A comparative study on the cold field electron emission properties of cubic nanocrystalline lead chalcogenide thin films

Abstract

A comparative study on the field electron emission properties of the nanocrystalline lead chalcogenide thin films has been made. The structure of the films was established by X-ray diffraction, transmission electron microscopy and atomic force microscopy, which revealed the formation of cubic structure with particle size in the range 5–8 nm. The threshold field was found to vary between 3.8 and 5.5 V μm⁻¹ for different systems. Due to strong quantum confinement, an enhancement in the emission properties was observed. The threshold fields and enhancement factors were calculated and we have tried to explain their emission mechanism.

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Enormous interest has been developed in recent years in the area of field electron (FE) emission properties of semiconductor thin films^1–4 (mainly II–VI and III–V) due to the ease of their low temperature and large area uniform deposition, which is normally difficult to achieve for the conventional carbon based nanostructures like carbon nanotubes (CNT), carbon nanofibers (CNF) and graphene. The FE emission properties of semiconductor films are mainly dependent on the variation of chemical bonding, doping and the crystal structure.^2–5 The decrease in particle size increases the FE emission at low turn-on fields by raising their Fermi level and lowering the work function.^2,3 In our previous work,¹ we have shown that electrochemically deposited PbSe nanocrystals (NCs) could act as a good FE emitter due to its low work function (0.51 eV), high enhancement factor (157), small size (ca. ∼8 nm) and regular shape. FE emission has crucial applications in electron guns, flat panel display screens, microwave power-amplifier tubes, X-ray tubes, high-luminescence light sources and micro-machined mass spectrometers.^6–8 FE emission is a surface-sensitive phenomenon and most of the experimental work on this involves CNT and CNF based materials. There are only a few reports on the studies of nanocrystalline lead chalcogenide thin film based field electron emitters.¹

This work reports a comparative study of the field electron emission properties of nanocrystalline lead chalcogenide thin films deposited electrochemically. The particle size of the different lead chalcogenide thin films was explored by structural and morphological analyses, which revealed the formation of cubic structure with nano dimension. The decrease in the threshold field and increase in the enhancement factor were explained in terms of the crystal structure and the work function (calculated using Fowler–Nordheim (F–N) theory).

The deposition technique for the nanocrystalline lead chalcogenide thin films has been reported in detail elsewhere.^9,10 In order to lower the crystallite size to a large extent, depositions were carried out for 15 min instead of 30 min, keeping all other parameters same, as described in ref. 11. Thus we have obtained lead chalcogenide films with a thickness of about 180 nm. The film thickness was measured using a Bruker Dektak XT Stylus Profiler fitted with a super-sharp tip of 50 nm radius of curvature operating under low stylus force of 3.0 mg and with a resolution of 5.0 μm per sample. High resolution X-ray diffraction (HRXRD), atomic force microscopy (AFM) and high resolution transmission electron microscopic (HRTEM) techniques were applied to learn about the crystal structure and morphology of the deposited materials, which is essential in order to explain the FE emission properties. HRXRD measurements of the PbX (X = S, Se, Te) thin films were carried out using a parallel beam X-ray diffractometer PANalytical X'PertPRO with a Cu target, k_α = 1.540598 Å, operating at 45 kV, 30 mA with a Bragg–Brentano goniometer and a θ–2θ scanning mechanism. HRTEM measurements were carried out using a JEOL JEM-2100 transmission electron microscope working at 200 kV. The topography measurements have been done by an ambient based multimode atomic force microscope (SPM, Solver P47H-PRO). All AFM measurements were done in semi-contact mode using a silicon probe having length = 95 μm, width = 30 μm and thickness = 2 μm. The resonance frequency was 240 kHz and force constant of 18 N m⁻¹ was applied for the scanning purpose. The detail of the field electron emission measurement was reported in ref. 1.

