Interband Tunneling Research Articles

Extremely Nonperturbative Nonlinearities in GaAs Driven by Atomically Strong Terahertz Fields in Gold Metamaterials.

Terahertz near fields of gold metamaterials resonant at a frequency of 0.88THz allow us to enter an extreme limit of nonperturbative ultrafast terahertz electronics: Fields reaching a ponderomotive energy in the keV range are exploited to drive nondestructive, quasistatic interband tunneling and impact ionization in undoped bulk GaAs, injecting electron-hole plasmas with densities in excess of 10^{19} cm^{-3}. This process causes bright luminescence at energies up to 0.5eV above the band gap and induces a complete switch-off of the metamaterial resonance accompanied by self-amplitude-modulation of transmitted few-cycle terahertz transients. Our results pave the way towards highly nonlinear terahertz optics and optoelectronic nanocircuitry with subpicosecond switching times.

Wannier-Stark states of graphene in strong electric field

We find theoretically the energy spectrum of a graphene monolayer in a strong constant electric field using a tight-binding model. Within a single band, we find quantized equidistant energy levels (Wannier-Stark ladder), separated by the Bloch frequency. Singular interband coupling results in mixing of the states of different bands and anticrossing of corresponding levels, which is described analytically near Dirac points and is related to the Pancharatnam-Berry phase. The rate of interband tunneling, which is proportional to the anticrossing gaps in the spectrum, is only inversely proportional to the tunneling distance, in a sharp contrast to conventional solids where this dependence is exponential. This singularity will have major consequences for graphene behavior in strong ultrafast optical fields, in particular, leading to nonadiabaticity of electron excitation dynamics.

Modeling direct interband tunneling. II. Lower-dimensional structures

We investigate the applicability of the two-band Hamiltonian and the widely used Kane analytical formula to interband tunneling along unconfined directions in nanostructures. Through comparisons with k·p and tight-binding calculations and quantum transport simulations, we find that the primary correction is the change in effective band gap. For both constant fields and realistic tunnel field-effect transistors, dimensionally consistent band gap scaling of the Kane formula allows analytical and numerical device simulations to approximate non-equilibrium Green's function current characteristics without arbitrary fitting. This allows efficient first-order calibration of semiclassical models for interband tunneling in nanodevices.

Modeling direct interband tunneling. I. Bulk semiconductors

Interband tunneling is frequently studied using the semiclassical Kane model, despite uncertainty about its validity. Revisiting the physical basis of this formula, we find that it neglects coupling to other bands and underestimates transverse tunneling. As a result, significant errors can arise at low and high fields for small and large gap materials, respectively. We derive a simple multiband tunneling model to correct these defects analytically without arbitrary parameters. Through extensive comparison with band structure and quantum transport calculations for bulk InGaAs, InAs, and InSb, we probe the accuracy of the Kane and multiband formulas and establish the superiority of the latter. We also show that the nonlocal average electric field should be used when applying either of these models to nonuniform potentials. Our findings are important for efficient analysis and simulation of bulk semiconductor devices involving tunneling.

