EECS 105 Fall 2003 Lecture 7 Lecture 7 IC Resistors and Capacitors Prof Niknejad Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Lecture Outline Department of EECS Review of Carrier Drift Velocity Saturation IC Process Flow Resistor Layout Diffusion Review of Electrostatics MIM Capacitors Capacitor Layout University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Thermal Equilibrium Rapid random motion of holes and electrons at thermal velocity vth 107 cm s with collisions every c 10 13 s 2 1 1 2 mn vth 2 kT Apply an electric field E and charge carriers accelerate for c seconds vth c zero E field 107 cm s 10 13 s 10 6 cm v th positive E x Department of EECS a c hole case vth University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Drift Velocity and Mobility For holes q c qE Fe E c c vdr a c m m m p p p vdr p E For electrons Fe qE q c c c E vdr a c m m m p p p vdr n E Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Mobility vs Doping in Silicon at 300 oK default values Department of EECS n 1000 p 400 University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Speed Limit Velocity Saturation c 3 1010 m s Thermal Velocity V cm V 4 V 10 10 1 4 cm cm 10 m m 4 The field strength to cause velocity saturation may seem very large but it s only a few volts in a modern transistor Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Drift Current Density Holes Hole case drift velocity is in same direction as E hole drift current density Jpdr vdp E x The hole drift current density is Jp Department of EECS dr q p p E University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Drift Current Density Electrons Electron case drift velocity is in opposite direction as E electron drift current density Jndr vdn E J ndr q n n E qn n E x The electron drift current density is Jndr q n vdn units Ccm 2 s 1 Acm 2 J J pdr J ndr qp p qn n E Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Resistivity Bulk silicon uniform doping concentration away from surfaces n type example in equilibrium no Nd When we apply an electric field n Nd J n q n nE q n N d E Conductivity n q n N d eff q n N d N a Resistivity Department of EECS 1 1 n n q n N d eff cm University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad IC Fabrication Si Substrate Pure Si crystal is starting material wafer The Si wafer is extremely pure 1 part in a billion impurities Why so pure Si density is about 5 10 22 atoms cm 3 Desire intentional doping from 10 14 10 18 Want unintentional dopants to be about 1 2 orders of magnitude less dense 10 12 Si wafers are polished to about 700 m thick mirror finish The Si forms the substrate for the IC Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad IC Fabrication Oxide Si has a native oxide SiO2 SiO2 Quartz is extremely stable and very convenient for fabrication It s an insulators so it can be used for house interconnection It can also be used for selective doping SiO2 windows are etched using photolithography These openings allow ion implantation into selected regions SiO2 can block ion implantation in other areas Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad IC Fabrication Ion Implantation oxide P type Si Substrate Si substrate p type N type diffusion region Grow oxide thermally Add photoresist Expose visible or UV source Etch chemical such as HF Ion implantation inject dopants Diffuse increase temperature and allow dopants to diffuse Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Diffusion Resistor N type Diffusion Region Oxide P type Si Substrate Using ion implantation diffusion the thickness and dopant concentration of resistor is set by process Shape of the resistor is set by design layout Metal contacts are connected to ends of the resistor Resistor is capacitively isolation from substrate Reverse Bias PN Junction Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Poly Film Resistor Polysilicon Film N or P type Oxide P type Si Substrate To lower the capacitive parasitics we should build the resistor further away from substrate We can deposit a thin film of poly Si heavily doped material on top of the oxide The poly will have a certain resistance say 10 Ohms sq Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Ohm s Law Current I in terms of Jn Voltage V in terms of electric field V IR I JA JtW I JA JtW t W E E V L Result for R L 1 R W t Department of EECS L R W t I JA JtW tW L V University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Sheet Resistance Rs IC resistors have a specified thickness not under the control of the circuit designer Eliminate t by absorbing it into a new parameter the sheet resistance Rs L L L R Rsq Wt t W W Number of Squares Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Using Sheet Resistance Rs Ion implanted or diffused IC resistor Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Idealizations Why does current density Jn turn What is the thickness of the resistor What is the effect of the contact regions Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Diffusion Diffusion occurs when there exists a concentration gradient In the figure below imagine that we fill the left chamber with a gas at temperate T If we suddenly remove the divider what happens The gas will fill the entire volume of the new chamber How does this occur Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 7 Prof A Niknejad Diffusion cont The net motion of gas molecules to the right chamber was due to the concentration gradient If each particle moves on average left or right then eventually half will be in the right chamber If the molecules were charged or electrons then there would be a net current flow The diffusion current flows from high concentration to low concentration Department of EECS University of California Berkeley EECS 105 Fall 2003 …
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