Ion Implantation and Synthesis of Materials - Studium

204 14 Application of Ion Implantation Techniques in CMOS FabricationFor a given choice of gate materials, the gate oxide thickness, t ox , and thedoping concentration, N B , are two parameters which can be used to adjust thethreshold voltage. t ox determines the value of V ox byVoxQoxQox= − = −C ( ε / t )ox ox ox(14.6)where Q ox is the fixed charge at the oxide–silicon interface, C ox is the oxidecapacitance per unit area and ε ox is the permittivity of SiO 2 .The substrate doping, N B , affects the threshold voltage through both V d and V ibyV qN x C (14.7)d = − B d /oxwhere x d is the depletion-layer width beneath the gate, and byVi=2kTNlnq nBi(14.8)where n i is the intrinsic carrier concentration.It is obvious from (14.7) and (14.8) that the threshold voltage can be adjusted tothe desired level by increasing the doping level through a low energy ionimplantation into the channel region. For simplicity, assuming that a shallow ionimplantation creates a boxlike shape profile of dopants with an uniformconcentration of N i over a depth of x i , the dopant concentration for a depth < x i isgiven by N B + N i , where N B is the substrate doping concentration before adding athreshold adjust implant. For a depth > x i , the dopant concentration is given by N B .The implantation causes a shift in the threshold voltage, ∆V T , given approximatelyby (Jaeger 1988)∆ V = (1/ C )( qQ )(1 − x / 2 x ), x x (14.9)T ox i i d i dwhere Q i = x i N i represents the implanted dose, and x d represents the depletionlayerwidth beneath the gate. The threshold-voltage shift is negative for donorimpurities and positive for acceptor impurities. An example of this technique isshown in Fig. 14.10, where the threshold voltages of both n-type (V Tn ) and p-type(V Tp ) transistors are adjusted and have positive shifts that increase with increasingboron implant doses.