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1 Electrical Engineering 2 Microelectronics 2 Dr. Peter Ewen (Room G08, SMC; - pjse) Lecture 4

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ELECTRICAL ENGINEERING 2 Microelectronics 2 Dr. P.J.S. Ewen LECTURES: Mondays Swann 7.20 Fridays JCMB 5327 Fridays JCMB 5327 TUTORIALS: Mondays Eng. CR 4 (Monday Lab Group) Tuesdays Eng. CR 4 Tuesdays Eng. CR 4 (Friday Lab Group) N.B. Tutorials run in weeks 3, 5, 7, 9, 11

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3 Fig. 20 Si SiSi +ve charge associated with vacancy the vacancy is mobile Electric field -ve +ve +ve the vacancy acts like a mobile +ve charge + - Semiconductor Electron-hole pair

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4 n i – intrinsic carrier concentration (N.B. n i ≠ n + p) At 300K: n i = 1.5x10 16 m -3 for Si n i = 2.5x10 19 m -3 for Ge INTRINSIC SEMICONDUCTORS Pure semiconductors are termed “intrinsic”: n = p = n i n – free electron concentration; p – hole concentration Si SiSi

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5 CARRIER LIFETIME - : < < s C.B. V.B. GENERATION RECOMBINATION Fig. 21 EgEgEgEg

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6n-typepentavalentdonoratomsp-typetrivalentacceptoratoms Substitutional impurities – they can be incorporated into the semiconductor lattice without distorting it. Typical doping concentrations: – m -3 EXTRINSIC SEMICONDUCTORS

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7 Fig. 22 Si As Si Si Si Donoratom Energy ~0.01 eV n-type Si C.B. V.B. Donor levels

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8 Fig. 22 Si B Si Si Si Acceptoratom Energy ~0.01 eV p-type Si C.B. V.B. Acceptor levels

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9 Fig. 23: Typical range of conductivities/resistivities for metals insulators and semiconductors. i i i i i

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10 The effect of increasing temperature on resistance/resistivity. MetalIntrinsicsemiconductorInsulator Extrinsic semiconductor As T RRRR RRRR RRRR R or R or R constant TCR+ve-ve-ve +ve, -ve or ~0 Fig. 24 def Temperature Coefficient of Resistance

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11 LECTURE 4 Influence of temperature on carrier Influence of temperature on carrier concentrations in semiconductors concentrations in semiconductors Majority and minority carriers The Fermi-Dirac distribution function

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12 Temperature / K (Free) electron concentration, n / m -3 Fig. 25: Free electron concentration vs. temperature for intrinsic and extrinsic silicon × ×10 21 nininini Intrinsic Si n-type Si doped with N D = m -3 EXTRINSIC REGION IONISATION REGION REGION INTRINSICREGION 0

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13 Si Si Si Si Si Donoratom Si As Si Si Si Energy required to break a silicon bond is ~1.1ev Intrinsic Si Energy required to detach a donor electron is ~0.01ev n-type Si

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14 Same considerations apply to p-type Si (p = N A in saturation region) Extrinsic material effectively becomes intrinsic above a certain transition temperature – bad news for devices! Temperature, T / K (Free) electron concentration, n / m × ×10 21 nininini Hole concentration, p / m -3 Hole concentration, p / m -3 Ge Si GaAs nininini nininini

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15 8. Maximum working temperature for a 8. Maximum working temperature for a semiconductor device semiconductor device The maximum temperature, T max, at which a device can operate is fixed by the semiconductor material from which it is made. At T max, n i = N D for n-type material and n i = N A for p-type material. If n i = C exp (-E g / 2kT) n i = C exp (-E g / 2kT) where E g is the energy gap, T the temperature in degrees K, C is a constant and k is Boltzmann's constant, determine T max for a GaAs sample doped with donors m -3, given that for GaAs, E g = 1.42 eV and C = 18.1x10 23 m -3.

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16 8. Maximum working temperature for a semiconductor device For an n-type semiconductor, by definition the (approximate) maximum working temperature, T max, is the temperature at which n i = N D.

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17 So for a GaAs sample doped with donors m -3 : The 1.6 in the above converts eV to joules.) (The 1.6 in the above converts eV to joules.) But at T = T max, n i = N D

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18 This calculation ignores the change in E g due to temperature: E g decreases from 1.42 to 1.2eV over this temperature range. However, even if you correct for this, the maximum working temperature for GaAs is still greater than 450 o C, much higher than for Si.

