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9
3239-3242
Therefore, the resistance of such materials is low or the conductivity is high FIGURE 14 2 Difference between energy bands of (a) metals, (b) insulators and (c) semiconductors FIGURE 14
9
3240-3243
FIGURE 14 2 Difference between energy bands of (a) metals, (b) insulators and (c) semiconductors FIGURE 14 1 The energy band positions in a semiconductor at 0 K
9
3241-3244
2 Difference between energy bands of (a) metals, (b) insulators and (c) semiconductors FIGURE 14 1 The energy band positions in a semiconductor at 0 K The upper band, called the conduction band, consists of infinitely large number of closely spaced energy states
9
3242-3245
FIGURE 14 1 The energy band positions in a semiconductor at 0 K The upper band, called the conduction band, consists of infinitely large number of closely spaced energy states The lower band, called the valence band, consists of closely spaced completely filled energy states
9
3243-3246
1 The energy band positions in a semiconductor at 0 K The upper band, called the conduction band, consists of infinitely large number of closely spaced energy states The lower band, called the valence band, consists of closely spaced completely filled energy states Rationalised 2023-24 327 Semiconductor Electronics: Materials, Devices and Simple Circuits Case II: In this case, as shown in Fig
9
3244-3247
The upper band, called the conduction band, consists of infinitely large number of closely spaced energy states The lower band, called the valence band, consists of closely spaced completely filled energy states Rationalised 2023-24 327 Semiconductor Electronics: Materials, Devices and Simple Circuits Case II: In this case, as shown in Fig 14
9
3245-3248
The lower band, called the valence band, consists of closely spaced completely filled energy states Rationalised 2023-24 327 Semiconductor Electronics: Materials, Devices and Simple Circuits Case II: In this case, as shown in Fig 14 2(b), a large band gap Eg exists (Eg > 3 eV)
9
3246-3249
Rationalised 2023-24 327 Semiconductor Electronics: Materials, Devices and Simple Circuits Case II: In this case, as shown in Fig 14 2(b), a large band gap Eg exists (Eg > 3 eV) There are no electrons in the conduction band, and therefore no electrical conduction is possible
9
3247-3250
14 2(b), a large band gap Eg exists (Eg > 3 eV) There are no electrons in the conduction band, and therefore no electrical conduction is possible Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation
9
3248-3251
2(b), a large band gap Eg exists (Eg > 3 eV) There are no electrons in the conduction band, and therefore no electrical conduction is possible Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation This is the case of insulators
9
3249-3252
There are no electrons in the conduction band, and therefore no electrical conduction is possible Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation This is the case of insulators Case III: This situation is shown in Fig
9
3250-3253
Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation This is the case of insulators Case III: This situation is shown in Fig 14
9
3251-3254
This is the case of insulators Case III: This situation is shown in Fig 14 2(c)
9
3252-3255
Case III: This situation is shown in Fig 14 2(c) Here a finite but small band gap (Eg < 3 eV) exists
9
3253-3256
14 2(c) Here a finite but small band gap (Eg < 3 eV) exists Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band
9
3254-3257
2(c) Here a finite but small band gap (Eg < 3 eV) exists Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band These electrons (though small in numbers) can move in the conduction band
9
3255-3258
Here a finite but small band gap (Eg < 3 eV) exists Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band These electrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the insulators
9
3256-3259
Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band These electrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the insulators In this section we have made a broad classification of metals, conductors and semiconductors
9
3257-3260
These electrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the insulators In this section we have made a broad classification of metals, conductors and semiconductors In the section which follows you will learn the conduction process in semiconductors
9
3258-3261
Hence, the resistance of semiconductors is not as high as that of the insulators In this section we have made a broad classification of metals, conductors and semiconductors In the section which follows you will learn the conduction process in semiconductors 14
9
3259-3262
In this section we have made a broad classification of metals, conductors and semiconductors In the section which follows you will learn the conduction process in semiconductors 14 3 INTRINSIC SEMICONDUCTOR We shall take the most common case of Ge and Si whose lattice structure is shown in Fig
9
3260-3263
In the section which follows you will learn the conduction process in semiconductors 14 3 INTRINSIC SEMICONDUCTOR We shall take the most common case of Ge and Si whose lattice structure is shown in Fig 14
9
3261-3264
14 3 INTRINSIC SEMICONDUCTOR We shall take the most common case of Ge and Si whose lattice structure is shown in Fig 14 3
9
3262-3265
3 INTRINSIC SEMICONDUCTOR We shall take the most common case of Ge and Si whose lattice structure is shown in Fig 14 3 These structures are called the diamond-like structures
9
3263-3266
14 3 These structures are called the diamond-like structures Each atom is surrounded by four nearest neighbours
9
3264-3267
