1. CHAPTER ONE SEMICONDUCTORS Copyright, 2006 © Ahmed S. Bouazzi 2e A G.I. Module Energie Solaire المدرسة الوطنية للمهندسين بتونس

2. The Crystal Lattice of Silicon Each silicon atom is situated at the center of a tetrahedron and connected to four other atoms occupying the summit of the tetrahedron.

3. A two dimension representation of the silicon crystal structure Intrinsic silicon Si Each silicon atom is situated at the center of four other atoms.

4. N-type Semiconductors n-doped silicon P P P P Si

5. P-type Semiconductors p-doped silicon Si B B B

6. Energy Interatomic distance Eg Permitted levels (a) (b) The Gap

7. Fermi Level [ F(E) is the probability for an electron to be in the E energy level] In intrinsic silicon, E F is situated in the middle of the gap. In doped silicon, the Fermi level goes up or down depending on the electron concentration.

8. Semiconductor Doping The doping atoms create localized levels inside the band gap.

9. Energy v E E F c E c E v E Semiconductor Metal Electron-hole Pairs

10. Intrinsic Carrier Concentration = 4 = 4 for silicon at 300 K, n i 2 = 2x10 20 cm -6 np = (m e m h ) 3/2 exp

11. In n-type silicon: Minority and Majority Carriers n = N D p no N D = n i 2 p no = n i 2 / N D In p-type silicon: p = N A n po N A = n i 2 n po = n i 2 / N A

12. In n-type silicon: Minority and Majority Carriers in Excess n n0 = N D ≈ 10 16 – 10 18 cm -3 p n0 N D = n i 2 ; p no = n i 2 / N D ≈ 2×10 4 – 2 × 10 2 cm -3 Creating  n =  p ( ≈ 10 11 – 10 14 cm -3 ) electron- hole pairs will give: n n = n n0 +  n ≈ N D and p n = p n0 +  p ≈  p

13. Minority and Majority Carriers in Excess In p-type silicon: p p0 = N A ≈ 10 16 – 10 18 cm -3 n p0 N A = n i 2 ; n po = n i 2 / N A ≈ 2×10 4 – 2 × 10 2 cm -3 Creating  n =  p ( ≈ 10 11 – 10 14 cm -3 ) electron- hole pairs will give: p p = p p0 +  p ≈ N A and n p = n p0 +  n ≈  n

14. Lifetime and Recombination N = N o exp In the bulk: At the surface: J sur = q(n p - n po )S  is the lifetime of the minority carriers. S is the surface recombination velocity of minority carriers.

15. Diffusion Length L = The diffusion length is the free path of the minority carriers before recombination.  is the lifetime of the minority carriers. D is the diffusion constant of minority carriers.

16. Absorption Coefficient The absorbed quantity of photons at the depth x is:  0 is the flux of photons arriving at the surface of the semiconductor and x is the depth. x 00 0

17. Drift Minority Carriers Current in a Semiconductor Electrons: J n = qn p µ n E and  n = qn p µ n

18. Holes: J p = qp n µ p E and  p = qp n µ p

19. J n = qD n  n p (x,y,z) J p = – qD p  p n (x,y,z) Diffusion Minority Carriers Current in a Semiconductor

20. J = J n + J p Electrons: J n = qn p µ n E + qD n  n p (x,y,z) Holes: J p = qp n µ p E – qD p  p n (x,y,z) Total Minority Carriers Current

21. E c E v E F E g p n Junction plane p-n Junction Depletion region

22. PHOTOVOLTAIC EFFFECT (1) The p-n Junction

23. E c E v E f Electrons current Holes current The photocurrent under illumination PHOTOVOLTAIC EFFFECT (2)

24. PHOTOVOLTAIC EFFFECT (3) The photovoltage under illumination

25. Depletion Region Where the built-in voltage is defined by:

26. Polarization of a p-n Junction direct inverse

27. I-V Characteristic

28. Saturation Current np =np =; p n =; L k = J o =

29. Metal/semiconductor junction E c E v Semiconductor E F metal E c E F E v (a) (b) (c) Schottky Diode and Ohmic Contacts