Two-dimensional (2D) materials display unique properties that could be useful for many applications ranging from electronics and optoelectronics to catalysis and energy storage. Entropically necessary defects are inevitably present in 2D materials in the form of vacancies and grain boundaries. Additional defects, such as dopants, may be intentionally introduced to tune the electronic structure of 2D materials. While defects are often perceived as performance limiters, the presence of defects and dopants in 2D materials results in new electronic states to endow unique functionalities that are otherwise not possible in the bulk. In this chapter, we review defect-induced phenomena in 2D materials with some examples demonstrating the relevance of defects in electronic and energy applications. In particular, we present how the (i) N-dopant configuration in graphene changes the electron-phonon interactions, (ii) zigzag defects and edges in graphene increase the quantum capacitance to improve energy density of graphene-based supercapacitors, and (iii) charged grain boundaries in exfoliated Bi2Te3 preferentially scatter low-energy electrons and holes to enhance the thermoelectric performance.
- Engineering defects
- 2D materials
- Quantum capacitance
- Energy storage
Two-dimensional (2D) materials have intrigued physicists and material scientists for many decades due to an abundance of unusual physical phenomena that result from the confinement of charge, heat, and entropy flow to a plane . For example, the ingenious harness of quantum mechanical phenomena, particular to lower dimensionality in graphene, has resulted in intriguing observations such as the quantum Hall effect at room temperatures, quantized optical transmittance, nonlocal hot carrier transport, and Klein tunneling [2, 3]. Despite such fundamental breakthroughs, the potential of 2D materials has not yet completely manifested into practical devices due to material limitations [1, 4]. For instance, the lack of a band gap resulted in serious limitations for using graphene in electronics . Defects in material science and engineering are often perceived as performance limiters, but in the case of 2D materials, defect engineering could provide a way to overcome many roadblocks and forge new frontiers. In this regard, others and we have shown that defects in 2D materials (e.g., dopants, vacancies) can provide an excellent handle to control material properties [5–8]. Specifically, we have shown that defects such as vacancies and N dopants in graphene could be used to control the electron-electron and electron-phonon scattering pathways . These results provided critical breakthroughs for improving the quantum capacitance of graphene and doping graphene without compromising its intrinsic characteristics . Defects also play a vital role in improving the properties of the so-called “beyond graphene” 2D materials. Previously, we used spark plasma sintering (SPS) to introduce charged grain boundaries (GB) in 2D Bi2Te3 for improving its thermoelectric (TE) figure of merit and compatibility factor . Similarly, it has been demonstrated that defect engineering in 2D materials could improve many qualities ranging from electronic levels, conductivity, magnetism, and optics to structural mobility of dislocations and catalytic activities [9, 10]. As discussed in this chapter, defect engineering in 2D materials leads to the discovery of potentially exotic properties, which can enable unprecedented technological applications. In particular, we present how dopants and defects in (i) graphene could be used for optical and electrochemical energy storage applications and (ii) 2D Bi2Te3 could be controlled for enhancing its thermoelectric efficiency.
2. Nitrogen dopants for tuning the electronic and optical properties of graphene
Graphene is an ideal platform for many optoelectronic devices due to its distinctive combination of high electron mobility (μ), optical transparency, and gate/dopant-tunable carrier density . However, to truly harness the potential of this combination and make graphene-based efficient optoelectronic devices a reality, optical and electronic properties of graphene must be tuned via substitutional doping . While doping graphene with boron (B) or nitrogen (N) can tune the Fermi energy (
The electronic and optical properties of a single-layer graphene (SLG) can be described in terms of massless Dirac fermions with linear dispersion near the Fermi energy (Figure 1b). The semimetallic nature and electronic band structure of SLG allow for the photogeneration of electron-hole pairs at any wavelength in the visible-light spectrum . This property is critical for many wide-bandwidth optoelectronic applications. As shown in Figure 1b, incident light excites electrons from the valence band (orange) into the conduction band (purple). Shortly after photoexcitation, incident photon-electron interactions create an out-of-equilibrium electron distribution (purple in Figure 1c), which initially relaxes on an ultrafast timescale (τ1 ~ 100–300 fs) to a hot Fermi-Dirac distribution and subsequently cools via phonon emission or defect scattering (τ2 ~ 1–2 ps) in graphene [8, 18]. In optoelectronic devices, when photoexcited electrons are scattered by phonons or defects, energy transferred to the lattice is dissipated as heat decreasing the net energy transported through charge carriers to drive a circuit. In the current scenario of graphene optoelectronic devices, a critical challenge is to increase the net charge carrier density and quench electron-defect relaxation pathways to extend photogenerated carrier lifetime.
