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The Matlab PDE Toolbox and Comsol Multiphysics coupling with Matlab via LiveLink are used in mathematical and computer modeling of field electron emission from emitter-arrays, as well as from single tip field electron emitter. Physical and mathematical models, computational methods and algorithms of stand alone Matlab application with graphical user interface are presented. The simulation results by the example of two different diode structures are also presented. Two generic cone-shape and cylindrical wedge-shape non-gated emitter-array diodes are considered. The effects of the variations in device geometrical structure and parameters on its potential distribution, electric field, and emission current are discussed.The current variation rate with respect to the tip-collector distance is calculated.Study of micro-scale non-uniformity of electric field with a software complex developed in Matlab has shown that field enhancement factor depends of the distance at which the field is applied to the sharp margin of cylindrical microemitter [1]. As this distance grows, the dependence becomes less significant, and at about 6 times the height of emitter protrusion becomes negligible. Numerical solutions of corresponding electrostatic boundary problems were carried out with Matlab and Matlab PDE Toolbox [2]. Software implementation should take into account the specifics of emission systems:• Calculation are of complex shape includes the emitter boundary with high curvature and multi-scale size, which leads to considerable diversity of characteristic measurements in the same geometric configuration. • The exponential dependence of current density on field strength requires increased precision when considering boundary conditions on the emitter. The solution has a rapidly changing gradient in the emission area (on edge of the cathode), thus the finite-element mesh has to become tighter in the neighbourhood of the emitter edge to avoid reduction of speed of convergence towards the exact solution and increase of the number of variables (i.e. the dimension of the finite-element system). With adaptable mesh it is natural to employ an error indicator, that would include the residual norm of the equation and fluctuations of the gradient of finite-element solution, as they are connected with one of the basic values given for this problem -that is, with the electric field strength. This indicator is implemented in pdejumps function which is called by adaptmesh function aimed for the adaptive solution of the problem. For making the mesh more fine a way of splitting finite elements was chosen, such that they are split along their longest side (rmethod=longest), i.e. a triangle (based on the value of error indicator) is replaced with two smaller triangles by splitting its longest side in half. For the case of conicalshape emitters in array the macro-scale field was calculated by Comsol Multiphysics coupling with Matlab via LiveLink.ACKNOWLEDGMENT

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