A Simple Formulation of the Saturation Current Density
in Heavily Doped Emitters
A. Zouari*, A. Ben Arab
Laboratoire de Physique Appliquée, Département de Physique,
Faculté de Sciences de Sfax,Université de Sfax, B.P. 802, 3018 Sfax, Tunisie
* Corresponding author. E-mail:Abdelaziz.Zouari@fss.rnu.tn
Received : 01 April 2002; revised version accepted : 05 August 2002
In non-uniformly and heavily doped emitter region of bipolar transistor, the continuity equation and the minority current equation cannot be exactly solved in closed form. This paper shows that the calculation of minority-carrier current density can be calculated by a simple approach. This approach is based on the average value of the equilibrium hole density p0, diffusion constant Dp, and lifetime t p of minority carrier and leads to two coupled differential equations of the first order. These equations can be solved very easily and can give a simple expression for the current density. Three definitions of the average value of p0, Dp, and t p are used and lead to three expressions for the emitter current density. One of them is identical to the one established by Rinaldi by another mathematical analysis and gives very accurate results for shallow emitter (W<1µm), whatever the range peak doping level (N(W)) and surface recombination velocity (S). On the other hand, the expressions obtained from the first or/and the second definition of the average value lead also to accurate results for the current density depending on the value of the surface recombination velocity, but cannot be used when N(W) is greater than 1020 cm-3 and W is superior to 0.1µm.
Keywords: Saturation current; Bipolar transistor; Recombination velocity.