Topic Covered



`color{blue} ✍️`From the V-I characteristic of a junction diode we see that it allows current to pass only when it is forward biased. So if an alternating voltage is applied across a diode the current flows only in that part of the cycle when the diode is forward biased.

`color{blue} ✍️`This property is used to rectify alternating voltages and the circuit used for this purpose is called a rectifier.

`color{blue} ✍️`If an alternating voltage is applied across a diode in series with a load, a pulsating voltage will appear across the load only during the half cycles of the ac input during which the diode is forward biased. Such rectifier circuit, as shown in Fig. 14.18, is called a `"half-wave rectifier."`

`color{blue} ✍️`The secondary of a transformer supplies the desired ac voltage across terminals A and B. When the voltage at A is positive, the diode is forward biased and it conducts. When A is negative, the diode is reverse-biased and it does not conduct.

`color{blue} ✍️`The reverse saturation current of a diode is negligible and can be considered equal to zero for practical purposes. (The reverse breakdown voltage of the diode must be sufficiently higher than the peak ac voltage at the secondary of the transformer to protect the diode from reverse breakdown.)

`color{blue} ✍️`Therefore, in the positive half-cycle of ac there is a current through the load resistor RL and we get an output voltage, as shown in Fig. 14.18(b), whereas there is no current in the negative halfcycle.

`color{blue} ✍️`In the next positive half-cycle, again we get the output voltage. Thus, the output voltage, though still varying, is restricted to only one direction and is said to be rectified. Since the rectified output of this circuit is only for half of the input ac wave it is called as half-wave rectifier.

`color{blue} ✍️`The circuit using two diodes, shown in Fig. 14.19(a), gives output rectified voltage corresponding to both the positive as well as negative half of the ac cycle. Hence, it is known as full-wave rectifier.

`color{blue} ✍️`Here the p-side of the two diodes are connected to the ends of the secondary of the transformer. The n-side of the diodes are connected together and the output is taken between this common point of diodes and the midpoint of the secondary of the transformer.

`color{blue} ✍️`So for a full-wave rectifier the secondary of the transformer is provided with a centre tapping and so it is called centre-tap transformer. As can be seen from Fig.14.19(c) the voltage rectified by each diode is only half the total secondary voltage.

`color{blue} ✍️`Each diode rectifies only for half the cycle, but the two do so for alternate cycles. Thus, the output between their common terminals and the centretap of the transformer becomes a full-wave rectifier output.
(Note that there is another circuit of full wave rectifier which does not need a centretap transformer but needs four diodes.) Suppose the input voltage to A with respect to the centre tap at any instant is positive. It is clear that, at that instant, voltage at B being out of phase will be negative as shown in Fig.14.19(b).

`color{blue} ✍️` So, diode `D_1` gets forward biased and conducts (while `D_2` being reverse biased is not conducting). Hence, during this positive half cycle we get an output current (and a output voltage across the load resistor RL) as shown in Fig.14.19(c).

`color{blue} ✍️`In the course of the ac cycle when the voltage at A becomes negative with respect to centre tap, the voltage at B would be positive. In this part of the cycle diode `D_1` would not conduct but diode `D_2` would, giving an output current and output voltage (across `R_L`) during the negative half cycle of the input ac.

`color{blue} ✍️`Thus, we get output voltage during both the positive as well as the negative half of the cycle. Obviously, this is a more efficient circuit for getting rectified voltage or current than the halfwave rectifier.

`color{blue} ✍️`Now we shall discuss the role of capacitor in filtering. When the voltage across the capacitor is rising, it gets charged. If there is no external load, it remains charged to the peak voltage of the rectified output.

`color{blue} ✍️`When there is a load, it gets discharged through the load and the voltage across it begins to fall. In the next half-cycle of rectified output it again gets charged to the peak value (Fig. 14.20).

`color{blue} ✍️`The rate of fall of the voltage across the capacitor depends upon the inverse product of capacitor C and the effective resistance `R_L` used in the circuit and is called the time constant.

`color{blue} ✍️`To make the time constant large value of C should be large. So capacitor input filters use large capacitors. The output voltage obtained by using capacitor input filter is nearer to the peak voltage of the rectified voltage. This type of filter is most widely used in power supplies.


`color{blue} ✍️`In the section, we shall discuss some devices which are basically junction diodes but are developed for different applications.

