9th International Vacuum Microelectronics Conference, St. Petersburg 1996

On the Capacitance of Vacuum Microelectronic Devices with Different Field Emitter Shapes

Baoping Wang', Yongming Tang, Johnny K.O. Sin* and Vincent M.C. Poon*

Electronic Engineering Department, Southeast University, Nanjing, Jiangsu, 210096, P.R. China.

*Department of Electrical and Electronic Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong.

Abstract

In this paper, capacitance of diode vacuum microelectronic devices with different field emitter shapes are studied. By using finite difference method, electric field and capacitance of field emitters with five different shapes are calculated. Calculation results show that the emitter shape has a larger effect on the field enhancement than on the capacitance. When the anode diameter is decreased from 8 pn to 4 pn. the capacitance can be decreased by ten times for the shiup tip-on-post field emitter. When the distance between the cathode and the anode and the height of the field emitter are increased by 2 pm, the capacitance w1 be increased by about 30% for the sharp tip-on-post field emitter.

1. Introduction

For the vacuum microelectronic devices to be used as RF power devices and FEDs, low capacitance and high transconductance are necessary in order to obtain higher frequency and better current drive. For practical use of these devices, attention should also be paid to other parameters such as field emission characteristics, electron traces and current distribution at the anode [l-31. In addition, other factors such as thermal contact and mechanical stability have to be considered. To study the optimum field emitter shape for vacuum microelectronic applications, field emitters with ten different shapes were presented last year [4]. Electric field at the tip of these field emitters and field enhancement factors for emitters with different shapes were calculated for a triode structure. In this paper, capacitances between cathode and anode for these different field emitters are calculated using finite difference method. Furthermore, results obtained for the different emitters are compared and discussed,

2. Numerical Analysis

To study the capacitance and electric field characteristic of the field emitters with different shapes, five important and practical shapes as shown in Fig. 1 are chosen. For the sake of simplicity, these field emitters are characterized as a diode with the configuration shown in Fig. 2. The structural parameters of these diodes are listed in Table 1.

In this study, two-dimensional analysis for these rotational symmetric structure is considered, and space-charge effects are neglected. Our interest is to find out how the different shapes of the &ld emitter in a given diode affects the capacitance and electron beam trajectories between cathode and anode. In order to achieve this goal, electric field in a given structure is calculated + He is now on leave and with the Hong Kong University of Science & Technology,

509

9th international Vacuum Microelectronics Conference, St. Petersburg 1996

using the finite difference method. The treatment of the boundary conditions and meshing are very important for accurate calculation. Linear interpolation is used in regions far away from the field emitter, and fine mesh and coarse mesh are appropriately used in different regions. In the vicinity of the apex of the field emitter, the size of the m s h is about 1 nm. After obtaining the electric field in a given structure, the capacitance between the cathode and anode is calculated by using the integration of electric field on the surface and the formula C = Q/V. Then the electron trajectories are calculated by using the fourth-order Runge-Kutta method.

Fig.1 Five shapes of field emitters.(a) pyramid with r = 10 nm;(b) sharp pynunid with r = 10 nm;(c) whisker with r = 50 nm;(d) pynmid-on- post with r = 10 nm;(e) sharp pyramid-on-post with r = 10 nm.

Table 1. The structural parameters

51 0

9th International Vacuum Microelectronics Conference, St. Petersburg 1996

r

Fig. 2. A rotational symmetric diode

3. Results and Discussion

The field emitters with five different shapes are used correspondingly to form the diode structure shown in Fig.2. Using finite difference method, electric field in the different structures is calculated. After obtaining the electric field, capacitance and electron trajectories can be calculated.

