A Self-consisitent Correction To The Gate Tunneling Current Model In The PSP Model For Submicron Process

As the dimension of metal-oxide-semiconductor field effect transistor(MOSFET)device scaling down,the leakage current in device becomes more and more significant in the device power consumption and performance.Consequently,the semiconductor process technology,device design and integrate circuit design in that field face a lot of challenges.People developed many improved MOSFET compact model to physically characterize the device characteristic and the leakage current to consummate the device design and then to reduce the influence of leakage current as far as possible.So far,the surface-potent-based PSP model is the relatively advanced MOSFET compact model,which uses surface potential as variable to physically model the electrical characteristic of devices.Surface-potential-based model for MOSFET channel uses the same value of surface potential in all positions of the channel,whereas,different expressions for the characteristic of different position use the average value of surface potential.With this nonself-consistent way,the channel current of PSP model is consistent with the condition that channel current is constant along the channel,indicating that PSP model is a compact model with high computational efficiency and accuracy.With the device scaling down,however,the nonlinear physical phenomena can not be ignored,and the channel current with respect to lateral coordinate of channel should be reconsidered.The thickness of the gate oxide of MOSFET is smaller than 1.4nm under the 90nm process technology so that the width of oxide barrier become narrower,which result in the higher possibility of particle tunneling across the oxide and into the gate so that the influence of gate tunneling current to MOSFET channel current become considerable.We note that different position with various surface potential in the channel of scaling MOSFET is affected by different value of gate tunneling current.PSP model,however,physically depicts the current continuity equation of gate tunneling current and channel current under the assumption that gate tunneling current only induces a small constant perturbation along the channel.It is noted that this one order assumption implies that PSP model simplifed model the current continuity equation,but it brings about nonself-consistent result.Hence,there is a range of device bias in which constant approximation would inaccurately describe the gate tunneling current effect resulting from the scaling down of gate oxide thickness in the integrate circuit with submicron process.We propose a self-consistent modified model on the influence of gate tunneling current effect to channel current.In this work,a mathematical analysis to obtain the series solution of the current continuity equationis is described to derive the high order term of surface potential with respect to channel lateral coordinate of MOSFET under the gate tunneling current effect.We generalize the expression of the first order derivative of the channel lateral coordinate with respect to surface potential under the symmetrical linearizotion method(SLM)framework to the higher order polynomials,and figure out the solution of the coefficient of the high order term.Consequently,ratio of the magnitude of the 2nd order term to the 1 st order term in the series solution being smaller than 1 determines the range device parameters that allow the application of constant channel current approximation in the presence of gate tunneling current.From the experiment,we finally found the bias range in which the gate voltage is bigger than 4.5V and ratio of the magnitude of the 2nd order term is bigger than 1st order term in the series solution,as well as the gate tunneling current significantly influence channel current.