Notes on Semi-Conductor Physics and Operating Silicon Photo-Diodes Emmett J. Ientilucci rev

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1 Notes on Semi-Conductor Physics and Operating Silicon Photo-Diodes Emmett J. Ientilucci rev INTRODUCITON This handout talks about how we dope silicon to create n- and p-type semiconductors, to the level pertinent in this class. An entire course can be devoted to this subject matter. We then talk about how we put these semiconductors together to create a pn junction. The simplest device that incorporates a pn-junction is called a diode. A light sensitive variant of the diode is called a photo-diode. Lastly, there is a discussion on how we amplify the output of a diode with a device called an operational amplifier. 2 SILICON Carbon, silicon and germanium (germanium, like silicon, is also a semiconductor) have a unique property in their electron structure, each has four electrons in its outer orbital. For silicon the orbital configuration is, Si: 1s 2 2s 2 2p 6 3s 2 3p 2 This is seen graphically in Figure 1. Figure 1 Shell configuration for silicon. The third orbital can hold up to 8 electrons but only 4 are in the valance band. This configuration allows silicon, as well as carbon and germanium, to form nice crystals. The four electrons form perfect covalent bonds with four neighboring atoms, creating a lattice (see Figure 2). In carbon, we know the crystalline form as diamond. In silicon, the crystalline form is a silvery, metalliclooking substance. 1

2 Figure 2 In a silicon lattice, all silicon atoms bond perfectly to four neighbors, leaving no free electrons to conduct electric current. This makes a silicon crystal an insulator rather than a conductor Metals tend to be good conductors of electricity because they usually have free electrons that can move easily between atoms, and electricity involves the flow of electrons. While silicon crystals look metallic, they are not, in fact, metals. All of the outer electrons in a silicon crystal are involved in perfect covalent bonds, so they can't move around. A pure silicon crystal is nearly an insulator hence, very little electricity will flow through it. 3 DOPING SILICON You can change the behavior of silicon and turn it into a conductor by doping it. In doping, you mix a small amount of an impurity into the silicon crystal. There are two types of impurities: N-type - In n-type doping, phosphorus (P) or arsenic (As) is added to the silicon in small quantities. Phosphorus and arsenic each have five outer electrons, so they're out of place when they get into the silicon lattice (see Figure 3). The fifth electron has nothing to bond to, so it's free to move around. It takes only a very small quantity of the impurity to create enough free electrons to allow an electric current to flow through the silicon. n-type silicon is a good conductor. Electrons have a negative charge, hence the name n- type. P-type - In p-type doping, boron (B) or gallium (Ga) is the dopant. Boron and gallium each have only three outer electrons (see Figure 3). When mixed into the silicon lattice, they form holes in the lattice where a silicon electron has nothing to bond to. The absence of an electron creates the effect of a positive charge, hence the name p-type. Holes can conduct current and are the majority carrier in this type of material. A hole happily accepts an electron from a neighbor, moving the hole over a space. p-type silicon is a good conductor. 2

3 (a) (b) Figure 3 (a) N-type doping with phosphorus showing an extra electron in the lattice and (b) doping with boron showing the creation of a hole. A minute amount of either n-type or p-type doping turns a silicon crystal from a good insulator into a viable (but not great) conductor. Hence the name semiconductor. N-type and p-type silicon are not that amazing by themselves; but when you put them together, you get some very interesting behavior at the junction. One such device that is created when p- and n-type silicon are brought together is called a diode. We will talk about this device and its variants later. 4 FORMING A PN JUNCTION A pn-junction is formed by combining p- and n-type semiconductors. When combined, a diffusion gradient is created. That is, an unevenness in the distribution of electrons and holes. We have a huge concentration of holes on the left side, with few electrons, and a huge concentration of electrons on the right side, with few holes. It only makes sense that the holes are going to start to diffuse from the p region into the n region, and the electrons will diffuse from the n region into the p region (see Figure 4.) Figure 4 When p- and n-type semiconductors are combined, a diffusion gradient is created. If we leave the sample for a while, the holes (diffusing to the right) and electrons (diffusing to the left) will eventually disperse such that they ve spread themselves evenly throughout the material, creating a single, uniform sample, right? Wrong. Let s take a look at the process one step at a time. We ll look at the n-type side first: When we attach the p-type region, the electrons, which are in extremely heavy concentration in the n-region will want to diffuse, or spread out into the p region. And they do. But consider what happens when the first electron leaves the n-region: we now have a charge imbalance. That free electron that diffused into the p-region left behind its donor atom, a donor atom with fifteen protons (phosphorus has 15 protons, for example), and now, only fourteen electrons. That donor atom now has a positive charge. Every other electron that leaves the n-region will likewise leave behind another positively charged acceptor ion (see Figure 5). 3

