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Introduction Formation Of Bond. Formation Of Band. Role Of Pauli Exclusion Principle. Fermi Dirac Distribution Equation Classification Of Material In Term Of Energy Band Diagram. Intrinsic Semiconductor. a)Drive Density Of State b)Drive Density Of Free Carrier. c)Determination Of Fermi Level Position Extrinsic Semiconductor. a) N Type Extrinsic Semiconductor b) P Type Extrinsic Semiconductor Compensated semiconductor. E Vs. Diagram. Direct and Indirect Band Gap. Degenerated and Non-degenerated. PN Junction.

- 1. Jamia Millia Islamia M.Tech Nanotechnology 2020-2022 Presentation on Solid State Electronics Submitted To: Submitted By: PROF. S.S ISLAM SULTAN SAIFUDDIN
- 2. Content • Introduction • Formation Of Bond. • Formation Of Band. • Role Of Pauli Exclusion Principle. • Fermi Dirac Distribution Equation • Classification Of Material In Term Of Energy Band Diagram. • Intrinsic Semiconductor. a)Drive Density Of State b)Drive Density Of Free Carrier. c)Determination Of Fermi Level Position o Extrinsic Semiconductor. a) N Type Extrinsic Semiconductor b) P Type Extrinsic Semiconductor • Compensated semiconductor. • E Vs. Diagram. • Direct and Indirect Band Gap. • Degenerated and Non-degenerated. • PN Junction.
- 3. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): – Insulators > 105 -cm (diamond = 1016 ) – Semiconductors 10-3 < < 105 -cm – Conductors < 10-3 -cm (copper = 10-6 ) • Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon. • Compound semiconductors are formed from combinations of elements of column III and V or columns II and VI. • Germanium was used in many early devices. • Silicon quickly replaced germanium due to its higher band gap energy, lower cost, and ability to be easily oxidized to form silicon-dioxide insulating layers. NJIT ECE-271 Dr. S. Levkov Chap 2 - 3
- 4. Solid-State Electronic Materials (cont.) • Band gap is an energy range in a solid where no electron states can exist. It refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors.
- 5. NJIT ECE-271 Dr. S. Levkov Chap 2 - 5 Semiconductor Materials (cont.) Semiconductor Bandgap Energy EG (eV) Carbon (diamond) 5.47 Silicon 1.12 Germanium 0.66 Tin 0.082 Gallium arsenide 1.42 Gallium nitride 3.49 Indium phosphide 1.35 Boron nitride 7.50 Silicon carbide 3.26 Cadmium selenide 1.70
- 6. Covalent Bond Model Silicon diamond lattice unit cell. Corner of diamond lattice showing four nearest neighbor bonding. View of crystal lattice along a crystallographic axis. • Silicon has four electrons in the outer shell. • Single crystal material is formed by the covalent bonding of each silicon atom with its four nearest neighbors.
- 7. Silicon Covalent Bond Model (cont.) Silicon atom Silicon atom Covalent bond
- 8. Silicon Covalent Bond Model (cont.) Silicon atom Covalent bonds in silicon
- 9. Silicon Covalent Bond Model (cont.) • Near absolute zero, all bonds are complete • Each Si atom contributes one electron to each of the four bond pairs • The outer shell is full, no free electrons, silicon crystal is an insulator • What happens as the temperature increases?
- 10. Energy Bands in Solids: • According to Quantum Mechanical Laws, the energies of electrons in a free atom can not have arbitrary values but only some definite (quantized) values. • However, if an atom belongs to a crystal, then the energy levels are modified. • This modification is not appreciable in the case of energy levels of electrons in the inner shells (completely filled). • But in the outermost shells, modification is appreciable because the electrons are shared by many neighboring atoms. • Due to influence of high electric field between the core of the atoms and the shared electrons, energy levels are split-up or spread out forming energy bands. • Consider a single crystal of silicon having N atoms. Each atom can be associated with a lattice site. • Electronic configuration of Si is 1s2 , 2s2 , 2p6 ,3s2 , 3p2 . (Atomic No. is 14)
- 11. Role Of Pauli Exclusion Principle The electronic system should obey Paulie’s exclusion principal , which states that no 2 e- are in the system can have same amount of energy. To obey this 3s and 3p level spilt into multiple levels so that each e- can occupy a district energy level. When inter atomic distance is further reduced. The 2N ‘s’ levels and 6N ‘p’ levels combined into a single band. At lattice spacing, single band is split into 2 bands with upper band containing 4N and lower band with 4N levels. At 00 k e- possess lowest energy , they fill up valence band and conduction band remaining empty.
