Analysis of Electrical Characteristics in 4H-SiC Trench-Gate MOSFETs with Grounded Bottom Protection p-Well Using Analytical Modeling

Abstract

A new analytical model to analyze and optimize the electrical characteristics of 4H-SiC trench-gate metal-oxide-semiconductor field-effect transistors (TMOSFETs) with a grounded bottom protection p-well (BPW) was proposed. The optimal BPW doping concentration (N_BPW) was extracted by analytical modeling and a numerical technology computer-aided design (TCAD) simulation, in order to analyze the breakdown mechanisms for SiC TMOSFETs using BPW, while considering the electric field distribution at the edge of the trench gate. Our results showed that the optimal NBPW obtained by analytical modeling was almost identical to the simulation results. In addition, the reverse transfer capacitance (C_gd) values obtained from the analytical model correspond with the results of the TCAD simulation by approximately 86%; therefore, this model can predict the switching characteristics of the effect BPW regions.

1. Introduction

Wide energy bandgap materials such as silicon carbide (SiC) and gallium nitride (GaN) are recognized as promising candidates for high-power devices due to a superior inherent property. They cause high critical electric field strength and high drift saturation velocity, which results in a high blocking capability with low on-resistance compared with Si devices. Especially, 4H-SiC trench-gate MOSFETs (TMOSFETs) have the benefit of low on-resistance due to their high cell density and absence of JFET regions [1,2,3,4,5]. It is possible to create a miniaturization application, such as an electric power converter, due to high-power operation, high frequency, and thermal capability. However, the TMOSFETs suffer reliability issues due to electric field crowding at the gate oxide in the blocking mode. To suppress electric field crowding, various technologies such as bottom protection p-wells (BPWs), bottom thick oxides, double trench structures, and double p-base structures were investigated [6,7,8,9,10,11,12].

BPW doping concentrations influence the electric field at the gate oxide, the effective thickness of the drift layer, and the parasitic capacitances. As the BPW doping concentration (N_BPW) increases, the electric field at the oxide decreases under 4 MV/cm by spreading the trench corner, so that the reliability of the gate oxide can be ensured [13,14]. However, this can decrease blocking characteristic because the effective thickness of the drift layer decreases when N_BPW exceeds the optimal condition. Thus, it is important to determine the optimal Al doping concentration in order to improve electrical characteristics and oxide reliability.

In previous studies on numerical TCAD simulations to determine the optimal value of the electrical characteristics, the effects of the BPW junction profile on the switching property, specific on-resistance, and blocking voltage were analyzed by varying the BPW process conditions, as presented in Refs. [15,16,17,18,19,20]. Even though this is useful to obtain the optimal points, considerable computational costs are incurred due to the enormous data set. On the other hand, an analytical model makes it possible to calculate the optimal N_BPW value by using Poisson’s equation with consideration of the depletion width, effective thickness of the drift layer, and electric field distribution.

In this study, an analytical model is proposed to investigate and optimize the electrical characteristics of 4H-SiC TMOSFETs, which are compared with numerical TCAD simulations. In addition, the reverse transfer capacitance (C_gd) was extracted using an analytical method for comparison with the C_gd of the numerical TCAD simulation results.

2. Device Structure Modeling

Figure 1 shows a cross-sectional view of the 1.2-kV 4H-SiC trench-gate MOSFET with a BPW structure. The 4H-SiC trench-gate MOSFET was constructed using Sentaurus TCAD simulation tools. The doping profiles of the P base, n⁺ source, p⁺ source, and BPW were formed by the Monte Carlo method. For a voltage rating of 1.2-kV, the drift doping concentration (N_drift) and the drift thickness (t_drift) were 6 $\times$ 10¹⁵ cm⁻³ and 13 μm, respectively. These parameters determine the breakdown voltage using a punch-through diode model and consider the two-dimensional effect and the reduction in the effective thickness between the trench and n-drift length [21]. The doping concentration and depth of the n⁺ source, p⁺ source, and P base were 1 $\times$ 10²⁰ cm⁻³, 1 $\times$ 10²⁰ cm⁻³, and 3 $\times$ 10¹⁷ cm⁻³, respectively. The length and depth of n⁺ source, p⁺ source, and P base were 1.25/0.3 μm, 0.5/0.4 μm, and 1.75/0.7 μm, respectively. The width, depth, and slope of the trench were 1 μm, 2 μm, and 88°, respectively; the trench depth effectively prevented the degradation of the current flow from the JFET resistance. At the trench bottom, a p-type region for BPW was constructed using multi-implantation energies and a spacer thickness of 0.1 μm. The implantation energies and spacer thickness were considered to prevent lateral penetration of the trench sidewall. N_BPW values from 1 $\times$ 10¹⁷ cm⁻³ to 3 $\times$ 10¹⁸ cm⁻³ were used to analyze electrical characteristics, and the contact metal was placed at the bottom of the trench to set BPW as ground [15,22].

