Layer-Dependent Pressure Effect on the Electronic Structure of 2D Black Phosphorus

Tunneling Magnetoresistance Transition and Highly Sensitive Pressure Sensors Based on Magnetic Tunnel Junctions with a Black Phosphorus Barrier

“…Considering that the thickness of monolayer black phosphorus is 0.524 nm, 18 we shall set where d is the thickness of the black phosphorus barrier. As for the pressure effect, according to ref ( 8 ), the parameters in eq 1 are set as follows: a = 0.18 eV/GPa, γ 0 = 1.76 eV, P coh = 1.4 GPa. In addition, because the magnitude of the intralayer primitive translational vector c = 4.3763 Å, 18 the magnitude of the intralayer reciprocal lattice vector K h = 2π/ c = 1.436 × 10 10 m –1 .…”

“…From eq 1 , it can be derived that the greater the number of layers, the larger the theoretical range of detection: for the number of layers N = 5, the theoretical range of detection is about 0–1.8 GPa; for N = 10, the theoretical range of detection is about 0–2.5 GPa; for N = 20, the theoretical range of detection is about 0–2.8 GPa. It is worth noting that the range of the experimental data in ref ( 8 ) only includes 0–2.5 GPa, and therefore the theoretical range of detection for N = 20 is only theoretically derived from eq 1 . In the present case, the sensitivity can be defined as (ΔTMR/TMR 0 )/ ΔP , where ΔTMR is the change in TMR, TMR 0 is the TMR under no pressure, and ΔP is the change in pressure.…”

“…Let us now turn to the pressure effect. According to ref ( 8 ), when N ≥ 5, the band gap of black phosphorus will decrease monotonically with pressure in the range of 0 GPa to 1 GPa, and the change is a few tens of meV/GPa. Considering the case that when the MTJs are without pressure, v ( K h ) is slightly larger than Δ – μ, and then a pressure is applied to the MTJs.…”

“… 1 , 3 , 5 , 7 On the other hand, quite recently, S. Huang et al investigated experimentally the pressure effect on the electronic structure of black phosphorus. 8 They found that the relative changes in band gap versus pressure depend on the number of layers of black phosphorus, which can be expressed as follows: where P is the magnitude of the pressure, N is the number of the layers, a is the changing rate, γ 0 is the difference of overlapping integrals for the conduction band and valence band under 0 GPa, and P coh is the cohesive pressure. In ref ( 8 ), both the experiments and the derivation of eq 1 are irrelevant to the substrate.…”

“… 8 They found that the relative changes in band gap versus pressure depend on the number of layers of black phosphorus, which can be expressed as follows: where P is the magnitude of the pressure, N is the number of the layers, a is the changing rate, γ 0 is the difference of overlapping integrals for the conduction band and valence band under 0 GPa, and P coh is the cohesive pressure. In ref ( 8 ), both the experiments and the derivation of eq 1 are irrelevant to the substrate. That is, eq 1 represents the physical properties of black phosphorus alone.…”