- 12. Formation of Energy Bands in Solids:
- 13. (i) r = Od (>> Oa): Each of N atoms has its own energy levels. The energy levels are identical, sharp, discrete and distinct. The outer two sub-shells (3s and 3p of M shell or n = 3 shell) of silicon atom contain two s electrons and two p electrons. So, there are 2N electrons completely filling 2N possible s levels, all of which are at the same energy. Of the 6N possible p levels, only 2N are filled and all the filled p levels have the same energy. (ii) Oc < r < Od: There is no visible splitting of energy levels but there develops a tendency for the splitting of energy levels. (iii) r = Oc: The interaction between the outermost shell electrons of neighboring silicon atoms becomes appreciable and the splitting of the energy levels commences. (iv) Ob < r < Oc: The energy corresponding to the s and p levels of each atom gets slightly changed. Corresponding to a single s level of an isolated atom, we get 2N levels. Similarly, there are 6N levels for a single p level of an isolated atom.
- 14. Since N is a very large number (≈ 1029 atoms / m3 ) and the energy of each level is of a few eV, therefore, the levels due to the spreading are very closely spaced. The spacing is ≈ 10-23 eV for a 1 cm3 crystal. The collection of very closely spaced energy levels is called an energy band. (v) r = Ob: The energy gap disappears completely. 8N levels are distributed continuously. We can only say that 4N levels are filled and 4N levels are empty. (vi) r = Oa: The band of 4N filled energy levels is separated from the band of 4N unfilled energy levels by an energy gap called forbidden gap or energy gap or band gap. The lower completely filled band (with valence electrons) is called the valence band and the upper unfilled band is called the conduction band. Note: 1. The exact energy band picture depends on the relative orientation of atoms in a crystal. 2. If the bands in a solid are completely filled, the electrons are not permitted to move about, because there are no vacant energy levels available.
- 15. 15 Fermi-Dirac distribution and the Fermi-level Density of states tells us how many states exist at a given energy E. The Fermi function f(E) specifies how many of the existing states at the energy E will be filled with electrons. The function f(E) specifies, under equilibrium conditions, the probability that an available state at an energy E will be occupied by an electron. It is a probability distribution function. EF = Fermi energy or Fermi level k = Boltzmann constant = 1.38 1023 J/K = 8.6 105 eV/K T = absolute temperature in K
- 16. 16 Fermi-Dirac distribution: Consider T 0 K For E > EF : For E < EF : 0 ) ( exp 1 1 ) ( F E E f 1 ) ( exp 1 1 ) ( F E E f E EF 0 1 f(E)
- 17. 17 If E = EF then f(EF) = ½ If then Thus the following approximation is valid: i.e., most states at energies 3kT above EF are empty. If then Thus the following approximation is valid: So, 1f(E) = Probability that a state is empty, decays to zero. So, most states will be filled. kT (at 300 K) = 0.025eV, Eg(Si) = 1.1eV, so 3kT is very small in comparison. kT E E 3 F 1 exp F kT E E kT E E E f ) ( exp ) ( F kT E E 3 F 1 exp F kT E E kT E E E f F exp 1 ) ( Fermi-Dirac distribution: Consider T > 0 K
- 18. 18 Temperature dependence of Fermi-Dirac distribution
- 19. 19
- 20. Classification of material in term of energy band picture
- 21. Metals: • The highest energy level in the conduction band occupied by electrons in a crystal, at absolute 0 temperature, is called Fermi Level. • The energy corresponding to this energy level is called Fermi energy. • If the electrons get enough energy to go beyond this level, then conduction takes place. The first possible energy band diagram shows that the conduction band is only partially filled with electrons. With a little extra energy the electrons can easily reach the empty energy levels above the filled ones and the conduction is possible. The second possible energy band diagram shows that the conduction band is overlapping with the valence band. This is because the lowest levels in the conduction band needs less energy than the highest levels in the valence band. The electrons in valence band overflow into conduction band and are free to move about in the crystal for conduction.
