What Is Tunneling?

Tunneling is a quantum mechanical phenomenon in which a particle passes through a potential energy barrier that it would be classically forbidden to surmount. Classical mechanics predicts that a particle with energy less than a barrier height simply reflects at the barrier boundary. Quantum mechanics, through the wave nature of particles, allows the wavefunction to decay exponentially within the barrier and emerge on the far side with nonzero amplitude, giving the particle a finite probability of transmission. This probability decreases exponentially with barrier width and height, so tunneling is significant only at atomic and nanometer length scales where barriers are narrow and particle energies are comparable to barrier heights. The phenomenon has profound consequences in nuclear physics, chemistry, and electronics, where it is both a design resource and a source of leakage currents that constrain device scaling.

Quantum Tunneling Fundamentals

The tunneling transmission coefficient for a rectangular barrier of height V and width d, for a particle of mass m and energy E less than V, falls off as exp(-2d sqrt(2m(V-E))/hbar), where hbar is the reduced Planck constant. This exponential dependence makes tunneling exquisitely sensitive to barrier geometry, a property exploited by the scanning tunneling microscope to image individual atoms on surfaces. Research on quantum tunneling phenomena documented through Physical Review Letters and Physical Review B underpins both the fundamental theory and its applications in surface science and device physics.

Gate Leakage and MOSFET Scaling

As silicon MOSFETs have scaled to gate oxide thicknesses below 2 nm, direct tunneling of electrons and holes through the gate dielectric has become a significant source of power dissipation and a fundamental limit on further oxide thinning. Gate leakage current increases exponentially as oxide thickness decreases, so the semiconductor industry replaced silicon dioxide with high-permittivity (high-k) dielectrics such as hafnium oxide, which achieve the same gate capacitance at a physically thicker layer, reducing tunneling current by orders of magnitude. NIST's semiconductor device metrology resources include measurement standards for gate dielectric characterization that support high-k process development.

Resonant Tunneling Devices

Resonant tunneling diodes (RTDs) consist of a thin quantum well layer sandwiched between two thin barrier layers in a semiconductor heterostructure. At specific applied voltages, the energy of conduction band electrons in the emitter aligns with a quasi-bound energy level in the quantum well, allowing resonant transmission and producing a current peak. As voltage increases beyond resonance, transmission falls and current decreases, producing a negative differential resistance (NDR) region. RTDs exhibit NDR at terahertz frequencies, making them candidates for high-frequency oscillators and detectors in terahertz sensing and communication systems.

Josephson Effect and Superconducting Tunnel Junctions

The Josephson effect describes the tunneling of Cooper pairs through a thin insulating barrier between two superconductors. A dc Josephson current flows without an applied voltage, and an ac current at a frequency exactly proportional to applied voltage provides a metrological link between frequency and voltage. This ac Josephson effect is the basis of the international volt standard, where superconductor-insulator-superconductor (SIS) junctions driven by microwave radiation produce voltage steps at integer multiples of hf/2e. NIST's quantum voltage program maintains Josephson junction arrays that define the volt with sub-nanovolt accuracy. Superconducting tunnel junctions are also used as ultra-low-noise photon detectors in X-ray astronomy and quantum information readout circuits.

Magnetic Tunneling

Magnetic tunnel junctions (MTJs) consist of two ferromagnetic metal layers separated by a thin insulating barrier, typically magnesium oxide. The tunneling conductance depends on the relative orientation of the magnetizations of the two ferromagnetic layers: parallel alignment yields higher conductance than antiparallel, a phenomenon called tunneling magnetoresistance (TMR). TMR ratios exceeding 600 percent have been measured at room temperature in optimized MgO-based junctions, enabling highly sensitive magnetic field sensors and the spin-torque magnetic random-access memory (STT-MRAM) used as non-volatile cache memory in embedded processors. IEEE Magnetics Letters publishes recent advances in MTJ materials and applications.

Applications

• Josephson junction arrays as primary voltage standards in national metrology institutes
• STT-MRAM non-volatile memory in embedded microcontrollers and cache hierarchies
• Resonant tunneling diode oscillators for terahertz spectroscopy and imaging
• Superconducting tunnel junction photon detectors in space-based X-ray telescopes
• Scanning tunneling microscope imaging and spectroscopy of atomic-scale surface structures
• High-k gate dielectric engineering in sub-5 nm CMOS nodes to suppress gate leakage