Stresses and strains in lattice-mismatched stripes, quantum wires, quantum dots, and substrates in Si technology

Abstract

We discuss recent advances made in the theory and measurements of stresses and strains in Si-based heterostructures containing submicron- and micron-size features. Several reports on theoretical as well as experimental studies of stresses in the substrates with local oxidation of silicon structures on the surface have been published recently. With the advent of GeXSi1−X strained layers and stripes extensive studies of both the stripe and the substrate stresses have also been made. Unlike the previous calculations and analytical models, recent finite element (FE) calculations take into account the coupling between the film–substrate stresses without making the approximation that the interface is rigid or that there is no variation of stresses in the stripes in a direction perpendicular to the interface. The results of these calculations have been compared with the analytical models and limitations of the analytical models have been pointed out. Micro-Raman measurements of the stresses in the stripes, quantum wires, quantum dots, and substrates have been made. The measured values of stresses in GeSi stripes and quantum structures agree well with the calculated values by the FE method. The micro-Raman measurements showed that as the ratio R=2l/h (2l is the width and h is the thickness of the stripe) decreases, the shape of the measured normal stresses in the substrate under the stripe (plotted in a direction parallel to the interface) changes dramatically, from concave upward to convex upward. Generation of dislocations in laterally small layers is also discussed briefly. FE calculations of trench-induced stresses which include the effect of the anisotropy of Si have also been made recently. In these calculations realistic experimental conditions were simulated to determine the oxide shape, oxide–interface stresses, and intrinsic and thermal stresses of the polysilicon fill. These values were then used as inputs for the FE calculations. Calculations of stresses induced by oxide-filled trenches were also made assuming that Si is isotropic and that the oxide fill has the same elastic constants as Si. These calculations and results of an earlier analytical model implemented under the same assumptions gave identical results; however, the calculated stress values were in error of 20%–30%. The maximum resolved shear stress for the 60° dislocation induced by a trench is 30% more if it is aligned in 〈110〉 direction rather than in the 〈100〉 direction. This explains the common observation that the 〈100〉-oriented trenches cause fewer dislocations than the 〈110〉 trenches. The characteristics of trench isolated as well as junction isolated bipolar transistors have been studied. The trench isolated transistors had 20% higher gain; however, the collector–base capacitance was higher by up to 50% in the trenched transistors. The increase in capacitance was caused by the anomalous diffusion of the antimony dopant from the buried collector layer induced by the stress field of the trenches. The effect could be eliminated by increasing the depth of the trench. The trenched devices also had higher emitter–collector leakage current caused by the dislocations generated by the trench induced stress field.