- 22. (a) Energy levels in a Li atom are discrete. (b) The energy levels corresponding to outer shells of isolated Li atoms form an energy band inside the crystal, for example the 2s level forms a 2s band. Energy levels form a quasi continuum of energy within the energy band. Various energy bands overlap to give a single band of energies that is only partially full of electrons. There are states with energies up to the vacuum level where the electron is free. (c) A simplified energy band diagram and the photoelectric effect. Energy Bands in Metals
- 23. (a) Above 0 K, due to thermal excitation, some of the electrons are at energies above EF. (b) The density of states, g(E) vs. E in the band. (c) The probability of occupancy of a state at an energy E is f(E). The product g(E)f(E) is the number of electrons per unit energy per unit volume or electron concentration per unit energy. The area under the curve with the energy axis is the concentration of electrons in the band, n. Energy Bands in Metals
- 24. Energy Bands in Metals T k E E E f B F exp 1 1 ) ( 2 / 1 2 / 1 3 2 / 3 ) 2 ( 4 ) ( AE E h m E e g Density of states Fermi-Dirac function dE E f E n F E 0 ) ( ) ( g 3 / 2 2 3 8 n m h E e FO
- 25. Semiconductors: As an electron leaves the valence band, it leaves some energy level in band as unfilled. Such unfilled regions are termed as ‘holes’ in the valence band. They are mathematically taken as positive charge carriers. Any movement of this region is referred to a positive hole moving from one position to another. At absolute zero temperature, no electron has energy to jump from valence band to conduction band and hence the crystal is an insulator. At room temperature, some valence electrons gain energy more than the energy gap and move to conduction band to conduct even under the influence of a weak electric field. Its conductivity can be tuned or tailored by addition of impurities.
- 26. (a) A simplified two dimensional view of a region of the Si crystal showing covalent bonds. (b) The energy band diagram of electrons in the Si crystal at absolute zero of temperature. The bottom of the VB has been assigned a zero of energy. Energy Bands in Semiconductors
- 27. (a) A photon with an energy hu greater than Eg can excite an electron from the VB to the CB. (b) Each line between Si-Si atoms is a valence electron in a bond. When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created. The result is the photogeneration of an electron and a hole pair (EHP) Energy Bands in Semiconductors
- 28. Insulators: Electrons, however heated, can not practically jump to conduction band from valence band due to a large energy gap. Therefore, conduction is not possible in insulators.
- 30. Intrinsic or Pure Semiconductor:
- 31. Intrinsic Semiconductor is a pure semiconductor. The energy gap in Si is 1.1 eV and in Ge is 0.74 eV. Ge: 1s2 , 2s2 , 2p6 ,3s2 , 3p6 , 3d10, 4s2 , 4p2 . (Atomic No. is 32) Si: 1s2 , 2s2 , 2p6 ,3s2 , 3p2 . (Atomic No. is 14) In intrinsic semiconductor, the number of thermally generated electrons always equals the number of holes. So, if ni and pi are the concentration of electrons and holes respectively, then ni = pi . The quantity ni or pi is referred to as the ‘intrinsic carrier concentration’.
- 33. Electrons and Holes: On receiving an additional energy, one of the electrons from a covalent band breaks and is free to move in the crystal lattice. While coming out of the covalent bond, it leaves behind a vacancy named ‘hole’. An electron from the neighboring atom can break away and can come to the place of the missing electron (or hole) completing the covalent bond and creating a hole at another place. The holes move randomly in a crystal lattice. The completion of a bond may not be necessarily due to an electron from a bond of a neighboring atom. The bond may be completed by a conduction band electron. i.e., free electron and this is referred to as ‘electron – hole recombination’.
- 34. A pictorial illustration of a hole in the valence band (VB) wandering around the crystal due to the tunneling of electrons from neighboring bonds; and its eventual recombination with a wandering electron in the conduction band. A missing electron in a bond represents a hole as in (a). An electron in a neighboring bond can tunnel into this empty state and thereby cause the hole to be displaced as in (a) to (d). The hole is able to wander around in the crystal as if it were free but with a different effective mass than the electron. A wandering electron in the CB meets a hole in the VB in (e), which results in the recombination and the filling of the empty VB state as in (f) Hole Motion in a Semiconductor
- 35. Fermi-Dirac Distribution for an Intrinsic Semiconductor Intrinsic Semiconductor with a Valence and Conduction Band EV EC g Band Gap Energy (E ) Eg ~2 eV Here, there is a high likelihood of the electrons remaining in the valence band due to the large gap in energy between the valence and conduction bands. This can be written as: E EF kT f (E) f (E) This Allows for the Fermi-Dirac Distribution to be Simplified 1 kT 1 exp(E EF ) 1 kT f (E) exp(EF E) 1 kT exp(E EF ) f(E) is the probability that a state at energy E IS populated. 1 – f(E) is the probability that a state at energy E IS NOT populated.
