In this article we will discuss about:- 1. Classification of pn Junctions 2. Characteristics of pn-Junction 3. Contact Potential 4. Breakdown in Diode.
Classification of pn Junctions:
A pn junction is a boundary between p-type region and n-type region of a single crystal semiconductor.
Based on the method of fabrication, the junctions may be classified as: 1. Grown Junctions 2. Alloyed Junctions 3. Diffused Junctions.
1. Grown Junctions:
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The grown junctions are formed by a technique called the grown junction technique. In this method, a single crystal semiconductor containing p-type or n-type impurity is grown from the melt and during the course of growth; the dopant in the melt is abruptly changed by adding a large quantity of dopant of the opposite type.
Such donors and acceptors are alternately added. Thus, we get a continuous single crystal which is composed of n-type and p-type regions. The pn junction is formed in a region where the concentration of acceptors and donors becomes equal. The width of this transition region may vary from 0.01 to 1 m.
2. Alloyed Junctions:
An alloyed or fused pn junction is formed by placing a small pellet of a dopant metal, such as trivalent indium, or an n-type semiconductor, such as germanium and heating the combination to about 160°C for a short duration. The indium melts and forms an alloy with Ge at the interface which is rich in In and hence is of p-type. Thus a p-n junction is formed between the n-type and p-type Ge.
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3. Diffusion Junctions:
The different junctions are fabricated by the impurity diffusion technique. If a wafer or slab of n-type Si is heated at about 100°C in a gaseous atmosphere containing a high concentration of boron atoms, the boron atoms diffuse slowly into the n-type Si under the effect of concentration gradient.
The concentration of boron atoms is the maximum at the surface and decreases gradually inside the wafer. If Na and Nd represent the concentrations of acceptors (B atoms) and donors respectively, then the region near the junction has Na < Nd and behaves n-types, whereas the region near the surface has Na > Nd and behaves p-types.
The pn junction is formed in the region where Na equals Nd. This is shown in Fig. 7.12. Impurity diffusion is the most common technique of forming pn junctions and, with the use of selective masking, has been employed for the fabrication of integrated circuits.
Based on the distribution of impurities near the junction, a pn junction may be classified as:
(a) Step graded junction.
(b) Linearly graded junction.
(c) Non-linearly graded junction.
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In a step graded junction, the concentration of donors or acceptors is constant upto the junction and abruptly decreases to zero at the junction. Alloyed junctions are nearly step graded junctions. In a linearly graded junction, the impurity concentration varies almost linearly with distance from the junction.
This type of junction can be produced by grown junction technique. In a non-linearly graded junction, the impurity concentration around the junction may have non-linear random distribution. The first two types of junctions are the most convenient to deal with.
Characteristics of pn-Junction:
The balance between the diffusion and drift currents is disturbed during forward or reverse bias and a net current flows through the junction. We will now determine the current-voltage relationship for the biased pn-junction.
At equilibrium, the minority carrier electron concentration in the p-region is related to the majority carrier electron concentration in the n-region by equation (viii) as;
When a small forward voltage V is applied, the effective barrier potential decreases to VB – V. This results in diffusion of some of the majority carriers across the junction, i.e., holes to n side and electrons to p side. Thus the minority carrier electron concentration at the edge of the transition region on the p side, n(-xp), becomes greater than its equilibrium value by a small amount Δnp.
Such an increase in the minority carrier concentration with forward bias is referred to as the minority carrier injection. The majority carrier electron concentration in the n region, however, changes only slightly with bias compared to its equilibrium value and hence can be taken as nearly constant, particularly for low level injection. Thus, for applied forward bias, eqn. (xii) can be written as-
This gives the excess electron concentration at the edge of the transition region, i.e., for x = -xp, in terms of the equilibrium electron concentration in the p region and the applied forward bias. Similarly, for excess holes on the n side, we have;
The injected minority carriers diffuse into their respective regions upto certain distances and then recombine with the opposite type of carriers. The diffusion currents produced by these charges can be determined by using the diffusion equations and the Fick’s first law of diffusion. The electron diffusion current injected into the p material at the junction is given by;
Where Dn is the diffusion coefficient of electrons in m2/s, A is the area of cross- section of the junction and Ln is the electron diffusion length which represents the average distance an electron diffuse before recombining. Ln is also related to the life time τn, of the electron as;
Similarly, the hole diffusion current injected into the n-type material at the junction is;
where, Dp and Lp represent the diffusion coefficient and diffusion length for holes respectively. The direction of both the currents is the same. The total diode current, I, is thus given by;
The current I0 is called the reverse saturation current. It is the same as the equilibrium diffusion current or drift current, both being equal at equilibrium. Equation (xix) is called the diode equation.
When the forward bias V is greater than a few KBT/e, the exponential term is much larger, than unity and equation (xix) gives the forward current as;
i.e., the current increases exponentially with forward bias. The equation (xix) also holds for reverse bias case. Putting V = -Vr in equations (xix), the current during reverse bias is given by-
For Vr greater than a few KgT/e, the exponential term is negligible and we obtain
IR = -I0 … (xxiii)
Thus the current IR is numerically equal to I0 and flows in a direction opposite to IF (i.e., from n to p side). Hence I0 is termed as the reverse saturation current. At a given temperature, the reverse current is very small and is almost constant. The reverse current has a magnitude less than or of the order of 1 A and is quite small as compared to the forward current which generally lies in the mA range. The empirical form of equation (xix) is
where is a numerical constant which depends on the material of the diode. Its value is 1 for Ge and 2 for Si. This equation is called the pn diode equation.
