WO2006061686A2

WO2006061686A2 - A cathodic device

Info

Publication number: WO2006061686A2
Application number: PCT/IB2005/003668
Authority: WO
Inventors: Johan Frans Prins
Original assignee: Johan Frans Prins
Priority date: 2004-12-10
Filing date: 2005-12-05
Publication date: 2006-06-15
Also published as: WO2006061686A3

Abstract

A method of forming a cathodic device includes the steps of forming a p-type layer (18) and an n-type layer (20) below a surface (20) of a substrate. The material has a conduction band which is at an energy level no more than 0.5 electron-Volts (eV) below the lowest vacuum energy level. The layers are formed so that they are in contact, with the p-type layer located between the surface and the n-type layer, and so that they form a p-n junction. The thickness of the p-type layer is somewhat less than the average distance which an electron injected into the p-type layer travels by diffusion and the thickness of the negatively charged depletion layer in the p-type layer is such that the difference between the thickness of the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer is substantially less than the said average distance.

Description

A CATHODIC DEVICE

THIS INVENTION relates to a method of forming a cathodic device and to a cathodic device, particularly when formed in accordance with the method.

According to the invention there is provided a method of forming a cathodic device, the method comprising, in a substrate of a material which is a large band gap semiconductor having a conduction band which is at an energy level no more than 0.5 electron-Volts (eV) below the lowest- energy vacuum level of electrons in a vacuum surrounding the substrate, so that the substrate material has near negative or preferably negative electron affinity characteristics: forming, under a surface of the substrate, a p-type layer to provide the substrate with a cathodic surface; and forming, under the p-type layer and in contact with the side of the p-type layer remote from the cathodic surface and at a p-n junction, an n-type layer, the formation of the p-type layer in contact with the n-type layer at the p-n junction giving rise to a positively-charged depletion layer on the n-side of the p-n junction and a negatively-charged depletion layer on the p-side of the p-n junction, the negatively-charged depletion layer and the p- type layer having respective thicknesses such that the thickness of the p-type layer is greater than that of the negatively-charged depletion layer by a value which is substantially less than the average distance which an electron injected into the p-type-layer from the n-type layer travels by diffusion before combining with a defect in the p-type layer, and the thickness of the p-type layer having a value which is somewhat less than said average distance.

The method may comprise forming the p-type layer before forming the n-type layer, or vice versa.

The invention thus provides a method of forming a cathodic device, the method including the steps of forming a p-type layer and an n-type layer below a surface of a substrate which is a large band gap semiconducting material, the material having a conduction band which is at an energy level no more than 0.5 electron-Volts (eV) below the lowest vacuum energy level so that the material has near negative or negative electron affinity characteristics, the layers being formed so that they are in contact, with the p-type layer located between the surface and the n- type layer, and so that the layers form a p-n junction with a positively charged depletion layer on the n side of the junction and so that the p-type layer comprises a negatively charged depletion layer on the p side of the junction, and a non-depleted layer, the thickness of the p-type layer being somewhat less than the mean free path length of an electron injected into the p-type layer from the n-type layer and the thickness of the non-depleted layer being substantially less than the said mean free path length.

Further according to the invention there is provided a cathodic device comprising a substrate material which is a large band gap semiconductor having a conduction band which is at an energy level no more than 0.5 eV below the lowest-energy vacuum level of electrons in a vacuum surrounding the substrate, so that the substrate has near negative or preferably negative electron affinity characteristics, the substrate having a cathodic surface under which there is a p- type layer and, under the p-type layer and in contact with the side of the p-type layer remote from the cathodic surface, an n-type layer, the contact between the p-type layer and the n-type layer being at a p-n junction giving rise to a positively-charged depletion layer on the n-side of the p-n junction and a negatively-charged depletion layer on the p-side of the p-n junction, the negatively- charged depletion layer and the p-type layer having respective thicknesses that the thickness of the p-type layer is greater than that of the negatively-charged depletion layer by a value which is substantially less than the average distance which an electron injected into the p-type layer from the n-type layer travels by diffusion before combining with a defect in the p-type layer, and the thickness of the p-type layer having a value which is somewhat less than said average distance.

L, ^■

The large band gap of the semiconductor substrate material may be manifested by its having a conduction band which is at an energy level no more than 0.5 eV below said lowest energy vacuum level, the conduction band preferably being at an energy level above the vacuum level, more preferably as high as practicable above the vacuum level.

