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Band-to-Band Tunneling Dominated Thermo-Enhanced Field Electron Emission from p-Si/ZnO Nano-Emitters Zhizhen Huang, Yifeng Huang, Ningsheng Xu, Jun Chen, Juncong She, and Shaozhi Deng ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b00140 • Publication Date (Web): 04 Jun 2018 Downloaded from http://pubs.acs.org on June 4, 2018

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ACS Applied Materials & Interfaces

Band-to-Band Tunneling Dominated Thermo-Enhanced Field Electron Emission from p-Si/ZnO Nano-Emitters

Zhizhen Huang, Yifeng Huang, Ningsheng Xu, Jun Chen, Juncong She*, Shaozhi Deng*

State Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key Laboratory of Display Material and Technology, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China

*Address correspondence to [email protected] and [email protected]

KEYWORDS: thermo-enhanced field emission, nano-template, solution-phase growth, p-Si/ZnO heterojunction, band-to-band tunneling

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ABSTRACT: Thermo-enhancement is an effective way to achieve high performance field electron emitters, and enables the individually tuning on the emission current by temperature and the electron energy by voltage. The field emission current from metal or n-doped semiconductor emitter at a relatively lower temperature (i.e., < 1000 K) is less temperature sensitive due to the weak dependence of free electron density on temperature, while that from p-doped semiconductor emitter is restricted by its limited free electron density. Here, we developed full array of uniform

individual

p-Si/ZnO nano-emitters and

demonstrated

the strong

thermo-enhanced field emission. The mechanism of forming uniform nano-emitters with well Si/ZnO mechanical joint in the nano-templates was elucidated. No current saturation was observed in the thermo-enhanced field emission measurements. The emission current density showed about ten-time enhancement (from 1.31 to 12.11 mA/cm2 at 60.6 MV/m) by increasing the temperature from 323 K to 623 K. The distinctive performance did not agree with the inter-band excitation mechanism but well-fit to the band-to-band tunneling model. The strong thermo-enhancement was proposed to be benefit from the increase of band-to-band tunneling probability at the surface portion of the p-Si/ZnO nano-junction. This work provides promising cathode for portable x-ray tubes/panel, ionization vacuum gauges and low energy electron beam lithography, in where electron-dose control at a fixed energy is needed.

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1. Introduction

Well integrated, actively controllable, and high density electron emission cathodes have attracted great attention because of their potential applications in vacuum electronics.1-4 Thermo-enhanced field emission cathode (working between room temperature and 1000 K) is one of the promising candidates, which benefits from heating the emitter to achieve higher current.2 The working temperature of the thermo-enhanced field emitter is much lower than that for thermionic cathode (i.e., ~1800 K) and electrons emit into vacuum by tunneling. It has been demonstrated that the energy distribution of the emitted electrons at < 1000 K is narrow which suggests that most of electrons are from energy states near the Fermi-level (metal) or the bottom of conduction band (semiconductor).5, 6 Namely, the thermo-enhancement is mainly contributed by the increase of electron density, while weakly influenced by the electrons with higher energy in the heated cathode.5 It enables the individually tuning on the emission current by temperature and the electron energy by the applied voltage. Moreover, the surface adsorption can be eliminated in a heated cathode, benefitting for cathode reliability.7-9 These merits are attractive for a wide range of applications. For example, the dose of x-ray in a portable x-ray tube should be modified by cathode temperature variation to meet the tolerance/requirement of different applications (i.e., imaging or sterilization) without changing the voltage.10 For ionization vacuum gauges11, high emission current is required for sufficient signal intensity, while low electron energy is expected to reduce the x-ray induced residual photocurrent and the electron stimulated desorption effect. In low energy electron beam lithography, ideally, it is desired to attain high 3



exposure efficiency by increasing the amount of injection electrons per unit time. Meanwhile, low energy of electrons is expected to avoid electron scattering effect and define high resolution patterns.12, 13

The thermo-enhanced field emission demonstrations so far are all based on the inter-band or inter-band defect states excitation mechanisms. The field emission current from metal or n-doped semiconductor thermo-enhanced emitter is less temperature sensitive due to the weak dependence of free electron density on temperature5, introduced.15,

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unless electron trap centers are

However, the quantity of electron trap centers is difficult to control. Gas

adsorption can also influence the thermo-enhanced field emission properties17, but this factor is still unpredictable. Alternatively, the emission current from p-doped cathode shows superior temperature sensitivity at the current saturation region.18 However, it is restricted by the limited free electron density in the conduction band. It is still challenging to develop integrated emitters with strong thermo-enhanced field emission.

