The skin effect, defined as the phenomenon of EM radiation penetrating only the near-surface area of the electrical conductor at high frequencies [
42], is influenced by the skin depth (
$\delta$) given by
$\delta =\frac{1}{\sqrt{\pi f\mu \sigma }}$[
43], where
$\sigma$ and
$\mu$ are the electrical conductivity and magnetic permeability of the shield, respectively, and
$f$ is the frequency. For non-magnetic materials with constant thickness, the skin depth is decreased with the increase in frequency [
5], resulting in improved attenuation of total electromagnetic waves (EMWs) beneath the surface of the shielding film. According to Simon’s formula, the EMI SE can be expressed as:
${\text{SE}}=50+10{\text{log}}\left(\sigma /f\right)+1.7t\sqrt{\sigma f}$ [
44,
45], where
f (MHz),
σ (S cm
−1), and
t (cm) are the electrical conductivity, frequency, and sample thickness, respectively. The EMI SE and electrical conductivity exhibit a proportional relationship, indicating that Ag–CNT film with higher electrical conductivity exhibits higher EMI SE (
Fig. 5b). Compared with CNT film (~ 7.7 × 10
4 S m
−1), Ag–CNT film-1 has a comparable electrical conductivity (~ 8.5 × 10
4 S m
−1). With the further increase in Ag content, the electrical conductivity of Ag–CNT film-2 and Ag–CNT film-3 increases to 3.24 × 10
5 and 6.82 × 10
5 S m
−1, respectively. The remarkable electrical properties primarily stem from the high conductivity of both Ag and single CNT, along with the robust tube–tube interactions among CNTs, which substantially facilitate electron transport and improve the electrical conductivity. The experimental results of Ag–CNT film-3 in the frequency range of 3–40 GHz are comparable to the theoretical calculation results based on Simon’s formula, as shown in
Fig. 5c. In addition, the formula predicts high EMI SE values for Ag–CNT film-3 at lower frequencies (Fig. S8a). Measurement of EMI SE of Ag–CNT film-3 at low frequency (30 MHz–1.5 GHz) using a coaxial transmission line method confirmed this prediction, showing similar EMI SE values at high and low frequencies (Fig. S8). As a result, Ag–CNT film maintains excellent EMI shielding capability over an ultra-broadband frequency range. To demonstrate the flexibility of CNT film after embedded with Ag particles, the EMI SE of Ag–CNT film-3 with different bending cycles was measured (
Fig. 5d), and the corresponding SEM images after bending are shown in Fig. S9. The Ag–CNT film-3 exhibits a negligible decay in EMI SE even after bending for 2000 cycles, which can be seen more intuitively by the negligible change in lamp brightness, as illustrated in
Fig. 5d. The EMI SE of Ag–CNT film-3 retains 94% of the original EMI SE, and this excellent flexibility characteristic of Ag–CNT film may be contributed to the strong interaction between Ag and CNT.