following equation: Therefore, Φ* can be written as: Since the x ≪ xd, the term (xd − x/2) ≈ xd, using this approximation equation () is solved as follows: , since (Φi − Va) > Vt. One obtains the equation of current caused due to diffusion: From equation (), one can observe that the current depends exponentially on the input voltage Va, also the barrier height ΦB. From equation (), Va can be written as the function of electric field intensity, which is as follows: Substituting equation () in equation () gives: From equation (), one can observe that when a zero voltage is applied to the semi-conductor diode, the drift current totally balances the diffusion current. Hence, the net current in a semiconductor diode at zero potential is always zero. The equation above can be applied to model semiconductor devices. When the density of electrons is not in equilibrium, diffusion of electrons will occur. For example, when a bias is applied to two ends of a chunk of semiconductor, or a light is shining in one place (see right figure), electrons will diffuse from high density regions (center) to low density regions (two ends), forming a gradient of electron density. This process generates diffusion current. See also Alternating current Conduction band Convection–diffusion equation Direct current Drift current Free electron model Random walk Maximal Entropy Random Walk – diffusion in agreement with quantum predictions References Encyclopaedia of Physics (2nd Edition), R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3 Concepts of Modern Physics (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, Solid State Physics (2nd Edition), J.R. Hook, H.E. Hall, Manchester Physics Series, John Wiley & Sons, 2010, Ben G. Streetman, Santay Kumar Banerjee; Solid State Electronic Devices (6th Edition), Pearson International Edition; pp. 126–135. Semiconductors Electric current Charge carriers