Analysis And Optimization Of Electromagnetic Characteristics Of Silicon Vias In 3D Integrated Circuits

The performance and integration of Integrated circuit have improved with each upgrade of its technology nodes.However,when the physical dimensions of transistors are close to the limit,problems such as short-channel effects,quantum effects,lithography realizability,and rising power consumption and heat dissipation will all seriously restrict the development of planar 2D ICs and make the Moore’s Law more challenging.Therefore,the planar two-dimensional integrated circuits have been unable to meet the rapid development requirements of integrated circuits.Three-dimensional integrated circuits(3-D ICs)based on through silicon vias(TSVs)are considered as one of the effective ways to continue Moore’s Law.By stacking a number of different functional circuit modules or chips together to form a stack structure,the delay and power consumption can be effectively reduced,and the I/O interconnect density can be increased and heterogeneous integration can be achieved.Therefore,the application prospect of 3-D ICs is optimistic and is favored,and will be the direction of the future development.However,3-D ICs still face many challenges,and there are some problems that need to be resolved.For example,the equivalent circuit model based on TSV is not perfect enough,the electromagnetic crosstalk model between TSVs is not accurate enough,and the noise interference between the array TSVs is still serious.Therefore,in order to solve the above problems,this thesis studies the electromagnetic properties,equivalent models,crosstalk noise,and array layout optimization of TSVs in 3D ICs,and obtains the following results: 1.In this thesis,we present an equivalent circuit model of coaxial-annular TSV and analyze 3-D integrated circuits characteristics based on this structure.By using the current continuity equation and Bessel function,the current density in the coaxial-annular TSV is solved,and the equivalent parasitic resistance and inductance are extracted.By considering the complex conductivity of the silicon substrate and the assumption of full depletion,the equivalent parasitic capacitance and conductance are extracted,which shows the skin effect at high frequencies and the semiconductor loss characteristics of silicon substrates.An electromagnetic field solver is used for comparison with the closed-form expressions,therein revealing good agreement between the results of the simulation and analytical models across the frequency range,and showing the faster speed characteristics of the proposed expressions.In addition,the variation trend of the resistance,inductance,capacitance,and conductance of the coaxial TSV and the key factors affecting the S-parameter are analyzed by changing physical parameters to further verify the accuracy of the proposed method and provide guidance for optimizes the circuit design2.In this thesis,we present a coupled inductance model between tapered TSVs in a stacked two-layer silicon substrate.According to the magnetic flux density and vector magnetic potential theory,a universal closed-form expression for the parasitic inductance with a frequency of up to 20 GHz is proposed by using the Taylor’s polynomial expansion theorem.A good agreement between the results of the proposed formulas and ANSYS HFSS simulation results is obtained.When the slope angle is equal to 90°,the formula can be simplified into the formulas of cylindrical TSVs.The mutual inductance and self-inductance also can be calculated only by changing the corresponding variable in the formula when the tapered TSV is located in the adjacent substrate layer or in the same substrate layer,which has higher versatility and superiority than other literatures.Therefore,it will help the designer to fully consider the noise distribution in the multilayer circuit.3.In this thesis,we present an equivalent crosstalk model between TSV and Re-Distribution Layer(RDL).The coupling capacitance is calculated based on cylindrical accumulation mode basis functions(AMBFs)and the scalar potential integral equation(SPIE).As a result of the numerical integration of capacitance is very complicated,we made an approximation by using Segmentation method and double-exponent transformation in order to improve calculation efficiency while guarantee accuracy.The accuracy and efficiency of the model are verified by analyzing the variation of coupling capacitance with physical parameters.In addition,coupling capacitance and crosstalk noise of several different TSV structures based on ground-signal-signal-ground are studied.It is pointed out that the crosstalk between TSV and RDL cannot be neglected;otherwise it is easy to overestimate the circuit performance.Especially when analyzing complex circuits such as large-scale array TSVs with long interconnects,ignoring the coupling between them may cause signal transmission errors.4.In this thesis,we investigate the electromagnetic crosstalk of array TSVs and propose a differential signal-ground TSV interlaced layout structure.The crosstalk between different numbers of signal TSVs on a single substrate is analyzed and the results show that the crosstalk noise is improved by 60% and 21% compared with the traditional single-ended and the differential signal layout,respectively.In addition,considering the multilayer substrate stack,a twisted-chain TSV structure is proposed.By inverting the upper and lower differential signals,the far-end inductive coupling is cancelled.Crosstalk is improved by up to 25% compared to the signal passing through the substrate.Moreover,the crosstalk improvement effect is more obvious for the odd-numbered substrate stack.