In the present work, we propose a featured cathode structure with ZnO nano-tip on the top of p-doped Si pillar (denoted as p-Si/ZnO nano-emitter). The p-Si/ZnO nano-emitters were fabricated using optimal nano-templates for local solution-phase growth of single ZnO nano-tips followed by a precisely controlled anisotropy etching of Si. The mechanism of forming uniform nano-emitters with well Si/ZnO mechanical joint in the nano-templates was elucidated. In the thermo-enhanced field emission measurement, no current saturation was observed, and a strong thermo-enhanced field emission was achieved. The experimental observation and numerical 4


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simulation results suggest that the energy band structure of the p-Si/ZnO nano-junction was modified by the penetrated electric field and thus induced the band-to-band tunneling. The distinctive thermo-enhanced performance did not agree with the inter-band excitation mechanism but fitted well with the band-to-band tunneling model. The strong thermo-enhancement was proposed to be benefit from the increase of band-to-band tunneling probability. This work elucidates the role of p-Si/ZnO nano-junction and provides a new device structure for thermo-enhanced field emission, which is distinguished from the earlier reports that mainly dopant/defect-dominated.2, 7, 15 The p-Si/ZnO nano-emitter cathode is promising for applications where electron-dose control at a fixed energy is needed.

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2. Experimental Section

Fabrication of Nano-Emitters. The fabrication of nano-emitters was started by defining PMMA (polymethyl methacrylate) nano-templates on a ZnO (~15 nm in thickness) coated boron doped (~1×1019 cm-3) Si wafer using electron beam (e-beam) lithography. The sputtering deposited ZnO thin film is a seed-layer for inducing growth of crystalline ZnO.19 The geometrical profile of the nano-template was finely-adjusted by tuning the e-beam dose during exposure, i.e., from 0.28 µC to 0.35 µC (with a fine interval of 0.01 µC), while maintaining the other parameters (acceleration voltage 28 kV) unchanged. The individual ZnO nano-tips were locally grown in the nano-templates by solution phase method while those grown outside the templates were removed by ultrasonic bathing.12 Individual ZnO nano-tips were obtained by cleaning up the PMMA with acetone and ethanol. The ZnO nano-tips prepared by this method is lightly n-type doped with a carrier concentration of ~1016 cm-3 (see the supporting information), which are well consistent with those in earlier literatures, i.e., 1016~1018 cm-3.20-23 After achieving uniform ZnO nano-tip array, the seed layer was etched with oxygen plasma by inductively coupled plasma (ICP, Oxford Instruments Plasma-lab System 100). The p-Si/ZnO nano-emitters were obtained by anisotropy etching the Si substrate using SF6 and C4F8 plasma, followed by a short duration (10 s) isotropy etch using SF6 plasma to smooth the substrate surface. The n-Si/ZnO nano-emitters were also fabricated for comparative studies using arsenic doped (~1×1019 cm-3) Si substrate.

Field Emission Measurement. The field emission measurements were performed in high 6


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vacuum (~3×10-10 Torr). The cathode-anode separation is 30 µm. The samples were baked for 24 hours at 773 K to eliminate the possible surface physical adsorption. Moreover, an ultraviolet illumination (with wavelength of 365 nm and power density of 5.2 mW/cm2) was performed after the baking to further eliminate the chemical adsorption.24 In the thermo-enhanced field emission tests, the temperature of the cathodes was adjusted by heating the sample holder. The output power of the heater was well controlled with a feedback circuit. The actual temperature of the sample was monitored by a thermocouple. To ensure that the thermal equilibrium was reached, the field emission tests were performed after the monitored sample temperature was stable for 10 min. In a specific temperature, field emission currents were recorded by changing the anode voltage in a scan mode, while the separation between anode and cathode remained unchanged. Keithley 248 and Keithley 6487 were used as power supply and field emission current measurement, respectively.

