The silicon substrate and adding to it—Part 1

1. The silicon substrate and adding to it—Part 1 • Explain how single crystalline Si wafers are made • Describe the crystalline structure of Si • Find the Miller indices of a planes and directions in crystals and give the most important direction/planes in silicon • Use wafer flats to identify types of Si wafers • Define • Semiconductor • Doping/dopant • Resistivity • Implantation • Diffusion • p-n junction • Give a number of uses of p-n junctions • Calculate • Concentration distributions for thermal diffusion • Concentration distributions for ion implantation, and • p-n junction depths

2. Silicon—The big green Lego® siliconsubstrate siliconsubstrate Surface micromachining Bulk micromachining

3. Three forms of material Grains Crystalline Amorphous Polycrystalline Glass and fused quartz, polyimide, photoresist Silicon wafers Polysilicon (in surface μ-machining)

4. Creating silicon wafers • Creates crystalline (cristalino) Si of high purity • A “seed” (semilla) of solid Si is placed in molten Si—called the melt—which is then slowly spun and drawn upwards while cooling it. • Crucible and the “melt” turned in opposite directions • Wafers cut from the cross section. The Czochralski method

5. Creating silicon wafers Grains Polycrystalline silicon (American Ceramics Society) Photo (foto) of a monocrystalline silicon ingot

6. It’s a crystal a a a Face-centered cubic (FCC) Body-centered cubic (BCC) Cubic Unit cells a - lattice constant, length of a side of a unit cell

7. It’s a crystal The diamond (diamante) lattice

8. Miller indices The Miller indices give us a way to identify different directions and planes in a crystalline structure. • How to find Miller indices: • Identify where the plane of interest intersects the three axes forming the unit cell. Express this in terms of an integer multiple of the lattice constant for the appropriate axis. • Next, take the reciprocal of each quantity. This eliminates infinities. • Finally, multiply the set by the least common denominator. Enclose the set with the appropriate brackets. Negative quantities are usually indicated with an over-score above the number. • Indices: h, k and l • [h k l ]  a specific direction in the crystal • <h k l >  a family of equivalent directions • (h k l ) a specific plane • {h k l } a family of equivalent planes

9. Tetoca a ti Find the Miller indices of the plane shown in the figure. • How to find Miller indices: • Identify where the plane of interest intersects the three axes forming the unit cell. Express this in terms of an integer multiple of the lattice constant for the appropriate axis. • Next, take the reciprocal of each quantity. This eliminates infinities. • Finally, multiply the set by the least common denominator. Enclose the set with the appropriate brackets. Negative quantities are usually indicated with an over-score above the number. 4 • Respuesta: (2 4 1) 3 2 1 c b a 1 1 2 2 For cubic crystals the Miller indices represent a direction vector perpendicular to a plane with integer components. Esdecir, [h k l] ⊥ (h k l) ¡Ojo! Not true for non-cubicmaterials!

10. Non-cubic material example Quartz is an example of an important material with a non-cubic crystalline structure. (http://www.jrkermode.co.uk/quippy/adglass.html)

11. Miller indices What are the Miller indices of the shaded planes in the figure below? • (1 0 0) • (1 1 0) • (1 1 1) Tetoca a ti: Find the angles between {1 0 0} and {1 1 1} planes, and {1 1 0} and {1 1 1} planes.

12. Wafer types Si wafers differ based on the orientation of their crystal planes in relation to the surface plane of the wafer. • Wafers “flats” are used to identify • the crystalline orientation of the surface plane, and • whether the wafer is n-type or p-type. <1 0 0> direction (1 0 0) wafer

13. Relative position of crystalline planes in a (100) wafer Orientations of various crystal directions and planes in a (100) wafer (Adapted from Peeters, 1994)

14. It’s a semiconductor Conductors Insulators Semiconductors The “jump” is affected by both temperature and light  sensors and optical switches

15. Conductivity, resistivity, and resistance • Electrical conductivity (σ)  • A measure of how easily a material conducts electricity • Material property • Electrical resistivity (ρ)  • Inverse of conductivity; esdecirρ = 1/σ • Material property By doping, the resistivity of silicon can be varied over a range of about 1×10-4 to 1×108Ω•m!