The actual thickness selected for the p-type layer will depend on the density, on the one hand, of electron donors in the positively-charged depletion layer and, on the other hand, on the density of electron acceptors in the negatively-charged depletion layer, and routine experimentation should be carried out to determine optimum or at least acceptable thicknesses for the various layers, bearing in mind practical and economic considerations, and bearing in mind that the average distance L which an electron injected from the n-type layer into the p-type layer travels by diffusion before combining with a defect can be calculated by the relationship:

L = ( Dr)* in which:

T is the average lifetime of such injected electron; and D is the diffusion coefficient.

The diffusion coefficient D can in turn be obtained from the Einstein relationship:

e in which: μ is the electron mobility; k_B is Boltzmann's constant; T is the temperature in °K; and e is the elementary charge of an electron.

By substantially less with regard to the degree to which the difference in thickness between the p-type layer and the negatively-charged depletion layer is less than the average distance which an electron injected into the p-type layer from the n-type layer travels by diffusion before combining with a defect in the p-type layer, is meant that the difference in thickness should amount to at most 70% of said average distance, preferably at most 50% and typically 10 - 50%. In turn, by somewhat less with regard to the degree to which the thickness of the p-type layer is less than said average distance, the p-type layer thickness should be 50 - 100% of said average distance, preferably 70 - 100% and typically 50 - 70%.

The minimum thickness of the p-type layer, i.e. the minimum depth of the p-n junction below the cathodic surface of the p-type layer, should be greater than the thickness of the negatively-charged depletion layer contained therein, and the thickness W_p of the negatively- charged depletion layer in the p-type layer can be calculated from the relationship:

in which:

N_A is the electron acceptor density in the p-type layer;

N_D is the electron donor density within the n-type layer; ε is the permittivity of the substrate; and

I Cp₀1 is the modulus of the contact potential between the n-type layer and the p-layer (roughly equal to the difference between the respective individual energies of the electron donors and the electron acceptors); and e is the elementary charge of an electron. .

It should be noted that the cathodic surface, under which the p-type layer exists or is formed, may comprise an area in the form of an island surrounded by a peripheral area under which an extension of the material of the n-type layer exists or is formed.

While, in principle, any suitable material having the necessary characteristics or properties set forth above may be used for the substrate, such as cubic boron nitride, aluminium nitride or silicon carbide, it is expected that diamond (including both single-crystal and polycrystalline forms thereof) will be preferred. Furthermore, while said characteristics or properties may be inherent in the substrate, which can in principle be manufactured or selected to have them, it is expected that at least some of the necessary characteristics or properties will typically be induced in the substrate by treatment thereof.

Thus, the necessary properties or characteristics may be achieved during crystal vapour deposition (CVD) growth of the substrate material, and/or they may be introduced, for example into a pre-formed substrate material having said large band gap, by ion implantation. Furthermore, the substrate may, for this purpose, be subjected to surface treatment to enhance the negative electron affinity of the substrate, particularly at the treated surface.

As indicated above, suitable substrate materials are characterized by having large band gaps, preferably such that they have conduction bands which are at higher energies than the vacuum level. Preferably the large band gap of the substrate material is thus at least 2eV, more preferably at least 5eV, and typically 5 - 7eV. This applies to the p-type layer and preferably also to the n-type layer, which are conveniently of the same semiconducting substrate material.

While a suitable diamond substrate can, as indicated above, in principle be formed by CVD growth, it may instead be obtained by the selection of an already pre-existing or preformed diamond substrate, for example a high purity (Type Ha) diamond, and by subjecting its surface to cleaning and polishing. The cleaning and polishing may be to provide the diamond with a flat cathodic surface. Instead, however, the diamond may be micromachined and polished to provide the diamond with a conical (more or less sharply pointed) cathodic surface (not primarily for field-effect purposes as is usually the case, but to provide for transmission of a focused electron beam of high electron density, although some degree of field emission could be beneficial).

