Modulation of graphene field effect by heavy charged particle irradiation

Graphene's sensitivity to changes in the local electric field makes it a promising material for implementation in a variety of sensor architectures.^1–3 It has been demonstrated that the unique properties of graphene can be used to develop graphene-based sensors to detect molecules, including those relevant for biochemical processes,^4–9 low-energy electromagnetic radiation,^10–16 and ionizing radiation, such as electrons, X rays, and gamma rays.^17–22 

Graphene can be used as a direct or indirect sensor. Direct sensing relies on the direct interaction of radiation, atoms, or compounds with the graphene, for example, by absorption,^23–28 or with a material immediately adjacent to graphene, such as a quantum dot or a nanomaterial layer deposited on graphene.^29–33 In these architectures, graphene current is modulated by the excitation of electrons within graphene or in the nanomaterial immediately adjacent to graphene.^34–36 In contrast, indirect sensing relies on the interaction of penetrating radiation with an underlying semiconducting substrate. In this approach, graphene is placed on a back-gated undoped semiconductor substrate in a graphene field effect transistor (GFET), as shown in Fig. 1(a). The energy deposited by the radiation modifies the conductivity of the substrate by production of electron-hole pairs, which are then transported within the substrate. The modification of substrate conductivity modulates the graphene current via the field effect principle, whereby the measured graphene current is sensitive to changes in the local electric field.^37–39 

Graphene-based devices have been used to sense photons, molecules, and high fluxes of charged particles by observing the graphene properties change due to its damage.^17,40–44 However, the interaction of heavy charged particles with the GFET at relatively low particle fluxes (on the order of 10³ cm⁻² s⁻¹ and lower) and high energies (on the order of MeV) has not been studied to date. Here, we investigate the effect of alpha (α) particle irradiation on the electrical response of a GFET. We first examine the graphene current response to α particle exposure at positive and negative gate polarities for two different radioactive sources. Next, we reveal the discrete step-like response of graphene, attributed to single α particle interaction, particularly for the negative gate polarity. Finally, we employ a simple electronic device model and Monte Carlo simulation to support the conclusions made from experimental measurements.

In a GFET, α particles are detected by measuring the change of the graphene current, I_sd, which occurs when the conductivity of the substrate is modified by ionization from α particle depositions in the substrate. The GFET studied in this work consists of graphene on a back-gated substrate. The dimensions of graphene are 20 × 4 μm² (see supplementary material Section I for additional information on GFET fabrication). The change of substrate conductivity acts to modify the electric field that is present in the vicinity of graphene, as illustrated in Figs. 1(b) and 1(c), before and after a single α particle absorption, respectively. For a change in graphene current to be attributed to α particles and be distinguishable from noise, the magnitude of the field effect must be sufficiently large. The magnitude of the field effect is dependent on the rate of α particle absorption in the substrate, the location of α particle absorption relative to the graphene, and the energy of the α particles.

Time-dependent, I_sd – t, and voltage-dependent, I_sd – V_g, measurements were conducted, which are used to evaluate the GFET response to α particle absorption and survey the field effect characteristics of the GFET. Measurement results with exposure to a ²¹⁰Po source and ²⁴¹Am source are shown in Fig. 2(a). These field effect measurements were taken after stabilization of the field effect or continuous exposure to ²⁴¹Am and ²¹⁰Po sources at V_g = −60 V for 5 min and 3 h, respectively. A greater field effect was observed when the higher activity (²⁴¹Am) α source was used. This is expected due to the greater change of substrate conductivity as the rate of ionization in the substrate is increased. As shown in Fig. 2(b), the difference in field effect characteristics for non-exposure and exposure to the ²¹⁰Po source at V_g = −40 V is measurable; the magnitude of this difference is important in interpretation of single α absorption events. The gate voltage at which all the field effect curves intercept is expected to be V_g = 0 V. Due to a possible combination of the effect of built-up charge in the substrate and doping of graphene by the ambient environment and during fabrication, the intercept gate voltage is shifted to positive V_g, whereby an additional application of electric field is required to induce an effective zero doping in graphene.^45–48 

Time-dependent measurements of graphene current resulted in a greater rate of change of I_sd when GFET was exposed to the higher activity ²⁴¹Am source compared to the lower activity ²¹⁰Po source, as shown in Figs. 3(a) and 3(b). Also, as predicted from the field effect characteristic measurements, I_sd – V_g, a greater rate of change of graphene current is observed for negative gate voltages. The total exposure times of the GFET were 35 min and 11 h for the ²⁴¹Am and the ²¹⁰Po source, respectively.

