--- title: "A proposal for a new type of thin-film field-emission display by edge breakdown of MIS structure" authors: ["V.N. Konopsky"] affiliation: "Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow region 142092, Russia" journal: "Journal of Physics D: Applied Physics" year: 1998 volume: "31" pages: "617-621" doi: "10.1088/0022-3727/31/6/014" type: journal-article site_group: "Field emission and MIS structures" url_abstract: "" url_pdf: "https://valery.konopsky.com/additional_pdf/A proposal for a new type of thin-film field-emission display by edge breakdown of MIS structure.pdf" language: en source_tex: "" source_pdf: "" --- ## Abstract A new type of field emission display (FED) based on an edge-enhance electron emission from metal-insulator-semiconductor (MIS) thin film structure is proposed. The electrons produced by an avalanche breakdown in the semiconductor near the edge of a top metal electrode are initially injected to the thin film of an insulator with a negative electron affinity (NEA), and then are injected into vacuum in proximity to the top electrode edge. The condition for the deep-depletition breakdown near the edge of the top metal electrode is analytically found in terms of ratio of the insulator thickness to the maximum (breakdown) width of the semiconductor depletition region: this ratio should be less than $2/(3\pi -2)\simeq 0.27$. The influence of a neighboring metal electrode and an electrode thickness on this condition are analyzed. Different practical schemes of the proposed display with a special reference to $\rm M/CaF_2/Si$ structure are considered. *Keywords: Field emission display, MIS structure, Edge breakdown.* $$A proposal for a new type of FED$$ # Introduction Flat panel field emission displays have the potential to be a low cost, high performance alternative to the currently dominant cathode ray tube and liquid crystal displays. The first major problem in FEDs is the development of a reliable and efficient cold cathode electron emitter. Current FED prototypes use sharp metal or semiconductor tips as field emitters , that requires expensive lithography and other difficult fabrication processes. Besides, the control voltage for such tip emitters is rather high (about 100 V). Some researchers use diamond-like films that contain nanoscale crystalline structure as the electron source , or use diamond and other coatings of the sharp tips to improve the emission properties of the tips . In the present paper we propose another type of field emitter, where electrons are produced by an avalanche breakdown in the semiconductor near the edge of the top metal electrode in the MIS structure. The plan of this paper is as follows: in Section 2 we describe the proposed display, based on the edge breakdown of the MIS structure. In Section 3 we discuss the condition under which edge breakdown in the MIS structure takes place. In Section 4 we estimate the influence of a neighboring electrode on the edge breakdown condition and in Section 5 we discuss and summarize our results. In Appendix we briefly estimate the influence of an electrode thickness on the edge breakdown condition. # Field emission display based on edge breakdown of MIS structure The display proposed is schematically shown in Figure 1(a). Glass substrate 1 with conductive metal column lines 2 is coated with a thin semiconductor layer 3, which contains low p-doped column lines 4 that coincide with the metal ones. The film of the insulator with NEA 5 is grown on semiconductor, and conductive metal row lines 6 are deposited on the insulator film. Above the MIS structure the fluorescent screen 7 is located. The anode (fluorescent screen) and cathode (MIS structure) regions are separated by a vacuum space 8. When a positive voltage pulse of duration which is short compared to the time constant of thermal generation of minority carriers (electrons in our case) is applied to the top electrode of the MIS structure, no inversion layer can form. Thus, a large potential drop across the semiconductor will take place. If the amplitude of the pulse voltage is increased, band bending reaches large values where minority carriers are generated by nonthermal effects (by avalanche in our case). The amplitude of the pulse voltage, at which avalanche occurs we designate by $V_{\mbox{{\scriptsize{\rm break}}}}$. When