- 36. Calculation of the Electron Density Recall the Density of States Equation EV EC Band Gap Energy (Eg) Eg ~2 eV Any electron in the conduction band must have an energy: 2me h2 k2 Ek so E Ec Ek and Ek E Ec E Ec Ec Ek or 2me h2 k2 Intrinsic Semiconductor with a Rearrangement of this equation yields: Valence and Conduction Band If we assume that we are working over a unit volume, substitution of these two equations leaves an expression density of states of the free electron k E1/2 2m 3/ 2 k k D(E ) dN V dE 2 2 h 2
- 37. Calculation of the Electron Density (Part II) c (E E )1/2 3/ 2 e 1 2m 2 2 h 2 e D (E) dE kT n F c e c EE (E E) exp E (E E ) 1 2m The Density of Electrons in the Conduction Band Must Just be Equal to the Density of States in the Conduction Band Multiplied by the Probability that an Electron Can Occupy One of Those States Integrated Over All Energies E n De (E) fe (E) dE EEc 1/2 3/ 2 2 2 h 2 The Integral Can be Simplified for Terms That Are Not Functions of Energy
- 38. Calculation of the Electron Density (Part III) dE E c F kT c E EE n (E) kT exp exp 1 2m (E E )1/ 2 3/2 e 2 2 h 2 Integrating Over the Definite Integral Yields The Following F c kT n 2e exp m kT 3/ 2 (E E ) 2 2 h Often, The Effective Density of States for the Conduction Band (Nc) is Defined: 2 2 h m kT 3/ 2 Nc 2e kT c So, The Following Holds Ec ) n N exp(EF
- 39. Absence of an Electron is Termed a Hole Intrinsic Semiconductor with a Valence and Conduction Band EV EC g Band Gap Energy (E ) g E ~2 eV If there is an electron present in the conduction band, that electron must have been promoted from the valence band and across the band gap. This “missing” electron in the valence band is termed a hole. 1 1 fh (E) 1 fh (E) 1 fe (E) 1 1 fe (E) exp (E E ) exp (E E ) kT kT F F The Probability of Not Finding an Electron is the Same as the Probability of Finding a Hole If EF – E >> kTThen: kT F h (E E ) f (E) exp
- 40. Calculation of the Hole Density E)1/ 2 (Ev 3/ 2 h 1 2m 2 2 h 2 h D (E) dE kT p F v h E E EEv (E E ) (E E)1/ 2 exp 3/ 2 1 2m The Density of Holes in the Valence Band Must Just be Equal to the Density of States in the Valence Band Multiplied by the Probability that a Hole Can Occupy One of Those States Integrated Over All Energies EEv p Dh (E) fh (E) dE 2 2 2 Again, We Simplify the Integral for Terms That Are Not Functions of Energy
- 41. Calculation of the Hole Density (Part II) dE EEv E v E kT (E E)1/ 2 exp F h E kT p exp 1 2m 3/ 2 2 2 h 2 Integrating Over the Definite Integral Yields The Following m kT 3/ 2 v F kT (E E ) exp p 2h 2 2 h Often, The Effective Density of States for the Conduction Band (Nc) is Defined: 2 2 h m kT 3/ 2 Nv 2h kT v So, The Following Holds EF ) p N exp(Ev
- 42. Solving in Terms of the Bandgap Energy If We Take the Product of n and p, We Obtain the Following v c e h e h g kT v c kT g v F kT F c kT kT kT ; E E E (E ) m m exp np 4 (E E ) m m exp np 4 (E E ) 2h exp (E E ) np 2e exp 3/2 3 2 3/2 3 2 h 2 h2 2 m kT 3/ 2 m kT 3/ 2 2 2 h 2 h kT g e h 2kT (E ) m m exp i i n p 2 3/4 3/ 2 This Expression is Only a Function of Masses, Temperature, and the Bandgap. Furthermore, Because in an Intrinsic Semiconductor, n = p np n2 p2 and i i 2 2 h
- 43. Fermi Energy of an Intrinsic Semiconductor If We Set the Equation We Found for n Equal to the Equation Found Earlier for p, We Obtain the Following Rearrangement of This Lower Equation Shows That: kT kT kT kT v F F c (E E ) 2h exp (E E ) 2e exp m kT 3/ 2 2 m kT 3/ 2 v F (E E ) exp p 2h m kT 3/ 2 2 F c n 2e exp m kT 3/ 2 (E E ) 2 h 2 2 h 2 h 2 2 h kT kT (E E ) 2E exp F exp c v kT EF ) exp(Ev kT h me (EF Ec ) m 3/ 2 exp
