Electron-Beam-Induced Charge Injection

• Electron-beam-induced charge injection is a process where incident electrons deposit and trap charge in insulators like hBN, generating localized electric fields.
• Experimental validation via SEM imaging, Raman spectroscopy, and space-charge profiling confirms controlled twist actuation and mobility modulation.
• This technique offers a contactless, tunable method for manipulating twist in van der Waals heterostructures and studying nonlinear charge dynamics in polymers.

Electron-beam-induced charge injection denotes the deposition or generation of charge by an incident electron beam, followed by trapping, transport, screening, or collection. In the literature considered here, it includes net negative charging of an insulating hexagonal boron nitride (hBN) flake on a grounded graphene layer, the formation of a broad negative charge packet in linear low-density polyethylene (LLDPE), and electron-beam-induced current (EBIC) regimes in which charge accumulation and field screening become non-negligible. A proof-of-concept demonstration in van der Waals heterostructures established that local charging of hBN under a $5\,\mathrm{keV}$ scanning electron microscopy (SEM) beam can create an interfacial electric field, generate in-plane electrostatic torque, and induce angular displacement, thereby enabling contactless manipulation of interlayer twist (Curreli et al., 2 Oct 2025).

1. Phenomenology and operating regimes

In insulating media, electron-beam-induced charge injection begins with primary electrons entering the target, losing energy, and generating secondary electrons (SE) and back-scattered electrons (BSE). For hBN irradiated with a $5\,\mathrm{keV}$ SEM beam at beam current $I<100\,\mathrm{pA}$ over a $\simeq 50\times 50\,\mu\mathrm{m}^2$ region, each primary electron penetrates only a few nanometres into hBN before coming to rest. The net charging rate depends on the secondary-electron yield $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$; for hBN at $V=5\,\mathrm{keV}$, $\delta_{\mathrm{SE}}\lesssim 1$, so more electrons are absorbed than emitted and negative charge accumulates. The wide bandgap of hBN ($\sim 6\,\mathrm{eV}$), its low intrinsic conductivity ($$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$), and its dielectric environment ($\epsilon_{\mathrm{hBN}}\approx 3$–$5\,\mathrm{keV}$0) allow a quasi-static surface charge density $5\,\mathrm{keV}$1 and a spatially inhomogeneous potential profile $5\,\mathrm{keV}$2 to build up on dwell-time scales of order $5\,\mathrm{keV}$3 (Curreli et al., 2 Oct 2025).

A related but distinct regime appears in polymer dielectrics. In the LLDPE/PVF multilayer designed for space-charge studies, high-energy electrons penetrate to a mean depth $5\,\mathrm{keV}$4 at $5\,\mathrm{keV}$5, deposit negative charge there, and form a broad “packet.” The blocking polyvinyl fluoride (PVF) films suppress charge injection from the aluminum electrodes under DC bias, so that only electrons delivered by the e-beam form the space-charge packet. This architecture isolates beam-induced charge transport from electrode-injection effects and makes the subsequent migration dynamics experimentally accessible (Zhao et al., 2018).

These cases differ from classical EBIC operation, in which the beam generates electron-hole pairs inside a semiconductor junction. In that setting, the electron beam is not primarily used to trap static charge in an insulator; rather, it excites carriers whose extraction, recombination, and screening determine the measured current. Haney et al. showed that sufficiently intense excitation can nonetheless drive EBIC into a nonlinear high-injection regime in which excess carriers accumulate and screen the built-in field (Haney et al., 2014).

2. Charge deposition, trapping, and electrostatics

For hBN, the injected charge density can be formalized through a beam-voltage-dependent charge-injection efficiency $5\,\mathrm{keV}$6. At each point $5\,\mathrm{keV}$7, the incremental charge per unit area delivered in a small time $5\,\mathrm{keV}$8 is $5\,\mathrm{keV}$9, and integration over the exposure time $I<100\,\mathrm{pA}$0 yields

$I<100\,\mathrm{pA}$1

Here $I<100\,\mathrm{pA}$2 is the local beam current density in $I<100\,\mathrm{pA}$3, while $I<100\,\mathrm{pA}$4 encapsulates primary-electron penetration depth and secondary-yield physics. With a focused $I<100\,\mathrm{pA}$5 aperture over a $I<100\,\mathrm{pA}$6 scan and $I<100\,\mathrm{pA}$7, the delivered dose is of order $I<100\,\mathrm{pA}$8–$I<100\,\mathrm{pA}$9 per second, corresponding to energy densities of $\simeq 50\times 50\,\mu\mathrm{m}^2$0–$\simeq 50\times 50\,\mu\mathrm{m}^2$1, stated to be well below damage thresholds for hBN/graphene (Curreli et al., 2 Oct 2025).

