SJ Electric Field Profiles
Figure 6.5 shows the simulation plots of SJ structure with W = 5 ^m and L = 15 fzm at different positive Vds bias when Vgs = 0 V produced by MEDICI.
Table 6.1. a values between E_{x},max and ?_{cr}j_{t} at different ratios of W/L.
1.5 x 10^{15} 

1.126 x 10^{5 }1.3 0.356 
1.430 X 10^{5 }0.975 0.453 
2.065 x 10^{5 }0.39 0.654 
3.2 x 10^{15} 

1.956 x 10^{5 }0.667 0.562 
2.158 x 10^{5 }0.5 0.620 
2.329 x 10^{5 }0.2 0.669 
1.27 x 10^{16} 7.1 x 10^{15} 
3 5 4.13 xlO^{15} 3.84 xlO^{15} 
2.773 x 10^{5} 2.546 x 10^{5 }0.2 0.333 0.671 0.663 
2.775 x 10^{5} 2.577 x 10^{5 }0.15 0.25 0.672 0.671 
2.775 x 10^{5} 2.585 x 10^{5 }0.06 0.1 0.672 0.673 
4.47 x 10^{16} 

3.256 x 10^{5 }0.067 0.673 
3.256 x 10^{5 }0.05 0.673 
3.256 x 10^{5 }0.02 0.673 
9.8 x 10^{16} 

3.569 x 10^{5 }0.033 0.670 
3.569 x 10^{5 }0.025 0.670 
3.569 x 10^{5 }0.01 0.670 
N (cm ^{3}) 
W (/j.m) E_{c} (V/cm) 
L = 15/xm Ex,max (V/cm) W/L иАЁ_{х},тга/E_{c} 
L = 20 /xm E_{x},max (V/cm) W/L ^{a} = E_{x}, max/E_{c} 
L = 50 /ли Ex,max (V/cm) W/L ^{а} — E_{x},max! E_{c} 
Fig. 6.3. Relationship between E_{x},max/Ec and W/L for SJ structure.
Fig. 6.4. R_{on},sp vs Vb_{r} performance merit of ideal unipolar silicon limit and SJ limits at W = 5 im, 0.5 im, and 0.05 im.
Fig. 6.5. Equipotential lines within SJ structure at different Eds bias before breakdown.
V_{br} is simulated to be 261V for this structure. The doping concentrations N_{A }and N_{d} for p and ncolumn in the structure are exactly equal to get the ideal result. However, in the practical fabrication, perfect match of N_{A} = N_{D} is difficult to achieve. The analysis of charge imbalance will be discussed in the later part of this chapter. When V_{DS} = 0 (see Fig. 6.5(a)), the depletion region that results from builtin potential between pn columns is very small. The builtin potential (V_{bi}) is approximated by
From Eq. (6.14) we know that in the case of N_{A} = N_{D} = 7 x 10^{15} cm^{3}, the builtin depletion width (W_{bi}) is about 0.5 fim. After V_{DS} > 0, the depletion region starts to extend. It is observed in Figs. 6.5(b)(d) that the depletion region first merges on the top part of the drift region at a small bias, then moves down with the increase of the bias.
At the breakdown, the entire drift region is fully depleted as shown in Fig. 6.6. The distribution of equipotential lines (the parallel curves shown in Fig. 6.6(a)) is nearly uniform within the drift region. The Efield vector plots in Fig. 6.6(b) represents that electric field crowds obviously at the pn column interface, especially at the top and bottom regions. Along the vertical direction at the center of the ndrift region, only vertical electric field is found. The above simulation result verifies the electric field profile as shown in Fig. 6.2.
Fig. 6.6. (a) Equipotential lines at 10 V interval, impact ionization representation and (b) Efield vector plots for SJ structure at breakdown.
As shown in Fig. 6.7(a), when increasing Ads, the vertical electric field profiles of SJ structure at the center of ncolumn (x = 5 p.m) start to transform from a triangle shape as that in the conventional case to a trapeziumlike distribution. The electric field at pn interface (x = 2.5 p.m) as shown in Fig. 6.7(b) is almost in the same shape at any bias but different in magnitude as determined by the applied bias.