Analytical Solution of the Space Charge Limited Current Using Lambert–Tsallis Wq Function

The space charge limited current (SCLC) has been studied since more than a century ago, and up to now, it remains a hot topic playing a key role in charge transport in microelectronic and nanoelectronic devices. Therefore, it would be useful for device engineers the existence of mathematical tools able to work with the different models of SCLC proposed in the literature. In this direction, the present work shows the applications of the Lambert–Tsallis
${W}_{q}$
function for solving some problems analytically related to different models of SCLC, like some generalizations of the 1-D Child–Langmuir (CL) law and SCLC of solids with carrier-density-dependent mobility.