Electron Device Potential of 2D Crystal Semiconductors

2D crystal semiconductors such as graphene and transition metal dichalcogenide are emerging as potentially attractive candidates for extending existing electronic device paradigms. More importantly, in the attempt to replicate existing electronic devices, the structural and electronic properties of these materials point towards potentially novel devices [1]. In this contribution, FOUR aspects of this emerging story will be presented, combining theory and experimental demonstrations. FIRST, the physical properties of 2D crystal materials such as graphene, MoS2, etc will be compared with conventional semiconductors such as Si, Ge, GaAs, GaN, etc. Structural properties, energy bandgaps, electron/hole transport properties, etc pertinent to electronic devices will be compared, and contrasted specifically as the dimensions are scaled down to nanoscale thicknesses.SECOND, the novel transport properties of 2D crystal semiconductors will be discussed. In particular, the mobilities of these materials within a band are affected by the coupling to surrounding dielectrics and by the presence of d-orbital band-edge states. The effect of out-of plane phonon vibrations and charged impurity scattering currently limits the mobilities severely in the MoS2 family of 2D semiconductors. Methods to boost the transport properties as predicted by the theoretical analysis will be presented. In addition, interband tunneling transport in both graphene and gapped MoS2-type chalcogenide semiconductors will be presented, with an eye towards novel electron device applications.THIRD, conventional FET-type devices using these materials will be discussed and contrasted with existing state-of-the-art performance with Si and III-V semiconductor devices. Challenges and opportunities in this arena for 2D crystal semiconductors such as advantages of electrostatic scaling advantages, and ohmic contact challenges will be discussed. Experimental results on 2D crystal semiconductor FETs with high on/off ratios, respectable mobilities, and robust current saturation will be presented.FOURTH, novel nanoelectronic devices that depend on tunneling transport will be presented. Specifically device proposals that exploit the intrinsic properties of 2D crystal semiconductors, such as graphene nanoribbon tunnel-FETs (TFET), Symmetric FET (SymFET), and TFETs with transition metal dichalcogenides will be presented. Finally, the very recent experimental demonstrations of some of these proposed devices will be discussed, and the challenges in realizing these devices, and their promise will be discussed. [1] D. Jena, Proceedings of the IEEE, 101, 1705 (2013).

III–V compound semiconductor transistors—from planar to nanowire structures

Abstract

Effect of Random, Discrete Source Dopant Distributions on Nanowire Tunnel FETs

The finite number, random placement, and discrete nature of the dopants in the source of an InAs nanowire tunnel field-effect transistor affect the drive current and the inverse subthreshold slope. The impact of source scattering is negligible, since the current is limited by the interband tunneling. The most significant effect of the discrete dopants is to create variations of the electric fields in the tunnel barrier, which cause variations in the current. The relative variation in the ON current decreases as the average doping density and/or nanowire diameter increases. Results from full self-consistent nonequilibrium Green's function calculations and semiclassical calculations are compared.

Performance limits of tunnel transistors based on mono-layer transition-metal dichalcogenides

Performance limits of tunnel field-effect transistors based on mono-layer transition metal dichalcogenides are investigated through numerical quantum mechanical simulations. The atomic mono-layer nature of the devices results in a much smaller natural length λ, leading to much larger electric field inside the tunneling diodes. As a result, the inter-band tunneling currents are found to be very high as long as ultra-thin high-k gate dielectric is possible. The highest on-state driving current is found to be close to 600 μA/μm at Vg = Vd = 0.5 V when 2 nm thin HfO2 layer is used for gate dielectric, outperforming most of the conventional semiconductor tunnel transistors. In the five simulated transition-metal dichalcogenides, mono-layer WSe2 based tunnel field-effect transistor shows the best potential. Deep analysis reveals that there is plenty room to further enhance the device performance by either geometry, alloy, or strain engineering on these mono-layer materials.

Self-consistent surface charges and electric field in p-i-n tunneling transit-time diodes based on single- and multiple-layer graphene structures

We develop a device model for p-i-n tunneling transit-time diodes based on graphene single- and multiple-layer structures operating at the reverse bias voltages. The model of the graphene tunneling transit-time diode (GTUNNETT) accounts for the features of the interband tunneling generation of electrons and holes and their ballistic transport in the device i-section, as well as the effect of the self-consistent electric field associated with the self-consistent charges of propagating electrons and holes. Using the developed model, we calculate the dc current-voltage characteristics and the ac frequency-dependent admittance as functions of the GTUNNETT structural parameters, in particular, the number of graphene layers.