The diamond substrate material may then, optionally after masking its surface, be subjected to various ion implantations, respectively to form the p-type layer and the n-type layer containing the necessary defects comprising electron acceptors and electron donors at appropriate densities, the p-type layer and the n-type layer being of appropriate thicknesses so that the p-n junction is at an appropriate depth below the surface having the negative electron affinity. In this way a positively-charged depletion layer of appropriate thickness comprising electron donors can be formed on the n-side of the p-n junction, and a negatively-charged depletion layer of appropriate thickness comprising electron acceptors can be formed on the p- side of the p-n junction. For example, boron ion implantation may be used to form the p-type layer, and oxygen- or particularly nitrogen ion implantation may be used to form the n-type layer, appropriate ion implantation energies being employed to obtain desired implanted ion densities at desired depths below the respective outer surfaces of the n-type layer and p-type layer. In addition, hydrogen-termination of carbon bonds at said surface, for example by hydrogenation of the surface after ion implantation, to form a dipole layer thereon, may be useful.

In the case of diamond of Type Ha described above, the Applicant has established that a suitable depth for the p-n junction below the outer surface of the p-type layer is at most ,10μm, preferably being 0.05 - 5μm, more preferably 0.1 - 1μm. The depth of the p-n junction below the outer surface of the n-type layer is not critical, and is determined by the substrate thickness.

The density of electron donors in the positively-charged depletion layer may be at least 1 x 10¹⁵ - 1 x 10¹⁹/cm³, preferably 1 x 10¹⁶ - 1 x 10¹7 cm³, e.g. 1 x 10¹7cm³. Similarly, the density of the electron acceptors in the negatively-charged depletion layer may be 1 x 10¹⁵/cm³ - 1 x 10¹⁹/cm³, preferably 1 x 10¹⁶ - 1 x 10¹⁸/cm³, e.g. 1 x 10¹7cm³.

In this regard it will be appreciated that, when the cathodic device of the present invention is connected into an electrical circuit in which it forms a cathode in opposition to an anode across a vacuum gap, the cathodic device will be connected to the circuit by an electrical or ohmic contact whereby its n-type layer is connected to the circuit at a position on the outer surface of the n-type layer under which position the positively-charged depletion layer is located, in spaced relationship from said outer surface. This outer surface may be on the opposite side of the substrate from the anode, so that the contact can be regarded as a so-called back contact, but it may indeed be on the same side of the substrate, as long as the material under the contact forms an extension of the material of the n-type layer. Furthermore, the electrical contact, particularly when in the form of a back contact, may be of silicon, the diamond in this case conveniently being grown on the silicon back contact.

The invention will now be described, in more detail and by way of a non-limiting example, with reference to the accompanying diagrammatic drawings, in which:

Figure 1 shows a schematic cross-sectional side elevation of a cathodic device in accordance with the -present invention, connected into an electrical circuit to form a cathode which is opposed across a vacuum gap by an anode, the anode and the cathodic device being shown grounded or earthed; and

Figure 2 shows the device of Figure 1 , but with a positive potential applied to the anode to generate an electric field across the vacuum gap directed from the anode towards the cathode, so that the field accelerates negatively-charged electrons from the cathode towards the anode; and

Figure 3 shows a graph of current as a function of potential of a device manufactured by ion implantation.

In the drawings, the electrical circuit is generally designated by reference numeral 10, and comprises a cathodic device 12 in accordance with the present invention, spaced across a vacuum gap 14 from an anode 16. The cathodic device 12 is in the form of a substrate comprising a large band gap material in the form of a high purityType Ha diamond, modified to be of layered construction. The cathodic device 12 thus comprises a p-type layer 18 under a surface 20 of negative electron affinity, and an n-type layer 22 on the side of the p-type layer 18 remote from the surface 20. The p-type layer 18 forms a cathode whose surface 20 opposes a conducting anode surface in the form of a gold-plated hemispherical surface 21 of the anode 16 across the vacuum gap 14; and the n-type layer 22 is integrally fast- and continuous with the p- type layer 18 at a p-n junction 24.

The side of the n-type layer 22 remote from the p-n junction is defined by a surface 26 connected to a back contact in the form of a gold-plated ohmic contact 28 shown grounded at 30 in Figure 1. The anode may have an annular construction, such that electrons extracted from the device 12 can be accelerated and steered towards a screen of a cathode ray tube where they are capable of switching pixels such as phosphor pixels. On opposite sides of the p-n-junction 24 are shown a positively-charged depletion layer 34 and a negatively-charged depletion layer 36. The layer 34 is spaced below the surface 26 and is in contact with the layer 36 at the p-n junction 24, the layer 36 in turn being spaced below the surface 20.