we apply a pulse voltage $V_{\mbox{{\scriptsize{\rm control}}}}$, which amplitude is less then $V_{\mbox{{\scriptsize{\rm break}}}}$, but more than $V_{\mbox{{\scriptsize{\rm break}}}}/2$ to one row line, and simultaneously apply such a pulse voltage with another polarity to one column line, the avalanche breakdown in the semiconductor will take place at the intersection of these lines. Under condition, which will be pointed out below, the breakdown will take place near the edges of metal lines. Inasmuch as velocities of the avalanche electrons at the semiconductor-insulator interface are directed in an arbitrary way, it is clear that at least a portion of the avalanche electrons, ballistically passing through the thin film of the insulator, will be extracted with a good efficiency (due to NEA of the insulator) into vacuum, instead of being impinged with the top metal layer. Then this portion of electrons will be accelerated by screen voltage $V_{\mbox{{\scriptsize{\rm screen}}}}$ ($\sim +100\div +1000$ V) and will be hit to the fluorescent screen as it is shown in Figure 1(b). # Edge breakdown condition The deep-depletition breakdown of MOS capacitors was first reported by Goetsberg and Nicollian , who experimentally investigated doping conditions under which uniform avalanche takes place. Later a “universal and normalized” criterion for “field uniformity” in MOS capacitors was offered in the form $d/W_{\mbox{{\scriptsize{\rm max}}}}>0.3$ (where $d$ is the insulator thickness and $W_{\mbox{{\scriptsize{\rm max}}}}$ is the maximum (breakdown) width of the semiconductor depletition region) . This criterion was suggested in  based on computer-calculated values of the field distribution in MOS capacitors. In this section we obtain this criterion in an analytical form, with an emphasis on physical explanation of the result, that helps us to analyze operating conditions and an ultimate resolution of the display proposed. For this purpose let us at first consider a simple two-dimensional model of the electric field near the edge of the metal plate (see Figure 2(a)). Here $A_1-A_2$ and $A_2-A_3-A_4$ are conductive plates. Let one plate have the potential $V$, and the other plate have the zero potential. We will use a method of conformal transformations (see  or any textbook in this field) to find an electrical field distribution in such a system. The Schwarz-Chrisoffel transform ``` math \begin{equation} z={\i h\over \pi}\left[ 2\sqrt{\omega-1}-\i\ln\left( {1-\i\sqrt{\omega-1}\over 1+\i\sqrt{\omega-1}}\right) \right] \end{equation} ``` relates the upper half $\omega$ plane (Figure 2(b)) to the interior of the region $A_1-A_2-A_3-A_4$ of the $z$ plane (Figure 2(a)) . Thus, half of the real axis $\Re{(\omega)} >0$ is at potential $V$ while $\Re{(\omega)} <0$ is at zero potential. The potential of the electric field in the $\omega$ plane is the real part of the complex potential given by the analytical function ``` math \begin{equation} F=\varphi +\i\psi ={V\over \i\pi}\ln\omega \; . \end{equation} ``` The electric field in the $z$ plane is ``` math \begin{equation} {\d F\over \d z} = {\partial\varphi\over \partial x} - \i {\partial\varphi\over \partial y} = E_x-\i E_y = {\d F\over \d\omega}{1\over \d z/\d\omega} \; . \end{equation} ``` Performing the differentiation with respect to $\omega$ in ([1]) and ([2]) ``` math \begin{equation} {\d z\over\d\omega}={\i h\over \pi}{\sqrt{\omega-1}\over\omega} \end{equation} ``` ``` math \begin{equation} {\d F\over \d\omega}={V\over \i\pi\omega} \end{equation} ``` we get ``` math \begin{equation} E_x-\i E_y = -{V\over h\sqrt{\omega-1}} \; . \end{equation} ``` Our main interest is the field near $z=0$ ($\omega=1$). Expanding logarithm in ([1]) in a Taylor series at $\omega=1$ and holding the first two terms, we obtain ``` math \begin{equation} \sqrt{\omega-1} = \left( {3\pi\over 2h\i}z \right)^{1/3} \end{equation} ``` and from ([6]) we have ``` math \begin{equation} E_x-\i E_y = -{V\over h\left(3\pi z/2h\i \right)^{1/3}} \end{equation} ``` or ``` math \begin{equation} \left| E\right|={V\over h}{\left( 2h/3\pi\right)^{1/3} \over\left( x^2+y^2\right)^{1/6}} \; . \end{equation} ``` We may define ``` math \begin{equation} z_{\mbox{{\scriptsize{\rm cr}}}}={2h\over 3\pi} \simeq {h\over 4.71} \end{equation} ``` as a “critical” distance from the edge at which field