Multiband effects on Fulde-Ferrell-Larkin-Ovchinnikov states of Pauli-limited superconductors

Multiband effects on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of a Pauli-limiting two-band superconductor are studied theoretically in the wide range of parameters, based on the Bogoliubov-de Gennes equation. First, we examine the phase diagrams of two-band systems with a passive band in which the intraband pairing interaction is absent and superconductivity is induced by a Cooper pair tunneling from an active band. The critical field of Bardeen-Cooper-Schrieffer to FFLO states becomes lower than the Lifshitz point with increasing the interband tunneling strength. We also study the thermodynamics of Pauli-limiting two-band superconductors with nonzero intraband pairing interactions. As a consequence of a competing effect between two bands, the FFLO phase is divided into two phases: ${Q}_{1}$- and ${Q}_{2}$-FFLO phases. In a particular case, the latter is further subdivided into a family of FFLO states with rational modulation lengths, where the spatial structure of the pair potential is approximately describable with sinusoidal functions with multiple modulation wave numbers. The resultant phase diagram is qualitatively different from that in a single-band superconductor and gives rise to a devil's staircase structure in the field dependence of physical quantities.

On the non-linear effects in graphene devices

We study several graphene devices able to generate non-linear effects in the current–voltage characteristics and in particular negative differential resistance (NDR) effects. This theoretical investigation is based on numerical charge transport simulation in the Green's function approach applied to a tight-binding Hamiltonian for particles in graphene. Depending on the device, the physical mechanism involved in the NDR effect may be different: (i) the mismatch of modes between left and right sides of a P+/P zigzag ribbon junction, (ii) the modulation of interband tunnelling in P/N junctions (tunnel diodes and tunnel field-effect transistors) or (iii) the modulation of chiral tunnelling in ‘conventional’ graphene transistors. We emphasize the advantages of exploiting different approaches of bandgap engineering in the form of graphene nanoribbons (GNRs) or nanomesh lattices (GNM), the latter resulting from a periodic array of nanoholes in graphene sheets. In particular, such nanostructuring allows us to design position-dependent bandgaps in devices, which is shown to make possible the optimization of device operation and, here, to get very high peak-to-valley ratio of the NDR. In the case of GNR nanostructuring, it is shown that appropriate bandgap engineering can even make the current–voltage characteristics of tunnel diodes weakly sensitive to the atomic edge disorder. Finally, GNM lattices are shown to be a very promising way to open large bandgaps in wide sheets of graphene and to introduce bandgaps locally with a view to optimizing the device operation and performance.

SPICE Modeling of Double-Gate Tunnel-FETs Including Channel Transports

SPICE modeling of double-gate (DG) tunnel FETs (TFETs) including channel transports is reported. An ideal drain current model neglecting the channel transport is developed first. It captures the interband tunneling characteristics, describes their geometry dependences, and is suitable for DG TFETs with limited drivability. The ideal current model and previously proposed charge model are then extended to include the channel transports. One way to model the transport is appending a DG MOSFET in series with the ideal TFET model. The dependences of TFETs current and terminal charges on channel transports are reproduced. Another way by inserting a resistance at the TFET source side is also proposed with reduced simulation time.

Single-trap-induced random telegraph noise for FinFET, Si/Ge Nanowire FET, Tunnel FET, SRAM and logic circuits

In this paper, we comprehensively review the impacts of single-trap-induced random telegraph noise (RTN) on FinFET, Ge/Si Nanowire FET and Tunnel FET (TFET). The resulting influences on the thermionic-based current conduction such as FinFET, Si-NW FET and Ge-NW FET (at low drain bias) as well as interband tunneling dominated current conduction such as TFET and high-drain-biased Ge-NW FET are extensively addressed in device and circuit level. The location of the trap is shown to have profound impacts and the impacts vary with bias conditions and trap types. The worst-case analysis of the stability/performance and leakage/delay for all possible trapping/detrapping RTN combinations are investigated for FinFET, Si-/Ge-NW FETs and TFET based 6T/8T SRAM cells and logic circuits.

An innovative band-to-band tunneling analytical model and implications in compact modeling of tunneling-based devices

In this paper, an analytical band-to-band tunneling model is proposed, validated by means of drift-diffusion simulation and comparison with experimental data, implemented in Verilog-A, and finally proven with SPICE simulator through simulation of circuits featuring tunneling diodes. The p-n junction current calculation starts from a non-local Band-to-Band tunneling theory including the electron-phonon interaction and therefore it is particularly suited for indirect semiconductor materials such as silicon- or germanium-based interband tunneling devices.

