Chapter 4: PN and Metal-Semiconductor Junctions

Transcription

1 Chater 4: P and Metal-Semiconductor Junctions 1

2 4.1 Building Blocks of the P Junction Theory Donor ions + V I P -tye P-tye I diode symbol Reverse bias Forward bias V P junction is resent in erhas every semiconductor device.

3 4.1.1 Energy Band Diagram of a P Junction (a) -region P-region E f E f is constant at equilibrium (b) E c E c E f E v E c and E v are known relative to E f E v (c) E c E f E v E c and E v are smooth, the exact shae to be determined. (d) eutral -region Deletion layer eutral P-region E c E f E v A deletion layer exists at the P junction where n 0 and 0. 3

4 4.1. Built-in Potential (a) -tye d d P-tye a a E c qf bi (b) E f E v V f bi (c) x x P x 0 Can the built-in otential be measured with a voltmeter? 4

5 4.1. Built-in Potential -region n d c e q A kt A kt q ln c d P-region n i n a c e qb kt B kt q ln c i n a f bi B A kt q c ln ni a ln c d f bi kt q ln d i n a 5

6 4.1.3 Poisson s Equation Gauss s Law: The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the ermittivity. (x) (x + Dx) s : ermittivity (~1 o for Si) : charge density (C/cm 3 ) Dx x Poisson s equation 6

7 4. Deletion-Layer Model (a) (b) 4..1 Field and Potential in the Deletion Layer eut ral Region d D eletion Layer x 0 n x P a eutral R egi on P P On the P-side of the deletion layer, = q a d dx q a s (c) x n q d q a x P x qa qa ( x) x + C 1 ( x P x) s s On the -side, = q d (d) x n 0 x P x qd ( x) ( x - x) s f bi V (e) 7

8 4..1 (a) Field and Potential in the Deletion Layer d a P (b) eut ra l Re gion D ele tion La yer e utral R egi on x n 0 x The electric field is continuous at x = 0. P P (c) q da x P = d x Which side x of the junction is deleted more? n q a x x A one-sided junction is called a + P junction or P + junction 8

9 (c) (d) (e) ECE Deartment- Faculty of Engineering - Alexandria University Field and Potential x in the Deletion Layer f bi x n q d q a x n x 0 P V x x On the P-side, qa V ( x) ( xp x) s Arbitrarily choose the voltage at x = x P as V = 0. (f) f bi, built-in otential x x n x P E c E f E v On the -side, qd V ( x) D ( x x s qd fbi ( x x s ) ) 9

10 (a) 4.. Deletion-Layer Width d a P (b) V is continuous at x = 0 If a >> d, as in a P + junction, (c) W de eut ra l Re gion D ele tion La yer e utral R egi on sfbi q d x 0 n x x x n q d x P x q a W de P x x P x sfbi 1 q d a a P x 0 1 d What about a + P junction? W de s f bi q where 1 1 d + 1 a 1 lighter doant density (d) 10

11 EXAMPLE: A P + junction has a =10 0 cm -3 and d =10 17 cm -3. What is a) its built in otential, b)w de, c)x, and d) x P? Solution: a) kt fbi q b) W de 0 17 d a cm ln 0.06V ln 0 6 n 10 cm sfbi q 6 i d / 1V 0.1 μm c) x W de 0.1 μm d) x P x d a μm 1. Å 0 11

12 4.3 Reverse-Biased P Junction V + P E c qf bi E c E f W de s ( fbi + Vr ) s q otential barrier q E f E v E v (a) V = 0 E c 1 1 d + 1 a lighter 1 doant density E c E fn qf bi + qv qv E f E v Does the deletion layer widen or shrink with increasing reverse bias? E v (b) reverse-biased 1

13 4.4 Caacitance-Voltage Characteristics d a P Conductor Insulator Conductor W de Reverse biased P junction is a caacitor. C de s A W de Is C de a good thing? How to minimize junction caacitance? 13

14 4.4 Caacitance-Voltage Characteristics 1/C de Caacitance data C 1 de W A de s ( fbi + V ) q A S Sloe = /q s A f bi Increasing reverse bias V r From this C-V data can a and d be determined? 14