`color{brown}bbul("Zener diode")`
`color{blue} ✍️`It is a special purpose semiconductor diode, named after its inventor C. Zener. It is designed to operate under reverse bias in the breakdown region and used as a voltage regulator. The symbol for Zener diode is shown in Fig. 14.21(a).

`color{blue} ✍️`Zener diode is fabricated by heavily doping both p-, and n- sides of the junction. Due to this, depletion region formed is very thin `(<10^–6 m)` and the electric field of the junction is extremely high `(~5×106 V//m)` even for a small reverse bias voltage of about 5V.

`color{blue} ✍️`The I-V characteristics of a Zener diode is shown in Fig. 14.21(b). It is seen that when the applied reverse bias voltage(V) reaches the breakdown voltage `(V_z)` of the Zener diode, there is a large change in the current.

`color{brown} {"Note"}` that after the breakdown voltage `V_z`, a large change in the current can be produced by almost insignificant change in the reverse bias voltage. In other words, Zener voltage remains constant, even though current through the Zener diode varies over a wide range. This property of the Zener diode is used for regulating supply voltages so that they are constant.

`color{blue} ✍️`Let us understand how reverse current suddenly increases at the breakdown voltage. We know that reverse current is due to the flow of electrons (minority carriers) from `p -> n` and holes from `n -> p.`

`color{blue} ✍️`As the reverse bias voltage is increased, the electric field at the junction becomes significant. When the reverse bias voltage `V = V_z,` then the electric field strength is high enough to pull valence electrons from the host atoms on the p-side which are accelerated to n-side. These electrons account for high current observed at the breakdown.

`color{blue} ✍️`The emission of electrons from the host atoms due to the high electric field is known as internal field emission or field ionisation. The electric field required for field ionisation is of the order of `10^6 V//m.`

`color{brown} bbul("Zener diode as a voltage regulator)"`
`color{blue} ✍️`We know that when the ac input voltage of a rectifier fluctuates, its rectified output also fluctuates. To get a constant dc voltage from the dc unregulated output of a rectifier, we use a Zener diode.
The circuit diagram of a voltage regulator using a Zener diode is shown in Fig. 14.22.

`color{blue} ✍️`The unregulated dc voltage (filtered output of a rectifier) is connected to the Zener diode through a series resistance Rs such that the Zener diode is reverse biased. If the input voltage increases, the current through Rs and Zener diode also increases.

`color{blue} ✍️`This increases the voltage drop across `R_s` without any change in the voltage across the Zener diode. This is because in the breakdown region, Zener voltage remains constant even though the current through the Zener diode changes.

`color{blue} ✍️`Similarly, if the input voltage decreases, the current through `R_s` and Zener diode also decreases. The voltage drop across `R_s` decreases without any change in the voltage across the Zener diode.

`color{blue} ✍️`Thus any increase/ decrease in the input voltage results in, increase/ decrease of the voltage drop across `R_s` without any change in voltage across the Zener diode. Thus the Zener diode acts as a voltage regulator. We have to select the Zener diode according to the required output voltage and accordingly the series resistance `R_s.`
Q 3169380215

In a Zener regulated power supply a Zener diode with `V_Z = 6.0 V` is used for regulation. The load current is to be 4.0 mA and the unregulated input is 10.0 V. What should be the value of series resistor `R_S` ?
Class 12 Chapter 14 Example 5

The value of RS should be such that the current through the Zener
diode is much larger than the load current. This is to have good load
regulation. Choose Zener current as five times the load current, i.e.,
`I_Z = 20 mA`. The total current through `R_S`
is, therefore, 24 mA. The
voltage dr op across RS is 10.0 – 6.0 = 4.0 V. This gives
`RS = 4.0V//(24 × 10^–3) A = 167 Omega`. The nearest value of carbon resistor
is `150 Omega`. So, a series resistor of `150 Omega` is appropriate. Note that slight
variation in the value of the resistor does not matter, what is important
is that the current `I_Z` should be sufficiently larger than `I_L`

Optoelectronic junction devices

`color{blue} ✍️`We have seen so far, how a semiconductor diode behaves under applied electrical inputs. In this section, we learn about semiconductor diodes in which carriers are generated by photons (photo-excitation). All these devices are called optoelectronic devices.

