The mechanical properties of semiconductor nanostructures, including nanowires, quantum dots, and two-dimensional materials, exhibit distinct behaviors compared to their bulk counterparts due to size effects, surface-dominated phenomena, and unique deformation mechanisms. These materials are critical for applications in flexible electronics, nanomechanical systems, and advanced composites, where mechanical robustness and reliability are essential.

Nanowires demonstrate size-dependent mechanical properties due to their high surface-to-volume ratio. The elastic modulus of semiconductor nanowires, such as silicon or gallium nitride, often deviates from bulk values as diameters decrease below 100 nm. For silicon nanowires, experimental measurements using nanoindentation and resonance techniques reveal elastic moduli ranging from 100 to 180 GPa, compared to the bulk value of approximately 170 GPa. The variation arises from surface stress effects and crystallographic orientation. Axially oriented nanowires typically exhibit higher stiffness than those with other orientations due to anisotropic bonding.

The elastic limit of nanowires also scales with size. Dislocation nucleation, the primary mechanism for plastic deformation, becomes increasingly suppressed as nanowire diameters shrink below 50 nm. Molecular dynamics simulations and in situ TEM experiments show that silicon nanowires can sustain elastic strains exceeding 5%, far beyond the 1% limit observed in bulk silicon. This enhanced elasticity is attributed to the lack of pre-existing defects and the dominance of surface energy in stabilizing the lattice.

Fracture toughness in nanowires is governed by surface flaws rather than bulk defects. For instance, brittle materials like silicon nanowires exhibit higher fracture strengths at smaller diameters due to reduced probability of critical crack formation. Experimental studies report fracture strengths approaching the theoretical limit of 12 GPa for defect-free silicon nanowires, compared to 1-2 GPa for bulk silicon.

Quantum dots, being zero-dimensional structures, exhibit mechanical behavior influenced by interfacial strain and lattice mismatch. Epitaxially grown quantum dots, such as InAs on GaAs, experience significant compressive or tensile strain due to lattice parameter differences. This strain affects their structural stability and can lead to misfit dislocations if critical thickness is exceeded. The elastic energy stored in strained quantum dots can be partially relieved through surface roughening or atomic rearrangement, but complete relaxation is rare in coherently embedded systems.

The mechanical response of quantum dots under external stress is challenging to probe directly, but indirect methods such as substrate bending tests reveal their influence on composite stiffness. For example, embedded silicon quantum dots in a silica matrix increase the effective Young’s modulus of the composite by 10-20%, depending on volume fraction and interfacial bonding.

Two-dimensional materials, such as graphene and transition metal dichalcogenides, exhibit exceptional in-plane stiffness and out-of-plane flexibility. Monolayer graphene possesses a Young’s modulus of approximately 1 TPa, rivaling diamond, while molybdenum disulfide (MoS2) monolayers exhibit moduli around 270 GPa. These values remain high even in multilayer stacks but decrease slightly due to interlayer shear.

The elastic limit of 2D materials is exceptionally high. Graphene can sustain tensile strains up to 25% before fracture, while MoS2 fails at around 10%. This extreme elasticity is enabled by the absence of out-of-plane defects and the strong covalent in-plane bonding. However, under compression, 2D materials undergo buckling, with critical strain thresholds dependent on layer number and boundary conditions. For instance, bilayer graphene buckles at compressive strains of 0.5-1%, whereas thicker sheets exhibit higher stability.

Deformation mechanisms in 2D materials differ markedly from bulk crystals. In graphene, strain is accommodated through bond stretching and angle bending, with no dislocation activity until extreme strains. In contrast, MoS2 and other TMDCs exhibit layer-dependent plasticity, where interlayer slip becomes significant in multilayers. Ripples and wrinkles commonly form in suspended 2D membranes under non-uniform stress, reducing effective stiffness but enhancing strain tolerance.

Size effects in 2D materials are less pronounced than in nanowires but still notable. Edge defects and grain boundaries dominate mechanical failure in finite-sized flakes. For example, the fracture strength of polycrystalline graphene is 30-50% lower than that of single-crystal flakes due to stress concentration at grain boundaries. Similarly, the presence of vacancies or adatoms reduces stiffness and strain tolerance.

Nanowires, quantum dots, and 2D materials also exhibit unique responses to cyclic loading and fatigue. Silicon nanowires show minimal fatigue degradation up to 10^8 cycles when surface oxidation is suppressed, whereas oxide-coated nanowires fail earlier due to crack initiation at the oxide interface. Graphene demonstrates near-perfect fatigue resistance under cyclic tension, with no measurable stiffness loss after millions of cycles, attributed to its defect-free lattice and reversible bond deformation.

Temperature dependence of mechanical properties is another critical factor. Nanowires generally maintain their stiffness at elevated temperatures better than bulk materials due to reduced phonon scattering and suppressed dislocation motion. For example, the elastic modulus of GaN nanowires decreases by less than 10% up to 600°C, whereas bulk GaN shows a 20% reduction. In 2D materials, thermal fluctuations introduce ripples that reduce effective stiffness but do not significantly weaken intrinsic bond strength until near-melting temperatures.

In summary, the mechanical behavior of semiconductor nanostructures is governed by size effects, surface and interface interactions, and unique deformation pathways. Nanowires exhibit enhanced elasticity and strength at small diameters, quantum dots influence composite mechanics through strain fields, and 2D materials combine ultrahigh stiffness with exceptional flexibility. Understanding these properties is crucial for designing reliable nanoscale devices and systems.