15 EXAMPLE: If the sloe of the line in the revious slide is x10 3 F - V -1, the intercet is 0.84V, and A is 1 mm, find the lighter and heavier doing concentrations l and h. Solution: l /( sloe q A /(10 3 s ) cm ) cm 3 qf kt hl n bi 18 3 fbi ln 10 i kt 0.06 e e cm h 15 q ni l 610 Is this an accurate way to determine l? h? 15

16 4.5 Junction Breakdown I V B, breakdown voltage Small leakage Current A Forward Current V R P R C A A Zener diode is designed to oerate in the breakdown mode. 3.7 V Zener diode B D IC 16

17 4.5.1 Peak Electric Field eutral Region increasing reverse bias + P a E 0 x (a) increasing reverse bias q ( 0) ( f + bi Vr ) s 1/ x (b) x V B s crit q f bi 17

18 4.5. Tunneling Breakdown Filled States - Emty States E c Dominant if both sides of a junction are very heavily doed. E v J G e H / ε I V crit 10 6 V/cm Breakdown 18

19 4.5.3 Avalanche Breakdown E c E f E v original electron imact ionization: an energetic electron generating electron and hole, which can also cause imact ionization. Imact ionization + ositive feedbackavalanche breakdown electron-hole air generation V B s crit q E c E fn 1 1 V B + a 1 d E v 19

20 4.6 Forward Bias Carrier Injection V=0 V = 0 I=0 Forward biased Forward biased V + E c P qf bi E f E v qf bi qv E fn - qv E c E f Drift and diffusion cancel out + E v Minority carrier injection 0

21 4.6 Forward Bias Quasi-equilibrium Boundary Condition n ( Ec E fn kt Ec E f kt E fn E x ) ( )/ ( )/ ( P ce ce e f )/ kt E c E c n ( E E f )/ kt P0e n P0 e qv fn / kt E fn fn E fn x x P E f E v E v 0 0 P x x The minority carrier densities are raised by e qv/kt Which side gets more carrier injection? 1

22 4.6 Carrier Injection Under Forward Bias Quasi-equilibrium Boundary Condition n qv kt ( x P ) np0e qv kt ( ) 0e x P i n a n i d e qv kt qv kt e qv kt n( xp ) n( xp ) np0 np0( e 1) ( x ) ( x ) 0 ( e qv kt 0 1)

23 EXAMPLE: Carrier Injection A P junction has a =10 19 cm -3 and d =10 16 cm -3. The alied voltage is 0.6 V. Question: What are the minority carrier concentrations at the deletion-region edges? Solution: n( x ) n e 10 e 10 P qv kt P0 cm qv kt e 10 e 10 ( x ) 0 cm Question: What are the excess minority carrier concentrations? Solution: n( x ) n( x ) n P P P cm cm ( x ) ( x ) 3

24 4.7 Current Continuity Equation J (x) area A J (x + Dx) A J ( x) q J J A ( x + Dx) J Dx ( x + Dx) q ( x) + ADx q D x Volume = A Dx dj dx q x 4

25 4.7 Current Continuity Equation qd dj dx d dx q q Minority drift current is negligible; J = qd d/dx d dx D L d n dx n L n L and L n are the diffusion lengths L D L n D n n 5

26 4.8 Forward Biased Junction-- Excess Carriers P + x P -x 0 x d dx ( ) L 0 ( x ) ( x) Ae x / L qv / kt 0( e 1) + Be x / L ( x) 0 ( e qv / kt 1) e xx / L, x x 6

27 4.8 Excess Carrier Distributions 1.0 P-side a = cm -3 n P ' e x/l n 0.5 -side d = cm -3 ' e x/l 3L n L n L n 0 L L 3L 4L ( x) 0 ( e qv / kt 1) e xx / L, x x n( x) n P0 ( e qv / kt 1) e xx P / L n, x x P 7

28 EXAMPLE: Carrier Distribution in Forward-biased P Diode -tye d = 5 cm -3 D =1 cm /s = 1 ms P-tye a = cm -3 D n =36.4 cm /s n = ms Sketch n'(x) on the P-side. n( x P ) n 0 qv kt ni qv / kt P0( e 1) ( e 1) e 10 cm 17 a 10 -side cm -3 n ( = ) P-side ' ( = n ) x x 8