The HRXRD patterns reveal the presence of cubic phase of PbTe (Fig. 1a), PbS (Fig. 1b) and PbSe (Fig. 1c). In PbTe, the diffractions were found due to the presence of (200), (220) and (420) planes (JCPDS ID 08-0028), in PbS from (111), (200), (220) and (400) planes (JCPDS ID 05-0592) and in PbSe the diffractions were observed from (111), (200), (220) and (222) planes (JCPDS ID 06-0354). Significant broadening of the peaks occurred due to the formation of NCs. The lattice parameter (a) was calculated using the equation ((1/d²) = (h² + k² + l²)/a²) and found to be 6.495 for PbTe, 5.958 for PbS and 6.141 for PbSe, which is in good agreement with literature value (6.443, 5.936 and 6.124 for PbTe, PbS and PbSe respectively). The crystallite sizes (D) were calculated by using Debye–Scherrer equation (D = 0.9λ/β cosθ) and found to be in the range 5–8 nm for the three systems, whereas the values of microstrain (ε = (β cosθ/4)) were found to be 6.9 × 10⁻³, 5.6 × 10⁻³ and 5.7 × 10⁻³ for PbTe, PbS and PbSe, respectively. The high microstrain value is associated with the low dimension of the deposited crystals.

Fig. 1 HRXRD plots of (a) PbTe (b) PbS and (c) PbSe and in inset corresponding HRTEM images. The peaks marked “*” were from the SnO₂ of the bottom FTO (SnO₂:F) substrates used for deposition.

The HRTEM images of the lead chalcogenide thin films are shown as the inset of Fig. 1a–c. The crystallite size was found to fall within 5 to 8 nm, with cubic shape. The lattice fringes in the HRTEM images (not shown here) were separated by 0.375 nm, 0.344 nm and 0.354 nm, which matched well with the ‘d’ spacing values for the (111) planes of cubic PbTe, PbS and PbSe respectively (JCPDS ID 08-0028, JCPDS ID 05-0592 and JCPDS ID 06-0354).

AFM imaging provides more detailed information involving the surface morphology and homogeneity of the lead chalcogenide thin films. From the AFM images (Fig. 2a–c) and the corresponding histograms, the particle sizes of PbTe, PbS and PbSe systems were found to vary between 5 and 8 nm. The particles were found to be distributed uniformly on the fluorine doped tin oxide (FTO) coated glass substrates with a regular morphology, making the film convenient for device applications. The average surface roughness (R_a) and root mean square (RMS) roughness were found to be 1.02 and 1.14 nm for PbTe, 1.09 and 1.35 nm for PbS and 1.13 and 1.54 nm for PbSe, respectively. Such low values of roughness indicate the smoothness of the surface for the deposited films. The surface roughness and RMS roughness increased with increase in particle size, reflecting the normal trend. The histogram for the particle size distribution (inset: Fig. 2a–c) again confirms that most of the particles in the deposited films were between 5 and 8 nm in diameter. This is in excellent agreement with the values of the crystallite sizes obtained from HRXRD measurements. As the exciton Bohr radius for different lead chalcogenide systems fall within 18–150 nm,^12,13 we can expect significant amount of quantum confinement in our deposited systems, as their diameters are about 3 to 30 fold lower than their exciton Bohr radii.

Fig. 2 AFM images of (a) PbTe (b) PbS and (c) PbSe and in inset corresponding histogram of grain size distribution.

Fig. 3a shows the emission current density (J) vs. macroscopic field (E) curves for the different lead chalcogenide thin films with fixed anode-sample separation (d) of 100 μm. The macroscopic field (E) is calculated from the external applied voltage (V), divided by the anode-sample spacing (d). Theoretically, the emission current I is related to the macroscopic electric field E as:

where, ϕ is the local work-function, β is the field enhancement factor, A is the effective emission area, ‘a’ is the first Fowler–Nordheim (F–N) Constant (1.541434 × 10⁻⁶ A eV V⁻²), ‘b’ is the second F–N Constant (6.83089 × 10⁹ eV^−3/2 V m⁻¹), and v_F and t_F are the values of the special field emission elliptic functions¹⁴ ‘v’ and ‘t’ evaluated for a barrier height ϕ. Field emission characteristics of the films were analyzed using the F–N theory. A simplified F–N equation for the local current density J at some point on the emitting surface may be written as¹⁴⁻¹⁶where, ‘r’ and ‘s’ are appropriate values of the intercept and slope correction factors, respectively. As ‘r’ and ‘s’ are relatively slowly varying functions of 1/E, so a F–N plot is expected to be a good straight line. The F–N plots of our samples are shown in Fig. 3b. It has been observed that all the J–E curves in the present work are satisfactorily fitted with the F–N equation (eqn (2)). This suggests that the electrons are emitted by the cold field emission process. The threshold field (E_th), which we define as the macroscopic field, needed to get an emission current density J = 10 μA cm⁻², were lying in the range 3.8 to 5.5 V μm⁻¹ for PbTe, PbS and PbSe respectively. This value is quite lower than that of amorphous carbon and DLC films^5,17 (6–15 V μm⁻¹), Si–C nanorods¹⁸ (13–20 V μm⁻¹), Mn doped ZnS³ (5.3–6.8 V μm⁻¹) etc.

