FIBER OPTICS Prof. R.K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture: 14 Optical Sources Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 1
The external quantum efficiency of a semiconductor material depends on a number of factors. We have already looked into one of those factors in the earlier discussion. However, we shall discuss it in more detail here and also investigate the contribution of all these factors on the overall external quantum efficiency of the semiconductor material. The very first factor (which we already have been introduced to) is the existence of an emission cone for the generated photon due to which it cannot be emitted out of the semiconductor material if it lies outside this cone. This means that all of the generated photons are not emitted out of the semiconductor material and hence there is a reduction in the overall external efficiency of the semiconductor material. Let us now derive an expression for this factor of efficiency. For the derivation, let us assume the photon to be generated at point A in the following figure 14.1. The triangle ABC signifies the emission cone of the generated photons at A. Figure 14.1: Photon generation and Emission Cone The refractive index n s of the semiconductor material is greater than that of the surrounding medium n a. The query, now, is to investigate the number of photons that actually lie inside the emission cone out of the total number of generated photons in the semiconductor material at point. This calculated quantity would be termed as η ext1 in order to signify it as the first factor affecting the external quantum efficiency of the semiconductor material. Let us assume that N photons are generated at point A of the semiconductor material by virtue of N radiative recombinations. The quantity η ext1 can be defined to be the ratio of the solid angle subtended at A by the emission cone to the total solid angle through which the N photons have equal probability to travel. Since the generated photons have equal probabilities to travel along all directions at A, the latter solid angle would correspond to 4π. Hence, ( ) (14.1) ( ) (14.2) Substituting equation 14.2 in 14.1, we can formulate the final expression as: Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 2
( ) (14.3) For a material like GaAs, the value of η ext1 is about 1.93%. This means that, out of every 100 generated photons, only 1-2 photons lie within the emission cone. Also, if we recall, the internal quantum efficiency of GaAs is about 50%, which indicates that out of 100 recombinations, only about 50 are radiative. Thus, to get 1-2 photons in the emission cone a total of 200 electron-hole recombinations have to take place. The second important factor that influences the external quantum efficiency is the partial reflection of the total photon energy at the semiconductor-medium interface in accordance to the boundary condition of refraction at media interface. That means, the photons which lie inside the emission cone are not all emitted out but part of them gets buried back into the semiconductor material due to partial reflection at the material boundary. Here we treat the photon as a wave and in order to calculate this factor, we require to find the reflection and transmission coefficients of the photons at the semiconductor-medium interface. If we assume all the photons to be incident at the semiconductor-medium interface almost normally, the power reflection coefficient Г and the power transmission coefficient τ can be expressed as: ( ) (14.4) ( ) (14.5) The quantity τ is, in fact, the expression for the second factor of external quantum efficiency that we are looking for. Let us denote this factor by η ext2. Hence, the expression for η ext2 is given as: ( ) (14.6) For a material like GaAs which has a refractive index of about 3.6, this quantity comes out to be about 0.68 or 68%. When the photons travel inside the emission cone towards the semiconductor material boundary to get emitted out, there are material absorptions that take place due to the intrinsic nature of the semiconductor material. This fact further reduces the number of available photons for emission. This can be hence considered as third factor influencing the external quantum efficiency and can be denoted by η ext3. Hence, For GaAs, this value of the quantity η ext3 is about 0.7 to 0.8. (14.7) Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 3
The next important factor which has to be taken into account for calculating the external quantum efficiency of the semiconductor material is the actual number of photons that get guided inside the optical fiber. From our earlier discussions, we are already familiar with the fact that only those light rays are launched or accepted into the fiber which lies in the numerical aperture (acceptance cone) cone of the optical fiber. So, the number of the emitted photons which lie inside this cone would get guided into the optical fiber. The region over which the photon emission takes place from the semiconductor material is a hemispherical region over the emission cone on the surface of the semiconductor material. So, the solid angle over which the photons are emitted from the semiconductor material is 2π. The solid angle subtended by the numerical aperture cone of the optical fiber is given as 2π (N.A.) 2. Here, N.A. is the numerical aperture of the optical fiber. A ratio of the above two solid angles would, hence, give the number of emitted photons that are actually guided into the optical fiber. Let us denote this factor of efficiency by η ext4. Hence, ( ) ( ) (14.8) A practical optical fiber, generally, has a numerical aperture ranging from 0.2 to 0.3 and so the above factor of efficiency ranges from 4% to 9%. Equations 14.3, 14.6, 14.7 and 14.8 give the four factors on which the external efficiency of an optical source depends. According to the definition, the product of all these factors determines the total external quantum efficiency of the optical source. Hence: (14.9) If we consider a semiconductor material like GaAs, the value of the External quantum efficiency is given by: This shows that out of 1000 photons generated in GaAs, only one photon is available for optical communication inside the optical fiber. If we include the internal quantum efficiency of GaAs which is about 50%, we see that out of 2000 electronhole recombinations, only 1 photon is available for optical communication inside the optical fiber. Thus GaAs can be said to be highly inefficient semiconductor for use in optical communication systems. The above discussion, thus, conclusively suggests that optical sources like LEDs have large spectral widths which do not allow high data rates and also, they have very low efficiencies. These drawbacks render LEDs to be inappropriate to be used for long-distance optical communication because; a long distance communication requires both- low spectral width and high optical efficiency. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 4