3 These structures are called the diamond-like structures Each atom is surrounded by four nearest neighbours We know that Si and Ge have four valence electrons
9
3265-3268
These structures are called the diamond-like structures Each atom is surrounded by four nearest neighbours We know that Si and Ge have four valence electrons In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour
9
3266-3269
Each atom is surrounded by four nearest neighbours We know that Si and Ge have four valence electrons In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour These shared electron pairs are referred to as forming a covalent bond or simply a valence bond
9
3267-3270
We know that Si and Ge have four valence electrons In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour These shared electron pairs are referred to as forming a covalent bond or simply a valence bond The two shared electrons can be assumed to shuttle back-and-forth between the associated atoms holding them together strongly
9
3268-3271
In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour These shared electron pairs are referred to as forming a covalent bond or simply a valence bond The two shared electrons can be assumed to shuttle back-and-forth between the associated atoms holding them together strongly Figure 14
9
3269-3272
These shared electron pairs are referred to as forming a covalent bond or simply a valence bond The two shared electrons can be assumed to shuttle back-and-forth between the associated atoms holding them together strongly Figure 14 4 schematically shows the 2-dimensional representation of Si or Ge structure shown in Fig
9
3270-3273
The two shared electrons can be assumed to shuttle back-and-forth between the associated atoms holding them together strongly Figure 14 4 schematically shows the 2-dimensional representation of Si or Ge structure shown in Fig 14
9
3271-3274
Figure 14 4 schematically shows the 2-dimensional representation of Si or Ge structure shown in Fig 14 3 which overemphasises the covalent bond
9
3272-3275
4 schematically shows the 2-dimensional representation of Si or Ge structure shown in Fig 14 3 which overemphasises the covalent bond It shows an idealised picture in which no bonds are broken (all bonds are intact)
9
3273-3276
14 3 which overemphasises the covalent bond It shows an idealised picture in which no bonds are broken (all bonds are intact) Such a situation arises at low temperatures
9
3274-3277
3 which overemphasises the covalent bond It shows an idealised picture in which no bonds are broken (all bonds are intact) Such a situation arises at low temperatures As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction)
9
3275-3278
It shows an idealised picture in which no bonds are broken (all bonds are intact) Such a situation arises at low temperatures As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction) The thermal energy effectively ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond as shown in Fig
9
3276-3279
Such a situation arises at low temperatures As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction) The thermal energy effectively ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond as shown in Fig 14
9
3277-3280
As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction) The thermal energy effectively ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond as shown in Fig 14 5(a)
9
3278-3281
The thermal energy effectively ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond as shown in Fig 14 5(a) The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q)
9
3279-3282
14 5(a) The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q) This vacancy with the effective positive electronic charge is called a hole
9
3280-3283
5(a) The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q) This vacancy with the effective positive electronic charge is called a hole The hole behaves as an apparent free particle with effective positive charge
9
3281-3284
The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q) This vacancy with the effective positive electronic charge is called a hole The hole behaves as an apparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh
9
3282-3285
This vacancy with the effective positive electronic charge is called a hole The hole behaves as an apparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh That is ne = nh = ni (14
9
3283-3286
The hole behaves as an apparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh That is ne = nh = ni (14 1) where ni is called intrinsic carrier concentration
9
3284-3287
In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh That is ne = nh = ni (14 1) where ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from electrons, the holes also move
9
3285-3288
That is ne = nh = ni (14 1) where ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from electrons, the holes also move Suppose there is a hole at site 1 as shown FIGURE 14
9
3286-3289
1) where ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from electrons, the holes also move Suppose there is a hole at site 1 as shown FIGURE 14 3 Three-dimensional dia- mond-like crystal structure for Carbon, Silicon or Germanium with respective lattice spacing a equal to 3
9
3287-3290
Semiconductors posses the unique property in which, apart from electrons, the holes also move Suppose there is a hole at site 1 as shown FIGURE 14 3 Three-dimensional dia- mond-like crystal structure for Carbon, Silicon or Germanium with respective lattice spacing a equal to 3 56, 5
9
3288-3291
Suppose there is a hole at site 1 as shown FIGURE 14 3 Three-dimensional dia- mond-like crystal structure for Carbon, Silicon or Germanium with respective lattice spacing a equal to 3 56, 5 43 and 5