Characterization and Simulation. The morphology of the Si/ZnO emitter arrays were characterized by scanning electron microscopy (SEM, Zeiss Supra 55). The measurements on the mechanical adhesion between the ZnO nano-tip and Si pillar were performed in the SEM system which integrated with a nanomanipulator (Klocke Nanotechnik). A fine tungsten tip which was fixed on the nanomanipulator was utilized to touch the Si/ZnO nano-emitter and force it to bend. The two-dimensional simulations were performed by using COMSOL Multi-physics software. In the simulations, the geometrical parameters were derived from the SEM images indicated in the present work, while the material properties parameters were referred to those of ZnO and Si 7



crystals that given in Refs (25, 26). The simulation model addressed two coupling processes, i.e., field induce electron accumulation and the resulted effect in field distribution. In the Si/ZnO junction, the correlation between the potential distribution and the carrier concentration was determined by Poison equation. The correlation between the applied electric field and the redistribution of carriers was depicted using the current continuity equations.

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3. Results and Discussion

3.1 Fabrication of Full-Array of Uniform Nano-Emitters

Figure 1. (a) The correlation between the template-diameter and exposure-dose. The experimental data are indicated as symbols, and the solid lines were obtained by linear fitting. (b) and (c) are the represented SEM images of the ZnO nano-tip with the PMMA-template obtained

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using the beam dose of 0.28 µC. The insets are the corresponding schematics illustrations. (d) The represented SEM image of a ZnO nano-tips array with missing and exfoliated tips.

The PMMA nano-template that fabricated by e-beam lithography is typically a hollow conical column. The cross-sectional view of the template is in a trapezoid-shape (inset in Figure 1a). The correlation between the diameter of the template-aperture and exposure-dose is showed in Figure 1a. Both the top-aperture (red line) and bottom-aperture (black line) diameters of the template increased linearly following the rise of the exposure-dose. By changing the dose from 0.26 to 0.35 µC (with 0.01 µC interval), the top-aperture diameter of the template increased from 37 to 76 nm, while that for the bottom-aperture was from 114 to 151 nm. Accordingly, the diameter of the template-aperture can be finely adjusted by changing the e-beam dose in the lithography. The diameter of template-aperture showed significant effect on the growth of well-defined ZnO nano-tip array. Dose in between 0.28~0.30 µC (shadow area in Figure 1a) is the critical “boundary”. No full array (i.e., without exfoliated nano-tips) can be achieved when using template with smaller aperture, i.e., those fabricated using exposure-dose of 0.28 µC and less. However, if the dose is increased to 0.30 µC or higher, uniform full array can be obtained with well repeatability. Figure 1b and 1c show the typical cross-sectional SEM images of individual ZnO nano-tips that embedded in the PMMA-templates obtained using the beam dose of 0.28 µC. The corresponding schematics illustrations are also indicated as insets. In Figure 1b, the bottom of the template was almost filled with ZnO, only a small portion (near the bottom 10


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corner; arrowed) was unfilled. The diameter of the ZnO-Si joint was about 116 nm, slightly less than that of the template (~137 nm). However, it is clearly indicated in Figure 1c that the nano-structured ZnO grown at the bottom of the template was only ~74 nm in diameter, about half of the aperture-diameter at the template bottom (~137 nm), resulting in a limited ZnO-Si joint-area. Both the corners at the bottom of the template were ZnO-unfilled (arrowed). In Figure 2a and 2b, the represented SEM images of a full array and an individual ZnO nano-tip taken from the sample with the PMMA-template obtained using the beam dose of 0.30 µC are indicated. Figure 2c shows the typical SEM image (with a schematics illustration) of the ZnO nano-tip before PMMA removing. Different to the observations showed in Figure 1b and 1c, it is clearly indicated that the bottom of the template was well-filled with ZnO-crystal, with very tiny unfilled corner (arrowed). The diameter of the ZnO-Si joint was about 136 nm, very close to that of the template (~141 nm). The evidences strongly suggest that the increase of the joint-area is crucial to obtain the full array.

