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Microelectronics 2

Electrical Engineering 2. Lecture 5. Microelectronics 2. Dr. Peter Ewen. (Room G08, SMC; email - pjse). 100 200 300 400 500 600. Fig. 25: Free electron concentration vs. temperature for intrinsic and extrinsic silicon. 3 × 10 21. Intrinsic Si.

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Microelectronics 2

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  1. Electrical Engineering 2 Lecture 5 Microelectronics 2 Dr. Peter Ewen (Room G08, SMC; email - pjse)

  2. 100 200 300 400 500 600 Fig. 25: Free electron concentration vs. temperature for intrinsic and extrinsic silicon 3×1021 Intrinsic Si n-type Si doped with ND = 1021 m-3 INTRINSIC REGION 2×1021 (Free) electron concentration, n / m-3 EXTRINSIC REGION 1021 ni IONISATION REGION Temperature / K

  3. 3×1021 *Provided semiconductor is in this temperature range 2×1021 Carrier concentration / m-3 1021 ni 100 200 300 400 500 600 Temperature, T / K Majority and Minority Carriers For intrinsic semiconductors: n = p = ni  np = ni2 For extrinsic semiconductors: nn >> pn for n-type pp >> np for p-type For extrinsic semiconductors it also turns out that: np = ni2 n – the electron concentration ni – the intrinsic carrier concentration p – the hole concentration *

  4. 3×1021 *Provided semiconductor is in this temperature range 2×1021 Carrier concentration / m-3 1021 ni 100 200 300 400 500 600 Temperature, T / K So for extrinsic semiconductors: nnpn = ni2 for n-type nppp = ni2 for p-type nn≈ ND for n-type pp≈ NA for p-type ND – donor concentration NA – acceptor concentration * Thus for n-type: nn≈ ND ; pn≈ ni2 / ND for p-type: pp≈ NA ; np≈ ni2 / NA Electrons in n-type – majority carriers Holes in n-type – minority carriers Holes in p-type – majority carriers Electrons in p-type – minority carriers

  5. F(E) is the Fermi-Dirac Distribution Function EF – the Fermi Level  A state at the Fermi level, EF, has a 50-50 chance of being occupied

  6. Fig. 26 F(E) for an INTRINSIC semiconductor E C.B. EC ½EG EF Energy, E ½EG EV V.B. 0 ½ 1 F(E) THE FERMI-DIRAC DISTRIBUTION

  7. EF Fig. 27 F(E) for an n-type semiconductor E C.B. EC donor levels Energy, E EV V.B. For n-type semiconductors the Fermi level lies closer to the conduction band edge, Ec 0 ½ 1 F(E) THE FERMI-DIRAC DISTRIBUTION

  8. Fig. 28 F(E) for a p-type semiconductor E C.B. EC acceptor levels Energy, E EF EV V.B. For p-type semiconductors the Fermi level lies closer to the valence band edge, Ev 0 ½ 1 F(E) THE FERMI-DIRAC DISTRIBUTION

  9. LECTURE 5  Electron scattering and mobility • Conduction by drift • Conductivity

  10. 10. The Fermi-Dirac distribution functionThe table below shows that although the energy gap for the diamond form of carbon is only about 5 times larger than that for Si, the resistivities of these materials differ by a huge amount - a factor of about 1010. To see why this is, use the Eg values in the table to compare F(Ec) for intrinsic Si and diamond at 300K. (F(Ec) is the value of the Fermi-Dirac distribution function at the conduction band edge, i.e. at E = Ec). At what temperature would Fdiam.(Ec) equal the room temperature value of FSi(Ec)?

  11. 10. The Fermi-Dirac distribution function The value of the Fermi-Dirac distribution function at the bottom of the conduction band, F(EC), is found by putting E = EC in the formula: For an intrinsic semiconductor EF will be approximately in the middle of the energy gap, i.e. it will lie ½Eg below the bottom of the conduction band, which is at E = EC, hence EC = EF + ½Eg.

  12. Hence: So

  13. In order that at some temperature, T, FDiam(EC) has the same value FSi(EC) has at room temperature, we require that:

  14. MOBILITY The MOBILITY,  , is a measure of the ease with which an electron can move through the solid. Electron movement is hindered by collisions, i.e. by SCATTERING. Electrons are scattered by: (A) The thermal vibrations of the atoms (i.e. PHONONS) – this is termed LATTICE SCATTERING.