The construction shown in Figure 2 is essentially similar to that shown in Figure 1 , except that the ohmic contact 28 is shown connected by an electrical (copper) lead 38 to a direct current (DC) power supply 40 which applies a positive potential to the surface 21 of the anode 16, to generate an electric field directed from the anode surface 21 towards the cathode surface 20.

Superimposed on the constructions shown in Figures 1 and 2 are shown the conduction band and valence band of the cathodic device 12, respectively designated 42 and 44 and shown in broken lines; and the Fermi-levels of the n-type layer 22 outside the positively- charged depletion layer 34, of the p-type layer 18 outside the negatively-charged depletion layer 36 and of the anode 16, respectively designated 46, 48 and 50. Finally, the depth of the p-n junction 24 (shown in dotted lines) below the cathode surface 20 is designated S, the thicknesses (shown in broken lines) of the negatively-charged depletion layer 36 and of the positively-charged depletion layer 34 respectively being designated W_p and W_n, and the vacuum levels at the surfaces 20, 24 and 26 (shown by doted lines) respectively being designated 52, 54 and 56.

The cathodic device 12 can be manufactured in different ways. When using diamond, the n-type and p-type layers respectively 22 and 18 can be generated by CVD growth. Instead, they can be generated by ion implantation. It may in fact not be necessary that the n- type layer 22, beneath the p-type surface layer 18 having negative electron affinity, has also to be a negative electron affinity material. However, when materials are used having different band gaps, a hetero-junction is formed. Such hetero-junction has band-energy offsets, and would not have an optimum efficiency for injecting electrons into the vacuum. Another aspect to take note of is that the negative electron affinity action can be amplified by forming other dipole layers on the surface of the substrate, for example by hydrogenating the surface 20, if it is that of a diamond.

To make the cathodic device 12 shown in the drawings for connection into the circuit 10, ion implantation was carried out on a diamond substrate. The diamond employed was a natural, insulating Type Ha diamond of high purity and having a flat square surface of 3.6 x 3.6mm². After polishing of this surface by techniques well known in the art using a standard diamond-polishing scaife with fine diamond powder to obtain a flat surface, and cleaning the flat surface by boiling in a 3:4:1 mixture (by volume) of concentrated sulphuric acid, concentrated nitric acid and concentrated perchloric acid as is well known in the art, the surface was masked to expose only a circular centrally-located area (20 in Figures 1 and 2) with a diameter of 2mm. The substrate was then ion-implanted, through this unmasked circular area, with boron ions in the energy range 25 - 70 keV, while maintaining the diamond substrate at the temperature of liquid nitrogen under a hard vacuum of 1 x 1Cr⁶TOn- (1.33 x 1Cr⁶ mbar).

Various doses of boron ions were implanted at various energies (except for the dose implanted at 25 keV), the doses being selected to generate a uniformly-doped p-type layer below the polished surface 20. The dose implanted at 25 keV was, however, increased to a value large enough to provide the substrate with a thin near-surface layer which was totally amorphous.

After the boron-ion implantation was complete, the diamond was rapidly heated from the temperature of liquid nitrogen used, up to 1000⁰C (by rapidly sliding it into a graphite crucible pre-heated to 1000⁰C), at which temperature it was held for 30 minutes to anneal it. This annealing activated the implanted boron ions to convert them into electron acceptors. Furthermore, the thin near-surface amorphous layer implanted with 25 keV boron ions was converted to graphite, which was etched off the surface 20 by boiling in the abovementioned concentrated acid cleaning solution comprising a mixture of concentrated sulphuric acid, concentrated nitric acid and concentrated perchloric acid in said 3:4:1 volume ratio. A very-near- surface layer of about 20 Angstrom units (A) thick remained, containing boron electron acceptors to a density of about 1 x 10²⁰ ions/cm³ in order to ensure that the Fermi-level would not be pinned at the surface 20.