Fig. 3 Emission current density (J) vs. macroscopic field (E) curves of lead chalcogenide (PbTe, Pbs and PbSe) thin films and (b) in inset corresponding F–N plot.

According to the F–N plot (Fig. 3b), the slope ‘m’ (given by eqn (3)) would represent the combined effect of work function and enhancement of local electric field and is given by:

Assuming an ideal flat emitter with field enhancement factor (β) equal to 1, the values of ϕ from the F–N plot (Fig. 3b) calculated to be 0.018 for PbTe, 0.022 for PbS and 0.026 for PbSe, respectively. Such low work functions might be due to an underestimation of the field enhancement factor β. But the true work function must be much larger than these values, as the factor β, which controls the work function, depends on the shape of the emitter. The emission mechanism may involve a strong field enhancement at the front surface. To understand the F–N emission process in our system, it is necessary to explain the origin of the large enhancement factor required to lower the barrier for easy electron emission. Forbes¹⁸ determined its value via the ‘hemisphere on post approximation’ as:

where, L = height of the post, R = radius of curvature of the hemisphere. The film thickness is ∼180 nm in our case and the average diameter of the particles fall in the range 5–8 nm. Assuming the sharp emission tip radii (R) of our sample to be around 10% of the particle size and the height of the post (L) is equal to the film thickness, the approximate β value was calculated to be 252, 210 and 157 for PbTe, PbS and PbSe, respectively.

The mechanism of the electron emission from these lead chalcogenide NCs might be related to the large band gap energy of the systems as explained by Robertson.¹⁹ The band structure of semiconductors NCs changes from a continuous to a discrete (atomic like) pattern with the reduction of the crystallite size, where, the lowest transition level E_l is blue shifted with respect to the original bandgap energy (E_g). The quantum confined or blue shifted energy ΔE can be expressed by the standard equation as:

ΔE = E_l − E_g = (h²π²/2μR²) − (1.8e²/4πεR) (5)

where ‘R’ is the radius of the NC, ‘μ’ is the effective mass of an electron, ‘e’ is the electronic charge, and ‘ε’ is the dielectric constant of the material. It can be seen from the above equation that the greater the reduction in crystallite size, the higher the amount of blue shifted energy. As we have a very small crystallite size here, a significant amount of blue-shift in the band gap energy is expected.

On the other hand, the semiconductor NCs can cause the conduction band minimum (CBM) to lie close to the vacuum level. This would produce a very low electron affinity in the material and hence field emission would be enhanced. This reasoning is supported by our approximate work function (ϕ) calculation from F–N plot. The ϕ-value obtained for our samples are in the range 0.47–0.51 eV, considering the corrected field enhancement factor as calculated from relation (3). So, the ‘ENH-material hypothesis’ given by Forbes,¹⁷ that electrically nanostructured heterogeneous (ENH) materials with quasi-filamentary conducting channels inside a less conducting matrix show low-macroscopic field emission, is also applicable to our film as the particle size of our film fall in the range 5–8 nm. Actually, due to the nanocrystalline nature of the films, the local field gets largely enhanced and hence showed improved field emission properties.

Conclusions

Surface morphology and structural analysis of lead chalcogenide NCs have been studied in details, which showed good field electron emission properties with a low threshold field varying from 3.8–5.5 V μm⁻¹. The field enhancement factor was found to fall in the range 252 to 157 for the three different lead chalcogenide systems. This low macroscopic filed emission is attributed to the nanocrystalline nature of the material, which shifts the CBM quite close to the vacuum level, thus enhancing the field emission properties.

Notes and references

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