The typical I-V characteristic of a pn junction is shown in Fig. 7.18. Unlike an ordinary resistor, a pn-junction exhibits highly nonlinear characteristic. The current flows relatively freely in the forward direction, whereas a negligible current flows in the reverse direction. It is due to these salient features of the I-V characteristic that pn-junction is considered to be a very useful device.
It is relevant to point out that besides the reverse saturation current produced by minority carriers, there also exists a small leakage current which flows in the direction of I0. The leakage current is small ohmic current which leaks along the surface edges of the junction during reverse bias as shown by the broken line in Fig. 7.18.
For small value of forward bias. OA, the diode current is very small and increases rapidly with further increase in voltage. This is because a small part of the applied voltage is used up in overcoming the barrier potential at the junction. The voltage at which the current begins to increase rapidly is known as the cut in, offset, or threshold voltage and is about 0.7 V for Si and 0.3 V for Ge.
Temperature Dependence of I-V Characteristics:
It has been observed theoretically that the variation of I0 with temperature T is ~8% per degree centigrade for Si and ~11%/°C for Ge, where contribution of leakage current has not been taken into account. Experimentally, the reverse saturation current I0 increases ~7%/°C for both Si and Ge. Since (1.07)10 ≈ 2.0, it is clear that the reverse saturation current approximately doubles for every 10°C rise in temperature. If I0 = I0, at T = T1, then at a temperature T, I0 is given by-
If the temperature is increased at a fixed voltage, the current increases. But if we now reduce V, then i may be brought back to its previous value. It has been found for Si and Ge at room temperature that-
in order to maintain a constant value of I. It is worth mentioning here that │dV/dT│ decreases with increasing temperature.
Contact Potential of pn Junction:
When a junction is formed between a p-type region and an n-type region, the Fermi levels of both the regions attain a constant value under equilibrium conditions as shown in Fig. 7.14.
It is assumed here that the junction is abrupt and the field exists only in the depletion region. Apparently, the conduction band edge, Ecp, in the p region occupies high energy position as compared to the conduction band edge, Ecn, in the n region; similarly Evp >Evn. The barrier energy is, therefore, given by-
EB = Ecp – Ecn = Evp – Evn = eVB … (i)
The relative shifts in the conduction band and valence band edge in the p region w.r.t. those in the n region depend on the two regions which further depends on the carrier concentration of these regions.
The concentration of electrons in the n regions is given by-
Where, Ec and EF has been replaced by Ecn and EFn respectively. The p region also contains some thermally generated electrons of concentration,
From above two eqns., we have-
For the same semiconducting material, the positions of the conduction and valence band edges do not change with doping, whereas the position of the Fermi level changes with both concentration and type of doping. Thus for n and p regions we must have;
ECn = ECp and EFn ≠ EFp
The different energy values attained by ECp and ECn in Fig. 7.14 are indicative of the fact that the Fermi levels of the two regions have been brought to the same position. Thus, we obtain-
Similarly, for holes in the n and p regions, we obtain
where pn and pp represent the concentration of holes in the n and p regions respectively. Since,
Breakdown in Diode:
The reverse breakdown may occur by any of the following two mechanisms: 1. Avalanche Breakdown 2. Zener Breakdown.
1. Avalanche Breakdown:
This type of breakdown occurs in lightly doped junction under the effect of relatively high reverse voltage ranging from a few volts to thousands for volts. The breakdown mechanism involves ionizing collisions of energetic carriers with host atoms which produce a large number of electron-hole pairs.
For example, when the electric field in the transition region is sufficiently high, an electron entering the transition region from the p side may acquire such a high kinetic energy as to collide with a host atom and break one of its covalent bonds with neighbouring atoms. The electron which earlier formed a part of the covalent bond now gets excited into the conduction band, thus producing an electron-hole pair.
The newly generated carriers produce additional electron hole pairs by the same process. Thus, the numbers of carriers keep multiplying and an avalanche of carriers is produced in a very short time. The electrons and holes move in opposite directions and constitute a large reverse current.
The avalanche breakdown is self-sustaining as long as the field is present in the transition region. The breakdown voltage is found to increase with temperature, i.e., the temperature coefficient is positive for this type of breakdown mechanism. As the temperature increases, the mean free path of the carriers decrease which means a large electric field is required to impart sufficient energy to the carriers to produce polarization.
2. Zener Breakdown:
The zener breakdown mechanism is dominant in heavily doped junctions and requires relatively low reverse voltage for its operation. In the band theory, the zener effect is considered to be the tunneling of electrons from the p side valence band to the n side conduction band, thus constituting a reverse current from n to p side. When the p and n regions across a junction are heavily doped, the crossing of bands may take place even at a few tenths of volt.
This means that the n side conduction band appears opposite to the p side valence band, thus bringing a number of empty states in the n side conduction band directly opposite to many filled states in the p side valence band as shown in Fig. 7.21. If the barrier separating these two bands is sufficient narrow, the electrons can directly tunnel through it under the effect of a small reverse bias.
The requirement of a narrow barrier of finite height is met firstly, by using an abrupt pn junction, such as an alloyed junction, who decreases the transition region width W, secondly, by heavily, assumed that the depletion region width does not increase appreciably with reverse bias which is true practically for low applied voltage and heavy doping. In case, the breakdown does not occur with reverse voltage of a few volts, the avalanche breakdown is likely to dominate.