Two dimensional quantum mechanical simulation of low dimensional tunneling devices

doi:10.1016/j.sse.2015.05.030

Solid-State Electronics

Volume 113, November 2015, Pages 167-172

https://doi.org/10.1016/j.sse.2015.05.030 Get rights and content

Abstract

We present a 2-D quantum mechanical simulation framework based on self-consistent solutions of the Schrödinger and Poisson equations, using the Finite Element Method followed by tunneling current (direct and phonon assisted) calculation in post-processing. The quantum mechanical model is applied to Germanium electron–hole bilayer tunnel FETs (EHBTFET). It is found that 2D direct tunneling through the underlap regions may degrade the subthreshold characteristic of such devices and requires careful device optimization to make the tunneling in the overlap region dominate over the parasitic paths. It is found that OFF and ON state currents for the EHBTFET can be classified as point and line tunneling respectively. Oxide thickness was found to have little impact on the magnitude of the ON current, whereas it impacts the OFF current.

Introduction

Steep slope devices with subthreshold swing (SS) lower than the 60 mV/dec are starting to gain a strong foothold in the research community [1], [2]. Tunnel FETs (TFETs) are among the most prominent of these novel devices. TFETs rely on band-to-band tunneling (BTBT), a quantum mechanical phenomenon which allows carriers to tunnel between valence and conduction bands. The reverse biased p–n junction at the tunneling interface acts as a bandgap filter, which effectively cools down the Fermi distribution at the source, thus resulting in sub-60 mV/dec switching [3].

Recently it was demonstrated in [4], [5], [6] that lowering the dimensionality of the gases involved in the tunneling might result in dramatic improvements of the SS and $I_{ON} / I_{OFF}$ ratio, which are essential figures of merit for a low power device.

In this paper we extend our previous 1-D quantum mechanical simulation framework [5] into 2-D by combining a 2-D self-consistent Schrödinger–Poisson solver with quantum mechanical models for both direct and phonon-assisted tunneling.

Section snippets

Simulation approach

The two-dimensional, fully self-consistent Schrödinger Poisson solver is based on the first order Finite Element Method (FEM) which enables simulations of devices with non-rectangular geometry rather easily.

The wavefunctions are found as the eigen-functions of the time independent, effective mass Schrödinger equation for both holes and electrons: $[\mp \nabla \cdot \frac{ℏ^{2}}{2} {[m_{α}]}^{- 1} \nabla + E_{(c, v)} (\vec{r})] ψ_{k α} (\vec{r}) = E_{k α} ψ_{k α} (\vec{r})$ where $α, k$ and ${[m_{α}]}^{- 1}$ indicates the valley index, ladder index and the inverse effective mass tensor,

Device structures

To verify that the new 2D models are consistent with the available 1D ones, we first use a fairly uniform structure, which can be described as a quantum well diode, as in Fig. 1. The P and N sides are both highly doped ( $N_{D} = N_{A} = 10^{20} {cm}^{- 3}$ ) with a thickness of $10 nm$ each. The uniformity of the device allows us to directly compare the results obtained by 1-D and 2-D models since the potential profiles are almost overlapping and the quantized energy levels are very close between 1-D and 2-D simulators.

Benchmarking of different direct BTBT models

The comparison of I–V curves for the device in Fig. 1 predicted by different models is given in Fig. 3. As can be seen from the plot, all the four models predict the same curvature and the same order of magnitudes for the tunneling current, which means that Eqs. (4), (7) are consistent with the 1-D models in the case of uniform structures. However it should be reminded that we are merely emulating the unquantized nature of the wavefunctions in the y-direction by taking a large width ( $L = 500 nm$ ).

Conclusion

Two different models for direct tunneling have been implemented in both 1-D and 2-D versions and general agreement has been observed for a uniform QW diode structure.

The I–V characteristics of the EHBTFET have been investigated and the SS was seen to be degraded by the leakage caused by the penetration of the wavefunction into the underlap region. For this reason, the 2-D model is a powerful tool to optimize the EHBTFET design with the aim to suppress the leakage paths through the underlap

Acknowledgments

The research leading to these results has received funding from the European Communitys Seventh Framework Programme under Grant agreement No. 619509 (Project E2-Switch). J.L.P. acknowledges a postdoctoral fellowship from the Ramon Areces Foundation. Helpful discussions with Profs. Andreas Schenk and Mathieu Luisier at ETH Zurich are also kindly acknowledged. Many thanks to Prof. Luca Selmi (University of Udine) for support and encouragement.

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View full text

Two dimensional quantum mechanical simulation of low dimensional tunneling devices

Abstract

Introduction

Section snippets

Simulation approach

Device structures

Benchmarking of different direct BTBT models

Conclusion

Acknowledgments

Solid-State Electron

Solid-State Electron

J Phys Chem Solids

Experimental demonstration of 100 nm channel length In0.53Ga0.47As-based vertical inter-band tunnel field effect transistors (TFETs) for ultra low-power logic and SRAM applications

Quantum mechanical study of the germanium electron–hole bilayer tunnel FET

IEEE Trans Electron Dev

Using dimensionality to achieve a sharp tunneling FET (TFET) turn-on

Experimental demonstration of 100 nm channel length ${In}_{0.53} {Ga}_{0.47} As$ -based vertical inter-band tunnel field effect transistors (TFETs) for ultra low-power logic and SRAM applications