As shown in Fig. 3(b), during measurements at V_g = −40 V with the ²¹⁰Po source exposure, I_sd exhibits discrete increasing steps. These discrete steps are shown in detail in supplementary material Section V. When the time derivative of the time-dependent current is calculated, the relatively fast and large step changes in I_sd are made more apparent and appear as spikes, as in Fig. 3(d). The discrete steps in I_sd are attributed to individual α particles depositing their energy directly under or near the edge of the graphene, which is corroborated by the following analysis: first, the electric field in the sensitive region of the substrate near graphene is modeled; second, energy deposition spectra of α particles expected in this sensitive region are calculated. The slow recovery of graphene current after α particle exposure is likely due to doping of graphene.

The electric field in the GFET was modeled using the COMSOL Multiphysics framework.⁴⁹ A region of modified conductivity was defined corresponding to energy deposition by a 3-MeV α particle, which is a typical energy deposited in the substrate by α particles from the ²¹⁰Po source, accounting for energy loss in air in our experiment and the source energy spectrum (a range of 1.88 cm is calculated for a 5 MeV α particle slowing to 3 MeV in air). Additional information about the model and related calculations is provided in supplementary material Section III. As shown in Fig. 1(c), when the modified conductivity region is present, the electric field lines are partially diverted toward the region where the α particle deposits its energy and where the conductivity is increased, and then toward graphene. To quantify the effect of this reconfiguration of the electric field near graphene, the average electric field along the width of graphene is plotted as a function of the distance (x) of the modified conductivity region from the center under graphene, x = 0 μm (Fig. 4(c)).

The electric field at graphene maintains an increased magnitude when energy deposition occurs under graphene but drops rapidly at the edge of graphene (x = 2 μm in Fig. 4(c)). The electric field reaches the magnitude equal to that when no modified conductivity region is present at a relatively small distance from the center of graphene, x ≈ 3 μm. These characteristic distances obtained from the two-dimensional model and shown in Fig. 4(c) correspond to the width of graphene in our GFET (2 μm); the model was also applied to the orthogonal dimension (graphene length, 20 μm), obtaining the result that the electric field is increased up to several μm from outside the edge of graphene. Thus, the area over which the GFET is sensitive to ionization extends over the region −3 ≲ x ≲ 3 μm (along graphene width) and −15 ≲ y ≲ 15 μm (along graphene length), or approximately as far as half of the graphene width or length beyond the edge of graphene. We define the highly sensitive region as −2.1 < y < 2.1 μm (along graphene width) and −10.25 < x < 10.25 μm (along graphene length) corresponding to a sensitive area of 20.5 × 4.2 μm². This represents an area within which the electric field is modified by >50% of the difference between the electric field at the center of graphene (x = 0 μm) and the electric field at x = 3 μm, corresponding to no modification of the electric field due to α exposure.

The occurrence of single α particle sensing can be further supported by the analysis of the discrete step changes in I_sd (Figs. 3(b) and 3(d)), the field effect measurements (Fig. 2(b)), and the electric field model (Fig. 4(c)). The change of the electric field due to a single discrete absorption event in experiment can be determined from the change in graphene current and compared to the modeled change in electric field due to single α particle absorption. The change in electric field due to α particle absorption in Fig. 4(c) is ≈1.4 × 10⁶ V/m or ≈24%. At V_g = −40 V, a 24% change of electric field would correspond to a change of back-gate voltage of approximately −10 V. The effect of this change of back-gate voltage on the current through graphene (I_sd) can then be estimated from the independently measured I_sd – V_g characteristic when graphene is exposed to the ²¹⁰Po source (Fig. 2(b)). A linear fit, I_sd = a + bV_g, with fit parameters of a = 1.02 × 10⁵ A and b = −1.367 × 10⁹ A V⁻¹, is obtained from the I_sd – V_g measurement in the range −55 V < V_g < −25 V. Typical large discrete steps of I_sd in Fig. 3(b) can be estimated as ≈1.5 × 10⁻⁸ A. Using the linear fit, a discrete step change of I_sd = 1.5 × 10⁻⁸ A corresponds to a back-gate voltage change ΔV_g ≈ −11 V, which is of the order of the change in V_g predicted from the correlation of the electric field model (Fig. 4(c)) and I_sd – V_g measurement (Fig. 2(b)). This analysis further establishes the correspondence between the electric field model to experimental I_sd – t and I_sd – V_g measurements and supports the conclusion that individual α particle interactions with the GFET are observed.

A Monte Carlo simulation was conducted to calculate the energy deposition spectra of α particles depositing energy under the effective area of graphene (20.5 × 4.2 μm²). Additional information on the Monte Carlo simulation is provided in supplementary material Section IV. The resulting energy deposition spectra for the region under the effective area of graphene for the α sources are shown in Fig. 4(d), and the information on the number of simulated α particles depositing energy under the effective area of graphene is given in Table I (⁠$αte [sim]$⁠). The number of α particles counted in the experiment is obtained from the distribution of the time derivative of the time-dependent graphene current (I_sd – t), shown in Figs. 4(a) and 4(b). The simulation provides an estimate of the rate of α particle incidence onto the effective area of GFET, which can be compared to the rate of discrete steps appearing in I_sd – t measurements. A good agreement is observed between the predicted (simulated) and experimentally measured rate of discrete steps appearing in the I_sd – t measurement for the ²¹⁰Po source at V_g = −40 V. The standard deviations are shown in the histograms of Figs. 4(a) and 4(b). The agreement further supports the hypothesis that the observed discrete steps in I_sd – t when the GFET is exposed to the ²¹⁰Po source are due to individual α particles depositing energy within the effective area of the GFET.

