Effects of Platinum on NiPtSiGe/n-SiGe and NiPtSi/n-Si Schottky Contacts

Solid phase reaction of NiPt/Si and NiPt/SiGe is one of the key issues for silicide (germanosilicide) technology. Especially, the NiPtSiGe, in which four elements are involved, is a very complex system. As a result, a detailed study is necessary for the interfacial reaction between NiPt alloy film and SiGe substrate. Besides using traditional material characterization techniques, characterization of Schottky diode is a good measure to detect the interface imperfections or defects, which are not easy to be found on large area blanket samples. The I-V characteristics of 10nm Ni(Pt=0, 5, 10 at.%) germanosilicides/n-Si₀/₇Ge₀.₃ and silicides/n-Si contact annealed at 400 and 500°C were studied. For Schottky contact on n-Si, with the addition of Pt in the Ni(Pt) alloy, the Schottky barrier height (SBH) increases greatly. With the inclusion of a 10% Pt, SBH increases ~0.13 eV. However, for the Schottky contacts on SiGe, with the addition of 10% Pt, the increase of SBH is only ~0.04eV. This is explained by pinning of the Fermi level. The forward I-V characteristics of 10nm Ni(Pt=0, 5, 10 at.%)SiGe/SiGe contacts annealed at 400°C were investigated in the temperature range from 93 to 300K. At higher temperature (>253K) and larger bias at low temperature (<253K), the I-V curves can be well explained by a thermionic emission model. At lower temperature, excess currents at lower forward bias region occur, which can be explained by recombination/generation or patches due to inhomogenity of SBH with pinch-off model or a combination of the above mechanisms.

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy.