Solar Cell (Photodiode)
A photodiode consists of a p-n junction (Fig. 8.21). If light of sufficiently high energy falls on or near the depleted area, electrons are lifted from the valence band into the conduction band, leaving holes in the valence band. The electrons in the depleted area immediately "roll down" into the n-region, whereas the holes are swept into the p-region. These additional carriers can be measured in an external circuit (photographic exposure meter) or used to generate electrical energy. In order to increase the effective area of the junction, the p-type region is made extremely thin (1 mm) and light is radiated through the p-layer (Fig. 8.21(a)). Since the p-layer is thin, the electric energy must be collected on the front surface, utilizing narrow metal electrodes (e.g., Al) which are arranged in the form of stripes, see Fig. 8.21(b). A single junction, single-crystalline silicon photovoltaic device has an open circuit voltage of approximately 0.6 V and a load voltage around 0.45 V. This performance can be considerably improved by multi-junction solar cells. As an example, Fig. 8.21(c) depicts a three-layer device which yields a load voltage of 2.3 V and an open circuit voltage of 2.66 V at 28°C. For understanding this increase in output voltage, one needs to know that semiconductors absorb the sunlight only in a small energy (wavelength) region which is determined by its bandgap.
Figure 8.21. Solar cells; (a) Side view; the p-region is only about 1 mm thick. (b) Front view. (c) Simplified schematic of a multilayer solar cell.
Stacking various semiconductors with different bandgaps uses the solar spectrum more completely and allows adding the individually obtained voltages. Each of the solar cells is connected to the next by a wide-bandgap tunnel junction (very heavily doped p- and n-layers, see Fig. 8.24). The top solar cell has the widest bandgap and thus, absorbs the green end of the solar spectrum. The photons that have a lesser energy and thus, have not yet been absorbed pass to the next (lower) junction which has a smaller bandgap and are absorbed there to a certain degree etc. Light with energies less than the smallest bandgap is not absorbed at all and cannot contribute to the power output of the solar cell. On the other hand, light with energies greater than the widest bandgap will be indeed absorbed, but this portion of the energy will quickly be lost via thermalization i.e., the created electron/hole pairs lose their energy via phonons (heat). In short, this higher energy is also not available for extracting useful power. Three additional items have to be considered: the semiconductor bandgaps in a multijunction device need to be current matched because the solar cell with the lowest generated current limits the output from the other two junctions. Further, the output voltage is temperature dependent; specifically, the higher the temperature, the lower the voltage. Finally, the doping level of a device also influences its open circuit voltage.
The electron-hole pairs that are created some distance away from the depleted region are generally not separated by the junction field and eventually recombine; they do not contribute to the electric current. However, some electrons or holes which are within a diffusion length from the depleted region drift into this area and thus contribute to the current. In semiconducting materials that contain only a few defects (such as grain boundaries, dislocations, and impurities) the electrons or holes may diffuse up to 200 mm before they get trapped, whereas in semiconducting materials containing a large number of defects the diffusion length decreases to 10 mm. The closer a carrier was created to the p-n boundary, the larger is its chance of contributing to the current (Fig. 8.22).
The thin p-type layer (Fig. 8.21(a)) introduces an internal resistance to the collection current, which reduces the efficiency of the energy conversion. At present, the maximal efficiency of a photovoltaic device, involving a three-layer technology (Fig 8.21(c)) and concentrated sunlight is 41.6%. Production cells always have a lower efficiency i.e. in the 20-25% range for terrestrial applications and about 30% for devices used in space. Current terrestrial concentrator solar cells have a minimum average efficiency at maximum power of 38.5% at 50 W/cm2. The energy needed to produce such a device (including mounting and installation) is recovered in about 6 years when the collector is located in North Africa or Central America. (Installation in central Europe or the northern states of the USA and Canada may double the energy recovery time.) The cost of photovoltaic devices (presently $6-$8 per installed watt) can be reduced by utilizing polycrystalline, less purified, or amorphous silicon, but at the expense of efficiency. As an example, photovoltaics made of commercial, hydrogen-doped amorphous silicon (see Section 9.4) have an efficiency of only 6-8%, but its invested energy for production and mounting is recovered in just 1 year. The efficiency of this device has been enhanced to 12% in laboratory experiments.
Figure 8.22. Schematic representation of the contribution of electrons and holes to the photocurrent (I) with respect to the distance x from the p-n junction.
The goal is to produce for terrestrial applications inexpensive solar cells having 20% efficiency or better and a lifetime of about 20 years. The lifetime is reduced when the metal contacts (grids) to the semiconductor corrode. Despite the fact that photovoltaics are still relatively inefficient, their worldwide sale has grown for the past 10 years by more than 15% per year and has reached now the $2 billion mark, while the cost has steadily decreased. The most recent development employs dye-coated titanium dioxide and an electrochemical cell which mimics the role of chlorophyll in photosynthesis.