strength is still higher than $V/h$ — the field strength between the plates far from the edge. Now the condition for edge breakdown is rather obvious: if insulator thickness is less than $z_{\mbox{{\scriptsize{\rm cr}}}}$ (as is shown in Figure 3) the breakdown takes place near the edge. But if $d>z_{\mbox{{\scriptsize{\rm cr}}}}$ the uniform breakdown occurs. The value $d+W_{\mbox{{\scriptsize{\rm max}}}}$ in the real MIS structure plays the role of the distance $h$ between the conductive plates in our model consideration. (The exception is the case when the distance $L$ (see Figure 1(b)) between the real metal plates is less than $d+W_{\mbox{{\scriptsize{\rm max}}}}$. In this case $h=L$.) From the equations ``` math \begin{equation} h=d+W_{\mbox{{\scriptsize{\rm max}}}} \end{equation} ``` ``` math \begin{equation} d1$ are at potential $V$ while part $-1<\Re{(\omega)} <1$ is at zero potential. The potential of the electric field in the $\omega$ plane is the real part of the complex potential given by the analytical function ``` math \begin{equation} F={V\over \i\pi}\ln{(w-1)} - {V\over \i\pi}\ln{(w+1)}\; . \end{equation} ``` Using the differentials with respect to $\omega$ of ([13]) ``` math \begin{equation} {\d z\over\d\omega}={2\i s\over \pi}{\sqrt{\omega^2-\lambda^2}\over(\omega^2-1)} \end{equation} ``` and ([15]) ``` math \begin{equation} {\d F\over \d\omega}={2V\over \i\pi(\omega^2-1)} \end{equation} ``` we may find the electric field in the $z$ plane from ([3]). ``` math \begin{equation} E_x-\i E_y = -{V\over s\sqrt{\omega^2-\lambda^2}} \; . \end{equation} ``` Our concern is the field near $z=\i h\pm s$ ($\omega=\pm\lambda$) points. Expanding arctanh and arctan in ([13]) in a power series at $\omega =\lambda$ and holding the first two terms, we have ``` math \begin{equation} \sqrt{\omega^2-\lambda^2} = {h\over s}\left[ {3\pi \over 2h\i}(z+h-\i s)\left(1+{h^2\over s^2}\right)^2 \right]^{1/3} \; . \end{equation} ``` and from ([18]) we have ``` math \begin{equation} E_x-\i E_y = -{V\over h\left[ (3\pi/2h\i)(z+h-\i s)\left(1+{h^2/s^2}\right)^2 \right]^{1/3}} \; . \end{equation} ``` Now the “critical” distance from the edge at which field strength is still higher than $V/h$ is ``` math \begin{equation} z_{\mbox{{\scriptsize{\rm cr2}}}}={2h\over 3\pi \left( 1+h^2/s^2\right)^2 }\; . \end{equation} ``` One can see that this value is coincident with ([9]) when $s\gg h$. For example, if $s=h$ so $z_{\mbox{{\scriptsize{\rm cr2}}}}$ is ``` math \begin{equation} z_{\mbox{{\scriptsize{\rm cr2}}}}={z_{\mbox{{\scriptsize{\rm cr}}}}\over 4}={h\over 6\pi}\; . \end{equation} ``` One can see that the distance $s$ between the top electrodes should be more than twice larger than $h=d+W_{\mbox{{\scriptsize{\rm max}}}}$ to avoid drastic decrease of $z_{\mbox{{\scriptsize{\rm cr2}}}}$. # Discussion and summary Firstly, let us mention the kind of insulator that may be used in this display. At least three kinds of insulators are appropriate for our purpose: hydrogen-terminated diamond (111), LiF and $\rm CaF_2$. Diamond has long attracted considerable attention as a cold cathode for FED due to its NEA and robust mechanical and chemical properties. LiF has the largest NEA of any solid. The NEA of LiF crystal is $-2.7$ eV . The possibility of epitaxial grown of LiF films on the Ge was also reported in . But we assume that the $\rm CaF_2/Si$ system is the best choice. The reasons for this are as follows: 1. $\rm CaF_2$ has a small but negative electron affinity . 2. A very attractive property of $\rm CaF_2$ is similarity of its crystal structure to Si: $\rm CaF_2$ has cubic m3m structure with only 0.6 % of lattice mismatch with Si(111) at room temperature. This fact makes it possible to grow perfect single crystal films of $\rm CaF_2$ on silicon by molecular beam epitaxy technique . The crystalline quality, chemical stability and electrical characteristics of $\rm CaF_2$ films grown on Si(111) may be further improved by rapid thermal annealing . 3. Barrier height between the conductive band minimum of Si and the conductive band minimum of $\rm CaF_2$ is only $\sim 2.2$ eV . 4. An additional attractive property of $\rm CaF_2$ is anomalously large low-energy electron escape depth of the order of 260 nm . 