The Superjunction Structure
The typical SJ structure is shown in Fig. 6.2 (Chen, 1993). Different from the conventional structure as shown in Fig. 6.1, SJ devices provide the superior performance on blocking voltage and on-state resistance by replacing the monotonic drift region with the alternative heavily doped p-n semiconductor layers. Figure 6.2 also gives the approximate electric field profiles within the SJ device under the bias of Vps > 0.
Optimum Doping Concentration
For the SJ device of a given breakdown voltage, there exists an optimum doping concentration Nd,op that results in the best performance. Equation (6.14) gives the depletion width of p-n junction under certain reverse bias voltage V.
where Na and Nd are the doping concentration of p- and n-column, respectively. In ideal SJ structure above-mentioned, it is required that
to have the best performance. Assume such a condition that, when the device is at breakdown, the depletion region of SJ structure is just pinched-off horizontally. That is, the p-n column width Wp = Wn = W is equal to the lateral depletion width of Wdep. By combining Eqs. (6.10), (6.14) and (6.15), the relationship between Nd,op and W is approximated as
SJ R0n,sp Calculation
From the device simulation, one knows that the breakdown of SJ structure always happens at the interface between p- and n-columns. In SJ structure, due to the influence from the sidewall p-column, there provides an additional horizontal electric field component (Ex) in comparison to that of the conventional p-i-n diode where the electric field is only in the vertical direction. Along the central vertical line of n or p-column, horizontal electric fields generated from neighboring p-n junction are in opposite direction and counteract each other. Thus, only the vertical electric field manifests. Where at the interface of p-n columns, Ex reaches the maximum value Ex,max0 and vertical electric field (Eу) maintains nearly constant, the total electric field (E) is the sum of both and becomes the highest. The profile of vertical field Ey is shown in Fig. 6.2. To simplify the derivation of blocking voltage, we assume that the p-n column length L is large enough, Ёу has a constant (average) value of EEyo and breakdown occurs when the total electric field reaches the critical electric field of silicon (Ec), which is expressed by
We define then
where a is the coefficient which has the value between 0 and 1.
From the p-i-n junction structure, Ex,max is given by
Combining Eqs. (6.18) and (6.20), it yields
Thus, the Ron,sp in the region of (0 < x < W) is
Therefore if L > W, Vbr is given by Combining Eqs. (6.22) and (6.23), it yields
Numerical simulations by MEDICI were carried out in order to find out the relationship between the electric field components of SJ structure and the critical electric field at various doping concentrations and different column width and length. Table 6.1 gives the results between Ex,max and Ec according to different dimensions and doping profiles of SJ structures. To guarantee the data accuracy, Ex,max is extracted from the mesh point at the center of the vertical line along the p-n interface. Ec is calculated from Eq. (6.9).
It was observed that, a = Ex,max/Ec has a nearly constant value when L > W is satisfied. As shown in Fig. 6.3, when W/L is less than 1/4, all the simulation results of Ex,max/Ec fall into the range of 0.669-0.673. Therefore, the average value of 0.672 is an acceptable value for a.
The minimum Ronsp is then calculated by Ron,sp ^ 2W% with a = 0.672.
By using the average constant mobility and Eqs. (6.9) and (6.10), the Ron,sp for the vertical structure can be calculated as
Using Eq. (6.25), the ideal SJ limits of specific on-resistance versus breakdown voltage at different column widths are plotted together with the ideal unipolar silicon limit of conventional MOSFET device, as shown in Fig. 6.4. Other detailed derivation by considering the mobility variation and lower critical electrical field within the SJ structure was made (Chen, 1999). Overall, the Ron,sp of an SJ structure can be considered to be proportional to the breakdown voltage in a range between Vbr17 and Vbr3.