29 EXAMPLE: Carrier Distribution in Forward-biased P Diode How does L n comare with a tyical device size? L n D n n μm What is '(x) on the P- side? 9

30 4.9 P Diode I-V Characteristics J total J total J = J total J n J n = J total J P-side J np 0 J -side J np P-side 0 J -side x J d( x) qv kt qd q 0( e 1) dx L D e xx L J dn( x) n qv kt np qdn q np0( e 1) dx Ln D e xx P Ln D D n Total current J ( x ) + J np( xp) q 0 + q n P0 ( e L L n J at all x qv kt 1) 30

31 The P Junction as a Temerature Sensor I I ( e qv kt 0 1) I 0 Aqn i L D d + Dn L n a What causes the IV curves to shift to lower V at higher T? 31

32 4.9.1 Contributions from the Deletion Region n qv n i e et recombination (generation) rate: n i de / kt qv /kt ( e 1) I I qnw qv / kt i de qv / kt 0( e 1) + A ( e τ de 1) I I + leakage 0 A qnw i τ de de Sace-Charge Region (SCR) current Under forward bias, SCR current is an extra current with a sloe 10mV/decade 3

33 4.10 Charge Storage -side cm -3 P-side Q I n' x I Q Q I s s What is the relationshi between s (charge-storage time) and (carrier lifetime)? 33

34 4.11 Small-signal Model of the Diode V I R C G 1 R q kt di dv d dv qv / kt I0( e ) I ( e 1 qv / kt 0 ) d dv What is G at 300K and I DC = 1 ma? I DC / kt q I 0 e qv / kt Diffusion Caacitance: dq di C s sg dv dv I s DC / kt q Which is larger, diffusion or deletion caacitance? 34

35 Part II: Alication to Otoelectronic Devices 4.1 Solar Cells Solar Cells is also known as hotovoltaic cells. Converts sunlight to electricity with 10-30% conversion efficiency. 1 m solar cell generate about 150 W eak or 5 W continuous ower. Low cost and high efficiency are needed for wide deloyment. 35

36 4.1.1 Solar Cell Basics light Short Circuit P I sc I Dark IV Eq.(4.9.4) V V E c Solar Cell IV Eq.(4.1.1) E v + (a) I sc Maximum ower-outut I qv kt I e 1) 0( I sc 36

37 Direct-Ga and Indirect-Ga Semiconductors Electrons have both article and wave roerties. An electron has energy E and wave vector k. direct-ga semiconductor indirect-ga semiconductor 37

38 4.1. Light Absortion Light intensity (x) e -x α(1/cm): absortion coefficient 1/α : light enetration deth hc Photon Energy (ev) 1.4 ( mm) A thinner layer of direct-ga semiconductor can absorb most of solar radiation than indirect-ga semiconductor. But Si 38

39 4.1.3 Short-Circuit Current and Oen-Circuit Voltage J (x) area A J (x + Dx) If light shines on the -tye semiconductor and generates holes (and electrons) at the rate of G s -1 cm -3, Dx Volume = A Dx d dx L G D x If the samle is uniform (no P junction), d /dx = 0 = GL /D = G 39

40 Solar Cell Short-Circuit Current, I sc Assume very thin P+ layer and carrier generation in region only. P + 0 P' 0 x L I sc G x J qd I ( ) L ( 0) 0 d dx G D ( x) G(1 e sc AJ (0) G D ( x) x / q Ge L AqL G is really not uniform. L needs be larger than the light enetration deth to collect most of the generated carriers. x G / L ) L 40

41 Oen-Circuit Voltage Total current is I SC lus the PV diode (dark) current: I n D i qv / kt Aq ( e 1) L d AqL Solve for the oen-circuit voltage (V oc ) by setting I=0 qv / (assuming e oc kt 1) n D i qvoc / kt 0 e LG L d G V oc kt q ln( G d / n i ) How to raise V oc? 41

