1. Thermal doping review example This presentation is partially animated. Only use the control panel at the bottom of screen to review what you have seen. When using your mouse, make sure you click only when it is within the light blue frame that surrounds each slide.

2. Cross section cut view that is not to scale Silicon wafer Oxide film Dopant containing film. Pattern a wafer and place an oxide film on top of the exposed silicon. Thermal Doping Example This section was protected by the mask Dopant will diffuse into the unprotected silicon as function of time and temperature in the furnace

3. Spin-on Dopant film sol-gel film Sources of dopants Thermal Doping Example Solid Source Cross section view of oven rack to hold wafers and solid dopant Wafer side that will house the functioning device. Solid wafer made of the dopant material Side of wafer that will have the functional device Wafer side that will house the functioning device. sol-gel film

4. for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002 Sources of dopants Thermal Doping Example Solid as vapor source Solid dopant placed in platinum boat

5. Liquid as vapor source Sources of dopants Thermal Doping Example for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002

6. Pure vapor source Sources of dopants Thermal Doping Example for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002

7. Thermal Doping Example Cross section cut view that is not to scale Silicon wafer Oxide film Dopant containing film. Pattern a wafer and place an oxide film on top of the exposed silicon. Place a dopant containing film on the wafer and heat for some time.

8. Silicon wafer Dopant containing film. Oxide film Thermal Doping Example Region of interest Cross section cut view that is not to scale

9. Silicon wafer Dopant containing film. Oxide film Cross section cut view that is not to scale

10. HEATHEAT

11. DEGLAZE then CLEAN Cross section cut view that is not to scale

12. HEATHEAT

14. Mask thickness (microns) Diffusion time (hours) Thermal Doping Example Oxide film needed to be thick enough to mask diffusion process for educational use only. Fig 3.7 p 53, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002 If your furnace is at 1100 degrees C, it will be at least 3.5 hrs before the boron gets through the1 micron thick oxide protective cover. 1 Practical factors How thick does the protective oxide have to be?

15. for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002 Thermal Doping Example Practical factors How much dopant will dissolve in the silicon? The real issue is how many dopant atoms will replace silicon atom. Impurity concentration (atoms/cm 3 ) You can dissolve more P and As atoms into crystal than can substitute for silicon atoms. N 0 At 900 C and maximum Boron concentration (solubility)at the surface is about 1.1 x 10 20 Boron atoms/ cm 3 1.1 x 10 20 Boron atoms/ cm 3 = Therefore,

16. Thermal Doping Example Practical factors How much does temperature influence the dopant transport into the silicon? for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002 B and P As D(T) = D 0 e - E A k T [] These plots can be modeled as exponential functions 86.2 x10 -6 ev/ K o AtomD 0 E A B10.53.69 ev Al8.03.47 ev Ga3.63.51 ev P10.53.69 ev As0.323.56 ev D(1173) = D 0 e - E A k (1173) [] From the model, what is the diffusion coefficient for P at 900 C? (900 C equals 1173 K) D( 1173 ) = P 10.5 e - 3.69 86.2 x10 -6 (1173) [] D( 1173 ) = P ? Come on! Work it out, its good for you. 1.48 x10 -15 cm /sec 2 10.53.69 ev

17. What are the model equations for the diffusion of dopant from an infinite source? Concentration profile through the diffusion region as a function of distance and time. Thermal Doping Example Practical factors X =0 at the outside edge of the wafer t =0 before the diffusion starts. Total dopant that was added to substrate. Distance into wafer were the concentration of the n and p materials is identical. Junction depth

18. What are the model equations for the diffusion of dopant from a constant or fixed source? Thermal Doping Example Practical factors Concentration profile through the diffusion region as a function of distance and time. X =0 at the outside edge of the wafer t =0 before the diffusion starts. Concentration at the surface as a function of time? Put X =0 and solve for all values of time. Distance into wafer were the concentration of the n and p materials is identical. Junction depth

19. X /4(Dt) 2 Function values Thermal Doping Example The error function and its complement are popular functions because they are solutions to differential equations that deal with diffusion problems. Values for the function are available from tables or plots like this one, What is erfc and how do I use it.? Practical factors erfc( ) -x e 2 or approximation functions like this one also found in common mathematics software packages. [] 1/2

20. for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002 Thermal Doping Example Practical factors The gaussian curve on the right is also often used as a substitute for the erf complement. For most of the model curves shown the plots have similar shape and functional response. for educational use only. From, R.C. Jaeger, Introduction to Microelectronic Fabrication, 2nd Ed., Prentice Hall, 2002

21. Thermal Doping Example Practical Problem You have a n-type silicon wafer that has a resistivity of 0.36 ohm-cm. You want to use boron to form the base region in the wafer for an npn transistor. You perform a solid-solubility limited boron “predeposition” at 900 C for 15 minutes followed by (after deglaze and clean) a 5 hour “drive-in” at 1100C. Find the boron surface concentration, the junction potential and the dose. (I) just after the “predeposition” step. (II) just after the “drive in” step.

22. Thermal Doping Example Find the boron surface concentration, the junction potential, and dose. Get N from the solubility graph for Boron at 900 C. 0 1) 2) Find the value for diffusion coefficient at 900 C. 900 C 1173 K D(1173) = B D 0 e - [ ] E A k (1173),B,B For Boron, B, the model becomes 3) Find the number of boron atoms, N ( x, t ) when x = 0 and t = 15 minutes (900 seconds). N ( x, t ) = N 0 erfc 1/2 [] x 2 D T t4,B,B (I) just after the “predeposition” step. (a) Boron surface concentration just after the “predeposition” step. Practical Problem

23. Determine the number of Boron atoms that correspond to the same resisitivity. (dopant concentration vs resistivity plot) 1) (I) just after the “predeposition” step. (b) Boron junction depth in the original resistivity of 0.36 ohm-cm n doped wafer. 2) Use the concentration profile model as a function of distance and time and solve for the junction depth distance. (II) just after the “drive-in” step. 1) Integrate the area under the concentration profile model for the pre- deposition or the “drive-in” process. 1) (c) Boron dose for this process. Find the boron surface concentration, the junction potential, and dose. Use the concentration profile model as a function of distance and time and solve when x = 0. (a) Boron surface concentration just after the “drive-in” step. N ( x, t ) = [] x 2 D T t4 e - Q 2  D t T [] 1/2 Thermal Doping Example Practical Problem

24. (II) just after the “drive-in” step. 1) Find the boron surface concentration, the junction potential, and dose. Use the concentration profile model as a function of distance and time and solve when x = 0. (a) Boron surface concentration just after the “drive-in” step. N ( x, t ) = [] x 2 D T t4 e - Q 2  D t T [] 1/2 1)Solve concentration profile model as a function of distance and time for junction depth. Thermal Doping Example Practical Problem (b) Boron junction depth, just after “drive in” step, in the original resistivity of 0.36 ohm-cm n doped wafer.

25. (II) just after the “drive-in” step. 1) Find the boron surface concentration, the junction potential, and dose. Use the concentration profile model as a function of distance and time and solve when x = 0. (a) Boron surface concentration just after the “drive-in” step. N ( x, t ) = [] x 2 D T t4 e - Q 2  D t T [] 1/2 1)Solve concentration profile model as a function of distance and time for junction depth. (b) Boron junction depth, just after “drive in” step, in the original resistivity of 0.36 ohm-cm n doped wafer.