The diamond was then again cleaned as described above, and implanted through its entire 3.6 x 3.6mm² surface with nitrogen ions, at said liquid nitrogen temperature, at energies of 70 - 170 keV. Most of the implanted nitrogen ions accordingly reached a greater depth under the 3.6 x 3.6 mm² surface than was reached under the surface 20 by the previously implanted boron ions. Doses of nitrogen ions were implanted at various energy levels in said .70 - 170 keV energy range to promote a uniformly doped nitrogen ion-containing layer, with evenly dispersed nitrogen ions at a more or less constant concentration therein, below the layer containing the implanted boron ions. After nitrogen ion implantation the diamond was again rapidly heated from the liquid nitrogen temperature, this time up to 500⁰C, by sliding it into a pre-heated graphite crucible at 500°C, at which temperature it was held to anneal it for 30 minutes. This annealing at 500⁰C activated the nitrogen ions by converting them to electron donors, providing donor sites or states in the diamond, each having an ionization energy of about 0.29 eV.

The diamond was then again cleaned as described above and the 3.6 x 3.6mm² surface was masked to cover the circular central area 20 through which the boron doping had taken place, and the remainder of the 3.6 x 3.6mm² surface, surrounding the masked area 20, was implanted with nitrogen ions, again at said temperature of liquid nitrogen. Implantation energies in the range 25 - 60 keV were used in this case, to promote the formation, outside and surrounding the boron-doped circular central area 20, of a nitrogen-doped n-type layer which extended all the way up to the 3.6 x 3.6mm² surface of the diamond.

After annealing by heating again to 500⁰C as described above, the central circular .area 20 was again masked and the entire exposed surface of the diamond was subjected to a nitrogen-plasma treatment by direct extraction of nitrogen ions from a nitrogen DC-plasma on to the diamond using equipment illustrated in Figure 1 of published International Patent Application WO 03/019597 (PCT/IB 02/03482) whereby a nitrogen plasma was generated between a grid and a plate having a hole in it, the ions being extracted from the hole by applying a 150V negative bias, which directed the nitrogen ions at and on to the surface 20 of the substrate. This plasma treatment increased the density or concentration of nitrogen ion electron donor states or sites at the surface 26 to permit achievement of ohmic-type contact by the contact 28 to the surface 26, by way of electron-tunneling into the n-type layer.

The ohmic contact at 28 was then made by clamping a gold-plated contact clamp to the surface 26. The anode 16 was formed by a gold-plated probe having a hemispherical tip having a radius of 0.5mm. When a DC_' potential difference of 20V was established between the surface 26 connected to the ohmic contact 28 and the anode 16, under a hard vacuum pressure of at most 0.75 x 10^"8 Torr (1 x 10^"8 mbar), this switched on the circuit 10 in the fashion of a diode junction, whereupon the device 12 injected copious numbers of electrons into the vacuum gap, which electrons were then accelerated towards the anode 16.

An example of the current-voltage (IV) characteristics of one of the devices manufactured by ion implantation is shown in Fig. 3. The dash-dot curve shows the IV- characteristics when the anode touches the diamond surface. This is a typical curve for a p-n junction which proves that such a junction has formed under the surface. The anode was then retracted by 5 μm from the diamond surface. The IV-characteristics changed, as shown by the solid curve in Fig. 3. The device still acts like a pn-junction but a larger voltage is required to also accelerate the electrons from the diamond's surface through the gap to the anode.

It was found that the circuit 10 could further be improved by providing an annular contact (not shown) on the surface 20, and by biassing this contact to cause a current to start to flow through the n-p junction 24, before applying said potential difference between the surface 20 and the anode 16. This allowed electrons immediately to be extracted through the annular contact, as soon as said potential difference was applied.

It should be noted that the values of the parameters mentioned above and related to the drawings, i.e of S, W_n, W_p, ΔΦ_A, eΦj and eΦ_v, are all a function of electron donor density, of electron acceptor density and, of applied potential, which can vary from zero up to 1000V or more.

Without being bound by theory, the Applicant sets forth hereunder the present understanding of the invention.

As emerges from the aforegoing, the present application discloses a method for accelerating electrons, extracted from the substrate 12 with negative electron affinity, towards the anode 16, by means of the cathodic device 12 which acts as a cold cathode, and which in principle can replace hot cathodes such as heated filaments.