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Figure 2. (a) and (b) are the representative SEM images of ZnO nano-tips (exposure dose: 0.30 µC). (c) The represented SEM images of the ZnO nano-tip with the PMMA-template obtained using the beam dose of 0.30 µC. The inset is the corresponding schematic illustration.

In our early work,12 it has been found that the growth of ZnO in the PMMA nano-template follows the well-accepted preferential growth model.27 The crystallization of ZnO is begun with the [0001] direction. The alignment of the [0001] crystal seeds on the ZnO seed-layer surface has been confirmed to be randomly distributed. Accordingly, the initial grown direction of the ZnO in the templates is random, but all along the (0001) facet. This early finding can be used to qualitatively interpret the above observations. Figure 3a shows the schematic illustration of the 12


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growth process in the case that the [0001] direction (indicated as blue arrow) is apart from the substrate normal. No matter the initial nucleation is located near the corner or center, the growth of (0001) facet could be eventually confined by the template sidewall and form a nano-cavity at the corner. Afterward, further growth of ZnO would follow other facets (indicated as black arrow) and finally fill the rest of the template. On the other hand, if the [0001] direction is parallel to the substrate normal, the growth would continue along the [0001] direction. The geometrical profile of the nano-structured ZnO at the bottom of the template would strongly depend on the location of the initial nucleation. When the growth is originated near the corner (Figure 3b), the structure would be similar to that showed in Figure 3a. However, if the growth is originated near the center (Figure 3c), cavities would form at both the corners, resulting in a limited ZnO-Si joint. The model is consistent well to the observations in Figure 1b and 1c, which showing the unfilled corner at the bottom of the template.

It is expectable that well ZnO-Si joint could be formed in the situations that showed in Figure 3a and 3b, with slight joint-area deviation, because the orientation of the crystal-seeds and the nucleation are randomly distributed. Most of the ZnO-tips in an array may grow follow the ways that indicated in Figure 3a and 3b. Exceptionally, a minimum ZnO-Si joint (as indicated in Figure 1c and Figure 3c) may form if the nucleation is originated near the center and grown right along the substrate normal. Those tips are much easier to be exfoliated during the lift-off of the PMMA template. The above discussion is consistent well with the SEM evidence in Figure 1d, i.e., most of the tips in an array were preserved while several tips were missing and exfoliated. 13



Our systematic growth experiments have demonstrated that by slightly increasing the template aperture, i.e., top-aperture diameter from 42 to 51 nm and bottom-aperature diameter from 137 to 141 nm, can result in a uniform well ZnO-Si joint (Figure 2b) and no tip-exfoliation was observed. It is worth noting that how this tiny increase in aperture can resulted in a well ZnO-Si joint, especially in the case that the nucleation is originated near the center and grown right along the substrate normal.

We propose that a larger aperture results in a longer duration before the blocking of zinc supply to the template bottom, which provides sufficient time for the growth of ZnO at the bottom to “full-fill” the template. Figure 3d shows the schematically illustration of the growth procedure, based on the geometrical parameters from templates defined with 0.28 and 0.30 µC. The dash line shows a smaller template while the solid line for a larger one. It is showed that the nano-structured ZnO (in blue) blocks the small template with unfilled cavity at the bottom. However, by slightly increasing the aperture-diameter (i.e., 10 nm), the ZnO would need to grow 59 nm in length to form a blocking. Ideally, the diameter of the ZnO at the bottom can have an increase of 59 nm (left panel of Figure 3d; in green), taking the estimation of that the growth rate of the certain facet of ZnO is half of that for the (0001) one.28 More significantly, a larger aperture can lead to a higher efficient supply of zinc source (Zn+) that allows the sufficient growth of ZnO at the bottom. Namely, in the same growth duration as that for the blocking happen at a smaller template, ZnO with larger bottom diameter can be achieved in a larger template (right panel in Figure 3d). With the contributions of the above effects, uniform full array 14


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of ZnO could be obtained.