Once charges are trapped on the hBN, the electrostatic potential in the heterostructure obeys Poisson’s equation,

$\simeq 50\times 50\,\mu\mathrm{m}^2$2

with boundary conditions

$\simeq 50\times 50\,\mu\mathrm{m}^2$3

for the grounded graphene layer and

$\simeq 50\times 50\,\mu\mathrm{m}^2$4

for the jump in displacement at the charged hBN surface $\simeq 50\times 50\,\mu\mathrm{m}^2$5, where $\simeq 50\times 50\,\mu\mathrm{m}^2$6 is the hBN thickness. In the parallel-plate approximation, the perpendicular field just above the graphene is

$\simeq 50\times 50\,\mu\mathrm{m}^2$7

The central electrostatic feature is therefore not merely charge deposition, but charge deposition under a specific boundary condition: the insulating layer is locally charged while the graphene beneath is electrically grounded, producing a well-defined interfacial field (Curreli et al., 2 Oct 2025).

The LLDPE packet experiments use an analogous electrostatic reconstruction at the transport stage. After e-beam charging, the local field at the packet front is obtained by integrating Poisson’s equation through the measured $\simeq 50\times 50\,\mu\mathrm{m}^2$8:

$\simeq 50\times 50\,\mu\mathrm{m}^2$9

This makes the packet-front mobility experimentally accessible through $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$0 and $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$1. The common element across hBN and polyethylene is that electron-beam injection establishes a non-equilibrium charge distribution whose subsequent behavior is governed by dielectric trapping and Poisson-consistent internal fields (Zhao et al., 2018).

3. From trapped charge to in-plane actuation

In the van der Waals actuator, the trapped charge produces not only a vertical field but also, because $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$2 need not be azimuthally uniform, a lateral field component $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$3. The electrostatic energy of the hBN-on-graphene two-plate capacitor can be written as

$$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$4

where $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$5 is the average potential difference induced across the hBN and $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$6 is the mutual capacitance between the twisted layers. The in-plane electrostatic torque about the $$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$7-axis follows from

$$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$8

In a refined treatment,

$$\delta_{\mathrm{SE}}(V)\equiv(\text{number of SE})/(\text{number of primary }e^-)$$9

which reflects the hexagonal symmetry of graphene/hBN and yields a sinusoidal torque that drives the rotor toward commensurate minima of the moiré energy landscape (Curreli et al., 2 Oct 2025).

This mechanism makes the electron beam an actuator rather than only a probe. Existing twist-control methods are described as often relying on mechanical contact, complex architectures, or extreme operating conditions. By contrast, the reported method uses local electron-beam-induced charge injection into the insulating hBN flake while the graphene layer below is grounded. The resulting interfacial field generates the in-plane torque without mechanical contact. A plausible implication is that the essential control variable is not simply deposited charge magnitude, but the spatial asymmetry of the trapped charge pattern, because that asymmetry determines the lateral component of the electrostatic field and hence the angular response (Curreli et al., 2 Oct 2025).

4. Experimental validation and metrology

The induced rotation was validated by in-situ SEM and by twist-dependent Raman spectroscopy. Under continuous $V=5\,\mathrm{keV}$0, $V=5\,\mathrm{keV}$1 irradiation, SEM imaging revealed irreversible rotations of hBN flakes by $V=5\,\mathrm{keV}$2–$V=5\,\mathrm{keV}$3 in six devices, with three clockwise and three counterclockwise rotations. The reported sense of rotation was in precise correlation with which graphene pads were grounded and biased. A Python-based image-registration method based on mean-squared-error minimization over a gold-marker region of interest returned $V=5\,\mathrm{keV}$4 for sample S1 and $V=5\,\mathrm{keV}$5 for S2, with $V=5\,\mathrm{keV}$6 uncertainty (Curreli et al., 2 Oct 2025).

Raman spectroscopy provided an independent twist-sensitive signature in the graphene $V=5\,\mathrm{keV}$7 band, but only in the graphene/hBN overlap region. One reported example changed from $V=5\,\mathrm{keV}$8 and $V=5\,\mathrm{keV}$9 before actuation to $\delta_{\mathrm{SE}}\lesssim 1$0 and $\delta_{\mathrm{SE}}\lesssim 1$1 after a $\delta_{\mathrm{SE}}\lesssim 1$2 counterclockwise rotation, with $\delta_{\mathrm{SE}}\lesssim 1$3. Using the empirical relation attributed to Eckmann et al. (2013),

$\delta_{\mathrm{SE}}\lesssim 1$4

with $\delta_{\mathrm{SE}}\lesssim 1$5 in nm, the post-actuation state implies $\delta_{\mathrm{SE}}\lesssim 1$6, which is stated to be consistent with the SEM-measured $\delta_{\mathrm{SE}}\lesssim 1$7. By contrast, bare-graphene regions with no hBN showed no significant $\delta_{\mathrm{SE}}\lesssim 1$8 or peak-position shifts (Curreli et al., 2 Oct 2025).