The influence of defects on photogenerated carriers could be accounted by the inclusion of an extra term (A) in the expression for carrier scattering rate τ−1 (N) = A + BN + CN2, where A represents nonradiative recombination, usually due to defects or traps, B represents radiative recombination, N is the carrier density, and C represents Auger recombination. The photogenerated carriers are quickly cooled to ground state through scattering by defects (represented by A) in addition to the existing carrier-carrier and carrier-phonon scattering (term B) and Auger recombination (term C). In the context of optoelectronic applications, it is imperative to identify ideal dopant concentration and configuration in graphene for which A in the carrier scattering rate equation is minimized. As mentioned earlier, heteroatomic doping can tune
2.1. CVD synthesis of N-graphene
Previously, we employed atmospheric pressure chemical vapor deposition (CVD) method for growing N-graphene . This CVD set up consisted of a Cu foil loaded inside a 1 in. quartz tube at a temperature of 1,000 °C. Methane gas was used as the carbon source for graphene growth, while acetonitrile (AN) and benzylamine (BA) were used as precursors for N dopants in varying concentrations. The reaction was carried out under inert atmosphere by passing a mixture of Ar and H2 through the quartz tube reaction chamber. In particular, 450 sccm of Ar and 50 sccm of H2 were used, and 2 sccm of methane was bubbled through the mixture of BA and AN. The volume percent of BA and AN varied in the ratio of 0:1, 1:1, and 3:1. Accordingly, the obtained samples were labeled S1, S2, and S3, respectively. Interestingly, we found that the N-dopant configuration (viz., graphitic, pyrrolic, and pyridinic) could be controlled using the ratio of BA to AN precursors.
2.2. The effects of N dopants in graphene: X-ray and Raman spectroscopy
We observed a strong correlation between the N-dopant configuration and the accompanying vibrational properties of N-doped CVD graphene: the N atoms bonded in the non-graphitic configurations (pyridinic and pyrrolic, observed using X-ray photoelectron spectroscopy or XPS) resulted in intense Raman disorder bands unlike the N atoms bonded in the graphitic configuration, even though the concentration of N dopants was higher in the latter case .
As shown in Figure 3a, we identified XPS peaks corresponding to graphitic, pyrrolic, and pyridinic configurations . For pyridinic configuration, the N1s peak positions reported in the literature are usually in the range 398.1–399.3 eV. Similarly, pyrrolic configuration gives rise to peaks in the range 399.8–401.2 eV, while the peak around 400.5 eV (blue colored) is associated with the graphitic configuration. The orange-colored peak at ~401.5 and 406 eV may be attributed to different nitrogenated adsorbents [20, 21]. XPS results confirmed that the atomic percentages of nitrogen in S1, S2, and S3 were 0.2, 2.5, and 3.8 %, respectively . It is important to note that S1 and S3 showed more non-graphitic N dopants compared to S2, which was purely graphitic doping. In order to further understand the effect of various nitrogen-doping configurations and concentrations on the electronic structure of graphene, we performed Raman spectroscopy of the samples S1, S2, and S3. The Raman spectrum of graphene displays four important bands [22, 23]: (i) the disorder or D band appears ~1350 cm−1 due to the presence of defects such as edges, grain boundaries, or any other type of defects including dopants in the graphene lattice; (ii) in some studies, researchers have also reported the presence of D′-band ~1600–1625 cm−1 in the Raman spectrum of highly disordered graphene ; (iii) the graphitic G band ~ 1585 cm−1 arises due to doubly degenerate optical phonon modes at the Brillouin zone center. It is a first-order Raman scattering process, and (iv) the 2D band ~ 2700 cm−1 is a consequence of second-order Raman scattering process involving intervalley scattering of in-plane transverse optical (
As seen in Figure 3b, the Raman spectra of pristine graphene samples did not exhibit strong D band in our studies. While samples S1 and S3, which contain non-graphitic doping configuration of nitrogen, showed strong D bands, the D band in sample S2 (graphitic) is similar to that in pristine sample despite higher dopant concentration (~2.5 %). These results are consistent with our observations in the XPS spectra shown in Figure 3a. When nitrogen atoms enter the graphene lattice in non-graphitic configuration, vacancies are needed and result in armchair-type edges. Previous reports showed that armchair edges in graphene allow intervalley scattering of
From the line-shape analysis of Raman 2D band (Figure 3c), we confirmed that our CVD-grown graphene samples are predominantly bilayers. As seen in Figure 3c, maximum downshift in 2D band (25 cm−1) was observed for sample S3 with relatively large dopant percentage (~3.5 %). On the other hand, sample S2 (graphitic configuration) showed little downshift in 2D band compared to sample S1 in spite of having higher dopant concentration. 2D band in S1 showed a downshift of ~10–15 cm−1 even in the presence of low dopant concentrations (~0.2 %). These differences in the 2D band shift in the Raman spectra can also be attributed to the nature of the dopant environment. For example, in samples S1 and S3 that are non-graphitic in nature, due to lattice symmetry breaking, electronic structure of graphene is strongly perturbed leading to possible renormalization of electron and phonon energies. Such a renormalization in electron energies results in a concomitant downshift in phonon energies of 2D band .