4 Figure 5 An electron diffuses from the n- to p- region, leaving behind a positively-charged donor ion. As more and more electrons leave, more and more positive charge is accumulated near the junction. As we all know, opposite charges attract, and so that immense positive charge begins to pull at the electrons. Like a powerful magnet, the positive ions start to haul some of the electrons, against their will to diffuse, back into the n-region. This is called electron drift (see Figure 6). Figure 6 As electrons diffuse into the p-type region, the positively charged ions left behind act to pull them back, causing an electron drift current in the opposite direction. Eventually, an equilibrium will be reached whereby electrons are diffusing out of the n region, and drifting (pulled by the huge positive charge left behind) back in at exactly the same rate. The result is an apparent balance of electrons outside the n region. In other words, the electric field caused by the positive ions left behind prevents all of the electrons from diffusing out of the n region. The majority stays put; only a few are able to diffuse out at any given moment before the field strength becomes so strong that they re pulled back. The exact same effect is observed if we consider the p-type side. The positively charged holes, as they diffuse out of the p region, leave behind negatively charged acceptor ions. As more and more holes leave, the amount of negative charge increases correspondingly, and serves to tug on the holes, pulling them back toward the p region. An equilibrium will again be reached when the rate at while holes diffuse out becomes equal to the rate at which they re pulled back in (see Figure 7). Figure 7 Hole drift and diffusion currents. 4.1 The Junction at Equilibrium (and Room Temperature) When we combine the two identical, but opposite effects in the form of a pn junction, we obtain something that looks like that of Figure 8. 4

5 Figure 8 As electron and hole drift and diffusion currents come into equilibrium, a region centered around the junction is formed known as the depletion region. Note the directions of the particle flow marked in Figure 8. Electrons diffuse from the n region into the p region, but the electric field causes them to drift (or rather, be pulled) back into the n region. Conversely, holes diffuse from the p into the n region, but the same electric field causes them to drift back into the p region. At equilibrium we have an electric field E, and an area void of moving charge or recombination. The area from which electrons and holes diffuse into the opposing material, leaving behind charged donor and acceptor atoms, or the area void of moving charge, is known as the depletion region. For the purposes of our review, we shall say that absolutely no recombination occurs within the depletion region. This makes sense, if we look at the image above. Consider an electron that diffuses out of the n region. When it enters the p region, it is met with a layer of negatively charged ions, and no holes (they all diffused into the n region). So there s nothing for the electron to recombine with. Instead, it must wait until it passes through the depletion region, and into the p-type region, where it is met with a huge concentration of holes, and can recombine. That is, outside the depletion region this is recombination. The same holds true for holes; a hole that diffuses into the n region is met immediately with a region devoid of electrons, and full of positive ions. It can t recombine, it must wait until it reaches the n-type area, with its abundance of free electrons, to do so. Thus we see that we can have two types of current flow across the junction. Because opposite charges are left on either side of the depletion region (positive left on the n side, and negative on the p side), the electric field lines all point in the same direction, n-side to p-side (see Figure 9). In other words, the field lines point from the positive, to the negative the electric fields from each side have combined to form a very strong, concentrated electric field within the depletion region. Figure 9 An electric field is established inside the depletion region, as noted by the arrows. Both the donor and acceptor ions left behind contribute to the strength of the field. Something very interesting takes place here. Remember what we have when there s an electric field over a region in space? We have a voltage. In fact, if we were to stick a meter on either end of our sample above, we would see that the p-type side is at a higher voltage than the n-type side. The diffusion of electrons and holes has resulted in a strong electric field, which means there s a voltage across our sample. This is known as the built-in voltage or contact potential, and can range from 0.1 to 0.8V for most junctions we will deal with. It is important to note, however, that the voltage differential occurs only in the depletion region. The rest of the n- and p- type material has no voltage. If we were to plot the voltage of our sample, it would look something like that of Figure 10. 5

