Trap-state mapping to model GaN transistors dynamic performance

Abstract

Trapping phenomena degrade the dynamic performance of wide-bandgap transistors. However, the identification of the related traps is challenging, especially in presence of non-ideal defects. In this paper, we propose a novel methodology (trap-state mapping) to extract trap parameters, based on the mathematical study of stretched exponential recovery kinetics. To demonstrate the effectiveness of the approach, we use it to identify the properties of traps in AlGaN/GaN transistors, submitted to hot-electron stress. After describing the mathematical framework, we demonstrate that the proposed methodology can univocally describe the properties of the distribution of trap states. In addition, to prove the validity and the usefulness of the model, the trap properties extracted mathematically are used as input for TCAD simulations. The results obtained by TCAD closely match the experimental transient curves, thus confirming the accuracy of the trap-state mapping procedure. This methodology can be adopted also on other technologies, thus constituting a universal approach for the analysis of multiexponential trapping kinetics.

Figure 1

(a) Distribution function $g\left(v\right)$ in Eq. (10) for different values of $\beta$ from 0.3 to 0.95. (b) Dependency between ${\tau }_{\mathit{pk}}/{\tau }_0$ and $\beta$. Notably, the difference between ${\tau }_{\mathit{pk}}$ and ${\tau }_0$ reaches several orders of magnitude for low values of $\beta$. (c) Comparison between the distribution function $g\left(v\right)$ using the asymptotic (red) and inverse Laplace (blue) approach. (d) $f\left(t\right)$ calculated by integrating $g\left(\nu \right)$ numerically calculated with the inverse Laplace transform varying $\beta$ from 0.3 to 0.95. (e) Relative error introduced using the asymptotic extraction (saddle point method) in respect to the inverse Laplace transform.

Figure 2

(a) Contour map of the $A_i$ distribution for different values of $\beta$ with ${\tau }_0=1$ s. (b) 3D plot of the $A_i$ distribution of time constants for a fixed ${\tau }_0=1$ s and different stretching coefficient. (c) $f\left(t\right)$ defined as three stretched exponential functions. (d) The sum of each exponential decay component ($A_i$) returns the stretched exponential behavior.

Figure 3

(a) Logarithmically spaced I_DV_G at $V_{\mathit{DS}}=0.4$ V after $t_{\mathit{fill}}=10$ µs at $V_{\mathit{fill}}=\left(2,50\right)$ V. (b) Normalized drain current transient at different temperatures and $V_{\mathit{ON}}=\left(4,0.4\right)$ V. The recovery is very slow compared to the fill time.

Figure 4

(a–b) $A_i$ distribution mapped extracted from the experimental data and mapper at different temperatures; (c) Distribution of activation energies, and (d) capture cross sections in the surface of the device under test.

Figure 5

(a) Trap distribution at the passivation/AlGaN interface implemented in TCAD structure. The activation energies and capture cross sections are defined according to the distributions obtained via trap-state mapping. (b) TCAD simulation of the recovery transient repeated at different temperatures, and (c–d) Vertical cross section of the dynamic behavior of the conduction band during the recovery along with the repopulation of the 2DEG Density.