Simple Circuits

Simple Circuits semiconductors. However, after , a few semiconductor devices using organic semiconductors and semiconducting polymers have been developed signalling the birth of a futuristic technology of polymer- electronics and molecular-electronics. In this chapter, we will restrict ourselves to the study of inorganic semiconductors, particularly elemental semiconductors Si and Ge. The general concepts introduced here for discussing the elemental semiconductors, by-and-large, apply to most of the compound semiconductors as well.

On the basis of energy bands According to the Bohr atomic model, in an isolated atom the energy of any of its electrons is decided by the orbit in which it revolves. But when the atoms come together to form a solid they are close to each other. So the outer orbits of electrons from neighbouring atoms would come very close or could even overlap. This would make the nature of electron motion in a solid very different from that in an isolated atom.

Inside the crystal each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges. Because of this, each electron will have a different energy level. These different energy levels with continuous energy variation form what are called energy bands. The energy band which includes the energy levels of the valence electrons is called the valence band.

The energy band above the valence band is called the conduction band. With no external energy, all the valence electrons will reside in the valence band. If the lowest level in the conduction band happens to be lower than the highest level of the valence band, the electrons from the valence band can easily move into the conduction band. Normally the conduction band is empty.

But when it overlaps on the valence band electrons can move freely into it. This is the case with metallic conductors. If there is some gap between the conduction band and the valence band, electrons in the valence band all remain bound and no free electrons are available in the conduction band. This makes the material an insulator.

But some of the electrons from the valence band may gain external energy to cross the gap between the conduction band and the valence band. Then these electrons will move into the conduction band. At the same time they will create vacant energy levels in the valence band where other valence electrons can move. Thus the process creates the possibility of conduction due to electrons in conduction band as well as due to vacancies in the valence band.

Let us consider what happens in the case of Si or Ge crystal containing N atoms. For Si, the outermost orbit is the third orbit (n = ), while for Ge it is the fourth orbit (n = ). The number of electrons in the outermost orbit is (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N.

The maximum possible number of electrons in the outer orbit is (2s + 6p electrons). So, for the 4N valence electrons there are 8N available energy states. These 8N discrete energy levels can either form a continuous band or they may be grouped in different bands depending upon the distance between the atoms in the crystal (see box on Band Theory of Solids). At the distance between the atoms in the crystal lattices of Si and Ge, the energy band of these 8N states is split apart into two which are separated by an energy gap Eg (Fig.

. ). The lower band which is completely occupied by the 4N valence electrons at temperature of absolute zero is the valence band. The other band consisting of 4N energy states, called the conduction band, is completely empty at absolute zero.

Simple Circuits The lowest energy level in the conduction band is shown as EC and highest energy level in the valence band is shown as EV. Above EC and below EV there are a large number of closely spaced energy levels, as shown in Fig. . .

The gap between the top of the valence band and bottom of the conduction band is called the energy band gap (Energy gap Eg). It may be large, small, or zero, depending upon the material. These different situations, are depicted in Fig. .

and discussed below: Case I: This refers to a situation, as shown in Fig. . (a). One can have a metal either when the conduction band is partially filled and the balanced band is partially empty or when the conduction and valance bands overlap.

When there is overlap electrons from valence band can easily move into the conduction band. This situation makes a large number of electrons available for electrical conduction. When the valence band is partially empty, electrons from its lower level can move to higher level making conduction possible. Therefore, the resistance of such materials is low or the conductivity is high.

FIGURE . Difference between energy bands of (a) metals, (b) insulators and (c) semiconductors. FIGURE . The energy band positions in a semiconductor at 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. Case II: In this case, as shown in Fig. .

(b), a large band gap Eg exists (Eg > 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.

Case III: This situation is shown in Fig. . (c). Here a finite but small band gap (Eg < 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. 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. Simple Circuits Suppose there is a hole at site as shown in Fig. . (a).

The movement of holes can be visualised as shown in Fig. . (b). An electron from the covalent bond at site may jump to the vacant site (hole).

Thus, after such a jump, the hole is at site and the site has now an electron. Therefore, apparently, the hole has moved from site to site . Note that the electron originally set free [Fig. .

(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.

The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih ( . ) 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 . Schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature (all bonds intact). + symbol indicates inner cores of Si or Ge. FIGURE .

(a) Schematic model of generation of hole at site 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 ) goes to the earlier hole site1, leaving a hole at its site indicating an apparent movement of the hole from site to site . EXAMPLE .

An intrinsic semiconductor will behave like an insulator at T = K as shown in Fig. . (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 > K, partially occupy the conduction band. Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig. . (b).

