4.3.3 Simulation Results

In standard vertical SJ devices the doping of the $n$- and $p$-column of the drift region must be balanced exactly. Most of the previous works assume that the charge of the $n$-column $Q_\mathrm{n}$ is equal to that of the $p$-column $Q_\mathrm{p}$. The BV depends on the critical electric field $E_\mathrm{c}$ of the device and the length of the $n$- and $p$-columns.

In the SOI-LDMOSFETs a large portion of the voltage is supported by the buried oxide layer and the charge of the $p$-body affects the RESURF condition significantly. Unlike in conventional RESURF devices, three-dimensional RESURF phenomena can be seen in this structure. $Q_\mathrm{n}$, $Q_\mathrm{p}$, and the charge $Q_\mathrm{db}$ of the p body depletion region should be balanced. Assuming that all columns are completely depleted before breakdown, the charges and BV are given by

$$Q_{n} = Q_{p} + Q_\mathrm{db} < 2 \frac{\varepsilon_{si}\,E_\mathrm{c}}{q}\,,$$ (4.1)

$$Q_{n} = N_\mathrm{D}\,W_\mathrm{N}; Q_{p} = N_\mathrm{A}\,W_\mathrm{P}\,,$$ (4.2)

$$\mathrm{BV} = E_\mathrm{c}\,t_\mathrm{N,P}\,,$$ (4.3)

where $t_\mathrm{N,P}$ is the length of the $n$- and $p$-columns, respectively. The BV depends both on the critical electric field $E_\mathrm{c}$ and the column length.

Figure 4.26 shows the $p$-column doping $N_\mathrm{A}$ dependence on the BV of the SJ SOI-LDMOSFETs, and the doping of the $p$-column is lower than that of the $n$-column. For the SJ SOI-LDMOSFET with an $n$-column doping $N_\mathrm{D}$ of 9.9 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$, a maximum BV of 124V is obtained at $N_\mathrm{A}$ $=$ 6.5 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$. With the $N_\mathrm{D}$ of 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$, a maximum BV of 127V is obtained at $N_\mathrm{A}$ $=$ 2.5 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$. These results demonstrate that the charge of the $p$-body strongly affects the charge balance condition of the SJ SOI-LDMOSFETs.

Figure 4.27 shows the $N_\mathrm{A}$ dependence on the electric field strength near the surface of the device along the $n$- and $p$-column junction.

Figure 4.26: $p$-column doping $N_\textrm {A}$ dependence on the BV of the SJ SOI-LDMOSFETs and lateral trench gate SJ SOI-LDMOSFET.

Figure 4.27: Comparison of the electric field in SJ SOI-LDMOSFET for different values of $N_\textrm {A}$ at the BV (along the $n$- and $p$-column junction in Fig. 4.24).

Figure 4.28: Potential distribution of a lateral trench gate SJ SOI-LDMOSFET at the $V_\textrm {DS}$ of 120 V.

At the gate edge a high electric field can be seen with a low $N_\mathrm{A}$ of 5.5 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$, and if the $N_\mathrm{A}$ is increased to the value of 9.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$, a high electric field is moved toward the drain edge. The optimum electric field strength distribution is obtained with the $N_\mathrm{A}$ of 7.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$. It proves that the optimum RESURF condition can be obtained with $N_\mathrm{A}$ much lower than $N_\mathrm{D}$.

A similar result can be seen for the lateral trench gate SJ SOI-LDMOSFET (dashed line in Figure 4.26). With an $n$-column doping $N_\mathrm{D}$ of 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$ and a width $W_\mathrm{N}$ $=$ 2 $\times$ $W_\mathrm{P}$ of 1.0$\mu$m, the maximum BV is 120V at $N_\mathrm{A}$ $=$ 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$. Even with a 2 times larger $n$-column width than that of the $p$-column the optimum doping $N_\mathrm{A}$ is the same as $N_\mathrm{D}$ in this case.