2.3. Nonlinear optical studies of N-graphene
We further explored the influence of defects on the carrier scattering rate using pump-probe (PP) spectroscopy . The differential transmittance (Δ
3. Defects in graphene for energy storage
The increasing global energy demands have spurred a rigorous search for new renewable energy sources. In recent times, fuel cells, photovoltaic devices/solar cells, and various other renewable energy sources have received much attention and are all promising candidates for clean energy production. However, today’s batteries and capacitors, which are the main components for energy storage, cannot meet the world’s demand for combined power and energy densities [24–27]. As an example, the plot in Figure 5 shows the general performance metrics for commercially available formats of charge/energy storage devices. This plot depicts
Nanocarbons including carbon nanotubes and graphene have been widely used as an electrode in EDLCs due to their high surface area (~2000 m2/g), modest electrical conductivity, electrochemical stability, and open porosity [25, 27]. However, the performance of the carbon-based EDLCs (particularly, graphene) is fundamentally limited by the so-called quantum capacitance (Cq), which is defined as Cq = e2DOS(EF) with
As shown in Figure 6, we found that the D band in the Raman spectrum of graphene increased with increasing power of plasma etching due to the introduction of new structural defects such as pores, which contain both armchair and zigzag edges. An important attribute of zigzag defects is that they may be electrically active and could contribute to an enhanced DOS much more than the armchair-type edge defects (which contribute less due to the two constituent carbon atoms belonging to different sublattices). We observed that the increase in plasma power resulted in a high device capacitance due to higher Cq arising from defect-induced DOS (EF). Indeed, we used cyclic voltammetry to quantify the changes in Cq and Cmeas (Figure 5b). The more than doubling of the Cmeas from 1.9 μF/cm2 (for the pristine sample) to 4.7 μF/cm2 (for the sample subject to 20 W plasma) is remarkable and suggests a novel means of substantially enhancing capacitance through defects. However, at higher plasma power (>20 W), high defect concentration results in poor electrical conductivity leading to a drop in Cmeas suggesting the importance of defect concentration in determining 2D material properties.
Thus, as evidenced by our data in graphene, the presence of defects does not necessarily deteriorate the material performance. Though there is only one way for a given material to be defect-free, there are many possibilities for it to be imperfect. While defect configuration is important in determining the mobility through carrier scattering rate, controlling defect concentration is critical for electrochemical applications. Accordingly, future efforts must be focused on finding new approaches to identify and control the right defect configurations (e.g., N in graphitic configuration to increase carrier concentration without compromising carrier scattering rates or mobility) and concentrations, which could improve material properties instead of dismissing all defects as detrimental for carrier mobility.
4. Defects in 2D bulk materials for thermoelectric power generation
Thermoelectric (TE) materials have the potential to reduce global energy crisis and global warming effects by converting waste heat to electricity. As of 2005, the world energy usage was ~15 terawatts of energy, of which ~90 % was first converted to heat and the remainder ~10 % of energy was utilized . In general, power plants and the transportation industry are the two main sources of heat energy losses that contribute to global warming. In recent years, prototype car models developed by automobile industries BMW and Ford have successfully transformed the waste heat from car exhausts to electricity using thermoelectric power generators, thus improving the fuel efficiency [24, 34].
