The Micro-Tip field emitter is essentially an ultra small electron gun. The device consists of a conical cathode with a tip radius in the range of 10 - 50 nm. A circular anode ring is placed in proximity to the tip so that when a potential difference of a few in the range 10 -100V DC is applied an extremely large electric field gradient is produced at the tip The electric field gradient is proportional to the sharpness of the tip. For this device the tip is so small , a large enough field gradient is produced to cause electrons in the bulk material of the tip to be physically "stripped off". The mechanism is quantum tunneling and the resulting emission phenomena is referred to as field emission. Once the electrons are "out" of the tip the electrostatic field exerts a force causing the electrons to follow extended trajectories away from the cathode. Many collide with the anode, but a high proportion are ejected almost vertically form the central open hole. By placing an phosphor screen above an array of these micro-tips, a miniature cathode ray tube (CRT) is realized (each pixel has one of more electron guns- In a conventional CRT one very large electron gun is used to illuminate all pixels). These micro tip or more correct Field Emission Displays (FED) promise flat screen display panels with brightness similar to that of a conventional CRT, but smaller, more rugged and energy efficient.
The micro tip device can also be used as an electronic switch. The basic two electrode device is a diode, (very similar to a vacuum tube diode popular before semiconductor revolution). Three electrode versions (triodes) function like switches, the third electrode is used to turn on /off the filed emission. Recent experiments have proved that micro- tip triodes can switch in the Tera Hertz (THz) range. That is approximately 1000 times faster than a semiconductor transistor.
ANSYS Can be used to compute the electrostatic field produced and the also compute the trajectories of the emitted electrons. The model can be 2D or 3D. In this example a 3D , quarter symmetry axis symmetric model is analyzed. The solid electrodes are surrounded by a meshed field domain, representing vacuum. The electrodes themselves do not need to be meshed as only the nodes on their surface, attached to the field domain are required to apply the voltage loads.
Solid mode details showing (on the left) part section of cathode tip, ground plane and annular anode. This model is efficiently analyzed as cylindrically symmetric section. Quarter symmetry section shown on the right hand side:
This was a H-element analysis, and the field domain needs to be surrounded with a single layer of infinite boundary elements. A Trefftz domain approach would also be appropriate. The fully meshed model is shown below. The red area is the vacuum surrounding the electrodes. The purple region are ANSYS infinite boundary elements that are used to represent the open domain. The bright green flags show the voltage loads applied to the electrodes.
This model has a relatively coarse mesh of about 10,000 DOF's in the field domain. The problem is solved in less than 5 minutes on an "old boatanchor" 233 MHz Pentium II laptop with 256 MByte of RAM.
Contour plot of electric field surrounding the tip field emitter:
Isosurface plot of voltage contours:
One the electrostatic analysis has been performed, charged particle can be introduced and their trajectories computed. ANSYS Multiphysics will allow up to 1000 trajectories with mixed mass to charge ratios, initial velocity vectors are also user defined. Both positive and negative particles can be traced. For the field emitter, the particles are electrons. In the image below approximately 50 electrons are introduced to the field in close proximity to the cathode tip.
Particle Trajectory Tracing in ANSYS, M. Gyimesi, V. Zhulin, D. Ostergaard, Fifth International Conference on Charged Particle Optics,Delft University, Netherlands, 1998. published in Nuclear Instruments & Methods in Physics Research, Section A, p.408-411,
Elsevier, 1999.
Electromagnetic Particle Trajectory Tracing, V. Zhulin, M. Gyimesi, ANSYS User Conference, 1998.
Micro-tip and FED references on the web:
Jing Li's Advanced Physics Topics (Department of Physics Kansas State University, USA)
Dr. Charles "Capp" Spindt - Vacuum Microelectronics at SRI
Developing Field Emitter Array Cathode Systems for Electrodynamic Tether Propulsion (University of Michigan & Naval Research Lab, 2000)
Silicon Tip Arrays with Thin Amorphous Diamond Apexes (Zhongshan University and RAL UK)