑈𝑇− 𝐼𝐵). It follows that 𝐼𝐵[1] = 𝐼𝐵[2] = 1 2𝐼𝐵. The total body current for this case, 𝐼_𝐵(𝑎), is thus given by Eq. (3.9).

𝐼_𝐵(𝑎)= 2𝑉𝐵𝐸,𝑜𝑛 𝑅_𝐵(𝑎)+ 𝑅𝑆 + 𝑅𝑆 𝑅_𝐵(𝑎)+ 𝑅𝑆 𝐼𝐷𝑈𝑇 (3.9) where 𝑅_𝐵(𝑎)= (𝑅𝑓𝑖𝑛𝑔𝑒𝑟 2 )‖ {𝑅𝑏𝑎𝑠𝑒,𝐷+ ( 𝑅𝑓𝑖𝑛𝑔𝑒𝑟 2 )‖ (𝑅𝑏𝑎𝑠𝑒,𝑆+ 𝑅𝑠𝑖𝑑𝑒)} (3.10)

Next consider the case that 𝐼𝐷𝑈𝑇≥ 𝐼̂𝐷𝑈𝑇 (“case (b)”). Due to the layout symmetry, 𝐼𝑆[1] = 𝐼𝑆[2] and

𝐼𝑆[3] = 𝐼𝑆[4]; also, 𝐼𝐵[1] = 𝐼𝐵[2] and 𝐼𝐵[3] = 𝐼𝐵[4]. It also follows that 𝐼𝑆[1] + 𝐼𝑆[3] = 1

2(𝐼𝐷𝑈𝑇− 𝐼𝐵).

The total body current, 𝐼_𝐵(𝑏), in this case is given by (3.11).

𝐼_𝐵(𝑏)= 4𝑉𝐵𝐸,𝑜𝑛 2𝑅_𝐵(𝑏)+ 𝑅𝑆 + 𝑅𝑆 (2𝑅_𝐵(𝑏)+ 𝑅𝑆) 𝐼𝐷𝑈𝑇− (𝑅𝑆‖2𝑅𝐵 (𝑏) ) 𝑅𝑏𝑎𝑠𝑒,𝑆+ 𝑅𝑠𝑖𝑑𝑒 (𝐼_𝑆[1] − 𝐼_𝑆[3]) (3.11) where 𝑅_𝐵(𝑏)= (𝑅𝑓𝑖𝑛𝑔𝑒𝑟 2 )‖ ( 𝑅𝑓𝑖𝑛𝑔𝑒𝑟 2 )‖ (𝑅𝑏𝑎𝑠𝑒,𝑆+ 𝑅𝑠𝑖𝑑𝑒) (3.12)

At the current level 𝐼𝐷𝑈𝑇= 𝐼̂𝐷𝑈𝑇, (3.9) and (3.11) yield different values of IB, indicating that the function is discontinuous. This becomes especially evident if one neglects the right-most term in (3.11), which is smaller than the others. This results in a linear relation between IB and IDUT, with the slope and y- intercept being different for cases (a) and (b). Eq. (3.8) also explains why in Figure 3.11 IB is observed to

39 be an increasing function of IDUT, even after all the fingers are operating in snapback; the increasing voltage drop across the source resistor RS causes VB[i] to rise.

The lowest current branch in Figure 3.11 is the result of conduction in just a single finger and will not appear in the simulation results unless it is forced to do so. The simulation results predict that the GGNMOS will have negligibly small IDUT until IB is large enough to turn on the first finger, but in measurement IDUT appears at lower IB levels than predicted. This discrepancy is attributed to non-uniform conduction across the finger width, which occurs at very low current levels [69],[70],[71].