9
3289-3292
3 Three-dimensional dia- mond-like crystal structure for Carbon, Silicon or Germanium with respective lattice spacing a equal to 3 56, 5 43 and 5 66 Å
9
3290-3293
56, 5 43 and 5 66 Å Rationalised 2023-24 Physics 328 in Fig
9
3291-3294
43 and 5 66 Å Rationalised 2023-24 Physics 328 in Fig 14
9
3292-3295
66 Å Rationalised 2023-24 Physics 328 in Fig 14 5(a)
9
3293-3296
Rationalised 2023-24 Physics 328 in Fig 14 5(a) The movement of holes can be visualised as shown in Fig
9
3294-3297
14 5(a) The movement of holes can be visualised as shown in Fig 14
9
3295-3298
5(a) The movement of holes can be visualised as shown in Fig 14 5(b)
9
3296-3299
The movement of holes can be visualised as shown in Fig 14 5(b) An electron from the covalent bond at site 2 may jump to the vacant site 1 (hole)
9
3297-3300
14 5(b) An electron from the covalent bond at site 2 may jump to the vacant site 1 (hole) Thus, after such a jump, the hole is at site 2 and the site 1 has now an electron
9
3298-3301
5(b) An electron from the covalent bond at site 2 may jump to the vacant site 1 (hole) Thus, after such a jump, the hole is at site 2 and the site 1 has now an electron Therefore, apparently, the hole has moved from site 1 to site 2
9
3299-3302
An electron from the covalent bond at site 2 may jump to the vacant site 1 (hole) Thus, after such a jump, the hole is at site 2 and the site 1 has now an electron Therefore, apparently, the hole has moved from site 1 to site 2 Note that the electron originally set free [Fig
9
3300-3303
Thus, after such a jump, the hole is at site 2 and the site 1 has now an electron Therefore, apparently, the hole has moved from site 1 to site 2 Note that the electron originally set free [Fig 14
9
3301-3304
Therefore, apparently, the hole has moved from site 1 to site 2 Note that the electron originally set free [Fig 14 5(a)] is not involved in this process of hole motion
9
3302-3305
Note that the electron originally set free [Fig 14 5(a)] is not involved in this process of hole motion The free electron moves completely independently as conduction electron and gives rise to an electron current, Ie under an applied electric field
9
3303-3306
14 5(a)] is not involved in this process of hole motion The free electron moves completely independently as conduction electron and gives rise to an electron current, Ie under an applied electric field Remember that the motion of hole is only a convenient way of describing the actual motion of bound electrons, whenever there is an empty bond anywhere in the crystal
9
3304-3307
5(a)] is not involved in this process of hole motion The free electron moves completely independently as conduction electron and gives rise to an electron current, Ie under an applied electric field Remember that the motion of hole is only a convenient way of describing the actual motion of bound electrons, whenever there is an empty bond anywhere in the crystal Under the action of an electric field, these holes move towards negative potential giving the hole current, Ih
9
3305-3308
The free electron moves completely independently as conduction electron and gives rise to an electron current, Ie under an applied electric field Remember that the motion of hole is only a convenient way of describing the actual motion of bound electrons, whenever there is an empty bond anywhere in the crystal Under the action of an electric field, these holes move towards negative potential giving the hole current, Ih The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih (14
9
3306-3309
Remember that the motion of hole is only a convenient way of describing the actual motion of bound electrons, whenever there is an empty bond anywhere in the crystal Under the action of an electric field, these holes move towards negative potential giving the hole current, Ih The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih (14 2) It may be noted that apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes
9
3307-3310
Under the action of an electric field, these holes move towards negative potential giving the hole current, Ih The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih (14 2) It may be noted that apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers
9
3308-3311
The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih (14 2) It may be noted that apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers The recombination occurs due to an electron colliding with a hole
9
3309-3312
2) It may be noted that apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination occurs in which the electrons recombine with the holes At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers The recombination occurs due to an electron colliding with a hole FIGURE 14
9
3310-3313
At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers The recombination occurs due to an electron colliding with a hole FIGURE 14 4 Schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature (all bonds intact)
9
3311-3314
The recombination occurs due to an electron colliding with a hole FIGURE 14 4 Schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature (all bonds intact) +4 symbol indicates inner cores of Si or Ge
9
3312-3315
FIGURE 14 4 Schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature (all bonds intact) +4 symbol indicates inner cores of Si or Ge FIGURE 14
9
3313-3316
4 Schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature (all bonds intact) +4 symbol indicates inner cores of Si or Ge FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron due to thermal energy at moderate temperatures
9
3314-3317