- 44. Fermi Energy of an Intrinsic Semiconductor (Part II) Simplification of the Previous Equation Yields: kT E exp g kT kT me me (E E ) exp c v h 2E exp F h m 3/ 2 m 3/ 2 Rearrangement of This Equation Demonstrates That: e mh EF 2 Eg 4 kTln m 1 3 If mh = me, We Find That the Fermi Energy is in the Middle of the Bandgap for an Intrinsic Semiconductor 2 1 EF Eg EV EC Band Gap Energy (Eg) Eg ~2 eV EF
- 45. Plots of D(E), f(E), n, and p as a Function of Energy Density of States Fermi-Dirac Distribution Electron and Hole Densities
- 46. Doping a Semiconductor: • Doping is the process of deliberate addition of a very small amount of impurity into an intrinsic semiconductor. • The impurity atoms are called ‘dopants’. • The semiconductor containing impurity is known as ‘impure or extrinsic semiconductor’. Methods of doping: • i) Heating the crystal in the presence of dopant atoms. • ii) Adding impurity atoms in the molten state of semiconductor. • iii) Bombarding semiconductor by ions of impurity atoms.
- 47. Extrinsic or Impure Semiconductor: N - Type Semiconductors: When a semiconductor of Group IV (tetra valent) such as Si or Ge is doped with a penta valent impurity (Group V elements such as P, As or Sb), N – type semiconductor is formed. When germanium (Ge) is doped with arsenic (As), the four valence electrons of As form covalent bonds with four Ge atoms and the fifth electron of As atom is loosely bound.
- 48. The energy required to detach the fifth loosely bound electron is only of the order of 0.045 eV for germanium. A small amount of energy provided due to thermal agitation is sufficient to detach this electron and it is ready to conduct current. The force of attraction between this mobile electron and the positively charged (+ 5) impurity ion is weakened by the dielectric constant of the medium. So, such electrons from impurity atoms will have energies slightly less than the energies of the electrons in the conduction band. Therefore, the energy state corresponding to the fifth electron is in the forbidden gap and slightly below the lower level of the conduction band. This energy level is called ‘donor level’. The impurity atom is called ‘donor’. N – type semiconductor is called ‘donor – type semiconductor’.
- 49. Extrinsic Semiconductors: n-Type a)The four valence electrons of As allow it to bond just like Si but the fifth electron is left orbiting the As site. The energy required to release to free fifth-electron into the CB is very small. b) Energy band diagram for an n-type Si doped with 1 ppm As. There are donor energy levels just below Ec around As+ sites.
- 50. Carrier Concentration in N - Type Semiconductors: When intrinsic semiconductor is doped with donor impurities, not only does the number of electrons increase, but also the number of holes decreases below that which would be available in the intrinsic semiconductor. The number of holes decreases because the larger number of electrons present causes the rate of recombination of electrons with holes to increase. Consequently, in an N-type semiconductor, free electrons are the majority charge carriers and holes are the minority charge carriers. Carrier Concentration in N - Type Semiconductors: If n and p represent the electron and hole concentrations respectively in N-type semiconductor, then where ni and pi are the intrinsic carrier concentrations. The rate of recombination of electrons and holes is proportional to n and p. Or, the rate of recombination is proportional to the product np. Since the rate of recombination is fixed at a given temperature, therefore, the product np must be a constant. When the concentration of electrons is increased above the intrinsic value by the addition of donor impurities, the concentration of holes falls below its intrinsic value, making the product np a constant, equal to ni2 .