6 Figure 10 Where there's an electric field, there's a voltage difference, and here we see that the internal electric field causes a voltage differential across the depletion region. The p-type region is at a certain voltage, and there s a constant increase in voltage across the depletion region due to the internal electric field (contact potential). As a result, the p-type side is at a noticeably higher voltage than the n-type side. (Remember that voltage is a potential, and is relative, so the absolute values of the voltages are not of consequence, just the difference between them. In other words, we could say the n-type side is at 10.0V, while the p-type side is at 10.7V. It would mean the exact same thing.) Now, our pn junction, as it sits there, has a very interesting property: it does not conduct. The p-type sample, on its own, conducted, as did the n-type sample, but when we combined them and allowed this internal diffusion/drift equilibrium to form, we would discover that the sample no longer allows current to pass. If we have some potential difference across the depletion region, then the bandgaps must be at a different levels on either side or offset from one another by the amount related to the contact potential. This is precisely the case. The built-in voltage or contact potential of the junction essentially drives the bandgaps apart, so that they look like that of the energy band diagram in Figure 11. Remember, the energy band diagram can tell us something about the amount of energy required to promote an electron from the valance band to the conduction band, where they can move freely (i.e., for conduction). Figure 11 The voltage differential means that the bandgaps have now been pushed apart, due to the internal electric field. Now think of a charge carrier an electron, say in the n-type region. Current is the movement of charge carriers, so for the sample to conduct, that electron would need to be able to flow across the depletion region, and into the p-type region. But the depletion region contains a very strong electric field which forces the bandgaps apart. The electrons are stuck in a lower energy level, and lack sufficient energy to break through the depletion region. Most students find it easiest to visualize this as a hill: the established built-in voltage causes a bandgap separation that acts like a hill which, in order to cross, the electron would have to climb (see Figure 12). Most of the electrons simply do not have the energy to climb the hill, therefore no charge carriers can cross the depletion region, so the sample cannot conduct. 6

7 Figure 12 The difference in the bandgaps acts like a 'hill' that electrons (or holes) must climb if they wish to cross the depletion region to aid in conduction. The same principle applies to holes attempting to move from the p- to n-type region; they re held back by the energy difference caused by the electric field. Electrons will not move in the other direction (from the p- to n-region) simply because their concentration is so low in the p-type area, and so high in the n-type area. It would be like the cream in your coffee mystically confining itself to one area. Again, the same holds true for holes in the opposite direction. So, all of a sudden, we now have a useless, non-conductive block of wood again, right? Not quite. Suppose we wanted to make this thing conduct. We might try to give the electrons more energy, so that they can make it up the hill; a logical, brute force solution. Or we can think outside the box remove the hill. 4.2 Forward Biasing the Junction Suppose I connect my p-n junction to a 0.5 volt battery. I ll connect the positive terminal to the p-side, and the negative terminal to the n-side. The battery forces a more positive potential on the p-type side, which acts to lower its energy relative to the n-side (see Figure 13). In other words, the applied voltage will act against the built-in voltage, and act to compress the bands back together. This is called forward biasing the junction (see Figure 13). P-side N-side Figure 13 A positive voltage applied to the p-type side acts to decrease the difference in the bandgaps. By applying 0.5V to the p-type side, we ve forward biased our junction, and effectively cancelled out 0.5V of the built-in voltage, leaving only 0.2V. The hill is that much smaller, but we re not quite there yet. The magic happens when we apply a voltage equal to, or greater than the built-in voltage. Watch what happens if we connect a 0.8V battery. 7

