in Figure 1.3. In a space-lattice of fcc-type, two identical atoms at 000 and form the primitive basis and are associated with each point of the fcc lattice. In the above picturesque, fractions are the heights over and above the base in units of a cube edge. In that case, points at lie on the fcc lattice, while those at and lie on the similar fcc lattice but are displaced along the line of body diagonal by a magnitude of ¼ of its length. It is a known fact that the unit cube of fcc lattice consists of 4 lattice points. As a result, diamond-type cubic lattice contains 2 × 4 = 8 atoms. The diamond-type fcc lattice in Si displays tetrahedral bonding characteristics [20, 21].
Figure 1.3 Schematic to show atomic positions in diamond-type cubic lattice.
Si is tetravalent and can be made p-type by adding dopants of boron (B), aluminium (Al) & gallium (Ga), and addition of antimony (Sb), phosphorous (P) & arsenic (As) generates n-type semiconductor material [10,11,20,21]. B and Ga possess only three valence electrons and when they are mixed into the Si lattice, deficiency of an electron is created which is termed as positively charged “vacancy” or “hole”. Holes take part in conduction accepting an electron from the neighbour and transitioning over the atoms. For making Si an n-type semiconductor, Sb, P and As are added into the Si lattice in small quantities each having five valence electrons, which creates an extra electron into the lattice. The availability of these free electrons as a whole in the material creates a net flow of negatively charged carriers to constitute current. Thus, addition of small amounts of either of two types of foreign atoms changes Si crystal into a medium-type of conductor, which is a semiconductor. Joining of two types of semiconducting materials constitutes a device entailed as nonlinear semiconductor diode [10,11,20-22]. Figure 1.4 shows a similar picture to portray the doping of two types of foreign atoms in Si lattice.
1.1.3 Introduction to Diode Physics
When p-type and n-type junctions are combined to form p-n junctions, they possess a characteristic called rectification [23-26]. Rectification is a property to allow flow of current easily in one direction only [28,29]. In the case of p-type material, the Fermi level (EF) is near the valence band edge and is close to conduction band edge in n-type material as shown in Figure 1.5. In p-type configuration, holes are the majority carriers, while electrons are minority carriers. Just the opposite happens in case of n-type materials in which electrons are majority carriers and holes are minority carriers. Upon joining, large carrier concentration gradients happen at the junction to cause carrier diffusion. Majority holes from the p-type are transported by diffusion into the n-type semiconductor, while majority electrons from n-type semiconductor are diffused towards the p-type. Holes continue to leave the side of p-type while electrons keep on moving from the side of n-type semiconductor till a saturation point is reached. In this exercise of charge carrier transportation, a minor concentration of negative acceptor ions
Figure 1.4 Figure showing the doping of two types of foreign atoms of B (p-type) and P (n-type) in Si to form semiconductor material with better conductivities.
Figure 1.5 Two semiconductor blocks of p-type and n-type before the formation of junction and also showing position of Fermi level (EF) in the corresponding dopes semiconductor material.
and positive donor ions at the semiconductor junction remains unreacted. The holes possess high mobility whereas acceptor atoms are permanently fixed in the semiconductor lattice. Similar explanation follows in case of electrons leaving the n-type semiconductor. A saturation point is attained after transportation of both types of charge carriers to oppositely doped semiconductor blocks. The result of large concentration gradient is that a part of the free electrons coming from donor impurity atoms migrates across the semiconductor junction filling up holes in the p-type semiconductor material to produce negative ions. On moving from n-type to p-type, positively charged donor ions (ND) are left behind on the side of n-type. Similarly, holes coming from acceptor foreign atoms are transported across the junction in an opposite direction having large number of free electrons. The transport mechanism of holes and electrons across the p-n junction is called diffusion. As a result, a space charge region is formed in the region combining p-type and n-type semiconductor blocks. On the side of p-type block, a negative space charge region is formed, while a positive space charge region is formed on the side of n-type semiconductor. The constitution of this space charge region in the junction develops an electric field that is directed from the holes towards the negative charge. The width of the p- and n-type layers is dependent on the degree of heavy doping of each layer with acceptor impurity atoms (NA) and donor impurity atoms (ND), respectively. Figure 1.6(a) below shows the space charge region formed between the joining of two semiconductor blocks of p-type and n-type. The electric field will be directed from positive charge towards the negative charge. Figure 1.6(b) shows the energy band diagram of a semiconducting p-n junction in thermal equilibrium. It needs to be pointed out that the flow of charge carriers can be due to both drift and diffusion. It is apparent from Figure 1.6(b) that the hole drift current flows from right to left, while hole diffusion current flows from left to right. The electron drift current flows from right to the left, while electron diffusion current flows from left to right. Thus, the free charge carriers (electrons and holes) produce current in two ways under the application of an electric field in a semiconductor, i.e. by drift and diffusion. The passage of charge carriers under the effect of an externally applied electric field generates a net current called as the drift current. In case of spatial variation of concentrations of charge carriers in the semiconductor, charge carriers have the tendency to move from regions of high concentration to regions of low concentration called as the diffusion current. The spatial variation in charge carrier concentration is called as the concentration gradient. Figure 1.7 shows the current-voltage characteristics of a typical p-n junction diode. When the junction is forward-biased (+ve terminal of the battery connected to p-type having positive vacancies as majority carriers), current (I) increases rapidly as a function of voltage (V). In case of application