  15. (B) DEFECTS (e.g. impurities) – DEFECT SCATTERING or IMPURITY SCATTERING. V: a vacancy – a place where an atom is missing. I: an interstitial – an extra atom that is residing in the space between regular atoms. D: a dislocation – here a region of the crystal has slipped relative to a neighbouring region. Im: an impurity – e.g. a donor or acceptor atom in the case of an extrinsic semiconductor V Im I D Fig. 30: Defect examples

  16. Note that the electrons are not scattered by the atoms themselves. The mobility for a perfect crystal at 0 K would be infinite:

  17. vd – drift velocity E – electric field def  = vd /E Note: • A mobility can also be defined for holes. • Units for mobility are: m2V-1s-1 • Mobility depends on temperature. For lattice scattering, mobility decreases as temperature increases because there are more thermal vibrations around at higher temperatures. For lattice scattering in semiconductors: l = KlT-3/2 l – indicates lattice scattering Kl – constant T – temperature in K

  18. High temperature – electron moving fast + Fig. 31 Low temperature – electron moving slowly + ionised donor atom + For impurity scattering: i = KiT3/2 For a metal:   T-1

  19. If the hole mobility for a sample of intrinsic silicon is 0.07 m2V-1s-1 at 300K, what will this mobility be at 100K? A. 1.35 x 10-2 m2V-1s-1 B. 0.21 m2V-1s-1 C. 0.36 m2V-1s-1 D. 2.33 x 10-2 m2V-1s-1

  20. l CONDUCTION BY CHARGE DRIFT Fig. 32 E (F = qE) Electron motion during time interval, t, in zero field. Electron motion during time interval, t, in field E. DRIFT VELOCITY: vd = l / t

  21. CONDUCTIVITY  – conductivity E – electric field J = I / A – current density J = E Ohm’s Law Metals:  = ne Semiconductors:  = nee + peh (intrinsic or extrinsic) special cases Intrinsic Semiconductors:  = eni(e + h) (n = p = ni for intrinsic) n-type:  ≈ nnee≈ NDee (nn >> pn for n-type) p-type:  ≈ ppeh≈ NAeh (pp >> np for n-type)

  22. 2 cm 2 cm 12 V 0.6 cm Intrinsic Si • 11. Drift velocity and current density (Bogart, 4th Edition, Ex. 2-2, p.13) • 12V is applied across a square plate of intrinsic Si as shown in the figure. • What are the electron and hole drift velocities? • What are the electron and hole components of the current density? • What is the total current density? • What is the total current through the plate? For Si: ni = 1.5 x 1016 m-3 e = 0.14 m2V-1s-1 h = 0.05 m2V-1s-1

  23. 11. Drift velocity and current density def  = vd/E 2 cm 2 cm 12 V 0.6 cm Intrinsic Si ni = 1.5 x 1016 m-3 e = 0.14 m2V-1s-1 h = 0.05 m2V-1s-1

  24. Electron and hole components of the current density?

  25. 2 cm 2 cm 12 V 0.6 cm Intrinsic Si electron -ve Je Jh -ve +ve +ve hole

  26. SUMMARY SCATTERING AND MOBILITY • The MOBILITY is a measure of the ease with which a carrier moves through the solid. • The mobility is limited by SCATTERING from: o THERMAL VIBRATIONS of the atoms o IMPURITIES and other DEFECTS

  27. The mobility is defined as the drift velocity achieved in unit electric field: • = vd / E • Units for  are: m2V-1s-1 • The mobility depends on temperature: For lattice scattering: l = KlT-3/2 For impurity scattering: i = KiT3/2 For a metal:   T-1

  28. l CONDUCTION BY CHARGE DRIFT • Conduction by drift is one of the two conduction mechanisms possible in solids • DRIFT refers to the net movement of carriers in a direction defined by the electric field. • The DRIFT VELOCITY is the distance drifted in time t, divided by t. E (F = qE) Vd = l / t

  29. CONDUCTIVITY Ohm’s Law: J = E Metal:  = ne General Semiconductor:  = nee + peh Intrinsic Semiconductor:  = eni(e + h) n-type:  ≈ nnee≈ NDee p-type:  ≈ ppeh≈ NAeh

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