8 The flood gates are open, and electrons start to pour across the barrier in huge quantities (see Figure 14 and Figure 15). Not only are they diffusing across the depletion region at a high rate, but now that the electric field is reversed, they re also being accelerated across. Because there s such a high concentration of electrons in the n-type region, the diffusion currents are extremely strong, and electrons flow at an enormous rate (i.e., large current). This can be seen in quadrant I of Figure 16. Essentially, the depletion region keeps narrowing until the threshold voltage (say 0.7V) is met, at which time the depletion region disappears. Holes do the same, in the opposite direction, of course. The current through the sample will increase exponentially as the voltage (forward biasing) increases; so fast, in fact, that if there is no external circuit in place to control the flow (a resistance), the current would increase so much that the junction would burn and destroy itself. Essentially, we now have a device that, if subjected to any voltage under 0.7V, will not conduct, but once exposed to greater than 0.7V, will conduct like crazy. P-side N-side Figure 14 When a strong enough forward bias is applied, the bandgaps level out, effectively cancelling out the internal electric field (i.e., no space charge), and allowing the diffusion currents to take over. Conduction is accelerated at this point. Figure 15 Forward biasing the p-n junction drives holes to the junction from the p-type material (sometimes called hole current flow) and electrons to the junction from the n-type material (sometimes called electron current flow). At the junction the electrons and holes combine so that a continuous current can be maintained. 8

9 Figure 16 Current-voltage relationship of a p-n junction. In quadrant I we can see that once the electric field is reversed, due to forward biasing, the electrons are actually accelerated across the junction thus producing a large amount of current. In quadrant III, reverse biasing initially causes a small amount of leakage. However, when enough voltage is applied, the device will function in such a way that it will conduct current. 4.3 Reverse Biasing the Junction What if we apply a negative voltage to the junction? Applying a negative voltage to the p-type side will have the opposite effect of forward biasing. The bands will be pulled further apart, resisting conduction. The depletion region effectively gets larger. This is known, unsurprisingly, as reverse biasing (see Figure 17). The amount of current produced for a given applied voltage for this mode of operation can be seen in quadrent III of Figure 16. A real p-n junction in this mode lets perhaps 10 microamps through. Theoretically, we could apply an infinite negative voltage to the p-side, and the device would not conduct. In fact, after a certain degree of reverse bias, the junction will go into what's known as breakdown (see Figure 16). This typically occurs at voltages in the neighborhood of 250V (reversed biased). Figure 17 The application of a reverse voltage to the p-n junction will cause a transient current to flow as both electrons and holes are pulled away from the junction. When the potential formed by the widened depletion layer equals the applied voltage, the current will cease except for the small thermal current. So basically we now have a device that conducts only in one direction, and only after a certain voltage. This is a diode, and its practical uses are vast. It doesn t take a Ph.D to realize the usefulness of a device that s essentially a current switch, flowing only in one direction, and that s essentially always on or off, never in between. Apply a certain voltage across it, and the gate is open; otherwise it s shut. This simple 9

10 structure has allowed the design of hundreds of devices including the photodiode which we will talk about in the next section. 4.4 Summary A p-n junction is the combination of a p- and n-type material. When combined, electrons diffuse from the n- to the p-type region, and holes visa versa. When they depart, the electrons leave behind positively charged donor ions. The holes likewise leave negative acceptor ions. The positively and negatively charged ions cause an electric field to form. The field acts against diffusion currents to pull the electrons and holes back to their original regions. These are called drift currents. Eventually, an equilibrium is reached when the diffusion and drift currents are exactly equal. The electric field that now exists, however, establishes a built-in voltage, which acts to drive the energy bands of the two halves apart. The difference in band energy levels makes it extremely difficult for charge carriers to cross the depletion region, effectively rendering the sample non-conductive. Applying a positive voltage to the p-type side, known as forward biasing, pushes the bands back together by overpowering the internal electric field. Once a voltage equal to the built-in voltage is applied, the junction starts to conduct very rapidly. If no external control (resistance) is present to slow the current flow, the junction will conduct so much that it overheats and burns. Conversely, we can reverse the polarity of the applied power supply to widen the depletion region. This structure is called a diode, and its uses in modern devices are vast. 5 DIODE A diode is the simplest possible semiconductor device. The universal symbol for a diode can be seen in Figure 18. The p-type end is also called the anode while the n-type end is called the cathode. A diode allows current to flow in one direction but not the other, as explained earlier. You may have seen turnstiles at a stadium or a subway station that let people go through in only one direction. A diode is a one-way turnstile for electrons. ( e- flow under forward bias ) Figure 18 Schematic symbol for a diode showing the p-type (anode) and n-type (cathode) ends. Diodes can be used in a number of ways. For example, a device that uses batteries often contains a diode that protects the device if you insert the batteries backward. The diode simply blocks any current from leaving the battery if it is reversed. This can protect the sensitive electronics in the device. 10