3. Design of Analytic Method

To investigate the relationship between the breakdown voltage and various N_BPW, we extracted the BPW charge, BPW junction depth, and depletion width by using a Gaussian distribution and Poisson’s equation. The depth profile of N_BPW was divided into two regions: the box profile region and the Gaussian profile region, as shown in Figure 2.

The charges for various N_BPW were calculated using the doping concentration distribution functions:

$$\mathrm{Q}\left(\mathrm{x}\right)={\mathrm{R}}_{\mathrm{p}}{\mathrm{N}}_{\mathrm{p}}+{{\displaystyle \int }}^{}{\mathrm{N}}_{\mathrm{p}}\exp \left[-\frac{{\left(\mathrm{x}-{\mathrm{R}}_{\mathrm{p}}\right)}^2}{2\Delta {\mathrm{R}}_{\mathrm{p}}^2}\right]\mathrm{dx}$$

(1)

The charge of the box profile region is approximated by the constant term R_pN_p, and that of the Gaussian profile region was calculated using the integral of the Gaussian distribution function term. The BPW junction depth (x_j) with various N_BPW was determined by solving the Gaussian distribution function [23]:

$$\mathrm{N}\left(\mathrm{x}\right)={\mathrm{N}}_{\mathrm{p}}\exp \left[-\frac{{\left(\mathrm{x}-{\mathrm{R}}_{\mathrm{p}}\right)}^2}{2\Delta {\mathrm{R}}_{\mathrm{p}}^2}\right]$$

(2)

where N_p is the highest N_BPW, R_p is the average distance when the doping concentration is N_p, and ΔR_p is the projected straggle standard deviation that is empirically used for 4H-SiC implantation data [24]. The BPW junction depth x_j can be obtained by integrating Equation (1), when the doping concentration is N_epi:

$${\mathrm{x}}_{\mathrm{j}}={\mathrm{R}}_{\mathrm{p}}+\Delta {\mathrm{R}}_{\mathrm{p}}\left[2\log \left(\frac{{\mathrm{N}}_{\mathrm{p}}}{{\mathrm{N}}_{\mathrm{epi}}}\right)\right]$$

(3)

In addition, the depletion width (W) was dependent on the doping concentrations, such as N_drift and N_BPW. It was calculated using Poisson’s equation [13,21].

$$\mathrm{W}=\sqrt{\frac{2{\mathsf{\epsilon }}_{\mathrm{s}}{\mathrm{v}}_{\mathrm{bi}}}{\mathrm{q}}\left(\frac{1}{{\mathrm{N}}_{\mathrm{epi}}}+\frac{1}{{\mathrm{N}}_{\mathrm{BPW}}}\right)}$$

(4)

where ${\mathsf{\epsilon }}_{\mathrm{s}}$ and q represent the dielectric constant and the charge of the electron, respectively, and ${\mathrm{v}}_{\mathrm{bi}}$ is the built-in potential. The junction depth (x_j) and the depletion width (W), as functions of N_BPW, affected the breakdown voltage. Therefore, we propose a breakdown voltage length factor that divides the depletion width by the junction depth. This parameter indicates the degradation of the breakdown voltage when N_BPW increases.