`color{blue} ✍️`We shall study the functioning of the following optoelectronic devices:
`color{blue} {(i)}` Photodiodes used for detecting optical signal (photodetectors).
`color{blue} {(ii)}` Light emitting diodes (LED) which convert electrical energy into light.
`color{blue} {(iii)}` Photovoltaic devices which convert optical radiation into electricity (solar cells).

`color{brown}bbul("(i) Photodiode")`
`color{blue} ✍️`A Photodiode is again a special purpose p-n junction diode fabricated with a transparent window to allow light to fall on the diode. It is operated under reverse bias. When the photodiode is illuminated with light (photons) with energy `(h_n)` greater than the energy gap `(E_g)` of the semiconductor, then electron-hole pairs are generated due to the absorption of photons.

`color{blue} ✍️`The diode is fabricated such that the generation of e-h pairs takes place in or near the depletion region of the diode. Due to electric field of the junction, electrons and holes are separated before they recombine.

`color{blue} ✍️`The direction of the electric field is such that electrons reach n-side and holes reach p-side. Electrons are collected on n-side and holes are collected on p-side giving rise to an emf. When an external load is connected, current flows. The magnitude of the photocurrent depends on the intensity of incident light (photocurrent is proportional to incident light intensity).

`color{blue} ✍️`It is easier to observe the change in the current with change in the light intensity, if a reverse bias is applied. Thus photodiode can be used as a photodetector to detect optical signals. The circuit diagram used for the measurement of I-V characteristics of a photodiode is shown in Fig. 14.23(a) and a typical I-V characteristics in Fig. 14.23(b).

Q 3189380217

The current in the forward bias is known to be more (~mA) than the current in the reverse bias (~μA). What is the reason then to operate the photodiodes in reverse bias?
Class 12 Chapter 14 Example 6

Consider the case of an n-type semiconductor. Obviously, the majority carrier density (n) is considerably larger than the minority hole density p (i.e., n >> p). On illumination, let the excess electrons and holes generated be `Deltan` and `Deltap,` respectively:
`n' = n + Deltan`
`p' = p + Deltap`

Here n' and p' are the electron and hole concentrations* at any particular illumination and n and p are carriers concentration when there is no illumination. Remember `Deltan = Deltap` and `n >> p.` Hence, the fractional change in the majority carriers (i.e., `Deltan//n`) would be much less than that in the minority carriers (i.e., `Deltap//p`). In general, we can state that the fractional change due to the photo-effects on the minority carrier dominated reverse bias current is more easily measurable than the fractional change in the forward bias current. Hence, photodiodes are preferably used in the reverse bias condition for measuring light intensity.

Light emitting diode (LED)

`color{blue} ✍️`It is a heavily doped p-n junction which under forward bias emits spontaneous radiation. The diode is encapsulated with a transparent cover so that emitted light can come out.

`color{blue} ✍️`When the diode is forward biased, electrons are sent from `n -> p` (where they are minority carriers) and holes are sent from `p -> n` (where they are minority carriers). At the junction boundary the concentration of minority carriers increases compared to the equilibrium concentration (i.e., when there is no bias).

`color{blue} ✍️`Thus at the junction boundary on either side of the junction, excess minority carriers are there which recombine with majority carriers near the junction. On recombination, the energy is released in the form of photons. Photons with energy equal to or slightly less than the band gap are emitted.

`color{blue} ✍️`When the forward current of the diode is small, the intensity of light emitted is small. As the forward current increases, intensity of light increases and reaches a maximum. Further increase in the forward current results in decrease of light intensity. LEDs are biased such that the light emitting efficiency is maximum.

`color{blue} ✍️`The V-I characteristics of a LED is similar to that of a Si junction diode. But the threshold voltages are much higher and slightly different for each colour. The reverse breakdown voltages of LEDs are very low, typically around 5V. So care should be taken that high reverse voltages do not appear across them.

`color{blue} ✍️`LEDs that can emit red, yellow, orange, green and blue light are commercially available. The semiconductor used for fabrication of visible LEDs must at least have a band gap of 1.8 eV (spectral range of visible light is from about `0.4 μm` to `0.7 μm`, i.e., from about `3 eV` to `1.8 eV`).

`color{blue} ✍️`The compound semiconductor Gallium Arsenide – Phosphide `(GaAs_(1–x)P_x)` is used for making LEDs of different colours. `GaAs_(0.6) P_(0.4) (Eg ~ 1.9 eV)` is used for red LED. GaAs `(Eg ~ 1.4 eV)` is used for making infrared LED. These LEDs find extensive use in remote controls, burglar alarm systems, optical communication, etc. Extensive research is being done for developing white LEDs which can replace incandescent lamps.

