Electronic transport properties of a-Si:H

Hydrogenated amorphous silicon (a-Si:H) is an excellent optical thin-film material. Owing to its efficient light absorption, low cost of fabrication, and ease of large-scale manufacturing, a-Si:H semiconductors are widely used as photovoltaic materials.¹ Much research on this material has been done for more than four decades; the improvement of the material’s stability and efficiency is still required. The efficiency of energy conversion is determined by several factors, among which electronic transport inside the material and in the region of contact with electrodes is the main target of this paper.

Recently, the electronic transport properties of atomic or molecular scale devices have attracted great attention, and various types of devices have been studied experimentally and theoretically.^2–9 Nano-scale devices using Si atoms or Si clusters have been vigorously investigated. For example, Liu et al.^10–12 investigated atomic chains of Si sandwiched between Au electrodes, reporting the influence of coupling morphology, coupling distance, and chain length on the electric conductance of the nanoscale junctions. The chain length effect was also discussed by Mozos et al.,¹³ while the coupling distance and the orientation for Si₄ cluster devices were thoroughly investigated by Dai et al.¹⁴ and an interesting phenomenon of negative differential resistance was found.

To theoretically investigate the electron transport, quantum simulations with the non-equilibrium Green’s function (NEGF) method are widely adopted. For example, Si nanoclusters with Al or Au atomistic contacts were reported,¹⁵ as well as other novel materials, such as Si nanowires,^16,17 Si₆₀ fullerene cage structures,¹⁸ and Si_mC_n/C_n clusters.¹⁹ 

Relatively low attention has been paid to the more conventional material, a-Si:H. The Staebler–Wronski effect is still problematic,^20,21 while the efficiency of energy conversion is governed by many factors, such as complicated band structure, carrier diffusion, and recombination. Although much progress has been done in aspects of structural, electronic, and optical properties of a-Si:H,^22–25 we need further understanding of this material, in particular, at atomistic scales.

In this paper, we describe the electronic transport properties of a-Si:H contacting with metallic electrodes investigated with quantum simulations. The relationship between the structural features reported in our previous analysis²⁴ and the transport properties investigated with the NEGF method is discussed.

For saving the computational resources, we focus on fairly small systems of a-Si:H with various hydrogen content. To obtain stable a-Si:H samples, a given number of silicon atoms in a crystalline silicon (c-Si) with normal density were randomly replaced with hydrogen atoms. The cell size was fixed to be 10.86 × 10.86 × 10.86 ų. The obtained configurations were annealed, or thermally equilibrated, at room temperature using a molecular dynamics (MD) method.

For the annealing, we utilized the DFTB + package,^26,27 which is a quantum simulation software based on the density functional theory (DFT) combined with the tight binding (TB) models. The matsci-0-3 parameter set^28,29 was used. The periodic boundary conditions (BCs) are assumed for all directions. For the electronic calculation part, we adopted the self-consistent charge (SCC) calculations. The time step of the MD simulation was chosen to be 1.0 fs.

Seven samples with different hydrogen concentration were prepared, as shown in Table I. By replacing the silicon atoms with the hydrogen atoms, the Si–Si bonds are broken; a part of the dangling bonds is passivated by the hydrogen atoms, as shown in Fig. 1, but an amount of dangling bonds still remain, as described in Table I. A detailed structural analysis of a-Si:H is described in our previous report.²⁴ 

The electronic transport calculations were performed by using the non-equilibrium Green’s function (NEGF) method with the density functional tight binding (DFTB)^30,31 model, which is also implemented in the DFTB + package.

To perform the NEGF calculation, we sandwiched each a-Si:H sample with two metallic electrodes, as shown in Fig. 2. The system is divided into three regions along the y direction; the source contact (SC) region, the target material (extended device region), and the drain contact (DC). The extended device region consists of previously obtained a-Si:H (64 atoms) and two atomic layers of electrode atoms to mitigate the influence of electrodes.¹⁹ We have chosen two metallic crystals with the fcc structure, copper and aluminum, as the electrodes to investigate how the atomistic contact with the electrodes affects the transport. The size of each electrode is 14.46 × 10.845 × 14.46 ų for copper and 16.2 × 12.15 × 16.2 ų for aluminum. The a-Si:H sample contacts on the (100) surface of electrodes. The distance between the two electrodes is chosen to be 13.5 Å based on our preliminary calculation ( Appendix).

The periodic BCs are assumed for all directions, but a vacuum region of 15 Å is inserted along the y direction to avoid unfavorable interaction between the adjacent images.^19,32 For the NEGF-DFTB calculation, the Dirichlet BC, where a constant electrostatic potential is given at each boundary along the y direction, is set to calculate the electrostatic potential in the system by solving the Poisson equation, and the Ohmic BC is assumed where the electrons are provided on the source and removed from the drain. To evaluate the electronic energy, 5 × 1 × 5 Monkhorst–Pack mesh for the Brillouin zone sampling is used. The electron temperature for the Fermi distribution is set to be 300 K.