Figure 4.28 shows the almost uniformly distributed potential lines of a lateral trench gate SJ SOI-LDMOSFET at the drain voltage $V_\mathrm{DS}$ of 120V. One can clearly see that most of the potential drops over the buried oxide layer. Curved potential lines at the top surface of the device by the lateral depletion along the $n$- and $p$-column junction are also visible.

The BV of SJ devices strongly depends on the charge balance condition. As has been shown in Figure 4.26, the BV decreases abruptly with decreasing $N_\mathrm{A}$. In practical manufacturing it is difficult to achieve perfect charge balance. Generally, it is assumed that the doping can be controlled within $\pm$10% of the nominal charge [32].

Figure 4.29 shows the sensitivity of the charge imbalance on the BV. By proper choosing the $p$-column doping $N_\mathrm{A}$ (near the value of the maximum breakdown region in Figure 4.26) the relations between the BV and the charge imbalance can be seen clearly. In this figure $N_\mathrm{A}$ of 7.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$ (SJ SOI-LDMOSFET with $N_\mathrm{D}$ of 9.9 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$), 3.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$ (SJ SOI-LDMOSFET with $N_\mathrm{D}$ of 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$), and 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$ (lateral trench gate SJ SOI-LDMOSFET with $N_\mathrm{D}$ of 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$) are used as reference values, respectively.

As shown in Figure 4.29, this sensitivity (slope of the line) is reduced if the doping of the drift region is lowered. The drastically reduced sensitivity can be seen in the SJ SOI-LDMOSFET with a doping concentration of $N_\mathrm{D}$ $=$ 6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$ (dotted line). The reduced BV (110V) with the $N_\mathrm{A}$ change from $-$20% to $+$20% is over 90% of the reference value (120V at zero charge imbalance).

Figure 4.29: Sensitivity of the BV to the charge imbalance for different values of $N_\textrm {D}$.

Figure 4.30: On-state characteristics of a conventional SOI-LDMOSFET, a SJ, and a lateral trench gate SJ SOI-LDMOSFET at $V_\textrm {GS}$ $=$ 12 V.

However, this results in an increasing on-resistance, which can be overcome by increasing the $n$-column width together with the lateral trench gate. Then it is possible to lower the doping of the drift region without degrading the on-resistance. The reduced BV (104V) of the lateral trench gate SJ SOI-LDMOSFET with the $N_\mathrm{A}$ change from 0% to $+$20% is about 87% of the reference value (120 V). Compared to the BV reduction (88 V) of the standard SJ SOI-LDMOSFET with $N_\mathrm{D}$ = 9.9 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$, the sensitivity of the BV to the charge imbalance is reduced in the proposed structure.

Table 4.3: DC performance comparison between a 120 V SJ and a lateral trench gate SJ SOI-LDMOSFET.

	SJ LDMOSFET on SOI	Lateral trench gate SJ SOI-LDMOSFET
$N_\mathrm{D}$	9.9 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$	6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$
$N_\mathrm{A}$	7.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$	6.0 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$
$R_\mathrm{sp}$	2.03m$\Omega$ $cm^2$	1.79m$\Omega$ $cm^2$
BV	117V	120V

Figure 4.30 and Table 4.3 show the results of the on-state characteristics of a conventional, a SJ SOI-LDMOSFET, and a lateral trench gate SJ SOI-LDMOSFET. From this figure it is clear that the lateral trench gate SJ SOI-LDMOSFET has superior current handling capability compared to the others. $R_\mathrm{sp}$ of this device is 1.79m$\Omega$ $cm^2$ at $V_\mathrm{GS}$ $=$ 12V and $V_\mathrm{DS}$ $=$ 0.5V. It is about 60% of the corresponding $R_\mathrm{sp}$ value of a conventional 120V SOI-LDMOSFET (about 3.0m$\Omega$ $cm^2$). Even the doping of the drift region is reduced by increasing the width of the $n$-column $R_\mathrm{sp}$ is lower than that of the SJ SOI-LDMOSFET with a much higher $n$-column doping up to 9.9 $\times$ $10^{16}$ $\mathrm{cm}^{-3}$.