In order to study the effects of the different emitter shapes and merent surface areas on the capacitance between the cathode and anode, the capacitances for different shapes in the structure with D = 4 pm and h = 2 pm are calculated. Results are shown in Table 2. For the relationship between the height of the field emitters and the capacitance, the capacitances for emitter shape (a) in the diode structure as a function of h are calculated and shown in Fig. 3. For the sake of simplicity, the radius r of the field emitter is 100 nm in the calculation. The capacitances for different emitters in the structure with D = 8 pm and h = 2.12 pm are calculated. The results are shown in Table 3. Furthermore, the capacitances for different emitters in the structure with D = 8 pm, H = 6 pm and h = 4.12 pm are calculated in order to study the effects of the distance between the cathode and anode, H, on the capacitance. The results are shown in Table 4.

Table 2. The capacitances ( x lW" F ) for five shapes in the structure with D = 4 p, H=4 pm and h = 2 p.

II Shape I Capacitance II 2.8975 2.8864 2.8815

( e ) 2.8798

51 1

9th International Vacuum Microelectronics Conference, St. Petersburg 1996

Shape

2.92

2.90

Capacitance 1.1910 1.1655

2.78 1 .

Shape ( a ) ( b )

2.76 I. 0 1 2 3

Height of Field Emitter ( ym )

Capacitance 9.1176 8.5703

Fig. 3. Capacitance vs. height of field emitter for shape ( a ).

Table 3. The capacitances ( x F )for five shapes in the structure with D = 8 pm, H = 4 pm and h = 2.12 pm.

1.1431 1.1414

( c ) 7.9932 ( d ) 7.9867

With the above results obtained, the following points can be made. First, with the emitter height less than 2 pm ( for H = 4 pm, D = 4 pm ), the capacitance of the diode is almost identical to the capacitance of the diode with no emitter ( C = 2.7916 x 10 -I7 F ), and the increase in emitter height only results in small increase in capcitance. When the height of the emitter is over 2 pm, the capacitance of the diode is increased drastically. Second, the shape of the field emitter has only a small effect on the capacitance of the diode. This is because the capacitance is related to the bulk of the field emitter, and there is little difference in the bulk among these five different field emitter shapes. Comparing with shape (a), the capacitance for shape (e) is only increased

512

9th lntemational Vacuum Microelectronics Conference, St. Petersburg 1996

by about 1%. Third, when the diameter of the anode, D, is decreased from 8 pm to 4 pm, the capacitance is almost decreased by ten times. This means that increase of the tip density does not only increase the transconductance but also decrease the capacitance. Fourth, when the distance between the cathode and anode, H, and the height of the field emitter, h, are increased by 2 pm, the capacitance is decreased by about 30%. Finally, the emitter shape has larger effect on the field enhancement factor than on the capacitance.

4. Conclusions

Electric field and capacitance evaluation of field emitters with different shapes used in a diode structure were presented. The electric kld and capacitances are calculated using finite difference method. Base on these results, it is concluded that the emitter shape has a larger effect on the &Id enhancement factor than on the capacitance. Therefore, the shape of a field emitter which can obtain high field enhancement in a given diode or triode structure is very important to practical applications. In addition, the increase in the tip density does not only increase the transconductance but also decrease the capacitance. When the distance between the cathode and anode and the height of the field emitter are increased by 2 pm, the capacitance can be decreased by about 30% for shape (e).

References

T. Utsurni, “What’s new and exciting”, IEEE Trans. Electron Devices, vol. 38, p. 2276, 1990. Zheng Cui and Linsu Tong, “Optimum geometry and space-charge effects in vacuum microelectronics devices”, IEEE Trans. Electron Devices, vol. 40, no. 2, p. 448,1993. H. F. Gray and J. L. Shaw, “Characterization of silicon tip-on-post field emitters and FEAs”, in Tech. Dig. 7th Int. Vacuum Microelectronics Conf. (Grenoble, France), p. 135,1994. Baoping Wang and Linsu Tong, “A study of the optimum field emitter shape for vacuum electronics applications”, in abstract f-1, 42nd Int. Field Emission Symposium ‘(Madison, USA), 1995.

34-1129 51 3