Here, some electrons are shown in the conduction band. These have come from the valence band leaving equal number of holes there. Example . C, Si and Ge have same lattice structure.

Why is C insulator while Si and Ge intrinsic semiconductors? Solution The 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. Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C.

Simple Circuits (ii) Trivalent (valency ); like Indium (In), Boron (B), Aluminium (Al), etc. We shall now discuss how the doping changes the number of charge carriers (and hence the conductivity) of semiconductors. Si or Ge belongs to the fourth group in the Periodic table and, therefore, we choose the dopant element from nearby fifth or third group, expecting and taking care that the size of the dopant atom is nearly the same as that of Si or Ge. Interestingly, the pentavalent and trivalent dopants in Si or Ge give two entirely different types of semiconductors as discussed below.

(i) n-type semiconductor Suppose we dope Si or Ge with a pentavalent element as shown in Fig. . . When an atom of + valency element occupies the position of an atom in the crystal lattice of Si, four of its electrons bond with the four silicon neighbours while the fifth remains very weakly bound to its parent atom.

This is because the four electrons participating in bonding are seen as part of the effective core of the atom by the fifth electron. As a result the ionisation energy required to set this electron free is very small and even at room temperature it will be free to move in the lattice of the semiconductor. For example, the energy required is ~ . eV for germanium, and .

eV for silicon, to separate this electron from its atom. This is in contrast to the energy required to jump the forbidden band (about . eV for germanium and about . eV for silicon) at room temperature in the intrinsic semiconductor.

Thus, the pentavalent dopant is donating one extra electron for conduction and hence is known as donor impurity. The number of electrons made available for conduction by dopant atoms depends strongly upon the doping level and is independent of any increase in ambient temperature. On the other hand, the number of free electrons (with an equal number of holes) generated by Si atoms, increases weakly with temperature. In a doped semiconductor the total number of conduction electrons ne is due to the electrons contributed by donors and those generated intrinsically, while the total number of holes nh is only due to the holes from the intrinsic source.

But the rate of recombination of holes would increase due to the increase in the number of electrons. As a result, the number of holes would get reduced further. Thus, with proper level of doping the number of conduction electrons can be made much larger than the number of holes. Hence in an extrinsic FIGURE .

(a) Pentavalent donor atom (As, Sb, P, etc.) doped for tetravalent Si or Ge giving n- type semiconductor, and (b) Commonly used schematic representation of n-type material which shows only the fixed cores of the substituent donors with one additional effective positive charge and its associated extra electron. semiconductor doped with pentavalent impurity, electrons become the majority carriers and holes the minority carriers. These semiconductors are, therefore, known as n-type semiconductors. For n-type semiconductors, we have, ne >> nh ( .

) (ii) p-type semiconductor This is obtained when Si or Ge is doped with a trivalent impurity like Al, B, In, etc. The dopant has one valence electron less than Si or Ge and, therefore, this atom can form covalent bonds with neighbouring three Si atoms but does not have any electron to offer to the fourth Si atom. So the bond between the fourth neighbour and the trivalent atom has a vacancy or hole as shown in Fig. .

. Since the neighbouring Si atom in the lattice wants an electron in place of a hole, an electron in the outer orbit of an atom in the neighbourhood may jump to fill this vacancy, leaving a vacancy or hole at its own site. Thus the hole is available for conduction. Note that the trivalent foreign atom becomes effectively negatively charged when it shares fourth electron with neighbouring Si atom.

Therefore, the dopant atom of p-type material can be treated as core of one negative charge along with its associated hole as shown in Fig. . (b). It is obvious that one acceptor atom gives one hole.

These holes are in addition to the intrinsically generated holes while the source of conduction electrons is only intrinsic generation. Thus, for such a material, the holes are the majority carriers and electrons are minority carriers. Therefore, extrinsic semiconductors doped with trivalent impurity are called p-type semiconductors. For p-type semiconductors, the recombination process will reduce the number (ni)of intrinsically generated electrons to ne.

We have, for p-type semiconductors nh >> ne ( . ) Note that the crystal maintains an overall charge neutrality as the charge of additional charge carriers is just equal and opposite to that of the ionised cores in the lattice. In extrinsic semiconductors, because of the abundance of majority current carriers, the minority carriers produced thermally have more chance of meeting majority carriers and thus getting destroyed. Hence, the dopant, by adding a large number of current carriers of one type, which become the majority carriers, indirectly helps to reduce the intrinsic concentration of minority carriers.

