Simulation Studies of a Trench MOS Device Structure with Small Figures of Merit

. We proposed a vertical high permittivity trench power MOS (HKTMOS) device with alternating N&P drift region and high permittivity (HK) trench sandwiched in between. The unique structure guarantees uniform potential distribution for wide voltage range at block state owing to both HK potential modulation effect and superjunction (SJ) charge balance. The specific on-resistance (Rons) of HKTMOS is in orders of magnitude lower than the SJ counterparts at the on state because of the strong accumulation effect brought by HK trench. Although the gate charge also significantly rises because of the accumulation, the figures of merit (FOM) of HKTMOS still reduces considerably than the SJ under same BV. An expression for FOM is derived demonstrating that the FOM of HKTMOS is proportional to the square of HK trench depth, which agrees on with simulation results well. The simulation results indicate that within the BV range of 500~2000V, the Rons and FOM of HKTMOS are in 1~2 orders of magnitude lower and 17.4%~44.1% of SJ, respectively under the same BV condition. Furthermore, HKTMOS also demonstrates better charge imbalance tolerance than SJ.


Introduction
The performance of silicon power devices are essential for the energy conversion system. The introduction of high permittivity (HK) material into power MOS device allows better potential distribution in silicon and therefore improves device breakdown voltage (BV) [1] . The effect is called the HK potential modulation (PM) effect [1] , which had been demonstrated both theoretically [2] and experimentally [3] . On other hand, because HK material exhibits large permittivity, it is potential to be used to activate the carrier accumulation (CA) effect in silicon to significantly reduce the device on-resistance (Ron). In this letter, we propose a novel HK trench MOS (HKTMOS), which utilizes both PM and CA effects from HK, resulting in specific-Ron(Rons) decrease in orders of magnitude compared with conventional superjunction device (SJ). Although such Rons decrease is at the cost of larger switch loss due to the extra accumulation charge on the gate, the relationship between Rons and gate charge is linear, and the total figures of merit (FOM) of HKTMOS still experiences a significant improvement than the SJ. Furthermore, HKTMOS also indicated strong doping-imbalance tolerance in N and P drift region.

Device structure and mechanism
The cross section view of HKTMOS is showed in Figure  1a. Similar with SJ, HKTMOS also features alternating N and P drift region pillar, whereas a layer of HK material is sandwiched in between. Together with the buried oxide in the N+ drain region, the P drift region is completely isolated from the N drift region and the drain, but directly contacts with the gate.
At the device blocking state, with the same mechanism as [4], although there is HK isolation between N and P drift region, their electric field still depleted with each other because of the large permittivity of HK, so that the charge balance effect still exists. Moreover, the total permittivity of drift region is also boosted with the introduction of HK trench, according to [1], the slope of electrical field in drift region is given by (1), Where Nd and εtotal are the doping concentration and total permittivity of the drift region, respectively. With large εtotal, the slope of the electric field is small, giving better potential distribution and higher BV on the basis on charge balance. The effect is attributing to the HK PM effect. As showed in Figure 1b, the potential distribution of HKTMOS is almost ideal at the blocking state. Besides, better doping imbalance tolerance between N and P pillar can be also realized with effect of HK, which will be verified later. Above all, at the device blocking state, both effect of HK PM and charge balance co-exists to guarantee the high BV not only for the short drift region, but also for long drift region devices. Although the reduction of device Rons by mean of CA effect has been reported in [5], the CA is generated by SiO2 layer, with the low permittivity of SiO2, its effect is limited. Moreover, small ε of the SiO2 also brings negative effect for BV according to (1). On contrast, HK material is capable of overcoming the above problems. When the device in Figure 1a is in on state, the gate voltage is high, the P pillar share the same high potential with gate as their directly contact. Whereas both drain and source voltage is much lower than the gate at the on state, consequently, CA effect happens at the interface of silicon and HK trench as showed in Figure 1c. The large permittivity of HK amplified the CA effect and forms a high carrier density path between drain and source, the device Rons is thereby significantly reduced.
CA effect allows significant Rons reduction with no additional drift region doping. However, large trench capacitance is necessary to accumulate enough charge at the device on-state to reduce the Rons. And the trench capacitor will be discharged at off-state to guarantee high BV, such charge-discharge cycle with large capacitance results in high switch loss. Rarely had any literatures qualitatively investigated such effect and its impact to FOM. For the HKTMOS device, as a low resistance path exists between drain and source generated by HK CA effect, the device Rons is major determined by the accumulation resistance (RA). According to [6], RA∝1/Cg, where Cg is the unit area trench capacitance, we can derive that Rons of HKTMOS is given by Where the KHKT, LHK, Vg, and W are the HKTMOS constant, depth of HK trench, gate voltage and width of the device, respectively. Although the N+ source junction and the drain not contributing to the total resistance are covered in the LHK in (2), both of their depth are overwhelming smaller than the drift region length and thereby negligible. We see that the Rons is proportional to LHK for HKTMOS from (2).
On the other hand, the gate charges are contributed by both HK trenches and SiO2 buries. The contribution from SiO2 buries is also overwhelming smaller than the HK trenches, for both permittivity and area. Therefore, it is neglected and gate charge is given by . According to (2) and (3), we see that the Rons is inverse proportional to the gate charge for a given device dimension. The definition [6] for FOM is FOM=Rons*Qg, which gives An interesting result is observable from (4) that FOM of the HKTMOS is irrespective of the unit area trench capacitance and device width. It is only proportional to the square of the HK trench depth with ratio of HKTMOS constant KHKT. According to analysis and simulation results, the analytical value of KHKT is 7.812×10 -4 Ω*nC/μm 2 .