Based on the NEGF scheme, we examined the electron transport along the y direction under various external electric field being imposed; we define the field as “positive bias” when the voltage of SC is higher than that of DC. After a self-consistent calculation of electronic states with the DFTB calculation, the transport properties, such as the density matrix, the transmission coefficient, and the electric current, were evaluated with the NEGF method.

Once the transmission coefficient T at an energy level E under an external voltage V_B is obtained, the Landauer formula³³ gives the electronic conductance G as

where G₀ is the quantum unit of conductance, G₀ ≡ 2e²/h (e: elementary charge, h: Planck’s constant).^34,35 The formula has been generalized to give the total electronic current I (Landauer–Büttiker formula^36–38) as

where f_SC and f_DC are the Fermi distribution functions of each electrode at the given temperature, respectively. The difference of the chemical potential μ_SC and μ_DC is related to the bias field,

In most cases where several transmission channels exist, the total transmission coefficient^32,39 is expressed as their sum,

To explore the possible contribution of hydrogen in the electron transport of a-Si:H, we first compare the density of states (DOS) for c-Si (diamond structure), a-Si, and a-Si:H (14%H). As shown in Fig. 3, no states exist in the bandgap for c-Si, while a-Si and a-Si:H have a significant amount of states in the bandgap, suggesting the defect states due to dangling bonds. Addition of hydrogen atoms passivates some of the defects, leading to a slight reduction of the defect states. No clear bandgap edge is seen for a-Si and a-Si:H, especially at the edge of the conduction band. This edge shape of the conduction band agrees well with the experimental measurements by Longeaud et al.⁴⁰ 

It is well known that a high-quality hydrogenated amorphous silicon works as a desirable passivation layer in various silicon-based heterojunction cells, which effectively reduces interfacial defects and improves cell efficiency,^41,42 although its quantum transport mechanism is not fully understood yet. We investigated the electronic transport properties of c-Si, a-Si, and a-Si:H (14%H) using Cu electrodes; the obtained transmission coefficient $TE,VB=0$ depending on the energy level is shown in Fig. 4. The transmission of c-Si and a-Si is essentially zero in the bandgap range. However, a-Si:H has significant transmission near the Fermi level ɛ_F, which is caused by resonances between the fuzzy boundaries of the valence and conduction bands. The transmission coefficient of a-Si:H has a sharp peak near E_F, which well extends over the entire bandgap range. This suggests that the added hydrogen atoms not only passivate the defects (dangling bonds) in a-Si but also enhance the electronic transmission capabilities.

In order to see the transmission mechanism in some details, the partial density of states (PDOS) is examined, as shown in Fig. 5. It is obvious that the peak of transmission coefficient in Fig. 4 corresponds to tunneling with p orbitals of Si atoms, while s and d orbitals have a negligible contribution. In this context, the role of hydrogen atoms seems indirect, i.e., enhancing the p orbitals of Si by passivating the dangling bonds.

Table I indicates that the hydrogen concentration strongly affects the structure properties.²⁴ Since we prepared the a-Si:H samples in this work by replacing a given number of Si atoms with H’s, the dangling bonds increase as well as the passivated sites as the hydrogen contents increases. Figure 6 depicts the transmission coefficient $TE,VB=0$ for these a-Si:H samples sandwiched between the Cu electrodes. At the Fermi level, the transmission is the largest for 3%H and 6%H cases. The sample of 25%H also exhibits large transmission, but the structural stability is not sufficient because it contains large amount of voids.

Since the Landauer–Büttiker formula [Eq. (2)] suggests that the electronic conductivity at zero bias field is determined by $TE=EF,VB=0$⁠, the value is plotted in Fig. 7, where the samples of 3%H and 6%H seem best in conductivity, although the concentration dependence is not large.

Based on the obtained electronic structure, we can evaluate the spatial distribution of charge density and electrostatic potential; examples are shown in Fig. 8. Since the electronegativity of Cu is similar to that of Si (both are equally 1.90 on the Pauling scale⁴³), there seems negligible electron transfer between a-Si:H and Cu electrodes, which differs from the Al electrode cases described later. At lower hydrogen contents, the charge is strongly localized, and a wide positive potential area exists, which should correspond to the non-passivated Si atoms. The increase of H content weakens the charge localization, and the positive potential region is dispersed, which seems to bring more channels of electron transport.

Next, we investigate the electric current I under the bias voltage V_B between the electrodes. The transmission coefficient $TE,VB$ of a-Si:H (3%H) is plotted for various V_B in Fig. 9. According to the Landauer–Büttiker formula, the current is determined by the transmission coefficient in the bias window, which is shown by the horizontal arrows in the figure. Although there exists slight asymmetry between the positive and negative biases, which should be brought by the asymmetry of the a-Si:H samples, the shape of the transmission spectrum is almost independent of the bias.