The semiconductor’s energy band structure is affected by doping. In the case of extrinsic semiconductors, additional energy states due to donor impurities (ED) and acceptor impurities (EA) also exist. In the energy band diagram of n-type Si semiconductor, the donor energy level ED is slightly below the bottom EC of the conduction band and electrons from this level move into the conduction band with very small supply of energy. At room temperature, most of the donor atoms get ionised but very few (~ – ) atoms of Si get ionised.

So the conduction band will have most electrons coming from the donor impurities, as shown in Fig. . (a). Similarly, FIGURE .

(a) Trivalent acceptor atom (In, Al, B etc.) doped in tetravalent Si or Ge lattice giving p-type semicon- ductor. (b) Commonly used schematic representation of p-type material which shows only the fixed core of the substituent acceptor with one effective additional negative charge and its associated hole. Simple Circuits EXAMPLE . for p-type semiconductor, the acceptor energy level EA is slightly above the top EV of the valence band as shown in Fig.

. (b). With very small supply of energy an electron from the valence band can jump to the level EA and ionise the acceptor negatively. (Alternately, we can also say that with very small supply of energy the hole from level EA sinks down into the valence band.

Electrons rise up and holes fall down when they gain external energy.) At room temperature, most of the acceptor atoms get ionised leaving holes in the valence band. Thus at room temperature the density of holes in the valence band is predominantly due to impurity in the extrinsic semiconductor. The electron and hole concentration in a semiconductor in thermal equilibrium is given by nenh = ni ( . ) Though the above description is grossly approximate and hypothetical, it helps in understanding the difference between metals, insulators and semiconductors (extrinsic and intrinsic) in a simple manner.

The difference in the resistivity of C, Si and Ge depends upon the energy gap between their conduction and valence bands. For C (diamond), Si and Ge, the energy gaps are . eV, . eV and .

eV, respectively. Sn also is a group IV element but it is a metal because the energy gap in its case is eV. FIGURE . Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type semiconductor at T > 0K.

Example . Suppose a pure Si crystal has × atoms m– . It is doped by ppm concentration of pentavalent As. Calculate the number of electrons and holes.

Given that ni = . × m– . Solution Note that thermally generated electrons (ni ~ m– ) are negligibly small as compared to those produced by doping. Therefore, ne ND.

Since nenh = ni , The number of holes nh = ( . × )/( × ) ~ . × m– Simple Circuits EXAMPLE . Initially, diffusion current is large and drift current is small.

As the diffusion process continues, the space-charge regions on either side of the junction extend, thus increasing the electric field strength and hence drift current. This process continues until the diffusion current equals the drift current. Thus a p-n junction is formed. In a p-n junction under equilibrium there is no net current.

The loss of electrons from the n-region and the gain of electron by the p-region causes a difference of potential across the junction of the two regions. The polarity of this potential is such as to oppose further flow of carriers so that a condition of equilibrium exists. Figure . shows the p-n junction at equilibrium and the potential across the junction.

The n-material has lost electrons, and p material has acquired electrons. The n material is thus positive relative to the p material. Since this potential tends to prevent the movement of electron from the n region into the p region, it is often called a barrier potential. Example .

Can we take one slab of p-type semiconductor and physically join it to another n-type semiconductor to get p-n junction? Solution No! Any slab, howsoever flat, will have roughness much larger than the inter-atomic crystal spacing (~ to Å) and hence continuous contact at the atomic level will not be possible. The junction will behave as a discontinuity for the flowing charge carriers.

Simple Circuits is not limited by the magnitude of the applied voltage but is limited due to the concentration of the minority carrier on either side of the junction. The current under reverse bias is essentially voltage independent upto a critical reverse bias voltage, known as breakdown voltage (Vbr). When V = Vbr, the diode reverse current increases sharply. Even a slight increase in the bias voltage causes large change in the current.

If the reverse current is not limited by an external circuit below the rated value (specified by the manufacturer) the p-n junction will get destroyed. Once it exceeds the rated value, the diode gets destroyed due to overheating. This can happen even for the diode under forward bias, if the forward current exceeds the rated value. The circuit arrangement for studying the V-I characteristics of a diode, (i.e., the variation of current as a function of applied voltage) are shown in Fig.

. (a) and (b). The battery is connected to the diode through a potentiometer (or reheostat) so that the applied voltage to the diode can be changed. For different values of voltages, the value of the current is noted.

A graph between V and I is obtained as in Fig. . (c). Note that in forward bias measurement, we use a milliammeter since the expected current is large (as explained in the earlier section) while a micrometer is used in reverse bias to measure the current.

You can see in Fig. . (c) that in forward FIGURE . (a) Diode under reverse bias, (b) Barrier potential under reverse bias.