- 51. Extrinsic Semiconductors: n-Type e d h d i e d eN N n e eN 2 Nd >> ni, then at room temperature, the electron concentration in the CB will nearly be equal to Nd, i.e. n ≈ Nd A small fraction of the large number of electrons in the CB recombine with holes in the VB so as to maintain np = ni 2 n = Nd and p = ni 2/Nd np = ni 2
- 52. P - Type Semiconductors: • When a semiconductor of Group IV (tetra valent) such as Si or Ge is doped with a tri valent impurity (Group III elements such as In, B or Ga), P – type semiconductor is formed. • When germanium (Ge) is doped with indium (In), the three valence electrons of In form three covalent bonds with three Ge atoms. The vacancy that exists with the fourth covalent bond with fourth Ge atom constitutes a hole.
- 53. Extrinsic Semiconductors: p-Type (a) Boron doped Si crystal. B has only three valence electrons. When it substitutes for a Si atom one of its bonds has an electron missing and therefore a hole. (b) Energy band diagram for a p-type Si doped with 1 ppm B. There are acceptor energy levels just above Ev around B sites. These acceptor levels accept electrons from the VB and therefore create holes in the VB.
- 54. The hole which is deliberately created may be filled with an electron from neighboring atom, creating a hole in that position from where the electron jumped. Therefore, the tri valent impurity atom is called ‘acceptor’. Since the hole is associated with a positive charge moving from one position to another, therefore, this type of semiconductor is called P – type semiconductor. The acceptor impurity produces an energy level just above the valence band. This energy level is called ‘acceptor level’. The energy difference between the acceptor energy level and the top of the valence band is much smaller than the band gap. Electrons from the valence band can, therefore, easily move into the acceptor level by being thermally agitated. P – type semiconductor is called ‘acceptor – type semiconductor’. In a P – type semiconductor, holes are the majority charge carriers and the electrons are the minority charge carriers. It can be shown that,
- 55. Extrinsic Semiconductors: P-Type • Na >> ni, then at room temperature, the hole concentration in the VB will nearly be equal to Na, i.e. p ≈ Nd • A small fraction of the large number of holes in the VB recombine with electrons in the CB so as to maintain np = ni 2 h a e a i h a eN N n e eN 2 p = Na and n = ni 2/Na np = ni 2
- 56. Intrinsic, i-Si n = p = ni Semiconductor energy band diagrams n-type n = Nd p = ni 2/Nd np = ni 2 p-type p = Na n = ni 2/Na np = ni 2
- 57. Semiconductor energy band diagrams Energy band diagrams for • (a) intrinsic • (b) n-type • (c) p-type semiconductors. • In all cases, np = ni 2. Note that donor and acceptor energy levels are not shown. CB = Conduction band, VB = Valence band, Ec = CB edge, Ev = VB edge, EFi = Fermi level in intrinsic semiconductor, EFn = Fermi level in n-type semiconductor, EFp = Fermi level in p-type semiconductor. c is the electron affinity. , n and p are the work functions for the intrinsic, n-type and p- type semiconductors
- 58. Compensated Semiconductor: A compensated semiconductor is one that contains both donor and acceptor impurity atoms in the same region Energy-band diagram of a compensated semiconductor showing ionized and un- ionized donors and acceptors
- 59. Compensation Doping Compensation doping describes the doping of a semiconductor with both donors and acceptors to control the properties. Example: A p-type semiconductor doped with Na acceptors can be converted to an n- type semiconductor by simply adding donors until the concentration Nd exceeds Na. The effect of donors compensates for the effect of acceptors. The electron concentration n = Nd Na > ni When both acceptors and donors are present, electrons from donors recombine with the holes from the acceptors so that the mass action law np = ni 2 is obeyed. We cannot simultaneously increase the electron and hole concentrations because that leads to an increase in the recombination rate which returns the electron and hole concentrations to values that satisfy np = ni 2. n = Nd Na p = ni 2/(Nd Na) Nd > Na
- 60. Summary of Compensation Doping a d N N n a d i i N N n n n p 2 2 i a d n N N More donors than acceptors More acceptors than donors i d a n N N d a N N p d a i i N N n p n n 2 2
- 61. Direct and Indirect band Gap Semiconductor
- 62. (a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is therefore a direct band gap semiconductor. (b) In Si, the minimum of the CB is displaced from the maximum of the VB and Si is an indirect band gap semiconductor. (c) Recombination of an electron and a hole in Si involves a recombination center . E vs. k Diagrams and Direct and Indirect Bandgap Semiconductors
- 63. Direct Band Gap Semiconductor • For these Semiconductor , Conduction band minima and valence band maxima occurs at same value of momentum. • An e- from CB directly return to VB without changing It’s momentum. And releases energy in the form of light (photon hv). • Ex: GaAS, Gap.GaAsP,
- 64. Indirect Band Gap Semiconductor • Conduction band minima and valance band maxima occurs at different value of momentum. • When e- from CB returns VB after changing its momentum is called indirect band gap sc. • E- changes its momentum by releasing phonon which is a heat particle. • Ex: Si, Ge
- 66. Degenerate and Non-degenerate Semiconductor
- 67. Degenerate and Non-degenerate Semiconductor • As the donor concentration further increases, the band of donor states widens and may overlap the bottom of the conduction band. • This overlap occurs when the donor concentration becomes comparable with the effective density of states. • When the concentration of electrons in the conduction band exceeds the density of states Nc , the Fermi energy lies within the conduction band. This type of semiconductor is called a degenerate n-type semiconductor. • In the degenerate n-type semiconductor, the states between Ef and Ec are mostly filled with electrons; thus, the electron concentration in the conduction band is very large.
