2.3 Tunneling and Quantum Interference

Quantum tunneling and interference are mind-bending phenomena that defy classical physics. These effects become super important in tiny nanoscale systems, where particles can sneak through barriers and create weird wave patterns.

Scientists and engineers are using these quantum tricks to make cool new gadgets. From super-sensitive microscopes to futuristic computer chips, quantum tunneling and interference are opening up a whole new world of nanoscale tech.

Quantum Tunneling and Interference in Nanoscale Systems

Quantum tunneling in nanoscale systems

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• Quantum tunneling leverages wave-particle duality allowing particles to penetrate potential barriers classically forbidden
• Particles possess finite probability of existing on opposite side of barriers defying classical physics
• Nanoscale systems amplify tunneling effects due to reduced dimensions approaching quantum scales
• Electron tunneling through thin insulating layers enables functionality of numerous nanoelectronic devices
• Scanning Tunneling Microscopy (STM) utilizes tunneling current to image surfaces with atomic resolution
• Tunneling current exhibits exponential dependence on barrier width providing extreme sensitivity to atomic-scale features
• Quantum tunneling enables operation of various nanoelectronic components (resonant tunneling diodes, single-electron transistors)
• Tunneling effects limit further miniaturization of conventional transistors due to increased leakage currents

Transmission probability of tunnel junctions

• Wentzel-Kramers-Brillouin (WKB) approximation estimates transmission probability for simple barrier shapes
• Transmission probability depends exponentially on barrier height and width
• Formula for transmission probability: $T \approx e^{-2\kappa d}$, where $\kappa = \sqrt{2m(V_0 - E)/\hbar^2}$
• Tunneling current relates to applied voltage: $I \propto V e^{-A\sqrt{\phi}/V}$
  • $\phi$ represents barrier height
  • $A$ denotes constant related to junction geometry
• Simmons model describes current density as function of applied voltage accounting for barrier shape modifications
• I-V characteristics influenced by:
  • Barrier material properties (work function, dielectric constant)
  • Temperature effects on electron distribution
  • Quantum capacitance arising from finite density of states

Quantum interference in nanodevices

• Quantum interference stems from superposition principle in quantum mechanics
• Matter waves exhibit constructive and destructive interference patterns
• Double-slit experiment for electrons demonstrates wave-like behavior of particles
  • Electrons pass through two slits and form interference pattern on screen
  • Pattern persists even with single electrons fired sequentially
• Aharonov-Bohm effect reveals phase shift due to magnetic vector potential
  • Observable in regions with zero magnetic field
  • Demonstrates non-local nature of quantum mechanics
• Quantum rings and interferometers exploit interference for device functionality
• Coherent transport in mesoscopic systems enables interference-based phenomena
• Fano resonances in quantum dots arise from interference between discrete and continuum states

Applications of tunneling and interference

• Resonant tunneling diodes (RTDs) utilize quantum well between two barriers
  • Exhibit negative differential resistance (NDR) region in I-V curve
  • Enable high-frequency oscillators and multi-valued logic circuits
• Quantum interference transistors employ Aharonov-Bohm ring interferometers
  • Control interference via electrostatic or magnetic fields
  • Offer potential for low-power switching devices
• Single-electron transistors (SETs) exploit Coulomb blockade phenomenon
  • Control transport of individual electrons
  • Function as ultra-sensitive electrometers (charge sensors)
• Tunneling magnetoresistance (TMR) devices leverage spin-dependent tunneling
  • Magnetic tunnel junctions for field sensors and memory devices (MRAM)
• Quantum cascade lasers employ intersubband transitions in coupled quantum wells
  • Generate terahertz and infrared light through engineered energy levels
• Scanning tunneling microscopy (STM) achieves atomic-scale imaging and manipulation
  • Scanning tunneling spectroscopy (STS) probes local density of states