42 4.1.4 Outut Power A articular oerating oint on the solar cell I-V curve maximizes the outut ower (I V). Outut Power I sc V oc FF Si solar cell with 15-0% efficiency dominates the market now Theoretically, the highest efficiency (~4%) can be obtained with 1.9eV >Eg>1.eV. Larger Eg lead to too low Isc (low light absortion); smaller Eg leads to too low Voc. Tandem solar cells gets 35% efficiency using large and small Eg materials tailored to the short and long wavelength solar light. 4

43 4.13 Light Emitting Diodes and Solid-State Lighting Light emitting diodes (LEDs) LEDs are made of comound semiconductors such as InP and Ga. Light is emitted when electron and hole undergo radiative recombination. E c Radiative recombination E v on-radiative recombination through tras 43

44 Direct and Indirect Band Ga Tra Direct band ga Examle: GaAs Direct recombination is efficient as k conservation is satisfied. Indirect band ga Examle: Si Direct recombination is rare as k conservation is not satisfied 44

45 LED Materials and Structure LEDwavelength ( m m) 1.4 hoton energy 1.4 ( ev) E g 45

46 LED Materials and Structure E g (ev ) E g (ev) Wavelength (μm) Color Lattice constant (Å) InAs In infrared 3.45 InP GaAs red Red Yellow yellow 5.66 GaP Green blue violet Blue 5.46 AlP Ga Al UV 3.11 comound semiconductors binary semiconductors: - Ex: GaAs, efficient emitter ternary semiconductor : - Ex: GaAs 1-x P x, tunable E g (to vary the color) quaternary semiconductors: - Ex: AlInGaP, tunable E g and lattice constant (for growing high quality eitaxial films on inexensive substrates) Light-emitting diode materials 46

47 Common LEDs Sectral range Material System Substrate Examle Alications Infrared InGaAsP InP Otical communication Infrared -Red GaAsP GaAs Indicator lams. Remote control Red- Yellow Green- Blue AlInGaP InGa GaA or GaP Ga or sahire Otical communication. High-brightness traffic signal lights High brightness signal lights. Video billboards AlInGaP Quantun Well Blue-UV AlInGa Ga or sahire Solid-state lighting Red- Blue Organic semiconductors glass Dislays 47

48 4.13. Solid-State Lighting luminosity (lumen, lm): a measure of visible light energy normalized to the sensitivity of the human eye at different wavelengths Incandescent lam Comact fluorescent lam Tube fluorescent lam White LED Theoretical limit at eak of eye sensitivity ( λ=555nm) Theoretical limit (white light) ? 683 ~340 Luminous efficacy of lams in lumen/watt Organic Light Emitting Diodes (OLED) : has lower efficacy than nitride or aluminide based comound semiconductor LEDs. Terms: luminosity measured in lumens. luminous efficacy, 48

49 4.14 Diode Lasers Light Amlification (a) Absortion (d) et Light Absortion (b) Sontaneous Emission (c) Stimulated Emission (e) et Light Amlification Light amlification requires oulation inversion: electron occuation robability is larger for higher E states than lower E states. Stimulated emission: emitted hoton has identical frequency and directionality as the stimulating hoton; light wave is amlified. 49

50 Light Amlification in P Diode Poulation inversion is achieved when qv E fn E f E g Equilibrium, V=0 Poulation inversion, qv > Eg 50

51 4.14. Otical Feedback and Laser light out Cleaved crystal lane P + + Laser threshold is reached (light intensity grows by feedback) when R R G 1 R1, R: reflectivities of the two ends G : light amlification factor (gain) for a round-tri travel of the light through the diode 1 R 1 R G Light intensity grows until, when the light intensity is just large enough to stimulate carrier recombinations at the same rate the carriers are injected by the diode current. 1 51

52 4.14. Otical Feedback and Laser Diode Distributed Bragg reflector (DBR) reflects light with multi-layers of semiconductors. Vertical-cavity surfaceemitting laser (VCSEL) is shown on the left. Quantum-well laser has smaller threshold current because fewer carriers are needed to achieve oulation inversion in the small volume of the thin small-eg well. 5

53 Laser Alications Red diode lasers: CD, DVD reader/writer Blue diode lasers: Blu-ray DVD (higher storage density) 1.55 mm infrared diode lasers: Fiber-otic communication 4.15 Photodiodes Photodiodes: Reverse biased P diode. Detects hotogenerated current (similar to Isc of solar cell) for otical communication, DVD reader, etc. Avalanche hotodiodes: Photodiodes oerating near avalanche breakdown amlifies hotocurrent by imact ionization. 53