The photovoltaic cell depicted in Fig. 8.21(a) has one inherent disadvantage: the impinging light has to travel first through the p-type layer (however thin it may be) before it eventually reaches the depleted (active) area. This attenuates its intensity to a certain degree. In addition, the incoming light is somewhat blocked by the metal electrodes, which cover part of the face of the cell. The resulting loss in efficiency is a trade-off for a large surface area (which is often desirable to increase power). For telecommunication applications however, for which high efficiency is more important, a rather ingenious alternative design can be used. Imagine that the light impinges transversely on (or better, along) the depletion layer. For this the beam is channeled-in from the side by a light-conducting device such as an optical fiber or a wave guide (Fig. 8.23). In order to increase the effective area, i.e., the width, W, of the depletion region, the photodiode is strongly reverse-biased and the doping of one of the semiconductors is comparatively light. (For details refer to Fig. 8.19(a).) The efficiency is further maximized by increasing the length of the depletion layer, L. This device yields almost 100% quantum efficiency.
The quantum efficiency can be calculated by the equation
where a is a parameter that determines the degree of photon absorption by the electrons (a is defined in (10.22)).
Figure 8.23. Schematic of a transverse-type photodiode that is connected to a light-carrying medium such as an optical fiber or a waveguide (L « 100 nm).
As an example, for a GaAs photodiode the n-region is lightly doped because the electron mobility in GaAs is much larger than the hole mobility, see topic 4. This shifts the depleted region towards the n-side. On the other hand, the p-region is heavily doped (and thin) in order to minimize its resistance.
The incoming light that is modulated by information (such as the spoken word in telecommunications) modulates, in turn, the electrical current in the photodiode. This transforms a signal which is transmitted by light into an electrical signal. We shall return to this topic and to other optoelectronic devices in Part III. In particular, organic photovoltaic cells will be extensively discussed in Section 13.8.15 once we have acquired some knowledge about organic semiconductors in topic 9.1.
Avalanche Photodiode
This device is a p-n photodiode that is operated in a high reverse bias mode, i.e., at near-breakdown voltage. The electrons and holes that were created by transitions from the valence band into the conduction band by the incident light are accelerated through the depleted area with a high velocity. As a consequence, they ionize the lattice atoms and generate secondary hole-electron pairs, which, in turn, are accelerated, thus generating even more hole-electron pairs. The result is a photocurrent gain, which may be between 10 and 1000. The avalanche photodiode is ideally suited for low-light-level applications, because of its high signal-to-noise ratio, and for very high frequencies (GHz). It is particularly used for detectors in long-distance, fiber-optics telecommunication systems. See in this context Fig. 8.23.
Tunnel Diode
So far, we have restricted our discussion mostly to the case for which the electrons drift from the n-type to the p-type semiconductor by way of "climbing" a potential barrier. Another electron transfer mechanism is possible, however. If the depleted area is very narrow (approximately 10 nm) and if certain other requirements (see below) are fulfilled, electrons may tunnel through the potential barrier. (See in this context Fig. 4.7, Fig. 8.20(b), and equation (4.39).) Heavy doping (e.g., 1020 impurity atoms per cubic centimeter) yields this condition.
The situation can best be understood by inspecting Fig. 8.24(a), in which a schematic band diagram of a tunnel diode is shown. Because of the high doping level, the Fermi energy extends into the valence band of the p-type semiconductor and into the conduction band of the n-type semiconductor.
Figure 8.24. (a)-(e) Schematic energy band diagrams for highly doped n- and p-type semiconductors (tunnel diode). (a) No bias. (b) Reverse bias. (c) Small forward bias. (d) Medium forward bias. (e) "Normal" forward bias. (f) Voltage-current characteristic for a tunnel diode.
In the equilibrium state, the same amount of electrons is tunneling through the potential barrier in both directions, i.e., no net current flows.
If a small reverse bias is applied to this device (Fig. 8.24(b)), the potential barrier is increased as usual and the Fermi energy, along with the top and bottom of the bands in the p-area, is raised. This creates empty electron states in the conduction band of the n-type semiconductor opposite from filled states in the valence band of the p-type semiconductor. As a consequence, some electrons tunnel from the p-type to the n-type semiconductor, as indicated by an arrow. An increase in the reverse voltage yields an increase in the electron current through the device (see Fig. 8.24(f)).
Let us now consider several forward voltages. A small forward bias (Fig. 8.24(c)) creates just the opposite of that seen in Fig. 8.24(b). Electrons are tunneling through the potential barrier from the conduction band of the n-type semiconductor into empty states of the valence band of the p-type semiconductor. The applied voltage needs to be only several millivolts and it produces a forward current of about one milliamp.
If, however, the voltage is increased to, say, 100 mV, the potential barrier might be decreased so much that, opposite to the filled n-conduction states, no allowed empty states in the p-area are present [Fig. 8.24(d)]. (The area opposite to the filled n-conduction states may be the forbidden band.) In this case, no tunneling takes place. As a consequence of this, the current decreases with increasing forward voltage, as shown in Fig. 8.24(f). We experience a negative current-voltage characteristic.
Finally, if the forward voltage is increased even more, the electrons in the conduction band of the n-type semiconductor obtain enough energy to climb the potential barrier to the p-side just as in a regular p-n junction. As a consequence, the current increases with voltage, just as in Fig. 8.16(a).
Of particular interest is the range in which a negative voltage-current characteristic is experienced. One has to bear in mind that all other electrical devices have a positive voltage-current characteristic, i.e., they dissipate energy. Therefore, if a tunnel diode is connected to properly dimensioned resistors and capacitors, a simple oscillator can be built which does not lose energy because the net resistance is zero. Those devices can oscillate at frequencies up to 1011 cycles per second.