In order to manufacture the cathodic device 12, it is preferable to start with a substrate 12 which has a surface 20 of negative electron affinity. Negative electron affinity implies that, before any depletion layer can form at the surface 20, in response to an outflow of electrons from the substrate 12 through the surface 20, the electrons will find themselves at a higher energy than the vacuum level 52. Although a diamond substrate 12 should be ideal for forming a cathodic device 12 capable of acting as a cold cathode, the present invention is not restricted to using only diamonds. Any substrate 12 with a surface 20 having a suitable negative electron affinity or near negative electron affinity may be used. The negative electron affinity can be an inherent property of the substrate 12, or it may be introduced by surface treatment of the substrate 12, for example by hydrogen-termination of carbon bonds on a diamond surface.

A thin surface layer of the substrate 12 should be doped to form the p-type layer 18, while below the p-type layer 18, the substrate 12 should be n-type, as in layer 22, such that the p-n junction 24 is generated below the surface 20 at a suitably shallow depth S. The actual depth S employed, is determined by the densities of the electron acceptors and of the electron donors, on opposite sides of the p-n junction 24. According to the depletion layer approximation, the positively-charged depletion layer 34 forms on the n-side of the p-n junction 24, and the negatively-charged depletion layer 36 forms on the p-side of the p-n junction. Assuming an abrupt transition at the p-n junction, the expected electron-energy situation can be modelled as shown in Figure 1 and Figure 2. The electron-energy band bending, within the substrate 12 having negative electron affinity, before any positive bias has been applied to the anode, is shown in Figure 1. In order to make the back contact 28 ohmic, the surface 26 of the n-type layer, on which the back-contact 28 is formed, should be highly doped, such that the depletion layer 34 which forms, within the substrate and underneath the back contact 28, is sufficiently narrow that electrons can easily tunnel through it.

The position of the p-n junction 24 at the depth S is shown, as well as the positions of the depletion layers 34 and 36 of widths W_n and W_p respectively. Electron-energy band bending, within the layers 34 and 36, is the same as for any p-n junction. It is assumed, in Figures 1 and 2, that there is no band bending at the substrate surface 20, i.e. there is no Fermi-level pinning, nor any other dipole layer on the surface 20. Because of the negative electron affinity of the surface 20, the conduction band 42 is at a higher energy at the surface 20 than the external vacuum level 52. Because the surface 20 is p-type, there are no, or very few, electrons in the conduction band 42, which can flow out of the surface 20 in order to generate an external electron-charge layer or cloud above the surface 20. Thus, a depletion layer and a barrier to electron emission, do not form below the surface 20.

Because the anode 16 shown in Figure 1 is grounded, it can be regarded as being in contact with the back contact 28, which is also grounded, and therefore the Fermi-levels respectively within the substrate 12, within the back contact 28 and within the anode 16 must be the same. In Figure 1 it has been assumed that the back contact 28 and the anode 16 have exactly the same work function. Thus, in order for the Fermi-levels 46, 48 and 52 to align, electrons have to flow from the substrate 12, through the back contact 28, and into the anode 16. Positive holes are left behind, and accumulate below the surface 20 of the substrate 12, and electrons arriving in the anode 16, in turn, accumulate under the surface 21 of the anode 16.

Thus the surfaces 20 and 21 , respectively of the substrate 12 and the anode 16, act as two capacitors plates-. Accordingly, an electric field, directed from the substrate 12 towards the anode 16, is generated. Because of this field, there is a potential difference ΔΦ_A between the substrate surface 20 and the anode surface 21. An electron, with a charge -e, will have a lower energy, namely when eΔΦ_A, immediately outside the surface 20 of the substrate 12, than it would have, when immediately outside the surface 21 of the anode 16. In other words and as shown in Figure 1, an electron experiences a lower vacuum level 52 at the surface 20 of the substrate 12 than at the surface 21 of the anode 16. Thus, in order to attract electrons from the surface 20 of the substrate 12 to the anode 16, a positive potential Φ, greater than ΔΦ_Aι must be applied to the anode 16. However, the back contact 28 and anode 16 need not have the same work function and their work functions may be different, if desired.