However, LEDs have something that is of interest. LED is a fairly linear device. This means that, the output optical power of the LED is almost linearly proportional to the input electric current into the LED. This is indicated by the characteristic shown in figure 14.2. Figure 14.2: Output characteristic of LED As seen from the above figure, the curve is a straight line. The slope of the line depends on various parameters of the material. This characteristic feature of the LED makes it a useful device for analog modulation because analog modulation requires the use of a linear device. A very simple electrical circuit does the job. Figure 14.3: Modulator circuit using LED The bias voltage maintains the threshold voltage level of the LED and the optical output is then modulated in accordance to the input modulating signal current. Thus the optical output varies linearly with respect to the input modulating signal current and we get a conversion from the electrical domain to the optical domain. In other words, we can modulate the light emitted by the LED, simply be modulating the input current to the LED. However, a very basic question to be investigated is what is the highest possible rate at which the modulation can be carried out? To put the question in a little simpler words- what is the highest rate of variation of the input current that can be successfully responded to by the LED? This rate of variation is, in fact, the frequency of the modulating signal. Hence, the question, essentially, is what is the highest modulating frequency supported by the LED? Although these questions look different, they enquire about the same aspect of the LED. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 5
The answer to the above query can be forwarded in two distinct ways. One approach would be in terms of the electric circuit parameters and the other in terms of the finite carrier recombination life-time. The LED circuitry shown in figure 14.3 above is, in fact, a circuit incorporating a semiconductor p-n junction diode. The semiconductor junction has its characteristic junction capacitance and resistance. This causes the circuit to have a finite electrical time constant τ which is the time constant of the p-n junction. So, the highest frequency of operation of the circuit is the reciprocal of the circuit time-constant and is called the bandwidth of the device. In view of the finite carrier life-time, the electron-hole pairs take a finite amount of time to recombine and generate a photon. So, if a variation of input current occurs within this time, it would not be responded to by the LED and would not be shown at the output. That is, the bandwidth of the device depends on the recombination lifetime of the charge carriers. Let us now investigate the highest modulating rate of the LED and also look for possible ways to alter this rate, preferably increase it to improve the bandwidth of the LED. For the above investigation, let us consider a p-n junction of a semiconductor material with electron density n 0 and hole density p 0 in the depletion region. If we assume r to be the recombination constant then, (14.10) Without any external injected carriers into the semiconductor material, n 0 and p 0 give the density of charge carriers generated thermally in the material due to ambient thermal conditions. Hence at thermal equilibrium, the rate of recombination (given by equation 14.10), without any external injection of carriers, equals the rate of thermal generation of charge carriers. If we now inject electrons and holes in the semiconductor material external such that the electron and hole density change to (n 0 + n) and (p 0 + p), respectively, then the net recombination rate is given by: ( )( ) (14.11) If we assume n= p, then the net rate of recombination can be re-written as: ( ) (14.12) Equation 14.12 gives the net recombination rate of both- electrons and holes inside the semiconductor material at any instant when the electron and hole densities are (n 0 + n) and (p 0 + p), respectively. Therefore, if the equation is rewritten for net recombination rate for electrons, then: ( ) (14.13) Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 6
In equation 14.13, the expression on the left hand side of the equation is the recombination rate of electron. Now, there are two possibilities of carrier injection into the semiconductor- very low injection and very high injection. Let us consider the two cases separately. For very low carrier injection or very low current, n<<(n 0 +p 0 ) and equation 14.13 modifies to: ( ) (14.14) Equation 14.14 is same as equation 13.12, and so, the carrier recombination life-time is given by: ( ) (14.15) As seen from the equation 14.15, the carrier recombination life-time is independent of the external current applied to it. The carrier recombination life-time or in other words, the photon generation life-time depends purely on the intrinsic charge carrier concentration and the recombination rate constant r. For very high carrier injection or high external current, n>>(n 0 +p 0 ) and the equation 14.13 modifies to: ( ) (14.16) In this case, the carrier recombination life-time can be calculated from the first principles. According to the definition of carrier recombination life-time, it is the ratio of the change in carrier density to the rate of change in carrier density. Therefore for high carrier injection densities: ( ) (14.17) The current in the external circuit is proportional to the quantity n. So, for high carrier injection densities, the carrier recombination life-time is inversely proportional to the external current, as seen from equation 14.17. This implies that the device can be switched ON/OFF at a faster rate at high currents. However, at high currents, the heat generated at the junction is high and the life of the device, thus, deteriorates. So, although LED can have good bandwidths at high currents, the life of the LED is uncertain at high currents and there is a possibility of excessive heat generation leading to the burning out of the LED. Let us now see the nature of the current required when the LED is to be used for digital modulation schemes. For a pulse of the digital data, an appropriate current profile has to be pumped into the device so that the LED behaves in accordance to Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 7
the data bits in the modulating signal. This requires the injection of a high current at a transition from digital 0 to a digital 1 so that the switching in the optical power in the LED takes place at almost the same rate as that of the data signal. Once the LED has turned ON, the current may be then allowed to die down because there is now high speed operation required. This strategy would be more clarified with the following diagram: Figure14.4: Current profile for digital modulation in LED The overshoot and undershoot (if necessary) can be calculated from the operating bandwidth required and can be appropriately generated by external circuitry. So, if a current profile shown in figure 14.4 is input to an LED, the output optical pulse would be similar to the data pulse shown in the figure. However, at high bandwidths the life of the LED is uncertain and deteriorates to generation of heat at the p-n junction of the device. From the above discussion we can conclude that, LED has two major drawbacks- low efficiency and large spectral width which make it unsuitable for longdistance optical fiber communication. Due to its isotropic emission nature, LED is more suitable with a multimode mode type of optical fiber which has a large numerical aperture. However, the linear relationship between the input current and the output optical power of the LED makes it suitable to be used in analog optical modulation circuits. For Long distance optical communication, another semiconductor type source is used which is known as the injection LASER diode (IED). This new device is rectified of all the drawbacks of LED and has a very narrow spectral width as well as a high optical efficiency. IED shall be discussed in subsequent section and a comparison shall be made between the two above devices at every characteristic point along the discussion. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 8