16. Conductivity, resistivity, and resistance • Tetoca a ti • Find the total resistance (in Ω) for the MEMS snake (serpiente) resistor shown in the figure if it is made of • Aluminum (ρ = 2.52×10-8Ω·m) and • Silicon 1 μm 100 bends total • Respuesta: • Al: 509 Ω • Si: 1.3 GΩ !! 100 μm 1 μm Entire resistor is 0.5 μm thick

17. Doping Phosphorus is a donor – donates electrons Boron is an acceptor – accepts electrons from Si  Charge carriers are “holes.” Phosphorus and boron are both dopants. P creates an n-type semiconductor. B creates a p-type semiconductor.

18. Doping • Two major methods • Build into wafer itself during silicon growth • Gives a uniform distribution of dopant •  Background concentration • Introduce to existing wafer • Implantation or diffusion (or both!) • Non-uniform distribution of dopant • Usually the opposite type of dopant (Esdecir, si wafer es p-type, el otroes n-type y vice versa) • Location where dopant concentration matches background concentration se llama p-n junction p-n junction • Uses of doping and p-n junctions: • Change electrical properties (make more or less conductive) • Create piezoresistance, piezoelectricity, etc. to be used for sensing/actuation • Create an etch stop

19. Doping How do we determine the distribution of diffused and/or implanted dopant? Mass diffusion: Often implantation and diffusion are done through masksin the wafer surface in order to create p-n junctions at specific locations. Concentration gradient Mass “flux” Diffusion constant Compare to Frequency factor and activation energy for diffusion of dopants in silicon

20. Doping by diffusion C time x At t = 0, or C(x, t = 0) = 0 Conservation of mass (applied to any point in the wafer) • Need • 1 initial condition • 2 boundary conditions C(x = 0, t > 0) = Cs C(x → ∞, t > 0) = 0 erfc() is the complementary error function: Appendix C Solución 

21. Doping by diffusion x Diffusion length  rough estimate of how far dopant has penetrated wafer Diffusion of boron in silicon at 1050°C for various times

22. Doping by diffusion Total amount of dopant diffused into a surface per unit area is called the ion dose. Cs C(x = 0, t > 0) = Cs Q = constant time Gaussian distribution x

23. Doping by implantation Distribution is also Gaussian, but it is more complicated. • CP – peak concentration of dopant • RP–the projected range (the depth of peak concentration of dopant in wafer) • ΔRP– standard deviation of the distribution • Range affected by the mass of the dopant, its acceleration energy, and the stopping power of the substrate material. Doping by ion implantation Peak concentration 

24. Doping by implantation Doping is often (de hecho, usually) a two-step process: 1st implantation – pre-deposition 2nd thermal diffusion – drive-in If projected range of pre-deposition is small, can approximate distribution with Typical concentration profiles for ion implantation of various dopant species Replace with Qi

25. Junction depth C implanted dopant background concentration p-n junction x

26. Tetoca a ti • A n-type Si-wafer with background doping concentration of 2.00×1015cm-3 is doped by ion implantation with a dose of boron atoms of 1015cm-2, located on the surface of the wafer. Next thermal diffusion is used for the drive-in of boron atoms into the wafer a 900°C for 4 hours. • a. What is the diffusion constant of boron in silicon at this temperature? • b. What is the junction depth after drive-in? • Hints: • Assume that the distribution of ions due to implantation is very close to the wafer surface • Useful information: • kb= 1.381×10-23 J/K • eV = 1.602×10-19 J

27. Tetoca a ti • A n-type Si-wafer with background doping concentration of 2.00×1015cm-3 is doped by ion implantation with a dose of boron atoms of 1015cm-2, located on the surface of the wafer. Next thermal diffusion is used for the drive-in of boron atoms into the wafer a 900°C for 4 hours. • a. What is the diffusion constant of boron in silicon at this temperature? • b. What is the junction depth after drive-in? Set = Cbg = 1.248×10-18 m2/s b. a. = 0.83×10-6 m Replace with Qi