Engineering Interband Tunneling in Nanowires With Diamond Cubic or Zincblende Crystalline Structure Based on Atomistic Modeling

We present an investigation in the device parameter space of band-to-band tunneling in nanowires with a diamond cubic or zincblende crystalline structure. Results are obtained from quantum transport simulations based on Nonequilibrium Green's functions with a tight-binding atomistic Hamiltonian. Interband tunneling is extremely sensitive to the longitudinal electric field, to the nanowire cross section, through the gap, and to the material. We have derived an approximate analytical expression for the transmission probability based on the Wentzel-Kramers-Brillouin theory and on a proper choice of the effective interband tunneling mass, which shows good agreement with results from atomistic quantum simulation.

(Invited) Si/SiGe Resonant Interband Tunnel Diodes Grown by Large-Area Chemical Vapor Deposition

Si/SiGe resonant interband tunnel diodes were successfully technology transferred from low-temperature molecular beam epitaxial growth to chemical vapor deposition (CVD) on 200-mm diameter p-doped silicon wafers in a production style reactor. The resonant interband tunnel diode structure consists of a p+-i-n+ diode that incorporates vapor phase doped δ-doping to enhance quantum mechanical confinement and tunneling probability. The tunneling barrier thickness was varied from 2 nm to 8 nm and a record high peak-to-valley current ratio of 5.2 for a CVD process is reported for a 6 nm barrier thickness. The CVD reactor is an active integral tool within a 200mm full CMOS process line and is suggestive that Si/SiGe RITDs could be seamlessly integrated into a full hybrid CMOS process flow.

Yield‐driven design of tunnelling SRAM cells

As an implementation of the static random access memory (SRAM), the tunnelling SRAM (TSRAM) uses the negative differential resistance of resonant (interband) tunnelling diodes (R(I)TDs) and potentially offers improved standby power dissipation and integration density compared with the conventional CMOS SRAM. TSRAM has not yet been realised with a useful bit capacity mainly because the level of reproducibility required of the nanoscale R(I)TDs has been demanding and difficult to achieve. In this reported work, the design of TSRAM cells is approached from the perspective of maximising their yield and specific results are presented for an RITD-based cell. With advances in the control of semiconductor multilayer growth, it is shown that achieving acceptable yields is now within sight.

Landau–Zener tunnelling in 2D periodic structures in the presence of a gauge field: I. Tunnelling rates

We study the interband Landau–Zener tunnelling of a quantum particle in the Hall configuration, i.e., in the presence of gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle) normal to the lattice plane. The interband tunnelling is induced by the potential field and for the vanishing gauge field is described by the common Landau–Zener theory. We generalize this theory for a nonzero gauge field. The depletion rates of low-energy bands are calculated by using a semi-analytical method of the truncated Floquet matrix.

Common path interference in Zener tunneling is a universal phenomenon

We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first `Zener oscillation' occurs at a transmission probability which is exponentially small when the co-efficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of $p$ in the low energy dispersion relation. Since odd powers of $p$ are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the $p^4$ term makes the leading contribution.

Tunneling Transistors Based on Graphene and 2-D Crystals

As conventional transistors become smaller and thinner in the quest for higher performance, a number of hurdles are encountered. The discovery of electronic-grade 2-D crystals has added a new “layer” to the list of conventional semiconductors used for transistors. This paper discusses the properties of 2-D crystals by comparing them with their 3-D counterparts. Their suitability for electronic devices is discussed. In particular, the use of graphene and other 2-D crystals for interband tunneling transistors is discussed for low-power logic applications. Since tunneling phenomenon in reduced dimensions is not conventionally covered in texts, the physics is developed explicitly before applying it to transistors. Though we are in an early stage of learning to design devices with 2-D crystals, they have already been the motivation behind a list of truly novel ideas. This paper reviews a number of such ideas.