The obtained I–V (current–voltage) curve is shown in Fig. 10. The current is essentially proportional to the bias, indicating the Ohmic resistance for all samples; this is in some sense amazing, when considering an extremely large electric field (e.g., V_B = 1.2 V corresponding to 0.9 × 10⁹ V/m) being applied. As for the hydrogen content dependence, the 3%H sample has the highest conductivity. The increase of H concentration lowers the conductivity, but the 14%H sample is the second best conductor. The “electron channels” generated by the structural change, discussed in Sec. III B, seems to contribute to this behavior.

The molecular orbital theory can give a large transmission for the a-Si:H systems. The peak of $TE$ below E_F corresponds to the resonance tunneling with HOMOs (highest occupied molecular orbitals) while the peak above E_F is the tunneling with LUMOs (lowest unoccupied molecular orbitals).⁴⁴ The relatively large defect peaks in the bandgap, as shown in Fig. 3, give large transmission in the bias window, similar to the graphene case discussed in Ref. 44.

The influence of applied bias is clearly seen in the spatial distribution views of charge and electrostatic potential in Fig. 11. The pattern of charge localization is essentially the same under the bias, which indicates that the dangling bonds and hydrogen-passivated sites are not affected much. However, the potential map exhibits some bias dependence. Since the local current should prefer regions of smaller potential gradient, current channels seem to depend on the bias, and the defect sites clearly make a large contribution.

To examine how the electrode contact affects the transport properties, we prepare another junction systems, i.e., a-Si:H sandwiched between two Al electrodes. The transmission coefficients are compared in Fig. 12, which indicates no significant difference between the Al electrode case and the Cu one.

Based on the measured current data I [A] under bias voltage −1.2 [V] $≤VB≤$ + 1.2 [V], the total electric conductivity σ is evaluated from the conventional definition

where A is the cross-sectional area of the sample (10.86 × 19.86 A²) and d = 13.5 A is the gap distance between the two electrodes. The results are shown in Fig. 13. The hydrogen content dependence is quite similar, but the Cu electrode cases generally have better conductivity than Al cases, partly because bulk Cu has larger conductivity than Al.

To further investigate the electrode effects, the charge density and the electrostatic potential distribution are plotted in Fig. 14. When compared with the Cu cases (Fig. 8), the largest difference is that the electrostatic potential inside the a-Si:H has negative values (typically −2.5 V $∼−1.5$ V), although the pattern of charge localization is essentially the same. This should be attributed to the difference of electronegativity, 1.90 for Si and Cu, and 1.61 for Al on the Pauling scale.⁴³ A part of electrons in Al electrodes are attracted to a-Si:H and generate an electric double layer at the electrode interface, which gives in part the reason of lower conductivity than Cu cases in Fig. 13. The abundance of electrons in a-Si:H smears the potential distribution to some extent, which helps the electron transport.

The electron transport properties of hydrogenated amorphous silicon (a-Si:H) were investigated with the density functional based tight binding (DFTB) simulation combined with the non-equilibrium Green’s function (NEGF) method.

1. A comparison of a-Si:H with crystalline and amorphous silicon systems confirms that passivation by the hydrogen atoms generally leads to the electronic transmission enhancement, by generating defect states in the bandgap and mitigating charge localization.

2. The hydrogen concentration affects the electron transmission. The 3%–6% hydrogen content gives the largest transmission due to the defect states resonance, but a large amount of hydrogen (14%) brings another transport channel, also showing large transmission.

3. All samples of a-Si:H behave as an Ohmic conductor under electrostatic bias, even with an extremely large field of ∼10⁹ V/m.

4. By comparing the copper electrode systems and the aluminum ones, the interface between a-Si:H and the electrodes is found to affect the electron transport, although the general trend of hydrogen concentration dependence is similar. Due to the electronegativity difference, electric double layers are generated on the Al/a-Si:H interface.

We have mainly investigated how the defects, the hydrogen passivation, and the a-Si:H/electrode interface affect the electron transport properties. Many other relevant factors exist to improve the photovoltaic efficiency of a-Si:H, such as the mid-range structural order and electron–hole recombination rate. Some need theoretical inspection on the quantum mechanics base, which is our future plan.

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article.

To determine an appropriate value of the gap distance d between the two electrodes (Fig. 2), we evaluated the electron transport as preliminary calculation with a similar setup with varying d from 13.3 to 15.5 Å. As shown in Fig. 15, the conductance depends on d; the conductance reduces with larger d due to the stretching of Si–Cu bonds. We have chosen d = 13.5 Å for the main calculations because it gives large conductance and reasonably stable structure.