4. Results and Discussion

Figure 3 shows the charges, length factor, and breakdown voltage for various values of N_BPW ranging from 1 $\times$ 10¹⁷ cm⁻³ to 3 $\times$ 10¹⁸ cm⁻³. As N_BPW increased, the charges reduced the electric field crowding at the trench edge by effective shielding in the BPW structure because the BPW charge gradually increased.

This means that the blocking voltage and gate oxide reliability were improved. However, along with the increase in the N_BPW, the effective thickness of the drift layer was reduced. This was caused by the degradation of the length factor, where x_j and W were increased and decreased, respectively. Therefore, the effect of the length factor reduces the breakdown voltage. In the case N_BPW of 8 $\times$ 10¹⁷ cm⁻³, the cross point between the effect of the charge and that of the length factor with various N_BPW was determined using the analytical method. This indicated that the gate oxide field was below 4 MV/cm. The electric field distributions of the trench corner in B-B’ for different N_BPW are shown in Figure 4.

When N_BPW was lower than 7 $\times$ 10¹⁷ cm⁻³, this was insufficient for the shielding effect at the gate oxide, and the peak electric field of the oxide was still higher than 4 MV/cm. This caused the dielectric breakdown to occur before avalanche breakdown in the drift layer. For this reason, although an N_BPW of 7 $\times$ 10¹⁷ cm^–3 has the highest breakdown voltage during the simulation, it can reduce oxide reliability in the long term. When N_BPW is higher than 8 $\times$ 10¹⁷ cm⁻³, the charges can effectively shield the oxide field, which is less than 4 MV/cm at the trench corner. However, the higher doping concentrations strongly influenced the degradation of the length factor, which caused the degradation of the blocking voltage. Therefore, in the case of N_BPW of 8 $\times$ 10¹⁷ cm⁻³, we found that the highest breakdown voltage of 1345 V was extracted by the TCAD simulation results and the analytic method considering the oxide electric field and the effect of the length factor.

Figure 5 shows the conduction band edge energy profiles at the poly-Si/oxide/BPW interface in the B-B’ of the trench corner with various N_BPW values under breakdown conditions. As N_BPW increased, the conduction band energy of the BPW region increased. This indicates that the higher doping concentration is not fully depleted in the BPW region under the breakdown voltage, so that the gate oxide was protected from the crowding electric field. In the case of an N_BPW value of 1 $\times$ 10¹⁷ cm⁻³, which was the lowest BPW concentration in the simulation conditions, the conduction band energy at the oxide region was pulled down. This means that a high electric field was applied at the edge of the trench gate oxide; consequently, a dielectric breakdown voltage was induced.

Figure 6 shows the C_gd of the analytical modeling and numerical simulation as the Drain-source voltage (V_ds). The C_gd was extracted using a Gaussian distribution and a TCAD simulator for comparative analysis, when the N_BPW was 8 $\times$ 10¹⁷ cm⁻³. The C_gd of the analytical modeling corresponds to that of the numerical simulation by approximately 86%. The analytical model was able to predict C_gd through the calculation of the BPW charge as the V_ds, but all parasitic capacitances of the TMOSFET device were not taken into account for the simple calculation. Thus, when the V_ds is less than 100 V, the slight discrepancy between the numerical simulation and analytical model exists, as shown in Figure 6. Although the C_gd was different between the analytical modeling and numerical simulation, analytical modeling was used to estimate the C_gd of the BPW region and predict the switching characteristics due to the effect of BPW.

5. Conclusions

We investigated the analytical modeling to optimize the electrical characteristics of a 4H-SiC trench-gate MOSFET with a grounded BPW. The optimized N_BPW was extracted using a Gaussian distribution and Poisson’s equation with consideration of the charge, depletion width, and junction depth of the BPW. We verified that analytical modeling was able to find the optimized N_BPW using a comparison with numerical TCAD simulation results of the breakdown mechanisms, with consideration of the electric field distribution and energy band diagram. In addition, C_gd was extracted using an analytical model. When the C_gd of the numerical TCAD simulation is compared with that of the analytical modeling, there is, approximately, an 86% correspondence. Therefore, this model can predict the switching characteristics of the effect BPW regions.