References 1 PROAKIS, J. G.: 'Digital communications' (McGraw-Hill, 1983) 2 ZENGJUN XIANG, and GUANGGUO BI: 'Complex neuron model with its applications to MQAM data communications in the presence of co-channel interferences'. Proc. IEEE ICASSP '92, USA, March 1992 3 ZENGJUN XIANG, and GUANGGUO BI: 'Fractionally spaced decision feedback multilayer perceptron for adaptive MQAM digital mobile radio reception'. Proc. IEEE ICC '92, USA, June 1992, 4 CHEN, s., GIBSON, G. J., and COWAN, c. F. N.: 'Adaptive channel equalisation using a polynomial perceptron structure', IEE Proc. I, 1990,137, (5), pp. 257-264 5 ZENGJUN XIANG : 'The theory of neural networks with its applica- tions to high efficiency digital mobile radio reception systems'. PhD Dissertation, Southeast University, June 1992 6 MATHEWS, v. J.: 'Adaptive polynomial filters', IEEE Signal Pro- cessing Mag., 1991,8, (3), pp. 10-27 NUMERICAL SIMULATION OF CARRIER TRANSPORT IN SCHOTTKY BARRIER DIODES A. Shibkov, M. Ershov and V. Ryzhii Indexing terms: Modelling, Schottky barrier devices, Diodes, Semiconductor devices and materials Carrier transport in Si Schottky diodes is analysed. A novel model for the recombination velocity suitable both for low and high biases has been derived and compared with pre- vious models. The influence of the boundary condition on simulation results was found to be more significant for C-V than for I-V characteristics. Introduction: The drift-diffusion model (DDM) is currently widely used as a basis for computer simulation of the carrier transport in Schottky barrier diodes due to its simplicity and reasonable accuracy [1, 2]. Among the most important prob- lems for the formulation of a carrier transport model in this case is the boundary condition for the current density at the metal-semiconductor (MS) interface. One of the earliest and most widely used models is the thermionic emission/diffusion model of Crowell and Sze [3] where the electron current density at the MS interface is defined by J = qv r (n s - n 0 ) (1) where n s is the electron concentration at the MS boundary, n 0 the electron concentration at the same point at equilibrium (zero bias condition) and v r is the surface recombination veloc- ity. Assuming that the velocity distribution of electrons is Maxwellian at the MS interface, the authors of Reference 3 found v r to be constant and equal to v r0 = v t JA where v th is the mean thermal velocity. The assumption of the Maxwellian velocity distribution is questionable under nonequilibrium conditions. The problem connected with the calculation of v r has been widely discussed recently. By using Monte-Carlo simulation, Baccarani and Mazzone [4] found the electron distribution function at the MS interface of an Si Schottky diode near flat-band to be semi-Maxwellian and recombination velocity to be twice that given in Reference 3. Adams and Tang [5] obtained an ana- lytical expression for the current-dependent recombination velocity assuming the electron velocities to be represented by a positive part of the drifted Maxwellian distribution at the MS interface. Their approach was followed by Mylander et al. [6] who introduced a 'compensating factor ... for the increase of the effective mass caused by the band structure changes at the Schottky contact' into an expression for recombination velocity. We present a new analytical description of the dependence of surface recombination velocity on the electron current and clarify the influence of recombination velocity on the Schottky diode electrical characteristics. New model for recombination velocity: We assume that the electron velocity distribution at the MS interface is drifted Maxwellian and therefore the recombination velocity is defined as _ fg> v x exp (-m*(v x - v d ) 2 /(2kT)) dv x Vrd J^ exp (-m*(v x - v d ) 2 /(2kT)) dv x = 0-5i?/l 4- erf {v d /t2J(n)v r0 ]}> + v r0 exp (- V 2 /(4KV 2 0 )) (2) where m* is the electron effective mass in the direction normal to the MS interface, and the drift velocity v d is defined as v d = J/qn (J is the current density and n is electron concentra- tion near the boundary). An electron distribution of this type was obtained in Refer- ence 8 where the image force effect was taken into account. We compare our model (eqn. 2) for the recombination velocity with models proposed earlier: (i) Crowell and Sze model [3]: v x exp (-m*v 2 J(2kT)) dv x = {kT/2nm*) 1/2 (ii) Adams and Tang model [5]: _ J? v x exp (-m*(v x - v d ) 2 /(2kT))dv x Vrd Jj exp (-m*(v x - v d ) 2 /(2kT))dv x exp(-v 2 /{4nv 2 0 )) (3) (iii) Nylander et al model [6]: 2v r0 exp (- rjv 2 /(4nv 2 0 )) Vrd = (4) (5) Our assumption differs from that of Reference 5 by a nor- malisation factor. The model of Reference 5 seems to be doubtful because at low bias (v d <t v r0 ), eqn. 4 tends to 2v r0 (see Fig. 1) in contrast with the model of Crowell and Sze (eqn. 3) which is more reliable under the conditions con- sidered. On the other hand, at high bias, eqn. 4 results in a v r about 50% higher than that calculated in Reference 4. The inconsistencies of the model of eqn. 4 are due to the neglection of electrons moving from the metal into the semiconductor. 1-6 (iii) & 0-8 -(iv) 0 <K 0-8 _ drift velocity, cm/s (x1Cr) 1-2 I Fig. 1 Recombination velocity as function of drift velocity for models proposed in References 5, 6 and in this Letter (i) [5] (ii) [6] (iii) this Letter (iv) [3] with constant recombination velocity ELECTRONICS LETTERS 10th September 1992 Vol. 28 No. 19 1841