While the discrete steps in I_sd – t are discernible when the ²¹⁰Po source is used, as in Figs. 3(b) and 3(d), this is not the case when the GFET is exposed to the ²⁴¹Am source, as in Fig. 3(a) or 3(c). This is attributed to the difference between the energy spectra of the ²¹⁰Po and ²⁴¹Am sources. As shown by simulation (Fig. 4(d)), the absorbed energy spectrum from the ²⁴¹Am source is weighted to lower energies, while the spectrum for the ²¹⁰Po source is weighted to higher energies. Thus, when the GFET is irradiated by the ²¹⁰Po source, a greater fraction of α particles incident on the GFET have the high energies needed to produce a large, discrete response. In contrast, the greater fraction of lower energy α particles emitted by the ²⁴¹Am source may obscure any discrete steps that occur in I_sd – t measurements. The higher incidence rate of α particles from the ²⁴¹Am source induces a relatively large continuous rate of change in I_sd; however, since the majority of α particles have lower energy, each particle causes only a small change of the substrate conductivity. Large numbers of such small energy depositions incrementally and collectively act to produce a significant change of conductivity. Conversely, the much lower rate of α particle absorption by the substrate when exposed to the ²¹⁰Po source allows for identification of discrete steps, especially as the average energy deposited by an α particle from the ²¹⁰Po source is higher. Discrete steps in I_sd – t measurements are not discernible for either source when positive gate voltage is applied (V_g = +40 V), as in Fig. 3(b). This is believed to be due to the lower field effect response of the GFET for positive gate voltage (V_g = 40 V) compared to negative gate voltage (V_g = −40 V), as also observed in field effect measurements in Fig. 2, especially for the ²⁴¹Am source. The greater sensitivity at negative gate voltage is believed to be due to the greater difference between the measurement voltage at V_g = −40 V and the charge neutrality point at approximately V_g = +20 V (as shown in Fig. 2(a)). Finally, measurements of a “dummy” device exposed to the ²⁴¹Am source, where graphene is replaced with gold, show no response to α particle exposure, as discussed in supplementary material Section VI.

In conclusion, experiments were conducted to develop an understanding of the effect of heavy charged particle irradiation on GFET electrical response. The GFETs consist of CVD graphene on SiC substrates in a back-gated architecture. The graphene field effect and time dependent response to α particle exposure from ²⁴¹Am and ²¹⁰Po radioisotope sources for both positive and negative gate voltages have been studied. For both α particle sources, a greater field effect is measured for negative gate voltages (V_g), which is likely due to doping of the graphene. Time-dependent measurements show cumulative graphene current response to both ²⁴¹Am and ²¹⁰Po sources, with greater current response for the higher activity ²⁴¹Am source. These time-dependent measurements are consistent with field effect measurements.

Of particular interest are the discrete step-like changes in graphene current when exposed to the ²¹⁰Po source at negative gate voltage. These discrete changes of graphene current are attributed to absorption of individual α particles in the area directly under graphene or near the edge of graphene. An analysis was conducted that includes an electric field model and Monte Carlo simulation. The results of the analysis support the single α particle sensitivity hypothesis by predicting the magnitude of change of the electric field at graphene due to single α particle absorption under graphene comparable to that observed in the experiment. The analysis also shows that the predicted number of α particles in simulation is in agreement with the number of discrete changes in graphene current for the ²¹⁰Po source.

Future work should focus on detailed experimental quantification of the dependence of discrete graphene current changes on the energy depositions of single charged particles in a GFET. To accurately perform such experiments, a monoenergetic particle source with ability to control both the particle energy and particle flux is desirable.

The experiments and analyses conducted within this work advance the understanding of charged particle interaction with GFETs and represent a step toward the utilization of graphene-based devices as ionizing radiation sensors operating in the pulse (single event) mode. GFETs could provide benefits of scalability to large sizes while maintaining low-power operation. In addition to the established sensing of electromagnetic radiation, GFETs show promise as heavy charged particle detectors for a variety of scientific and engineering applications.

See supplementary material for more detail on the GFET fabrication process, calculation of conductivity within the substrate, experimental setup, and electrical measurements. Also discussed are the Monte Carlo simulation method, testing of dummy devices, and the effects of radiation damage on graphene.

This work was funded by the Department of Homeland Security (DHS) and the National Science Foundation (NSF) through the Academic Research Initiative (ARI) (2009-DN-077-ARI036-02) and by the Defense Threat Reduction Agency (DTRA).