Analytical Carrier Transport Model for Arbitrarily Shallow p-n Junctions Miloš Popadić, Gianpaolo Lorito and Lis K. Nanver Abstract - This paper presents for the first time an analytical model of arbitrarily shallow p-n junctions. Depending on the junction depth, electrical characteristics of ultra-shallow p-n junctions can vary from the characteristics of standard Schottky diodes to standard deep p-n junctions. Therefore, this model successfully unifies the standard Schottky and p-n diode expressions. In the crossover region, where the shallow doping can be totally depleted, electrical characteristics phenomenolog- ically substantially different from typical diode characteristics are predicted. These predictions and the accuracy of the presented model are evaluated by comparison with the MEDICI simulations. Furthermore, ultra-shallow n + -p diodes were fabricated, and the anomalous behavior in the crossover regime was experimentally observed. I. INTRODUCTION In the ever downscaling of silicon technology, ultrashallow junctions and Schottky diodes are playing an important role as basic building blocks of devices such as CMOS transistors [1] and heterojunction bipolar transistors. The electrical behavior of such devices can to a great extent be simulated by physics-based simulators [2]- [4]. Compact and efficient analytical models can, for many evaluations, be the more time- and cost-efficient solution [5], but analytical modeling of ultra-shallow contacts has received little attention [6]. This paper presents a novel analytical model that for the first time makes it possible to calculate the I-V characteristics of arbitrarily thin p-n junctions with a metal contact. The model covers the transition of the structure from a Schottky diode (zero junction thickness), over a punch-through diode (the junction region to the metal can be depleted), to a conventional deep p-n diode. The model successfully calculates punch-through in the reverse characteristics, and, very interestingly, in the forward region new effects related to the depletion of the junction surface from the metal contact are identified. These effects can lead to forward I-V characteristics that very significantly differ from the conventional diode behavior with ideality factor n = 1. The results are verified by MEDICI simulations and the novel forward current behavior is also observed experimentally. II. ANALYTICAL TRANSPORT MODEL We have established an analytical model for carrier transport in a metal/p-Si/n-Si stack where the p-region may be arbitrarily shallow and forms a Schottky contact to the metal. The following common approximations were used: uniform doping, depletion-region approximation, low- injection regime, constant mobility, constant carrier lifetimes, direct recombination in the quasi-neutral region, negligible recombination in the depletion region, finite surface recombination velocity, constant Schottky barrier height without tunneling, Maxwellian carrier distribution and quasi Fermi level (QFL) approximation. The departing point of the derivation was the set of transport equations for both types of carriers: thermionic emission at the metal/Si interface, minority carrier diffusion and recombination in the quasi-neutral region and also drift and diffusion across the depletion regions. The complete derivation with its approximations and physical models followed the principles long established (e.g. [7]). The main peculiarity of the problem of ultra-shallow junctions was that the p- region, if it is thin enough, may be totally depleted. Therefore the solution was reached in two steps: first, the Poisson equation for the band diagram was solved to obtain the dependencies on the applied voltage of the intrinsic p- region width and the highest potential in the p-region; second, the transport equations were solved by demanding current and QFL continuity. The solution is presented in Fig. 1. An analogous solution can be found for the metal-n- p junction situation by reversing the relevant signs. III. TRANSITION FROM P-N JUNCTION TO SCHOTTKY ON N-SI The equations (1) to (5) from Fig. 1 therefore represent a closed-form unified solution covering the whole spectrum of junction configurations from a Schottky contact on n-Si to a conventional deep p-n junction. Formulae for the ψ MB and L p int are not given here, but can be easily derived in the case of totally depleted p-region or obtained from the current continuity in the case where an intrinsic p-region exists. In both cases there is no need to introduce an iterative algorithm. Details of the derivation will be published elsewhere. Indeed, it is observed that the total-current expressions for a p-region width of either zero or going to infinity are the standard Schottky and p-n junction I-V expressions, respectively, which have been included in Fig. 2 for comparison. This limit behaviour was All authors are with the Laboratory of Electronic Components, Technology and Materials, Faculty of Electrical Engineering and Computer Science, Delft University of Technology and with the Delft Institute for Microsystems and Nanoelectronics, Feldmannweg 17, 2628CT Delft, The Netherlands. E-mail: m.popadic@tudelft.nl