- 68. Degenerate Semiconductors (a) Degenerate n-type semiconductor. Large number of donors form a band that overlaps the CB. Ec is pushed down and EFn is within the CB. (b) Degenerate p-type semiconductor .
- 69. Degenerate and Non-degenerate Semiconductor
- 70. What is a PN Junction? • A PN junction is a device formed by combining p-type ( doped with B,Al) and n-type (doped with P,As,Sb) semiconductors together in close contact. • PN junction can basically work in two modes, – forward bias mode (as shown below: positive terminal connected to p- region and negative terminal connected to n region) – reverse bias mode ( negative terminal connected to p-region and positive terminal connected to n region) PN junction device
- 71. Law of the Junction Apply Boltzmann Statistics (can only be used with non-degenerate semiconductors) N1 = ppo N2 = pno E1 = PE2 = 0 E2 = PE1 = eVo T k E E N N B ) ( exp 1 2 1 2 T k eV p p B o po no ) 0 ( exp T k eV p p B o po no exp
- 72. Law of the Junction Apply Boltzmann Statistics T k eV p p B o po no exp T k eV n n B o no po exp 2 ln ln i d a B no po B o n N N e T k p p e T k V
- 73. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Figure: The pn junction with no applied voltage (open-circuited terminals). n-type semiconductor filled with free electrons p-type semiconductor filled with holes junction Step #1: The p-type and n-type semiconductors are joined at the junction.
- 74. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Figure: The pn junction with no applied voltage (open-circuited terminals). Step #2: Diffusion begins. Those free electrons and holes which are closest to the junction will recombine and, essentially, eliminate one another.
- 75. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. The depletion region is filled with “uncovered” bound charges – who have lost the majority carriers to which they were linked. Step #3: The depletion region begins to form – as diffusion occurs and free electrons recombine with holes. Figure: The pn junction with no applied voltage (open-circuited terminals).
- 76. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Step #4: The “uncovered” bound charges effect a voltage differential across the depletion region. The magnitude of this barrier voltage (V0) differential grows, as diffusion continues. voltage potential location (x) barrier voltage (Vo) No voltage differential exists across regions of the pn-junction outside of the depletion region because of the neutralizing effect of positive and negative bound charges.
- 77. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Figure: The pn junction with no applied voltage (open-circuited terminals). Step #5: The barrier voltage (V0) is an electric field whose polarity opposes the direction of diffusion current (ID). As the magnitude of V0 increases, the magnitude of ID decreases. diffusion current (ID) drift current (IS)
- 78. Step #6: Equilibrium is reached, and diffusion ceases, once the magnitudes of diffusion and drift currents equal one another – resulting in no net flow. diffusion current (ID) drift current (IS) Once equilibrium is achieved, no net current flow exists (Inet = ID – IS) within the pn-junction while under open-circuit condition. p-type n-type depletion region
- 79. Ideal pn Junction Depletion Widths n d p a W N W N ) ( net x dx d E Field (E) and net space charge density Field in depletion region x Wp dx x x ) ( 1 ) ( net E Acceptor concentration Donor concentration Net space charge density Permittivity of the medium Electric Field
- 80. Ideal pn Junction Built-in field n d o W eN E 2 ln i d a o n N N e kT V Built-in voltage Depletion region width 2 / 1 2 d a o d a o N eN V N N W = o r where Wo = Wn+ Wp is the total width of the depletion region under a zero applied voltage ni is the intrinsic concentration
- 81. Working of a PN junction . Forward Bias Reverse Bias Zener or Avalanche Breakdown Voltage Current I-V characteristic of a PN junction diode. •PN junction diode acts as a rectifier as seen in the IV characteristic. •Certain current flows in forward bias mode. •Negligible current flows in reverse bias mode until zener or avalanche breakdown happens.