Figure 3. The schematic illustrations of the ZnO nano-tip growth process. (a) The case that the [0001] direction (indicated as blue arrow) is apart from the substrate normal. (b) and (c) showed the cases that the [0001] directions (indicated as blue arrow) of ZnO are parallel to the substrate normal. The initial nucleation are located near the corner and center in (b) and (c), respectively. (d) The schematic illustrations showing how the tiny increase in template aperture can resulted in a well ZnO-Si joint, in the case that the nucleation is originated near the center and grown right along the substrate normal. 15



Full array (300×300 emitters with 4 µm separation) of ZnO nano-tips was fabricated for the following field emission studies using the templates defined with exposure-dose of 0.31 µC. Figure 4a shows the typical SEM image of a uniform array of p-Si/ZnO nano-emitter, which was obtained by isotropic plasma etching the Si substrate using the ZnO nano-tip as mask. The height of the ZnO nano-tip and the p-Si pillar are ~510 nm and ~660 nm, respectively. The radius of the ZnO nano-tip apex is about 56 nm. We further confirmed that the ZnO nano-tip was possessed of excellent mechanical adhesion with the Si pillar. SEM images in Figure 4b and 4c demonstrate a well preserved ZnO-Si joint even when the nano-emitter was forced to bend with an angle of ~40 degree as respect to the substrate normal.

Figure 4. (a) The SEM image of a uniform Si/ZnO nano-emitters array (75° tilt-angle view). (b) and (c) are the SEM images showing a Si/ZnO nano-emitter before and after bending (both are 45° tilt-angle view).

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3.2 Thermo-Enhanced Field Emission

Figure 5 gives the field emission current versus applied electric field (I-F) curves and the corresponding Fowler-Nordheim (F-N) plots of the p-Si/ZnO and n-Si/ZnO emitters obtained at different temperature (323~623 K with 50 K interval), respectively. The emission current showed a clear temperature dependency and no saturation. When the temperature increased from 323 to 623 K, the emission current of the p-Si/ZnO nano-emitters increased from 18.31 to 169.57 µA (current density: 1.31~12.11 mA/cm2) at 60.6 MV/m, while the current of the represented n-Si/ZnO nano-emitters increased from 0.20 to 4.69 µA (current density: 0.01~0.34 mA/cm2) at 100 MV/m. The emission current density was obtained by dividing the emission current by the area that the nano-emitters array occupied, i.e., ~0.014 cm2.

The field emission properties of the individual n-Si/ZnO nano-emitter in an array is in weak uniformity.29 This non-uniformity cause the sample-to-sample variation in field emission properties of the n-Si/ZnO emitter. However, with the integrated p-Si/ZnO junction, the individual p-Si/ZnO emitters in an array showed better uniformity and reliability due to the current-limited effect of the reversely biased p-n junction.29 Accordingly, although the current of the individual p-Si/ZnO emitters was limited, the improvement in uniformity would lead to an increasing number of contributed emitters, thereby, increasing the total emission current. In our thermo-enhanced field emission measurements, all the n-Si/ZnO emitters (either with better or worse primary emission properties) showed weaker thermo-enhanced field electron emission than that of the p-Si/ZnO emitters. The represented I-F curves of the n-Si/ZnO nano-emitters in 17



Fig. 5(c) possesses a clear thermo-response (i.e., higher ∆I/I ratio) was given here to provide better and clear comparison between the p-Si/ZnO and n-Si/ZnO emitters and emphasize the superiority of p-Si/ZnO in thermo-enhanced field electron emission.

It has been reported that the field emission current density of the primary ZnO nanowires rose from 0.003 to 0.148 mA/cm2 at 4.93 MV/m by increasing the temperature from 323 to 723 K10, while the saturation current density of the p-type Si nano-emitters rose from 1.39 × 10-4 to 0.19 mA/cm2 at 6.90 MV/m when the temperature increased from 256 to 340 K.2 Our p-Si/ZnO nano-emitters showed a wider current density regulation range than the ZnO nanowires and a higher current density than the p-type Si nano-emitters. The lower driving electric field for the nano-cathodes in Ref 2 and Ref 10 was mainly due to their higher aspect ratio that brought a stronger geometrical field enhancement. Further increasing the aspect ratio (sharpen the tip apex or increase tip height) of the Si/ZnO nano-emitter or coating them with low work function materials are potential options to achieve enhancing emission. Among the nano-structured emitters mentioned above, our Si/ZnO emitters are robust for working under a higher electric field. The F-N plots of the p-Si/ZnO (Figure 5b) and n-Si/ZnO (Figure 5d) nano-emitters fit well to straight lines, suggesting that electrons emitted into the vacuum by tunneling rather than “climbing” over the vacuum potential barrier. On that account, the thermo-enhanced field emission is believed to be mainly induced by the tremendous increase of electron density in the conduction band of ZnO nano-tip.