Simulation verification and discussion
We use TMA-MEDICI to make 2D simulation and verify above analysis. Figure 2 shows the BV dependence for Rons and switch delay for both HKTMOS with different HK permittivity εHK (a) and SJ device (b). As revealed in Figure 2b, the Rons of the SJ rises rapidly with increase of BV at the exponential of 1.33 [4]. On contrast, under the effect of strong CA effect brought by HK, the Rons of HKTMOS is in the orders of magnitude lower than the SJ as showed in Figure 2a. Higher εHK always brings smaller Rons, owing to the reason that higher permittivity always provides larger trench capacitance, thereby stronger CA effect and smaller Rons. Moreover, expression (2) suggests that the Rons of HKTMOS is proportional of the drift region length. Because the BV is also proportional to the drift region length, the Rons of HKTMOS rises linearly with the increase of BV as Figure 2a reveals, which agrees on with (2).
Although the CA effect of HK reduces Rons in orders of magnitude, the large trench capacitance also slow down the switching speed. As showed in Figure 2, the switch delay of the HKTMOS is much larger than the SJ device, in the orders of magnitude as well. Higher εHK value always causes worse switch delay. To investigate the comprehensive performance of the HKTMOS, the device FOMs are simulated and calculated as shown in Figure 3a. Rons is simulated under the condition of a 15 V gate voltage and 0.1 V drain voltage. Qg is simulated schematically as shown in Figure 3a, where a 15 V square wave voltage is applied on the gate. Qg is determined by the current integral at the time interval when the drain drops from 100 V to the voltage of the fully on-state. As Figure 3a shows, both Rons and Qg increase linearly with the rise of LHK, which is consistent with (3) and (5). (3) and (5) also indicated that Rons and Qg are proportional and inversely proportional to εHK, respectively. The relation is also verified by simulation, as Figure 3a shows; a larger εHK always provides a smaller Rons but a larger Qg and vice versa. Figure 3b shows the FOM and BV vs. LHK for both HKTMOS and SJ, where the FOM of HKTMOS with changing εHK are plotted in different line styles. As mentioned above, Rons and Qg are inversely proportional and proportional to LHK, respectively, which cancel each other out when the multiplication for FOM occurs. It can be observed that all of the lines almost overlap with each other for different εHK when LHK ranges from 30 μm to 120 μm (Figure 3b) according to simulation, which agrees with (6) very well. The proportional coefficient between the FOM and LHK square may be different depending on the cell geometry; however, for a device with a given cell geometry, the FOM is only determined by LHK regardless of the HK permittivity and trench thickness. For HKTMOS with the size displayed in Figure 2a, the analytical value of the proportional coefficient is derived as 7.812×10 -3 Ω*nC/μm 2 . Utilizing such a coefficient, we are able to calculate the FOM using (6), which is shown by the round dots in Figure 3b. It is clear that the calculation results agree well with the simulation results. Figure 3b also reveals that for the HKTMOS with smaller εHK (εHK=50), the FOM by simulation is slightly smaller than the calculated value, especially at larger LHK. This is because Qg is determined by the sum of QHK and QDC, then, Qg will drop linearly with the linear decrease of εHK as long as QHK is still larger than QDC according to (4). However, as RA parallels with Rdrift, with smaller εHK, RA in (2) is less dominant, and the contribution to Rons from the drift region Rdrift becomes more significant although RA is still much lower than Rdrift. Consequently, the total Rons will rise sub-linearly with the decrease of the small εHK due to the contribution from the drift region bypass, which has been neglected in previous analysis. Moreover, according to (6), the FOM of HKTMOS is proportional to the square of LHK; the square amplifies the model inaccuracy if LHK is large, which causes a larger FOM difference between the calculated and simulated values under the condition of a large LHK and a small εHK as shown in Figure 3b. Figure 3b also shows the relationship between BV and LHK for both HKTMOS and SJ. The BVs of HKTMOS with different εHK completely overlapped with each other so that only one curve is shown for HKTMOS. As the BV of SJ relies on CB only, while HKTMOS takes both effects of PM and CB to achieve high BV, the BV of HKTMOS will be slightly better than that of SJ, as shown in Figure 3b. Last but not least, HKTMOS always demonstrates significant FOM improvement over that of SJ under all LHK in the figure; the FOM of HKTMOS is 48% of that of SJ at the LHK of 120 µm, and only 17% at the LHK of 30 µm. Although the FOM takes the total gate charges into consideration instead of the gate-to-drain charges only, HKTMOS still exhibits a significant FOM improvement over that of SJ.