5. And lastly, the good emission properties of the $\rm CaF_2/Si$ structure has recently been demonstrated in the experiment . The thickness of the insulator film about $d\sim 10$ nm seems to be nearly optimum because it is large enough to avoid direct tunneling of electrons from semiconductor to metal, but it is small enough for ballistic passing of electrons through insulator film. So, if one has 10 nm thick $\rm CaF_2$ film on the $1~\mu$m thick Si layer with p-dopant concentration $n\sim 10^{16}$cm${^{-3}}$ ($W_{\mbox{{\scriptsize{\rm max}}}}\sim 1~\mu$m ), one may be sure that when pulse voltages with the amplitude $V_{\mbox{{\scriptsize{\rm control}}}}\sim\pm 10$ V are applied to one row and one column lines an avalanche breakdown will occur at the edges of metal lines ($d/W_{\mbox{{\scriptsize{\rm max}}}}\sim 0.01$). The control voltage may be still decreased if the distance between metal electrodes $L$ will be less than $d+W_{\mbox{{\scriptsize{\rm max}}}}$ (but $L$ must always be more than $3\pi d/2$). The avalanche electrons will be injected into insulator at the $\alpha - \beta$ line, which shown in Figure 3. From geometrical considerations, up to several tens percent of electrons may be injected into vacuum. To summarize, we have proposed a simple design of the field-emission display based on the deep-depletition edge avalanche breakdown of the MIS structure. The control voltage of this display may be as small as tens volts and its ultimate resolution may reach several microns. # Appendix Here we mention the influence of the top electrode thickness on the edge breakdown condition. To avoid complicated expressions, we give only a simple estimation of the effect by solving the problem presented in Figure 5(a), where top electrode has zero thickness. The equation ``` math \begin{equation} z={h\over \pi}(\omega-\ln{(w)}-1) \end{equation} ``` relates the upper half $\omega$ plane (Figure 5(b)) to the interior of the region $A_1-A_2-A_3-A_4$ of the $z$ plane (Figure 5(a)). The potential of the electric field in the $\omega$ plane is the real part of the complex potential given by the analytical function ``` math \begin{equation} F={V\over \i\pi}\ln\omega \; . \end{equation} ``` The electric field in the $z$ plane is ``` math \begin{equation} {\d F\over \d z} = {\d F\over \d\omega}{1\over \d z/\d\omega} \; . \end{equation} ``` Performing the differentiation with respect to $\omega$ in ([A1]) and ([A2]) ``` math \begin{equation} {\d z\over\d\omega}={h\over \pi}{{\omega-1}\over\omega} \end{equation} ``` ``` math \begin{equation} {\d F\over \d\omega}={V\over \i\pi\omega} \end{equation} ``` we get ``` math \begin{equation} E_x-\i E_y = {V\over \i h(\omega-1)} \; . \end{equation} ``` Our main interest is the field near $z=0$ ($\omega=1$). Expanding logarithm in ([A1]) in a Taylor series at $\omega=1$ and holding the first two terms, we obtain ``` math \begin{equation} {\omega-1} = \left( -{2\pi\over h}z \right)^{1/2} \end{equation} ``` and from ([6]) we have ``` math \begin{equation} E_x-\i E_y = -{V\over h\left(2\pi z/h \right)^{1/2}}\; . \end{equation} ``` One can see that the “critical” distance in this case is: ``` math \begin{equation} z_{\mbox{{\scriptsize{\rm cr0}}}}={h\over 2\pi }\; . \end{equation} ``` And the edge breakdown condition is ``` math \begin{equation} {d\over W_{\mbox{{\scriptsize{\rm max}}}}}<{1\over 2\pi -1}\simeq 0.19\; . \end{equation} ``` This edge breakdown condition should be used when top electrode thickness is less than any other dimensions in the system. Essentially it means that top electrode thickness should be less than thickness of the insulator film. # References ## References [1] Brodie I and Spindt C A 1992 *Adv. Electron. 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Lett.* **60** 183 [2] **Figure 1:** Sectional view (a) and side view (b) of the FED based on edge breakdown of MIS structure. 1 — glass substrate, 2 — metal column lines, 3 — semiconductor layer, 4 — p-doped column lines, 5 — insulator with NEA, 6 — metal row lines, 7 — fluorescent screen, 8 — vacuum spacing. \ **Figure 2:** Plane $z$ (a) and plane $\omega$ (b) related by the equation ([1]) \ **Figure 3:** Distance $z_{\mbox{{\scriptsize{\rm cr}}}}$ and electron emission area $\alpha - \beta$ near the edge. \ **Figure 4:** Plane $z$ (a) and plane $\omega$ (b) related by the equation ([13]) \ **Figure 5:** Plane $z$ (a) and plane $\omega$ (b) related by the equation ([A1]) (Appendix)