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Figure 5. The I-F curves and the corresponding F-N plots of the Si/ZnO nano-emitters obtained at different temperature. (a) and (b) for the typical p-Si/ZnO nano-emitters while (c) and (d) for the represented n-Si/ZnO nano-emitters. The insets are the magnified F-N plots at the high field regions.

We attribute the thermo-enhanced field emission of the n-Si/ZnO nano-emitters to the defect states excitation model30, because the n-Si/ZnO (n-n) junction showed weak current ballasted effect. The amount of electrons in the conduction band of ZnO is increased due to the thermal-excitation from the defect states, resulting in an enhanced electron emission. However, 19



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this model is not valid for the p-Si/ZnO nano-emitters because the electron supply was ballasted by the p-Si/ZnO (p-n) diode. Field emitter with a reversely biased p-n diode has been well studied and demonstrated an emission current saturation region.2,

14, 31

The saturated current

origins from the inter-band excitation in the depletion region of the nano-junction (generation current). However, no current saturation was observed in our p-Si/ZnO nano-emitters. To figure out the role of p-n diode, the generation current at 323 K and 623 K were numerically estimated. In semiconductor physics, the depletion region behaves essentially like an intrinsic semiconductor. The intrinsic carrier concentration (beff) in p-Si is:  E  beff = BT 1.5 exp  − gp   2 kT 

,26

(1)

where B is a coefficient, Egp is the band-gap of p-Si because the free electrons are provided by p-Si, k is the Boltzmann constant, T is the cathode temperature. The relationship between Egp and temperature can be described as:

αT 2 32 Egp (T ) = Egp (0) − , T +β

(2)

where Egp(0) is the extrapolated value of the band-gap at 0 K and α, β are fitting parameters. For Si, Egp(0) = 1.17 eV, α = 4.73 × 10-4 eV/K, β = 636 K. The generation current is proportional to the intrinsic carrier concentration (J ∝ beff). Accordingly, we combined eq 1 and eq 2 to obtain:

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 αT1   E (0) Egp (0)  J1 T13/2 αT2 = 3/2 exp  gp − − ,  exp  J 2 T2 2kT1  2 k T 2 k T β β + + ( ) ( ) 1 2  2kT2  

(3)

where J1 and J2 are the generation current density at temperature T1 and T2 , respectively. The reported generation current density from a p-Si/ZnO heterojunction at 333 K was 0.01 mA/cm2.33 The cross-section area of a p-Si/ZnO nano-emitter herein was about 4.01 × 10-10 cm2 and the total area of an array (300×300) was about 3.61 × 10-5 cm2. Accordingly, the generation currents of all the p-Si/ZnO nano-emitters were estimated to be 1.81× 10-4 µA (at 323 K) and 17.49 µA (at 623 K). It was apparently a small proportion of the emission currents obtained in the measurements (Figure 5a), which were 18.31 µA (at 323 K) and 169.57 µA (at 623 K). Furthermore, higher current should lead to more Joule-heat in the depletion region, resulting in a larger amount of nonequilibrium carriers.34 This is a positive feedback process and thus predicts an upward bended F-N curve. However, it is contrary to our observation (Figure 5b) which implies a limited electron supply. Both the generation current estimation and F-N plots behavior suggest that the inter-band excitation via the interior p-Si/ZnO (p-n) diode cannot give reasonable interpretation for the strong thermo-enhancement.

