Solid State Devices EE 3311 SMU Chapter 4 Diffusion of Dopants Revised September, 2015

Impurity Diffusion Diffusion in Semiconductors a process that allows atoms to move within a solid at elevated temperatures takes place in a concentration gradient atoms move in direction of decreasing concentration changes type (n or p) of carrier changes the conductivity Diffusion Mechanisms Substitutional Interstitial

Point Defects & Doping Self Interstitial Vacancy Substutional

Diffusion Process T ~ 900 to 1100C (Si) Dopants spread vertically and laterally

3D View of Diffusion

Constant Source Diffusion

Drive-in Diffusion

Diffusion Fick’s First Law Units: D (cm2/sec); DN (particles/cm3); Dx (cm); so J (particles/cm2/sec)

Diffusion Fick’s Second Law

Constant Source Diffusion Solution Complementary Error Function Profiles

Constant Source Math Details

Constant Source Math Details, cont’d 1

Constant Source Math Details, cont’d 2

Constant Source Math Details, cont’d 3

Constant Source Math Details, cont’d 4

Limited Source Diffusion Solution Gaussian Profiles Initial Impulse with Dose Q

Limited Source Math Details

Limited Source Math Details, cont’d 1

Limited Source Math Details, cont’d 2

Two Step Diffusion

Diffusion Profile Comparison Complementary Error Function and Gaussian Profiles are Similar in Shape

Diffusion Coefficients Substitutional Diffusers Interstitial Diffusers

Diffusion Coefficients limited source constant source

Successive Diffusions Successive Diffusions Using Different Times and Temperatures Final Result Depends Upon the Total Dt Product

Diffusion Solid Solubility Limits There is a limit to the amount of a given impurity that can be “dissolved” in silicon (the Solid Solubility Limit) At high concentrations, all of the impurities introduced into silicon will not be electrically active

Point Defects & Doping Self Interstitial Vacancy Substutional

Diffusion p-n Junction Formation

Junction Depth of Limited Source Diffusion

Junction Depth of Constant Source Diffusion And the junction xj occurs at

Resistivity vs. Doping For EE 3311, wafer resistivities range from ~ 1 to ~ 10 ohm-cm Implies NB ~ 4x1014 to 4.5x1015 atoms/cm3

Two Step Diffusion Short constant source diffusion used to establish dose Q (“Predep” step) Longer limited source diffusion drives profile in to desired depth (“drive in” step) Final profile is Gaussian

Diffusion Calculation Example 4.3 - Boron Diffusion A boron diffusion is used to form the base region of an npn transistor in a 0.18 W-cm n-type silicon wafer. A solid-solubility-limited boron predeposition is performed at 900o C for 15 min followed by a 5-hr drive-in at 1100oC. Find the surface concentration and junction depth (a) after the predep step and (b) after the drive-in step.

Diffusion Calculation, cont’d 1 Boron Diffusion: Constant Source constant source/pre-deposition:

Diffusion Calculation, cont’d 2 Boron Diffusion: Limited Source limited source/drive-in:

Diffusion Calculation, cont’d 4 Wafer Background Doping

Diffusion Calculation, cont’d 3 Junction Depths

Diffusion Calculation, cont’d 5 Calculated profiles Short constant source diffusion used to establish dose Q (“Predep” step) Longer limited source diffusion drives profile in to desired depth (“drive in” step) Final profile is Gaussian

Lateral Diffusion Under Mask Edge Diffusion is really a 3-D process. As impurities diffuse vertically, they also diffuse horizontally in both directions. Diffusion proceeds laterally under the edge of the mask opening

Lateral Diffusion Under Mask Edge Original Mask

Concentration Dependent Diffusion

Concentration Dependent Diffusion

Resistors and Sheet Resistance

Stop Diffusion Slides for 3311

Resistors: Counting Squares Top and Side Views of Two Resistors of Different Size Resistors Have Same Value of Resistance Each Resistor is 7  in Length Each End Contributes Approximately 0.65  Total for Each is 8.3  Figure 4.14

Resistors Contact and Corner Contributions Effective Square Contributions of Various Resistor End and Corner Configurations Figure 4.15

Sheet Resistance: Irvin’s Curves Irvin Evaluated this Integral and Published a Set of Normalized Curves Plot Surface Concentration Versus Average Resistivity Four Sets of Curves n-type and p-type Gaussian and erfc

Sheet Resistance Irvin’s Curves

Sheet Resistance Irvin’s Curves (cont.)

Two Step Diffusion Sheet Resistance - Predep Step

Two Step Diffusion Sheet Resistance - Drive-in Step

Resistivity Measurement Four-Point Probe

Four-Point Probe Correction Factors

Sheet Resistance van der Pauw’s Method

Junction Depth Measurement Groove and Stain Method

Junction Depth Measurement Angle Lap Technique

Impurity Profiling Spreading Resistance Region of Interest is Angle-Lapped Two-Point Probe Resistance Measurements vs. Depth Profile Extracted

Impurity Profiling Secondary Ion Mass Spectroscopy (SIMS)

Diffusion Simulation After Predep After Drive-in SUPREM Simulation

Diffusion Systems Open Furnace Tube Systems Wafers in Quartz Boat Solid source in platinum source boat Liquid Source - carrier gas passing through bubbler Gaseous impurity source Wafers in Quartz Boat Scrubber at Output

Diffusion Systems Boron Diffusion

Diffusion Systems Phosphorus Diffusion

Diffusion Systems Arsenic & Antimony Diffusion

Diffusion Toxicity of Gaseous Sources Silane and Dichlorosilane Used for Polysilicon Deposition

Diffusion Gettering Improves Quality of Wafers Backside Treatment Removes Metallic Impurities: Cu, Au, Fe, Ni (Rapid Diffusers) Removes Crystal Defects: Dislocations Backside Treatment Surface Damage e. g. Sandblasting Phosphorus Diffusion Argon Implantation Internal Stress Crystal Defects Oxygen Incorporation During Growth Implantation

Diffusion References

End of Diffusion Slides