P. H. Cutler

THEORETICAL STUDY OF FIELD EMISSION FROM DIAMOND

The electron field emission from diamond surfaces is investigated theoretically using a model consisting of the projection of the energy band surfaces in the 〈111〉, 〈110〉, and 〈100〉 emission directions. The effect of the negative electron affinity, the band bending, the image interaction, and surface states is examined in detail. It is found that the conventional theory of electron field emission applied to crystalline diamond cannot explain the measured high‐current emission at low fields. We postulate two subbands in the intrinsic band gap, which may be generated by defects or impurities. With reasonable band parameters, the calculated I‐V characteristics agree with experimental data.

Model calculations of internal field emission and J–V characteristics of a composite n-Si and N–diamond cold cathode source

A model to describe internal field emission through the interface between highly n-doped Si and nitrogen (N)-doped diamond is presented. We describe the roughness on the Si surface as a collection of sharp, spherically pointed Si asperities embedded in the diamond film. These “tips” provide enhancement of the applied electric field, which, in conjunction with the high N doping of diamond, results in the formation of a Schottky barrier which allows for tunneling or internal field emission from the Si into the conduction band of diamond. This enhanced electric field is also sufficient to induce valence band tunneling from the Si into the diamond conduction band. In our model limitations on the field mediated transport of holes from the n-doped Si/diamond interface to the cathode base leads to charging of the Si asperities. This charge accumulation results in band bending in Si and a significant reduction in the valence band current. The calculated J–V characteristics for the internal field emission lead to ...

Reflection and transmission of electrons through surface potential barriers

Abstract A numerical treatment has been made of the reflection properties of several 1-dimensional surface potential barrier models. Curves of reflection coefficient versus energy have been obtained for the classical image barrier, the modified or corrected image barrier and the Bardeen potential in both the zero and finite field cases. For zero field, the smoothly varying Bardeen potential yields smaller reflection except for energies close to zero. This result suggests that the presence of the discontinuous derivative in the potential function introduces spurious reflection. There is no appearance of the elastic scattering component found in low-energy electron diffraction for any of the 1-dimensional models investigated. With fields, the curves are qualitatively similar except near the barrier maximum. However, for incident energies above the barrier, the image and modified image are larger in magnitude than the Bardeen model. The present treatment is compared with a recent numerical computation of the periodic deviations in the Schottky effect.

Theoretical analysis of field emission from a metal diamond cold cathode emitter

Recently, Geis et al. [J. Vac. Sci. Technol. B 14, 2060 (1996)] proposed a cold cathode emitter based on a Spindt-type design using a diamond film doped by substitutional nitrogen. The device is characterized by high field emission currents at very low power. Two properties, the rough surface of the metallic injector and the negative electron affinity of the (111) surface of the diamond are essential for its operation. We present a first consistent quantitative theory of the operation of a Geis–Spindt diamond field emitter. Its essential features are predicated on nearly zero-field conditions in the diamond beyond the depletion layer, quasiballistic transport in the conduction band, and applicability of a modified Fowler–Nordheim equation to the transmission of electrons through the Schottky barrier at the metal-diamond interface. Calculated results are in good qualitative and quantitative agreement with the experimental results of Geis et al.

Calculation of electron field emission from diamond surfaces

The electron field emission from diamond surfaces is investigated theoretically using a model consisting of the projection of the energy‐band surfaces in the 〈111〉, 〈110〉, and 〈100〉 emission directions. The effect of the negative electron affinity, the band bending, the image interaction, and surface states are examined in detail. It is found that the tunneling from the bulk conduction and valence bands is negligible in p‐type diamond. While emission from surface states located about 1 eV below the conduction band has sufficient transmission probability to produce currents observed in experiments, there is no obvious transport mechanism in intrinsic, doped, or polycrystalline diamond to sustain a direct field emission current. We postulate two subbands in the intrinsic band gap, which may be generated by defects or impurities. With reasonable band parameters, the calculated j–F characteristics agree with experimental data.