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3.3 Band-to-Band Tunneling Enhancement

Figure 6. The numerical simulation results. (a) Plots that show the correlation between the local electric field and applied anode voltage. Herein, Ft and Fr are the electric fields that perpendicular to the ZnO nano-tip apex and side-wall surface at the p-Si/ZnO joint (see the inset), respectively. (b) The built-in electric field (Fb-surface) of the surface portion (in green; not in scale) of a p-Si/ZnO junction under the conditions of thermal equilibrium (red line) and with electron accumulation (black line), at an applied anode voltage of 400 V. The abscissa represents the position in height (the inset) as respect to the substrate. The Si/ZnO interface is at the height of 650 nm. (c) and (d) are schematics for the bottom of conduction band at the interior/surface (illustrated as red/black lines) portions of the p-Si/ZnO and n-Si/ZnO nano-junctions, 22


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respectively. The Fermi-level was taken as zero (E=0) for reference. The insets are the corresponding energy band diagrams of the Si/ZnO surface portions.

A two-dimensional electrostatic model was built using COMSOL Multi-physics software to analyze the field distributions and the energy band structures of the Si/ZnO nano-junctions. The simulation results are showed in Figure 6. Figure 6a shows the correlation between the local electric field and applied anode voltage. Herein, Ft and Fr are the electric fields that perpendicular to the nano-tip apex and side-wall surface at the Si/ZnO joint (see the inset of the figure), respectively. The fields increased lineally following the anode voltages. The Ft (~109 V/m) is sufficient for inducing field electron emission35, while the Fr (~108 V/m) would lead to an electron accumulation (resulted from field penetration) at the junction surface. The electron accumulation “layer” would significantly influence the build-in field (denoted as Fb-surface) of the p-Si/ZnO junction at the surface portion (the inset of Figure 6b). At an applied anode voltage of 400 V, the peak Fb-surface were 17 MV/m and 76 MV/m for the thermal equilibrium and electron accumulation situations, respectively. On account of the limited depth of field penetration, the Fr may show weak effect on the build-in field in the interior portion of the p-Si/ZnO junction. The increase on the Fb-surface could lead to a significant energy band bending. Figure 6c shows the bottom of conduction band at the interior/surface portion (illustrated as red/black lines) of the p-Si/ZnO nano-junction. A wide depletion region (~100 nm) formed in the interior portion of ZnO at the p-Si/ZnO nano-junction. It is because that the solution-phase grown crystallized ZnO 23



is intrinsically lightly n-doped36 while the Si is heavily p-doped. However, the width of the depletion region at the surface portion shrank to ~50 nm owing to the electron accumulation. With the help of electric field and narrow depletion region, the band-to-band tunneling may occur at the surface portion of the p-Si/ZnO junction, which means the electron in the valence band of p-Si could tunnel to the conduction band of ZnO (the inset of Figure 6c). For comparison, similar simulations were performed based on the n-Si/ZnO (n-n) junction. In Figure 6d, the potential barriers of the n-n junction showed similar heights of 0.205 eV and 0.175 eV for the interior and surface portion, respectively. Therefore, Fr showed weak effect on the electron transportation at the n-Si/ZnO junction. This finding further supports that the defect states excitation model in explaining the thermo-enhanced field emission from n-Si/ZnO nano-emitters.

The above analysis showed that the p-Si/ZnO diode was reversely biased with weak generation current, while the electron transport from p-Si to ZnO for field emission may dominated by the band-to-band tunneling at the surface portion of the junction (Figure 6a-6c). Therefore, it is reasonable to propose that the band-to-band tunneling current (It) is approximately equal to the field emission current (I). In the following discussions, we take It = I for exploring the applicability of the model. The band-to-band tunneling could be approximated by an electron penetrating a triangular potential barrier37, with a width related to the electric field at the depletion region and a height related to the effective band-gap (Eeff).38 As indicated in the band diagram showed in the inset of Figure 6c, the effective band-gap at the interface of the heterojunction is defined as Eeff = Ec/n-ZnO – Ev/p-Si with Ec/n-ZnO the n-doped region conduction 24


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band edge and Ev/p-Si the p-doped region valence band edge. The Eeff can be written as: Eeff = ( Ec /p − Si − Ev /p − Si ) + ( Ec /n − ZnO − Ec /p − Si ) = E gp − ∆Ec ,

