2.3.1 Conventional RESURF in JI

For a conventional lateral RESURF structure as shown in Figure 2.16 and at an applied reverse voltage $V_R$, the lateral diode ($p^+ n$-epi) breakdown voltage $BV_\mathrm{ld}$ and the vertical junction ($p$-substrate/$n$-epi) depletion extension $d_\mathrm{nepi}$ into the $n$-epi, are given by

$$BV_\mathrm{ld} = \frac{\varepsilon_{si}\,E_\mathrm{c}^2}{2q\,N_\mathrm{epi}}\,,$$ (2.6)

$$d_\mathrm{nepi}(V_\mathrm{R}) = \sqrt{\frac{2\varepsilon_{si}\,V_... ...\, C_\mathrm{sub}} {q\,N_\mathrm{epi}\,(C_\mathrm{sub} + N_\mathrm{epi})}}\,.$$ (2.7)

Here, $\varepsilon_{si}$ is the dielectric constant of silicon, $E_\mathrm{c}$ is the silicon critical electric field ($~$ 3 $\times$ $10^5$ V$/$cm), and $q$ is the electronic charge. The requirement for such a structure to achieve a benefit from the RESURF principle is that the vertical full depletion of the $n$-epi region takes place before the lateral diode breaks down. Since the lateral diode is the junction most susceptible to a high electric field (i.e., represents the weakest breakdown point), this requirement causes the electric field at that junction to reduce and leads the structure to breakdown at a different voltage than the one predicted by (2.2). Therefore, to ensure full vertical depletion of the $n$-epi region, it is required that

$$d_\mathrm{nepi} (BV_\mathrm{ld}) \geq t_\mathrm{nepi}\,.$$ (2.8)

where $d_\mathrm{nepi} (BV_\mathrm{ld})$ is the vertical depletion extension into the $n$-epi at $BV_\mathrm{ld}$. As a result in single-RESURF devices, the optimal $n$-epi integrated charge $Q_{n}$ $=$ $N_\mathrm{epi}$ $\times$ $t_\mathrm{nepi}$ is given by

$$Q_{n} = \frac{\varepsilon_{si}\,E_\mathrm{c}}{q} \sqrt{\frac{C_\mathrm{sub}}{C_\mathrm{sub} + N_\mathrm{epi}}}\,.$$ (2.9)

When processing and forming doped regions in IC technologies, and in order to have reasonable control over the thickness and doping concentrations of these regions, it is essential that the doping concentration of the $n$-epi region is higher than that of the $p$-substrate. In other words, $N_\mathrm{epi} > C_\mathrm{sub}$. Consequently, an upper theoretical bound for $Q_{n}$ can be obtained by setting $N_\mathrm{epi} = C_\mathrm{sub}$ in (2.9) which is given by

$$Q_{n,\mathrm{max}} = \frac{\varepsilon_{si}\,E_\mathrm{c}}{q \sqrt2}\,.$$ (2.10)

Figure 2.18 and Figure 2.19 show the optimum potential distribution and electric field strength of 150V lateral $pn$-diode with drift length $L_\mathrm{d}$ $=$ 7$\mu$m, respectively. Generally, electric fields are focused at the anode and cathode edge.

Figure 2.18: Potential distribution of a RESURF diode at the cathode voltage 150 V.

Figure 2.19: Electric field of a RESURF diode for different values of the $n$-drift doping concentration.

Figure 2.20: Electric field distribution of a RESURF diode at the cathode voltage of 150 V.

Field plates are introduced to reduce the electric fields at these region. Without a field plate at the anode region the required $n$-drift doping will be lowered, which significantly increases the on-resistance. In addition the BV will decrease due to the field crowding at the anode and cathode edges. From Figure 2.18, almost uniformly distributed potential lines of the lateral diode can be seen at a cathode voltage of 150V (optimum doping of the $n$-drift is $5 \times 10^{15}$ $\mathrm{cm^{-3}}$). The theoretical maximum BV is determined by the breakdown of the vertical diode structure (by the depletion layer width at the $p$-sub and $n$-drift junction).

Figure 2.19 shows the $n$-drift doping dependence of the electric field strength near the surface of the device. At the cathode edge a high electric field can be seen with a low $n$-drift doping of 2 $\times$ $10^{15}$ $\mathrm{cm^{-3}}$, and if the $n$-drift doping is increased to $10^{16}$ $\mathrm{cm^{-3}}$, a high electric field is moved toward the anode edge. The optimum electric field distribution is obtained with an $n$-drift doping of 5 $\times$ $10^{15}$ $\mathrm{cm^{-3}}$. At this optimum doping the peak electric field can be seen both at the anode and cathode edge, and the distribution between them forms a parabolic shape. It shows that the optimum RESURF condition can be obtained with an $n$-drift doping higher than that of the $p$-substrate.

With the higher $n$-drift dose the peak electric field occurs only at the $p^+ n$-drift junction (dotted line in Figure 2.19) of the anode side, and the BV decreases. The vertical diode depletes rapidly, and the electric field at the anode side exceeds critical value of silicon before the lateral depletion is achieved. Therefore, a premature breakdown occur at the surface of the $p^+ n$-junction.

With the lower $n$-drift doping the peak electric field moves towards $n^+$-cathode. It causes a BV lower (dashed line in Figure 2.19). If the $n$-drift doping is lower compared to that of the $p$-substrate, depletion mainly occurs in the $n$-drift region and the BV decreases. The optimal case is obtained when the depletion region extends equally in the $n$-drift and $p$-substrate regions. If the lateral distance is sufficient, breakdown occurs vertically in the semiconductor bulk under the $n^+$-region. Figure 2.20 shows the electric field distribution of the optimized lateral diode, where the peak electric field can be seen under the cathode edge.