54 Part III: Metal-Semiconductor Junction Two kinds of metal-semiconductor contacts: Rectifying Schottky diodes: metal on lightly doed silicon Low-resistance ohmic contacts: metal on heavily doed silicon 54

55 f Bn Increases with Increasing Metal Work Function Vacuum level, E 0 qy M c Si = 4.05 ev y M : Work Function of metal qf Bn E c c Si : Electron Affinity of Si E f E v Theoretically, f Bn = y M c Si 55

56 4.16 Schottky Barriers Energy Band Diagram of Schottky Contact Metal Deletion layer eutral region qf Bn -Si E c E f Schottky barrier height, f B, is a function of the metal material. P-Si E v E c E f f B is the most imortant arameter. The sum of qf Bn and qf B is equal to E g. qf B E v 56

57 Schottky barrier heights for electrons and holes Metal Mg Ti Cr W Mo Pd Au Pt f Bn (V) f B (V) Work Function y m (V) f Bn + f B E g f Bn increases with increasing metal work function 57

58 Fermi Level Pinning qy M qf Bn c Si = 4.05 ev + Vacuum level, E 0 Ec E f A high density of energy states in the bandga at the metalsemiconductor interface ins E f to a narrow range and f Bn is tyically 0.4 to 0.9 V E v Question: What is the tyical range of f B? 58

59 Schottky Contacts of Metal Silicide on Si Silicide: A silicon and metal comound. It is conductive similar to a metal. Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deosited on Si, an annealing ste is alied to form a silicide-si contact. The term metal-silicon contact includes and almost always means silicide-si contacts. Silicide ErSi 1.7 HfSi MoSi ZrSi TiSi CoSi WSi isi Pd Si PtSi f Bn f Bn (V) f B f B (V)

60 Using C-V Data to Determine f B qf qf Bn bi qf Bn q(f bi + V) qv E c E f E v E c E f E v qf W bi de C qf qf s W Bn Bn ( E s ( fbi q de A E + V ) d c kt ln Question: How should we lot the CV data to extract f bi? f c d ) 60

61 Using CV Data to Determine f B 1/C 1 C ( f bi + V ) q A d s V qf Bn qf bi E c f bi E f Once f bi is known, f B can be determined using qf bi qf Bn ( E E ) qf kt c f Bn ln c d E v 61

62 4.17 Thermionic Emission Theory v thx - q(f B V) E c V Metal -tye Silicon E fm qf B qv E fn E v n v J th SM c e q( f V )/ kt 3kT J 1 0 B / m n mn kt h v thx o 3/ kt 4qmnk qnvthx T e 3 h qv / kt e, where J 100e e q( f V )/ kt / m n qf / kt B qf / kt B B e x qv / kt A/cm 6

63 4.18 Schottky Diodes V = 0 Forward biased I Reverse biased Reverse bias V Forward bias 63

64 4.18 Schottky Diodes I 0 AKT 4qmnk K 3 h I I + I SM e qf / kt B 100 A/(cm M S I 0 e qv / kt K I 0 ) I 0 ( e qv / kt 1) 64

65 4.19 Alications of Schottly Diodes I I Schottky diode I I ( e 1 qv / kt 0 ) I 0 AKT e qf / kt B f B P junction diode V I 0 of a Schottky diode is 10 3 to 10 8 times larger than a P junction diode, deending on f B. A larger I 0 means a smaller forward dro V. A Schottky diode is the referred rectifier in low voltage, high current alications. 65

66 Switching Power Suly 110V/0V AC utility ower P Junction rectifier Hi-voltage DC AC AC 1V DC MOSFET inverter Transformer 100kHz Hi-voltage Lo-voltage Schottky rectifier 50A feedback to modulate the ulse width to kee V out = 1V 66

