Current Density Scaling Expressions for a Bipolar Space-Charge-Limited Cylindrical Diode

Abstract

Exact analytical solutions for the currents in a bipolar space-charge-limited (SCL) diode in cylindrical geometry do not exist. Expressions for the electron and ion current densities as functions of the diode cathode and anode radii and the applied voltage are developed and fit to numerical solutions. The results are provided for nonrelativistic and relativistic electrons. These provide scaling relations for the diode, which were not previously available. They also converge to known planar diode expressions in the appropriate limit. The relativistic scaling relations are then combined with nonrelativistic results using a fit function technique to provide a general expression for the current densities valid for all values of the diode voltage. The results are presented for both negative and positive polarities. For completeness, single-species SCL flow results in cylindrical geometry are also developed using the same techniques presented here for bipolar SCL flow and are included in the Appendix.

Bulk Polymerization of Acrylic Acid Using Dielectric-Barrier Discharge Plasma in a Mesoporous Material

“…Research on the applications of discharged plasma is currently thriving in various fields, including biomedical devices, environmental science, and agriculture [16,17]. Among the wide range of plasma techniques, DBD plasma stands out due to its exceptional safety and selectivity when interacting with biological systems [18,19].…”

A Numerical Approach for Space Charge Limited Bipolar Flow in Cylindrical diodes

“…For different applications, the classical CL law may be inapplicable. Therefore, there are extensions to the CL law to the cylindrical and spherical geometries [5]− [9], multidimensions [10]− [13], quantum regime [14]− [16], relativistic effect [17]− [20], time dependent current injection [21]− [23], and influence of initial velocity [24]− [27]. Moreover, the theories of SCL have been used to make an investigation of some space charge dominated systems, such as THz oscillation [28]− [32], Coulomb blockade [33], bipolar flow [34]− [37], optical field emission at high field [38]− [44], photon-enhanced thermionic energy converters (PETEC) [45], and nanodiodes [46].…”

“…For high power applications and thermionic energy converters (TEC), outgassing and thermionic emission typically occur [34], [45]. In [9], an approximate current density scaling expressions for cylindrical bipolar diodes in positive and negative polarity for non-relativistic and relativistic regimes are provided. Such a bipolar flow problem is of fundamental interest since positive ions are commonly used to mitigate the space charge effect [45].…”

Polymerization of D-Ribose in Dielectric Barrier Discharge Plasma

“…The studies on the applications of discharged plasma are currently very active in the medical, environmental, and agriculture fields [1][2][3][4][5][6][7][8][9][10]. Among various plasma techniques, dielectric barrier discharge (DBD) plasma [11,12] is of special interest due to the safety and selectivity in its effects on biological systems [13,14].…”