INTEGRATED CIRCUITS Dr. Esam Yosry Lec. #3

Diffusion  Introduction  Diffusion Process  Diffusion Mechanisms  Why Diffusion?  Diffusion Technology  Diffusion Equation  Lateral Diffusion  Measuring Dopant Concent. & Depth

Introduction ( Chip Fabrication Cycle)

Introduction ( Processes)  Oxidation  Diffusion  Ion Implantation  Deposition  Etching  Lithography  Deposition  Removal  Patterning  Modification of electrical properties

Diffusion Process  Diffusion: is a process by which impurity atoms move through a crystal  Diffusion is the redistribution of atoms from high concentration regions to low concentration regions  Diffusion is becoming the old way of doping, but it is still used for deep doping

Diffusion Process  Diffusion process is carried out at 1000 °C to give atoms thermal energy  There are more than one possible mechanism by which the heated atoms can move through the heated crystal

Diffusion Mechanisms Substitutional : B, P, As Interstitial : Au, Cu, Fe Thermal activation E (eV) E s > E i

Why Diffusion?  Placement of doped regions (Source/Drain) determine the short- channel c/cs of MOS device

Diffusion Technology  The introduction of impurities by diffusion into wafer is usually carried out by exposing the wafer to an inert (nitrogen) gas containing the desired dopant in a diffusion furnace  The Two-Step diffusion is: Predeposition then Drive-In

Diffusion Technology  Predeposition : doping often proceeds by initial predep step to introduce the required dose of dopant into the substrate (source on Infinite source)  Drive-In: a subsequent drive-in anneal then redistributes the dopant giving the required junction depth and surface concentration (source off limited source)

Diffusion Technology SiO 2 P-type dopant atoms P-doped region n-type wafer Masked part of the wafer Typically, a thermally grown oxide mask is used, and openings are made in the oxide over the regions where you want to dope.

Diffusion Technology  Oxide can be relatively thin, since the diffusivity of dopants in SiO2 << in Si. Need thicker oxide for longer predeposition processes  Oxide grows on the Si wafer during diffusion and traps the dopant in the wafer so it does not diffuse out.

Diffusion Technology  A junction is the separation between a region n-dopant and p-dopant region  Junction location is where the concentration of electrons = concentration of holes Metallurgical Junction

Diffusion Sources Diffusion Technology

Diffusion Furnace Exactly the same as the oxidation furnace. The nature of the ambient gas depends on the type of diffusion required. BatchTube Boat

Diffusion Equation Fick’s 1st Law: Continuity Equation: Fick’s 2nd Law (Diffusion Equastion): D is the diffusion constant in cm 2 /s

Diffusion Equation Dopant redistribution is described by Fick’s 1st Law, how the flux of dopant depends on the doping gradient -ve indicates that the flow is down the concentration gradient

Diffusion Equation Fick’s 2nd Law describes how the change in concentration in a volume is determined by the change in fluxes in and out of the volume ∆N∆N

Solution of the Diffusion Equation Under constant surface concentration N s (Infinite source): (Predeposition) Under constant dose Q (Limited source): (Drive-In) surface concentration diffusion length L d Shallow highly concentrated doped region near the surface D d t d >> D p t p

Solution of the Diffusion Equation Predeposition: (Diffusion from infinite source for short time at low temperature) x XjXj log scale NsNs NBNB Shallow Junction

Solution of the Diffusion Equation Deep Junction Drive-in: (Diffusion from a limited source for long time at high temperature) XjXj

Solution of the Diffusion Equation At any given time we can plot the concentration versus distance

Solution of the Diffusion Equation Error Function

Solution of the Diffusion Equation Error Function

Solution of the Diffusion Equation Error Function

Example 1 Calculate the junction depth and the dose of dopant Q introduced into an n-type silicon substrate with a bulk background concentration of cm -3 after a diffusion from infinite source at 975 °C for 60 min with 3.5 x cm -3 surface concentration and diffusion constant is 1.5 x cm 2 /s. Solution N B =10 15 cm -3,T=975 °C, t=60 min, N S = 3.5x10 20 cm -3, D=1.5x cm 2 /s. N B / N S = 2.9x10 -6, 2√Dt =1.47x10 -5 cm. From table erfc -1 (2.9x10 -6 ) =3.3 X j =3.3x1.47x10 -5 =49 µm = 0.49 micron Q=N s L d /√ Π = 1.47x10 -5 x 3.5x10 20 /1.77 = 2.9x10 15 cm -2

Solution T=1100 °C, t=4.5 hr, D=2.5x cm 2 /s. We must first make sure that the condition D d t d >> D p t p is valid. √( D d t d )= √ (2.5x x 4.5x60x60) = 0.64 micron √ D p t p = √ 1.5x x 60x60 = micron Thus the condition is valid and we can use where Example 2 Calculate the junction depth for the sample predep-diffused in example1 after a drive-in for 4.5 hours at 1100 ° C and diffusion constant at this temperature is 2.5 x cm 2 /s. N o =(2x3.5x10 20 / Π) x 0.074/0.64= 2.5x cm -3. X j =12.8x10 -5 x √ln(2.5x10 19 /10 15 )= 4 micron

Solution Obtain the diffusion coefficient at 1100 C,  D = 0.2  / hr 1/2 from the graph on the previous page T=1100 °C, t=5 hr. Example 3 Calculate the concentration of a boron diffusion into silicon (doped with Phos. to 1X10 15 /cm 3 ) after a 5 hour diffusion at 1100 C. The boron Q o is 5X10 11 /cm 2. Calculate the N(x) at 1 , 2  and 3 .

Example 3 Q/(  Dt) 1/2 = 6.0X10 15 boron atoms / cm 3 At x = 0, N(x) = 6.0X10 15 atoms / cm 3 At x = 1 , N(x) = 4.4X10 15 atoms / cm 3 At x = 2 , N(x) = 1.7X10 15 atoms / cm 3 At x = 3 , N(x) = 0.36X10 15 atoms / cm Distance in the silicon in microns 6.0X X10 15 x N(x)

Lateral Diffusion Dopant diffuses laterally under the oxide diffusion mask % X j XjXj Diffusion through an oxide window

There are several techniques: 1.Sheet Resistance 2. Bevel and Etch Mechanically groove the wafer surface. 3. Capacitance-Voltage Measurement 4. Spreading Resistance Profilometry Can measure doping between – atoms/cm 3 5. Secondary Ion Mass Spectroscopy Takes a long time Measuring Dopant Concentrations and Depth

 Sheet Resistance is defined by looking at a small piece (square) of silicon with dimension “L” on a side and x j deep Sheet Resistance L

Measuring Dopant Concentrations and Depth  The resistivity of a cube is given by: Sheet Resistance L L L + V - I

Measuring Dopant Concentrations and Depth  The sheet resistance of a shallow junction is Sheet Resistance L L L + V - I Sheet Resistance sq For uniformly doped material

Measuring Dopant Concentrations and Depth  Place a biased metal contact on the semiconductor surface to form a depletion region of width W and a capacitance of C Capacitance-Voltage Measurement

Measuring Dopant Concentrations and Depth  Measure the capacitance of the depletion region as a function of bias voltage so the substrate doping is given by:  Dose not work for high doping (>10 18 atoms/cm 3 ) Capacitance-Voltage Measurement

Many thanks to Prof. Hany Fikry and Prof Wael Fikry for their useful materials that help me to prepare this presentation. Thanks