The variations on V
fb for encapsulated and bare MOSCAPs are positively shifted with the increase of bending deformations under concave and convex conditions, as mentioned in
Section 4.1. It may be attributed to that the more electrons are injected by increasing mechanical strains but the behavior of fluctuated magnitude of V
fb from planar to bent state is varied with Ø for MOSCAPs w/ and w/o encapsulation. It is significant to compare the V
fb and effective oxide charge (N
eff) in encapsulated and bare MOSCAPs. The V
fb corresponding to C
fb is extracted from C-V curves, C
fb and N
eff are calculated as follows [
20]:
where C
max and C
min are the maximum and minimum capacitance of measured C-V curves, N
A is the acceptor concentration, N
D is the donor concentration, n
i is the intrinsic carrier concentration, ΔV
fb is the theoretical V
fb minus extracted V
fb, q is the electron charge, and A is the gate surface area of MOSCAPs.
Figure 11 summarizes the V
fb and N
eff for encapsulated and bare MOSCAPs with Ø from 160 μm to 320 μm under bending conditions. Compared to the encapsulated devices with Ø 160 μm and Ø 320 μm, the encapsulated MOSCAP of Ø 240 μm presents the most desirable ability to alleviate the instability of V
fb in bare devices. Specifically, the precise variations that V
fb at four bending radii of (-)110.5 mm, (-)85 mm, (+)77.5 mm, and (+)38.5 mm minus V
fb at planar state (i.e., V
fb - V
fb,o), which are extracted as small as 0.005 V, 0.034 V, 0.009 V, and 0.023 V. It manifests that encapsulated MOSCAPs with Ø 240 μm is beneficial to relieve the strain in gate dielectric layer leading to the enhancement of stability on J
g and V
fb. At the planar state, the N
eff in encapsulated MOSCAPs with Ø of 160 μm, 240 μm, and 320 μm is 4.14 × 10
11 cm
-2, 5.74 × 10
11 cm
-2, and 6.99 × 10
11 cm
-2. The N
eff increased to 7.0 × 10
11 cm
-2, 10.61 × 10
11 cm
-2, and 11.38 × 10
11 cm
-2 for bare MOSCAPs with Ø of 160 μm, 240 μm, and 320 μm. However, as the applied bending deformations, the decrease of N
eff is obvious in the bare MOSCAPs, probably because the physical thickness of the gate dielectric layer with larger size is more sensitive to being altered and affected by bending strains without the protection of ultrathin encapsulation layer.
Figure 12 illustrates the C
max divided by C
max at 1 kHz (i.e., normalized C
max (ω)) changed with Ø of 160 μm, 240 μm, and 320 μm in encapsulated and bare MOSCAPs.
Figure 13 illustrates the extracted values of frequency dispersion according to the varied Ø under bending conditions. Notably, the frequency dispersion from Ø 160 μm to Ø 320 μm is 9.19 %/Dec, 7.67 %/Dec, and 8.3 %/Dec at the planar state for bare MOSCAPs, which is relatively large and fluctuating. But the frequency dispersion at the planar state is extremely stable for encapsulated MOSCAPs from Ø 160 μm to Ø 320 μm, which is 6.29 %/Dec, 6.63 %/Dec, and 6.68 %/Dec. Among three types of Ø in encapsulated MOSCAPs, Ø 160 μm maximally maintains stability on frequency dispersion under four bending conditions but the larger areas of Ø 240 μm and Ø 320 μm only performed better under concave bending conditions than convex. The C
max performances for encapsulated MOSCAPs with Ø 320 μm under concave and convex bending deformations are consistent with the properties of the frequency dispersion. While the increased frequency dispersion for encapsulated MOSCAPs with Ø 240 μm denotes the substantial changes in interface states. In addition, compared to Ø 160 μm and Ø 320 μm, the frequency dispersion of bare MOSCAPs with Ø 240 μm is most stable under bending deformations which is due to the robustness of both C
max and interfacial properties. Hence, the results of frequency dispersion denote that the smallest Ø of 160 μm is the favorable choice in the ultrathin encapsulation strategies, but it needs optimizations on the strain insensitivity of both the ultrathin dielectric layer and interface between dielectric and ultrathin channel as Ø increases.