(4)

where Ec/p-Si is the conduction band edge of p-Si, ∆Ec is the conduction band offset. The conduction band offset is well known to be 0.3 eV for a Si/ZnO heterojunction.25, 26 Thus, It can be given as:

It =

2π eAFb2− surface 9h2

 π 2 m* E 3/2  39 m* eff , exp  −  hFb −surface  Eeff  

(5)

where A is the cross section area of the electron accumulation “layer” at the junction surface, e is the electron charge, h is Planck constant, m* is the effective mass of an electron. The eq 5 can be rewritten as:

ln( I t

 2π eA F 2 m*  π 2 m* b − surface − E eff ) = ln  E 3/ 2 .   hFb − surface eff 9h2  

(6)

The eq 6 shows that (Eeff)3/2 and ln(It ⋅(Eeff)1/2) are in a linear relationship. Eeff can be obtained from the combination of eq 2 and eq 4, while It can take the values of field emission currents (I) (Figure 5a) as mentioned above. The analysis on how well the Eeff and It data fit a linear relationship can provide the information on the applicability of the band-to-band model to the thermo-enhanced emission. Accordingly, the correlations between (Eeff)3/2 and ln(It ⋅(Eeff)1/2) at different applied field in a temperature range of 323 to 623 K were plotted (Figure 7a), with the corresponding linear fitting lines. In statistics, the coefficient of determination (R2), which is 25



the proportion of the variance in the dependent variable that is predictable from the independent variable, is utilized to assess how well a model explains and predicts future outcomes.40 Herein, the R2 values of the fitting lines under different applied field were 0.81 (@45.2 MV/m), 0.87 (@50.0 MV/m), 0.90 (@55.2 MV/m) and 0.96 (@ 60.6 MV/m), respectively. All the R2 values were higher than 80%, implies that the band-to-band tunneling model has high applicability. It is worth mentioning that the R2 increased following the applied field which means a higher applicability of the tunneling model under the higher applied field. The deviation were occurred at the (Eeff)3/2 values between 0.65~0.7. The Eeff is significantly temperature depended. We alternatively plotted the emission current versus temperature (I-T; Figure 7b) for showing the clearer physical image for analysis. In the band-to-band tunneling model, It (and thus the corresponding I) increases exponentially following the rising of the temperature. However, the I-T curves in Figure 7b were not exactly in an exponential behavior. The curves were sketchily discriminated into three sections. In section-I and section-III, the curves generally fitted to an exponential behavior. Noticeably, the growth rate of the emission current declined in section-II, suggesting a weaker thermo-enhancement. It is worth mentioning that by using the slope of the fitting line and Fb-surface may possible to extract the effective mass. The difficulty comes from the accurately measurement of Fb-surface and further studies are needed.

In the above analysis, only the decrease of band-gap of p-Si (Egp) that leads to a narrower effective band-gap (Eeff) at the heterojunction during the temperature increasing was considered. However, it has been demonstrated that the Si/ZnO interface was filled with ZnO nano-crystals.29 26


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Double Schottky barriers (DSBs) with defect states may form between the grain boundaries.41 The defect states trap electrons. Less electrons may be excited from defect states at the relative lower temperature (section-I in Figure 7b) in thermo-enhanced field emission. Therefore, the band-to-band tunneling model showed well fit. Following the increase of temperature (section-II in Figure 7b), significant amount of electrons were excited from defect states. The excitation of electron could lead to a decrease of built-in potential difference (Vb) in the depletion region of ZnO and thus result in a lower Fb-surface. Accordingly, as indicated in Figure 7c and 7d, the increase of temperature from T1 to T2 may result in Vb1>Vb2 and Egp1>Egp2. The decrease in Vb restrains while the narrower Egp enhances the band-to-band tunneling, respectively. These inverse effects would result in a weaker thermo-enhancement on the emission current, which can qualitatively explain the deviation from exponential behavior of the I-T curves in section-II (Figure 7b). The trapped electrons would almost be excited when the temperature is increased to a higher level (section-III in Figure 7b). Namely, at T2

Band-to-Band Tunneling-Dominated Thermo ... - ACS Publications

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