The case is shown in Figure 1 where the work functions of the back contact 28 and the anode 16 are the same. Where a potential Φ is applied to the anode 16 is greater than ΔΦ_A, the situation would be as depicted in Figure 2. Assuming that the electrical fields generated within the n-type layer 22 and the p-type layer 18 are small enough to be neglected, a portion Φ_v of the applied potential Φ, should appear across the vacuum gap 14, between the substrate surface 20 and the anode 16, and the remainder of the applied potential Φ, i.e. Φj, should appear across the depletion layers 34, 36 at the sub-surface p-n junction, such that:

φ = φ_v + φ_j

In Figure 2 these potentials are shown as energy offsets eΦ_v and eΦj, respectively between the Fermi-levels 50 and 48 of the anode 16 and of the p-type layer 18, and between the Fermi-levels 48 and 46 of the p-type layer 18 and of the n-type layer 22, respectively.

The potential Φj acts as a forward bias over the p-n junction 24. Electrons are thus injected into the conduction band 42 of the p-type layer 18, within which they can move towards the surface 20. Provided that the depth S is small enough, such that very few of these electrons combine with holes within the p-type layer 18, these electrons will arrive at the surface 20, will exit the surface 20, and will then be accelerated by the electric field within the vacuum gap 14 from the substrate surface 20 to the anode 16. It should be noted that this field is, in the case under discussion, not given by Φ_v divided by the distance between, the substrate surface 20 and the anode 16. The reason for this is that a part of Φ_v has to cancel the initial potential difference ΔΦ_A. Accordingly, the field experienced by the electrons is given by:

in which:

E_v is the electrical field in the vacuum gap 14; and d is the distance between the surface 20 and the anode 16.

In order for the device 12 to work as a cold cathode, S should be greater than W_p. The width W_p of the positive depletion layer is given by the relationship, set forth above, of:

In this regard it is to be noted that | Φ_o| , the modulus of the contact potential at the p-n junction between the n-type.and p-type substrate layers 22 and 18, is roughly equal to the difference between the energies of the electron donors and the electron acceptors. The larger N_A becomes, the smaller W_p becomes. It is thus possible to calculate, from the above relationship, the minimum depth S which is required for such a p-n junction, being no less than W_p.

As already mentioned above, S should also not be too large, otherwise the electrons, Injected into the p-layer 18, will, before they can exit the surface 20, recombine with holes. Once in the conduction band 42 of the p-type layer 18, the electrons move principally by diffusion (provided the electric field within this layer is negligible as has been assumed above). If the average lifetime of an injected electron, before recombining with a hole is T and the diffusion coefficient is D, then the average distance L which the injected electron can diffuse before recombination, can be written, as indicated above, by the relationship:

L = (Drf

By using the Einstein relationship, also set forth above, which gives D as a function of the electron mobility μ, Boltzmann's constant k_B, and the temperature T, it is possible to obtain the relationship:

Thus, the higher the mobility μ, the larger L can be. In order to get most of the injected electrons to reach the surface, the difference between S and W_p should be substantially less than L. It is known that the higher the acceptor density N_A, the more the electrons will be scattered and the lower their mobility μ will be. Thus to increase L, N_A should be as small as possible. On the other hand, by decreasing N_A, the larger W_p will become, and this should be taken into account when selecting the depth S for the p-n junction 24.

Claims

1. A method of forming a cathodic device, the method including the step of forming a p-type layer and an n-type layer below a surface of a substrate which is a large band gap semiconducting material, the material having a conduction band which is at an energy level no more than 0.5 electron-Volts (eV) below the lowest vacuum energy level so that the material has near negative or negative electron affinity characteristics, the layers being formed so that they are in contact, with the p-type layer located between the surface and the n-type layer, and so that they form a p-n junction with a positively charged depletion layer on the n side of the junction and a negatively charged depletion layer on the p side of the junction, the thickness of the p-type layer being somewhat less than the average distance which an electron injected into the p-type layer from the n-type layer travels by diffusion before combining with a defect in the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer being such that the difference between the thickness of the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer is substantially less than the said average distance.

2. A method as claimed in claim 1, in which either the p-type layer or the n-type layer is formed first.

3. A cathodic device which comprises a substrate which is a large band gap semiconducting material, the material having a surface, a p-type layer and an n-type layer below the surface, and a conduction band which is at an energy level no more than 0.5 electron-Volts (eV) below the lowest vacuum energy level so that the material has near negative or negative electron affinity characteristics, the p-type layer being located between the surface and the n-type layer arid the layers being in contact so that they form a p-n junction with a positively charged depletion layer on the n side of the junction and a negatively charged depletion layer on the p side of the junction, the thickness of the p-type layer being somewhat less than the average distance which an electron injected into the p-type layer from the n-type layer travels by diffusion before combining with a defect in the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer being such that the difference between the thickness of the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer is substantially less^ than the said average distance.