- 82. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. • Figure to right shows pn- junction under three conditions: – (a) open-circuit – where a barrier voltage V0 exists. – (b) reverse bias – where a dc voltage VR is applied. – (c) forward bias – where a dc voltage VF is applied. Figure 3.11: The pn junction in: (a) equilibrium; (b) reverse bias; (c) forward bias. 1) no voltage applied 2) voltage differential across depletion zone is V0 3) ID = IS 1) negative voltage applied 2) voltage differential across depletion zone is V0 + VR 3) ID < IS 1) positive voltage applied 2) voltage differential across depletion zone is V0 - VF 3) ID > IS
- 83. Forward biased pn junction and the injection of minority carriers (a) Carrier concentration profiles across the device under forward bias. (b). The hole potential energy with and without an applied bias. W is the width of the SCL with forward bias Forward Biased pn Junction
- 84. Forward Bias: Apply Boltzmann Statistics Note: pn(0) is the hole concentration just outside the depletion region on the n-side N1 = ppo N2 = pn(0) T k E E N N B ) ( exp 1 2 1 2 T k eV T k eV T k V V e p p B B o B o po n exp exp ) ( exp ) 0 ( pno/ppo T k eV p p B no n exp ) 0 (
- 85. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Forward-Bias Case • Observe that decreased barrier voltage will be accompanied by… – (1) decrease in stored uncovered charge on both sides of junction – (2) smaller depletion region • Width of depletion region shown to right. 0 0 p p p p p p 0 width of depletion region electrical permiability of silicon (11.7 1.04 12 ) magnitude of electron charge con replac P P P / e with 0 2 1 1 ( ) A F S F c V W q m S n p F A D N V V W x x V V q N N action: E p p p p p p 0 p p centration of acceptor atoms concentration of donor atoms barrier / junction built-in voltage externally applied forward-bias voltage P P P 0 P 2 ( D F A D J S F A D N V V N N Q A q V V N N 0 p p 0 magnitude of charge stored on either side of rep dep lace wit letion regionP h ) J F V V Q V action:
- 86. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Reverse-Bias Case • Observe that increased barrier voltage will be accompanied by… – (1) increase in stored uncovered charge on both sides of junction – (2) wider depletion region • Width of depletion region shown to right. p p p 0 p 0 0 width of depletion region electrical permiability of silicon (11.7 1.04 12 ) magn replace with itude of electron ch / 0 arge P P (eq3.31) 2 1 1 ( ) S R F cm S n p R V V V W q A D W x x V V q N N action: E p p p p p p p 0 p p p concentration of acceptor atoms concentration of donor atoms barrier / junction built-in voltage externally applied reverse-bias volta P P P g P e P (eq3.3 2 2) A D R N N V J V Q A 0 p p 0 magnitude of charge store 0 d on either side of depletion re replace with gi P on ( ) J R V V V A D S R A Q D N N q V V N N action:
- 87. Built in charge, electric field and potential at equilibrium. Built in charge Built in electric field N-region P-region P-region N-region Built in potential, Vbi= 0.834V
- 88. Built in charge, electric field and potential at forward bias Decreasing charge with applied bias due to thinning of depletion width. P-region N-region N-region P-region Decreasing electric field with applied bias due to thinning of depletion width. Potential difference Vbi-Va= 0.234V Positive bias at P side reduces the barrier leading to increase in diode current. Increased diffusion of electrons across the barrier lowered by Va.
- 89. Doping= 1e16 cm3 Doping= 1e18 cm3 • Increasing doping leads to increasing built in potential, Vbi [1],[2]. Na : P region doping level (cm-3). Nd : N region doping level (cm-3). ni : Intrinsic carrier density (cm-3). KbT : Thermal voltage (= 0.0259 V). = V bi On changing doping for both n-type and p-type regions from 1e16 cm3 to 1e18 cm3. i d a b bi n N N T K V . log
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