67 4.19 Alications of Schottky diodes Question: What sets the lower limit in a Schottky diode s forward dro? Synchronous Rectifier: For an even lower forward dro, relace the diode with a wide-w MOSFET which is not bound by the tradeoff between diode V and leakage current. There is no minority carrier injection at the Schottky junction. Therefore, Schottky diodes can oerate at higher frequencies than P junction diodes. 67

68 4.0 Quantum Mechanical Tunneling Tunneling robability: P 8 m ex h ( T ( V E)) H 68

69 4.1 Ohmic Contacts 69

70 4.1 Ohmic Contacts W de sf q Bn d Silicide + Si f Bn E c, E f E fm f Bn V V E c, E f Tunneling robability: P e Hf Bn d x E v x E v T H J W SM de 4 h / 1 s m q d n v / s q thx f P Bn / q q d d kt / m n e H ( f V ) / Bn d 70

71 4.1 Ohmic Contacts R c dj dv SM 1 e qv Hf thx Bn H / d d e Hf Bn / d Ωcm 71

72 4. Chater Summary Part I: P Junction f bi kt q ln d i n a The otential barrier increases by 1 V if a 1 V reverse bias is alied deletion width W de s otential barrier q junction caacitance C de s A W de 7

73 4. Chater Summary Under forward bias, minority carriers are injected across the jucntion. The quasi-equilibrium boundary condition of minority carrier densities is: n( x ) np0 ( x ) 0 Most of the minority carriers are injected into the more lightly doed side. e qv e qv kt kt 73

74 4. Chater Summary Steady-state continuity equation: d dx D L Minority carriers diffuse outward e x /L and e x /L n L and L n are the diffusion lengths L D I 0 qv kt I I0( e 1) Aqn i D L d + Dn L n a 74

75 4. Chater Summary Charge storage: Q I s Diffusion caacitance: C G s Diode conductance: G I DC / kt q 75

76 4. Chater Summary Solar cell Part II: Otoelectronic Alications ower I sc V oc FF ~100um Si or <1um direct ga semiconductor can absorb most of solar hotons with energy larger than E g. Carriers generated within diffusion length from the junction can be collected and contribute to the Short Circuit Current I sc. Theoretically, the highest efficiency (~4%) can be obtained with 1.9eV >E g >1.eV. Larger E g lead to too low I sc (low light absortion); smaller E g leads to too low Oen Circuit VoltageVoc. Si cells with ~15% efficiency dominate the market. >x cost reduction (including ackage and installation) is required to achieve cost arity with base-load non-renewable electricity. 76

77 4. Chater Summary Solar cell Part II: Otoelectronic Alications ower I sc V oc FF ~100um Si or <1um direct ga semiconductor can absorb most of solar hotons with energy larger than E g. Carriers generated within diffusion length from the junction can be collected and contribute to the Short Circuit Current I sc. Theoretically, the highest efficiency (~4%) can be obtained with 1.9eV >E g >1.eV. Larger E g lead to too low I sc (low light absortion); smaller E g leads to too low Oen Circuit VoltageVoc. Si cells with ~15% efficiency dominate the market. >x cost reduction (including ackage and installation) is required to achieve cost arity with base-load non-renewable electricity. 77

78 4. Chater Summary Laser Diodes Light is amlified under the condition of oulation inversion states at higher E have higher robability of occuation than states at lower E. Poulation inversion occurs when diode forward bias qv > E g. Otical feedback is rovided with cleaved surfaces or distributed Bragg reflectors. When the round-tri gain (including loss at reflector) exceeds unity, laser threshold is reached. Quantum-well structures significantly reduce the threshold currents. Purity of laser light frequency enables long-distance fiber-otic communication. Purity of light direction allows focusing to tiny sots and enables DVD writer/reader and other alication. 78

79 4. Chater Summary Part III: Metal-Semiconductor Junction I 0 AKT e qf B Schottky diodes have large reverse saturation current, determined by the Schottky barrier height f B, and therefore lower forward voltage at a given current density. Ohmic contacts relies on tunneling. Low resistance contact requires low f B and higher doing concentration. / kt 4 ( fb h R c e m s n / q d ) Ω cm 79

80 f Bn Increases with Increasing Metal Work Function Vacuum level, E 0 qy M c Si = 4.05 ev Ideally, f Bn = y M c Si qf Bn E c E f E v 80