+4 symbol indicates inner cores of Si or Ge FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron due to thermal energy at moderate temperatures (b) Simplified representation of possible thermal motion of a hole
9
3315-3318
FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron due to thermal energy at moderate temperatures (b) Simplified representation of possible thermal motion of a hole The electron from the lower left hand covalent bond (site 2) goes to the earlier hole site1, leaving a hole at its site indicating an apparent movement of the hole from site 1 to site 2
9
3316-3319
5 (a) Schematic model of generation of hole at site 1 and conduction electron due to thermal energy at moderate temperatures (b) Simplified representation of possible thermal motion of a hole The electron from the lower left hand covalent bond (site 2) goes to the earlier hole site1, leaving a hole at its site indicating an apparent movement of the hole from site 1 to site 2 (a) (b) Rationalised 2023-24 329 Semiconductor Electronics: Materials, Devices and Simple Circuits EXAMPLE 14
9
3317-3320
(b) Simplified representation of possible thermal motion of a hole The electron from the lower left hand covalent bond (site 2) goes to the earlier hole site1, leaving a hole at its site indicating an apparent movement of the hole from site 1 to site 2 (a) (b) Rationalised 2023-24 329 Semiconductor Electronics: Materials, Devices and Simple Circuits EXAMPLE 14 1 An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig
9
3318-3321
The electron from the lower left hand covalent bond (site 2) goes to the earlier hole site1, leaving a hole at its site indicating an apparent movement of the hole from site 1 to site 2 (a) (b) Rationalised 2023-24 329 Semiconductor Electronics: Materials, Devices and Simple Circuits EXAMPLE 14 1 An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig 14
9
3319-3322
(a) (b) Rationalised 2023-24 329 Semiconductor Electronics: Materials, Devices and Simple Circuits EXAMPLE 14 1 An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig 14 6(a)
9
3320-3323
1 An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig 14 6(a) It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band
9
3321-3324
14 6(a) It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band These thermally excited electrons at T > 0 K, partially occupy the conduction band
9
3322-3325
6(a) It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band These thermally excited electrons at T > 0 K, partially occupy the conduction band Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig
9
3323-3326
It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band These thermally excited electrons at T > 0 K, partially occupy the conduction band Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig 14
9
3324-3327
These thermally excited electrons at T > 0 K, partially occupy the conduction band Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig 14 6(b)
9
3325-3328
Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig 14 6(b) Here, some electrons are shown in the conduction band
9
3326-3329
14 6(b) Here, some electrons are shown in the conduction band These have come from the valence band leaving equal number of holes there
9
3327-3330
6(b) Here, some electrons are shown in the conduction band These have come from the valence band leaving equal number of holes there Example 14
9
3328-3331
Here, some electrons are shown in the conduction band These have come from the valence band leaving equal number of holes there Example 14 1 C, Si and Ge have same lattice structure
9
3329-3332
These have come from the valence band leaving equal number of holes there Example 14 1 C, Si and Ge have same lattice structure Why is C insulator while Si and Ge intrinsic semiconductors
9
3330-3333
Example 14 1 C, Si and Ge have same lattice structure Why is C insulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit
9
3331-3334
1 C, Si and Ge have same lattice structure Why is C insulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit Hence, energy required to take out an electron from these atoms (i
9
3332-3335
Why is C insulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit Hence, energy required to take out an electron from these atoms (i e
9
3333-3336
Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit Hence, energy required to take out an electron from these atoms (i e , ionisation energy Eg) will be least for Ge, followed by Si and highest for C
9
3334-3337
Hence, energy required to take out an electron from these atoms (i e , ionisation energy Eg) will be least for Ge, followed by Si and highest for C Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C
9
3335-3338
e , ionisation energy Eg) will be least for Ge, followed by Si and highest for C Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C 14
9
3336-3339
, ionisation energy Eg) will be least for Ge, followed by Si and highest for C Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C 14 4 EXTRINSIC SEMICONDUCTOR The conductivity of an intrinsic semiconductor depends on its temperature, but at room temperature its conductivity is very low
9
3337-3340
Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C 14 4 EXTRINSIC SEMICONDUCTOR The conductivity of an intrinsic semiconductor depends on its temperature, but at room temperature its conductivity is very low As such, no important electronic devices can be developed using these semiconductors
9
3338-3341
14 4 EXTRINSIC SEMICONDUCTOR The conductivity of an intrinsic semiconductor depends on its temperature, but at room temperature its conductivity is very low As such, no important electronic devices can be developed using these semiconductors Hence there is a necessity of improving their conductivity