4. A cathodic device as claimed in claim 2, in which the conduction band is at an energy level which is above the vacuum energy level.

5. A cathodic device as claimed in claim 3 or claim 4, in which the difference between the thicknesses of the p-type layer and the thickness of the negatively charged depletion layer in the p-type layer is equal to or less than 70% of the said average distance.

6. A cathodic device as claimed in claim 5, in which the difference is equal to or less than 50% of the said average distance.

7. A cathodic device as claimed in claim 6, in which the difference is between 10 and 50% of the said average distance.

8. A cathodic device as claimed in any one of claims 3 to 7 inclusive, in which the thickness of the p-type layer is between 50 and 100% of the said average distance.

9. A cathodic device as claimed in claim 8, in which the thickness is between 70 and 100% of the said average distance.

10. A cathodic device as claimed in any one of claims 3 to 9 inclusive, in which the depth of the p-n junction below the surface is less than or equal to 10 μm.

11. A cathodic device as claimed in any one of claims 3 to 10 inclusive, in which the depth of the p-n junction below the surface is between 0.05 and 5 μm.

12. A cathodic device as claimed in any one of claims 3 to 11 inclusive, in which the depth of the p-n junction below the surface is between 0.1 and.1 μm.

13. A cathodic device as claimed in any one of claims 3 to 12 inclusive, in which the positively charged depletion layer has an electron donor density of between 1x10¹⁵ and 1x10¹⁹ cm ^"

14. , A cathodic device as claimed in any one of claims 3 to 13 inclusive, in which the positively charged depletion layer has an electron donor density of between 1x10¹⁶ and 1x10¹⁸ cm

15. A cathodic device as claimed in any one of claims 3 to 14 inclusive, in which the positively charged depletion layer has an electron donor density of about 1x10¹⁷ cm Λ

16. A cathodic device as claimed in any one of claims 3 to 15 inclusive, in which the negatively charged depletion layer has an electron acceptor density of between .1x10¹⁵ and 1x10¹⁹ cm ^"3.

17. A cathodic device as claimed in any one of claims 3 to 16 inclusive, in which the negatively charged depletion layer has an electron acceptor density of between 1x10¹⁶ and 1x10¹⁸ cm ^"3.

18. A cathodic device as claimed in any one of claims 3 to 17 inclusive, in which the negatively charged depletion layer has an electron acceptor density of about 1x10¹⁷ cm ^"3.

19. A cathodic device as claimed in any one of claims 3 to 18 inclusive, in which the band gap of the substrate is at least 2eV.

20. A cathodic device as claimed in any one of claims 3 to 19 inclusive, in which the band gap is at least 5eV.

21. A cathodic device as claimed in any one of claims 3 to 20 inclusive, in which the band gap is between 5 and 7eV.

22. A cathodic device as claimed in any one of claims 3 to 21 inclusive, in which the surface is in the form of an island surrounded by a peripheral area which is an extension of the n- type layer.

23. A cathodic device as claimed in any one of claims 3 to 22 inclusive, in which the substrate is formed by a method which includes a step selected from at least one of a chemical vapour deposition step and an ion implantation step.

24. _. A cathodic device as claimed in any one of claims 3 to 23 inclusive, which includes a surface treatment step to enhance the negative electron affinity of the substrate.

25. A cathodic device as claimed in any one of claims 3 to 24 inclusive, in which the substrate is selected from diamond, cubic boron nitride, aluminium nitride and silicon carbide.

26. A cathodic device as claimed in claim 25, in which the substrate is a diamond substrate and in which the p-type layer is formed by ion implantation using boron.

27. A cathodic device as claimed in claim 25 or claim 26, in which the substrate is a diamond substrate and in which the n-type layer is formed by ion implantation using one of oxygen and nitrogen.

28. A cathodic device as claimed in any one of claims 24 to 27 inclusive, in which the substrate is a diamond substrate and in which the surface treatment step is a surface hydrogenation step for hydrogen termination of carbon bonds at said surface.

29. A cathodic device as claimed in any one of claims 3 to 28 inclusive in which the surface is conical or pointed.