A basic thermoelectric energy conversion module consists of
4.1. Quantum confinement effects in 2D thermoelectric materials
In the early 1990s, Hicks et al.  predicted intriguing changes in transport properties upon lowering the dimensionality of existing bulk materials (e.g., from 3D to 2D) that were not observed in the corresponding bulk materials. A dramatic increase in the density of states (DOS) of low-dimensional materials was predicted that could increase the Seebeck coefficient and potentially decouple the electronic transport properties. Moreover, the presence of numerous interfaces in low-dimensional materials also increased phonon scattering effects that reduced the lattice thermal conductivity, thus introducing opportunities to independently vary all the parameters constituting the
Nevertheless, it is challenging to fabricate low-dimensional materials for commercial thermoelectric applications and devices, which must be a cost-effective and facile process. In addition, the nanostructured thermoelectric materials have to be thermodynamically stable to retain the desired 2D properties over time, to make the devices reliable and long lasting. To be able to make use of the advantages of low-dimensional materials as well as robustness of the bulk materials, bulk nanomaterials or nanocomposites have been used to enhance the thermoelectric performance of existing thermoelectric materials such as SiGe and PbTe [40, 41].
Controlling the multi-scale microstructures via defect engineering and consequently the length scales of the electrical and thermal transport is essential for enhancing TE performance. However, material properties (thermopower, electrical, and thermal conductivity) dictating the ultimate compatibility factor and
4.2. Impact of charged grain boundaries in few-layered Bi2Te3
Discovered in the early 1950s by Goldsmid , Bi2Te3 is one of the most used and commercialized TE materials for room-temperature power generation and refrigeration applications . The first TE refrigerator was designed using the
Recently, Puneet et al.  utilized a novel technique of chemical exfoliation followed by spark plasma sintering (CE-SPS) in the
The bulk bismuth telluride (Bi2Te3) exhibits a rhombohedral crystal structure belonging to the space group R m(D5), which is more commonly represented by a hexagonal crystal structure as shown in Figure 7a. The hexagonal unit cell of Bi2Te3 is composed of three quintuples with lattice constants
The nanostructuring of the commercial
The rapid densification technique by SPS has distinct advantages over other types of sintering techniques, such as the hot pressing. The SPS process is capable of sintering material powders within a very short time, in the order of minutes [49, 50]. As a result, it is possible to retain the metastable micro-/nanostructures of materials by limiting their grain growth and excessive diffusion during the sintering process. Furthermore, unlike other sintering techniques like hot pressing which uses furnace heating, only the graphite cylinder, rods, and sample are heated by the joule heating produced by pulsed dc in the SPS, which leads to even shorter processing times.
Contrary to the general understanding that defects in a crystal lattice are detrimental to the transport properties of materials, the defects in 2D materials are extremely useful and could be manipulated to generate controlled defects for novel and innovative applications. As observed in the few-layered bulk Bi2Te3, the localized positive charges in the grain boundaries introduced extra electrons in the material, thereby increasing the carrier concentration
In summary, the CE-SPS processing of 2D Bi2Te3 leads to preferential scattering of electrons at charged grain boundaries and optimizes the band filling, thereby increasing the electrical conductivity despite the presence of numerous grain boundaries, and mitigates the bipolar effect via band occupancy optimization leading to an upshift in
As exemplified by graphene and Bi2Te3, the presence of defects and dopants imparts the host material with new micro/quantum states or energy configurations that can strongly influence optical, electronic, and thermal properties. In addition to the above properties, S and F dopants are being explored to make graphene magnetic [10, 52–55], while N dopants are expected to provide much higher enhancements in quantum capacitance without compromising electrical conductivity . Similar to Bi2Te3, defects in other layered systems such as SnSe and TaSe2 could be engineered to achieve better thermoelectric performance [56–62]. Although this chapter presented only some examples of defects in 2D materials, the same concepts also hold true for other 2D materials such as MoS2, WS2, and BN. Indeed, some properties (e.g., luminescence and catalytic activity) of these materials can be tuned using defects [63–68]. As the design and development of new 2D materials are costly, complex, and limited due to the relatively poor air stability of many materials (e.g., silicene and phosphorene), the realization of desired properties and functionalities through control of defects (e.g., vacancies, dopants) in 2D materials is necessary. Though there is only one way for a given material to be defect-free, there are many possibilities for materials to be imperfect. The global scientific endeavors on understanding defects, such as the efforts presented in this chapter, provide a glimpse of the enormous potential of defects warranting further interdisciplinary research efforts.