The polyethylene work illustrates a different validation chain. There, a Q-switched Nd:YAG laser at $\delta_{\mathrm{SE}}\lesssim 1$9, $\sim 6\,\mathrm{eV}$0 pulse width, and $\sim 6\,\mathrm{eV}$1 energy was used in Laser Induced Pressure Propagation (LIPP) to recover the spatial charge distribution $\sim 6\,\mathrm{eV}$2 after e-beam charging. Tracking the leading edge of the negative packet yielded $\sim 6\,\mathrm{eV}$3 and therefore the packet-front velocity and mobility. This methodology is not a twist metrology, but it demonstrates that electron-beam-induced charge injection can be validated either by structural observables such as SEM/Raman or by direct space-charge profiling (Zhao et al., 2018).

5. Relation to EBIC, recombination, and screening

Electron-beam-induced charge injection is often conflated with EBIC, but the two are not identical. EBIC is a current-measurement technique in which a focused electron beam generates electron-hole pairs inside a device, and the measured current reflects charge collection. In the linear regime, current is proportional to the generation rate. In the high-injection regime analyzed by Haney et al., however, the total pair-generation rate $\sim 6\,\mathrm{eV}$4 can exceed the rate at which carriers are extracted, so excess carriers accumulate, screen the internal field over a region of size $\sim 6\,\mathrm{eV}$5 or $\sim 6\,\mathrm{eV}$6, and drive the device into a nonlinear regime. The onset criterion is

$\sim 6\,\mathrm{eV}$7

The corresponding critical generation rates were given as

$\sim 6\,\mathrm{eV}$8

$\sim 6\,\mathrm{eV}$9

and

$$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$0

These expressions make explicit that beam-induced carrier accumulation can become a dominant electrostatic effect rather than a small perturbation (Haney et al., 2014).

A complementary EBIC model applies when recombination within the depletion region is substantial. In that formulation, the local collection efficiency in a uniform-field toy model is

$$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$1

with

$$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$2

and, locally,

$$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$3

The reduced collection efficiency in CdS-CdTe EBIC was reproduced only if the mobility-lifetime product $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$4 is spatially varying within the depletion region, and that reduction was speculated to be related to high-injection effects and increased radiative recombination. This places EBIC within the broader field of electron-beam-induced charge phenomena, but in a diagnostic rather than actuation-oriented role (Haney et al., 2014).

The misconception to avoid is therefore terminological: electron-beam-induced charge injection may refer to trapped surface charge in an insulator, a mobile space-charge packet in a dielectric, or a beam-generated carrier population whose collection is measured as EBIC. The unifying feature is beam-driven non-equilibrium charge creation; the physical observable is system-dependent.

6. Transport behavior, current limitations, and prospective devices

In polymer dielectrics, the injected charge packet can be driven by an applied field and used to extract field-dependent mobility. After charging the multilayer LLDPE sample at $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$5, $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$6, and $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$7 in vacuum $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$8, a DC field in the range $$\sigma_{\mathrm{hBN}}\lesssim 10^{-12}\,\mathrm{S/m}$$9–$\epsilon_{\mathrm{hBN}}\approx 3$0 was applied. Using the packet front as the reference point, the observed average mobility ranged from $\epsilon_{\mathrm{hBN}}\approx 3$1 to $\epsilon_{\mathrm{hBN}}\approx 3$2 under calibration local field. The measured $\epsilon_{\mathrm{hBN}}\approx 3$3 rose with field up to a peak $\epsilon_{\mathrm{hBN}}\approx 3$4 at $\epsilon_{\mathrm{hBN}}\approx 3$5 and then fell to $\epsilon_{\mathrm{hBN}}\approx 3$6 beyond $\epsilon_{\mathrm{hBN}}\approx 3$7, which was interpreted as clear negative differential mobility consistent with a Gunn-effect-like model (Zhao et al., 2018).

In the hBN/graphene twist actuator, the current limitations are different. The induced rotations are at present irreversible because the system settles into the nearest local minimum of the moiré energy landscape, with interlayer friction and elastic relaxation pinning the flake. Angular precision is limited by the stochastic evolution of the asymmetric charge pattern under beam scanning, with spatial resolution $\epsilon_{\mathrm{hBN}}\approx 3$8. The maximum achievable $\epsilon_{\mathrm{hBN}}\approx 3$9 appears capped at a few degrees unless the stator is subdivided into multiple independently biased segments to tailor $5\,\mathrm{keV}$00 more finely. These constraints indicate that the present implementation is a proof of concept rather than a fully programmable twist platform (Curreli et al., 2 Oct 2025).

The same work also identifies an integrated route beyond SEM actuation. By patterning via-hole contacts to the graphene stator and a top metal collector on hBN, fast voltage pulses $5\,\mathrm{keV}$01 could in principle replace the stationary SEM beam and enable on-chip, reversible twist control. The stated prospects are reconfigurable moiré devices for dynamic tuning of correlated-electron phases, strain-engineered optoelectronic functionalities, and programmable nanoelectromechanical systems that exploit twist as an active degree of freedom. This suggests that electron-beam-induced charge injection currently serves both as a physical mechanism and as a prototyping method for electrostatic architectures in which twist, space charge, or screening is the operative variable (Curreli et al., 2 Oct 2025).