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19 Majority and Minority Carriers For intrinsic semiconductors: n = p = n i np = n i 2 For extrinsic semiconductors: n n >> p n for n-type n n >> p n for n-type p p >> n p for p-type p p >> n p for p-type For extrinsic semiconductors it also turns out that: np = n i 2 np = n i 2 n i – the intrinsic carrier concentration n – the free electron concentration p – the hole concentration * Temperature, T / K Carrier concentration / m × ×10 21 nininini * Provided semiconductor is in this temperature range

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20 So for extrinsic semiconductors: So for extrinsic semiconductors: n n p n = n i 2 for n-type n p p p = n i 2 for p-type Temperature, T / K Carrier concentration / m × ×10 21 nininini * Provided semiconductor is in this temperature range n n ≈ N D for n-type p p ≈ N A for p-type N D – donor concentration N A – acceptor concentration * Thus for n-type: n n ≈ N D ; p n ≈ n i 2 / N D for p-type: p p ≈ N A ; n p ≈ n i 2 / N A for p-type: p p ≈ N A ; n p ≈ n i 2 / N A Electrons in n-type – majority carriers Holes in n-type – minority carriers Holes in n-type – minority carriers Holes in p-type – majority carriers Holes in p-type – majority carriers Electrons in p-type – minority carriers Electrons in p-type – minority carriers

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21 9. Carrier concentrations (Bogart, 9. Carrier concentrations (Bogart, 4 th Edition, Ex. 2-18, p.41) 4 th Edition, Ex. 2-18, p.41) A silicon wafer is doped with 1.8x10 20 m -3 atoms of As. If n i = 1.6x10 16 m -3 determine the electron and hole concentrations, n and p. (Assume the temperature is in the extrinsic region of operation.) of operation.) Temperature, T / K Electron concentration / m -3 4× ×10 20 nininini * Provided semiconductor is in this temperature range 2×10 20

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22 9. Carrier concentrations Arsenic is an n-type dopant hence:

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23 Which of the following statements is true: Holes in an n-type semiconductor are… A)Majority carriers that are thermally produced B)Minority carriers that are produced by doping C)Minority carriers that are thermally produced D)Majority carriers that are produced by doping

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24 Energy C.B. V.B. Donor levels EgEgEgEg Statisticalprocesses E N(E) Total number of electrons at energy E Probability that a state at energy E is occupied Total number of states at energy E The Fermi-Dirac Distribution Function F(E) x n(E) =

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

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26 Fig. 26 Energy, E C.B. V.B. E ECECECEC EFEFEFEF EVEVEVEV ½E G 0 ½ 1 F(E) F(E) for an INTRINSIC semiconductor THE FERMI-DIRAC DISTRIBUTION

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27 Fig. 27 Energy, E C.B. V.B. E ECECECEC EFEFEFEF EVEVEVEV 0 ½ 1 F(E) F(E) for an n-type semiconductor THE FERMI-DIRAC DISTRIBUTION donorlevels For n-type semiconductors the Fermi level lies closer to the conduction band edge, E c

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28 Fig. 28 Energy, E C.B. V.B. E ECECECEC EFEFEFEF EVEVEVEV 0 ½ 1 F(E) F(E) for a p-type semiconductor THE FERMI-DIRAC DISTRIBUTION acceptorlevels For p-type semiconductors the Fermi level lies closer to the valence band edge, E v

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29 Fig. 29 Energy C.B. V.B. Donor levels EFEFEFEF C.B. V.B. C.B. V.B. EFEFEFEF EFEFEFEF Metal Degenerate n-type Degenerate p-type Degenerate Semiconductors Acceptor levels EGEGEGEG EGEGEGEG

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30 For a semiconductor sample at 0 K, what is the probability that a state at the top of the valence band is occupied by an electron? A. 0 B. 1 C. ½ D. Between 1 and ½ D. Between 1 and ½

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31 The Fermi level, E F, for a silicon sample lies 0.8eV above the valence band edge. If the energy gap for silicon is 1.1eV, is this sample A. p-type B. n-type C. intrinsic

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32 SUMMARY INFLUENCE OF TEMPERATURE ON CARRIER CONCENTRATIONS For intrinsic semiconductors the carrier concentrations increase steadily as T increases. In Si, n i is small below 400K but increases rapidly above this temperature.

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33 For extrinsic semiconductors the concentration vs. T plot has three regions: 1. Ionisation region – the impurities are being ionised 2. Extrinsic region – all the impurities are ionised; few electron hole pairs 3. Intrinsic region – electron-hole pairs produced in large numbers – material effectively becomes intrinsic There is a transition temperature below which devices must operate, otherwise pn junctions will be lost. There is a transition temperature below which devices must operate, otherwise pn junctions will be lost. 33

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34 MAJORITY AND MINORITY CARRIERS MAJORITY AND MINORITY CARRIERS Majority carriers - electrons in n-type and holes in p-type Minority carriers - electrons in p-type and holes in n-type np = n i 2 np = n i 2 In n-type: n n ≈ N D ; p n ≈ n i 2 / N D In p-type: p p ≈ N A ; n p ≈ n i 2 / N A

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35 THE FERMI-DIRAC DISTRIBUTION FUNCTION THE FERMI-DIRAC DISTRIBUTION FUNCTION This is a statistical function giving the probability that a state at energy E is occupied by an electron This is a statistical function giving the probability that a state at energy E is occupied by an electron E F is the FERMI LEVEL - the energy at which a state has a chance of occupancy.

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36 The Fermi Level is approximately in the middle of the gap for an intrinsic semiconductor. The position of the Fermi Level is a measure of how n-type or p-type the material is. A degenerate semiconductor is one which is very heavily doped.

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