Energy exchange processes in electron emission at high fields and temperatures

A new more complete theory for energy exchange processes in electron emission is formulated. It is found that the tunneling contribution to the availability of vacant states is necessary to explain the replacement process occurring in the emitter region. The introduction of the tunneling states now makes it possible to obtain both the average energies of the emitted and replacement electrons using the same formalism. At T=0 K, the average energy of replacement electrons, 〈er〉, is the same as the average energy of the emitted electrons, 〈ee〉. As T increases, 〈er〉 increases rapidly until it reaches a maximum and then decreases slowly, while 〈ee〉 increases monotonically. When T equals the inversion temperature Ti, 〈ee〉=〈er〉 and the energy exchange Δe=0. We have also calculated both Δe and Ti as a function of field F. For high temperature and fields, the value of Ti differs considerably from that obtained without the tunneling state contribution and Ti exhibits nonlinear behavior as a function of field. Tunne...

Nanoscale Devices for Rectification of High Frequency Radiation from the Infrared through the Visible: A New Approach

We present a new and viable method for optical rectification. This approach has been demonstrated both theoretically and experimentally and is the basis fot the development of devices to rectify radiation through the visible. This technique for rectification is based not on conventional material or temperature asymmetry as used in MIM (metal/insulator/metal) or Schottky diodes, but on a purely sharp geometric property of the antenna. This sharp “tip” or edge with a collector anode constitutes a tunnel junction. In these devices the rectenna (consisting of the antenna and the tunnel junction) acts as the absorber of the incident radiation and the rectifier. Using current nanofabrication techniques and the selective atomic layer deposition (ALD) process, junctions of 1 nm can be fabricated, which allow for rectification of frequencies up to the blue portion of the spectrum. To assess the viability of our approach, we review the development of nanoantenna structures and tunnel junctions capable of operating in the visible region. In addition, we review the detailed process of rectification and present methodologies for analysis of diode data. Finally, we present operational designs for an optical rectenna and its fabrication and discuss outstanding problems and future work.

Generalization of Fowler-Nordheim field emission theory for nonplanar metal emitters

Field emitter tips can now be fabricated with radii of curvature of the order of nm or even the size of a single atom. To include these geometric effects, we have calculated the field emission tunneling currents for hyperboloidal and conical free‐electron tip models using geometry‐dependent image interactions and bias fields. The numerical results can be fitted by an equation of the form J=AV2 exp(−B/V−C/V2), where A, B, and C are constants depending on material and geometric parameters. The calculated results, plotted as log J/V2 vs 1/V, do not exhibit the straight line behavior predicted by the Fowler–Nordheim model for field emission from a planar surface. Furthermore, the calculated current densities are dramatically enhanced for both the hyperboloidal (rt=10 nm) and conical (cone half‐angle=70°) emitter models. In addition, field emission energy distributions for both models are significantly different from that of the Fowler–Nordheim planar model.

The use of internal field emission to inject electronic charge carriers into the conduction band of diamond films: a review

Abstract Several thin film composite metal(semiconductor) diamond cold cathode sources have recently been fabricated exhibiting high current–low power characteristics. We have modeled the field emission in these thin film diamond electron sources as a three-step process (electron injection, transport and vacuum emission). Critical to the operation of these devices is a mechanism for populating the conduction band (CB) of diamond with charge carriers. Internal field emission has been proposed for the injection of electrons by tunneling from metal (semiconductor) substrates into the diamond CB. A thin (Schottky) tunneling barrier is created at the substrate–diamond interface by heavily doping the diamond with nitrogen and roughening the metal (semiconductor) interface to enhance the internal field. In this paper we review model calculations of the internal field emission process for both metal and semiconductor substrates. The results show good agreement with experiment, implying the usefulness of the internal field emission mechanism to provide electronic charge carriers in the CB of diamond films.

Monte Carlo study of hot electron and ballistic transport in diamond: Low electric field region

A Monte Carlo simulation of electron transport in the conduction band of diamond as a function of field and film thickness has been performed. It predicts that the energy distribution of field emitted electrons ‘‘heats up’’ when the internal electric field is of the order of 1 V/μm and greater. The energy distribution shifts and becomes broader as the width of the sample increases. With increasing field (≥10 V/μm), there is a transition to quasi‐ballistic‐like behavior. For thinner films (≤0.1 μm), the transport is more clearly ballistic with the peak energy scaling roughly with the field. It is suggested that if a realistic and viable electron injection mechanism into the conduction band of a diamond–metal or diamond–semiconductor interface could be found for those crystal faces of diamond exhibiting negative electron affinity, then a copious cold cathode electron emitter with field tunable energies is feasible.