`color{blue} {(i)}` Low operational voltage and less power.
`color{blue} {(ii)}` Fast action and no warm-up time required.
`color{blue} {(iii)}` The bandwidth of emitted light is `100 Å` to `500 Å` or in other words it is nearly (but not exactly) monochromatic.
`color{blue} {(iv)}` Long life and ruggedness.
`color{blue} {(v) }` Fast on-off switching capability.

Solar cell

`color{blue} ✍️`A solar cell is basically a p-n junction which generates emf when solar radiation falls on the p-n junction. It works on the same principle (photovoltaic effect) as the photodiode, except that no external bias is applied and the junction area is kept much larger for solar radiation to be incident because we are interested in more power.
A simple p-n junction solar cell is shown in Fig. 14.24.

`color{blue} ✍️`A p-Si wafer of about `300 μm` is taken over which a thin layer `(~0.3 μm)` of n-Si is grown on one-side by diffusion process. The other side of p-Si is coated with a metal (back contact).

`color{blue} ✍️`On the top of n-Si layer, metal finger electrode (or metallic grid) is deposited. This acts as a front contact. The metallic grid occupies only a very small fraction of the cell area `(<15%)` so that light can be incident on the cell from the top.

`color{blue} ✍️`The generation of emf by a solar cell, when light falls on, it is due to the following three basic processes: generation, separation and collection—

`color{blue} {(i)}` generation of e-h pairs due to light (with `hv > E_g` ) close to the junction; (ii) separation of electrons and holes due to electric field of the depletion region. Electrons are swept to n-side and holes to p-side;
`color{blue} {(iii)}` the electrons reaching the n-side are collected by the front contact and holes reaching p-side are collected by the back contact. Thus p-side becomes positive and n-side becomes negative giving rise to photovoltage.
the Fig. 14.25(a) a photocurrent `I_L` flows through the load. A typical `I-V` characteristics of a solar cell is shown in the Fig. 14.25(b).

`color{brown} {"Note"}` that the `I – V` characteristics of solar cell is drawn in the fourth quadrant of the coordinate axes. This is because a solar cell does not draw current but supplies the same to the load.

`color{blue} ✍️`Semiconductors with band gap close to `1.5 eV` are ideal materials for solar cell fabrication. Solar cells are made with semiconductors `color{purple}((E_g = 1.43 eV), CdTe (E_g = 1.45 eV), CuInSe_2 (E_g = 1.04 eV),)` etc.

`color{blue} ✍️`The important criteria for the selection of alike `color{purple}(Si (E_g = 1.1 eV),)` GaAs material for solar cell fabrication are (i) band gap `color{purple}((~1.0 "to" 1.8 eV),)` (ii) high optical absorption `(~104 cm^(–1)),` (iii)electrical conductivity, (iv) availability of the raw material, and (v) cost. Note that sunlight is not always required for a solar cell. Any light with photon energies greater than the bandgap will do.

`color{blue} ✍️`Solar cells are used to power electronic devices in satellites and space vehicles and also as power supply to some calculators. Production of low-cost photovoltaic cells for large-scale solar energy is a topic for research.
Q 3109380218

Why are Si and GaAs are preferred materials for solar cells?
Class 12 Chapter 14 Example 7

The solar radiation spectrum received by us is shown in Fig. 14.26.
The maxima is near `1.5 eV.` For photo-excitation, `hv > E_g`. Hence, semiconductor with band gap ~1.5 eV or lower is likely to give better solar conversion efficiency. Silicon has `E_g ~ 1.1 eV` while for GaAs it is `~1.53 eV.` In fact, GaAs is better (in spite of its higher band gap) than Si because of its relatively higher absorption coefficient. If we choose materials like CdS or CdSe `(E_g ~ 2.4 eV),` we can use only the high energy component of the solar energy for photo-conversion and a significant part of energy will be of no use. The question arises: why we do not use material like `PbS (E_g ~ 0.4 eV)` which satisfy the condition `hv > E_g` for n maxima corresponding to the solar radiation spectra? If we do so, most of the solar radiation will be absorbed on the top-layer of solar cell and will not reach in or near the depletion region. For effective electron-hole separation, due to the junction field, we want the photo-generation to occur in the junction region only.