target="_blank" rel="nofollow" href="#ulink_ba2a2b44-dea6-5bf2-b69e-c032a73ee55e">equation (1.3) [10,11,23,24],
(1.14)
Figure 1.9 The above figure (a) displays band diagram of an abrupt junction in steady state and (b) displays an approximation of space charge distribution.
Similarly, in case of n-type neutral region, NA = 0 and n ≫ p Now, setting NA = p = 0 in equation (1.13), we get, n = ND and putting in equation (1.3) [10,11,23,24],
(1.15)
In the steady state, the total electrostatic potential difference between p-type and n-type neutral regions is defined as the built-in-potential (Vbi) and is given as follows [10,11,23,24],
(1.16)
In between the neutral regions and semiconductor barrier, a narrow transition region exists which has a width smaller in comparison to the width of the barrier or the depletion region. This is true for regions existing on both sides of the depletion region. On neglecting the transition regions in comparison to the depletion region, a nearby rectangular space charge distribution is obtained as shown in Figure 1.9(b) [10,23,24]. Here, xp and xn are the widths of the depletion layer of p- and n-type blocks. In case of completely depleted region, the amount of p and n dopants will be zero, and then from equation (1.11) [10,24],
The physics of Poisson’s equation lies in the fact that distribution of impurities can be performed in the form of shallow diffusion or low energy ion implantation or in the form of deep diffusions or high-energy ion implantations [10,23,24]. The type of ion implantation describes the doping profile according to the energy dose applied [30]. Shallow diffusion or low-energy ion implantation introduces foreign atoms at low depths to form abrupt p-n junction as shown in Figure 1.10(a). In this case, the doping concentration profile shows a rapid changeover between the p-type and n-type regions. In case of high-energy ion implantations, distribution of doping profiles can be approximated almost linearly across the barrier called as linearly graded junction as shown in Figure 1.10(b).
In case of an abrupt junction, the free charge carriers are completely depleted such that under the condition, -xp ≤ x < 0, equation (1.17) becomes [10],
In case of an abrupt junction, the free charge carriers are completely depleted such that under the condition, 0 < x ≤ xn, equation (1.17) becomes [10],
Figure 1.10 Approximation of foreign atom doping profiles in semiconductor forming (a) abrupt junction due to shallow diffusion and (b) linearly graded junction as a result of deep diffusion.
For the space charge neutrality of the semiconductor as a whole,
(1.20)
The total depletion layer width is given as follows,
(1.21)
The electric field distributed in the barrier can be obtained by integrating equations (1.18) & (1.19) [10,11,23,24].
In case of -xp ≤ x < 0,
In case of 0 < x ≤ xn,
Now, integrating equations (1.22) & (1.23) over the barrier gives Vbi as follows,
(1.24)
(1.25)
Hence, area covered under the shaded triangle in Figure 1.11 corresponds to built-in-potential or Vbi. Using above equations, Vbi as a function of the total width of depletion layer is given as,
(1.26)
The p-n junction circuit diagrams along with energy band diagrams for steady-state and in case of forward- and reverse-biased states are shown in Figure 1.12. Figure