11 6 PHOTO-DIODE (Interaction of Light and P-N Junction) A photodiode is simply a light sensitive diode where the resistance (or amount of current generated) of the device changes as a function of illumination. With out applying a bias (forward or reverse) we can revisit our energy band diagram for the p-n junction and observe its behavior as a function of incident light energy. This can be seen in Figure 19. If the light energy is greater than the band gap energy Eg, the electrons are pulled up into the conduction band, leaving holes in their place in the valence band. These electron-hole pairs occur throughout the p-layer, depletion layer and n-layer materials. In the depletion layer, however, the electric field (acting against electron diffusion, for example) accelerates these electrons toward the n-layer and the holes toward the p-layer. Of the electron-hole pairs generated in the n-layer, the electrons, along with electrons that have arrived from the p-layer, are left in the n-layer conduction band. The holes at this time are being diffused through the n-layer up to the depletion layer while being accelerated, and collected in the p-layer valence band. In this manner, electron-hole pairs which are generated in proportion to the amount of incident light are collected in the n- and p-layers. This results in a positive charge in the p-layer and a negative charge in the n-layer. If an external circuit is connected between the p- and n-layers, electrons will flow away from the n-layer, and holes will flow away from the p-layer toward the opposite respective electrodes. Again, these electrons and holes that generate a current flow in a semiconductor are called the carriers. This phenomena is the basis for a solar cell and is called the photo-voltaic effect. The total current due to the flow of electrons (and holes) is proportional to the amount of incident radiation. Figure 19 P-N junction energy diagram showing its behavior with incident illumination, which typically enters from the p-side of the material. The construction of such a device is illustrated in Figure 20. The important regions are the active area (ptype material), the depletion region, and the n-type region, all of which have been reviewed in previous sections. 11

12 Figure 20 Planar diffused silicon photodiode. The current-voltage characteristic of a photodiode with no incident light is similar to the standard diode discussed earlier. However, when incident flux is present the amount of overall current generated increases. This can be seen in Figure 21 for various levels of incident flux, P. Again, for a given incident flux level, we can apply a forward, reverse, or no-bias to the detector. Figure 21 Characteristic I-V curves of a photodiode. P 0 -P 2 represents different light levels. 6.1 Biasing the Photo-diode Biasing the photo-diode has the exact same effect as biasing our diode, as previously described. After all, they are effectively the same device. Typically, however, the photodiode is operated in a zero bias mode (i.e., no forward or reverse bias applied). 6.2 Spectral Sensitivity and Penetration Depth In a substrate, different energy photons can get absorbed at different depths in the material. The depth at which this occurs, for a given material, is called the penetration depth. A plot of this depth for various 12

13 materials can be seen in Figure 22. For silicon, the band gap energy at room temperature is Eg = 1.12 ev, which equals 1.1 um, hence the cutoff for silicon. Figure 22 Penetration depth (or absorption coefficient) for various types of materials. 7 AMPLIFIERS One method of measuring a photodiodes output is to simply measure the voltage across a resistor connected to the photodiodes output. A resistor used in this scheme is sometimes called a load resistor (see Figure 23). Since the photodiode is a variable current source, we can measure the change in voltage with a meter. A better scheme, however, is to use an operational amplifier. V out I s R L V out = I s x R L Figure 23 Measuring the voltage drop (due to the photodiode) across a load resistor. An op-amp or (operational amplifier) is simply an integrated circuit that performs amplification, among other things. The standard symbol or schematic notation for an op-amp can be seen in Figure 24. Here we see two inputs, an output and two connections to power the device. 13

14 Figure 24 Standard op-amp symbol showing inputs, output, and power requirements. A better configuration for an op-amp is to place a resistor, usually called a feedback resistor, from the input to the output (see Figure 25). This produces lots of gain, as a function of the resistor size. In this configuration, a current is generated through R 2. The amount of current is simply I 2 =V in /R 2. Now, the input resistance of an op-amp is very high so (almost) all the current is forced to travel through R 1, the feedback resistor. If we fix the resistance of R 2 and make R 1 big, we can get a lot of gain. This is why we will have different values for the feedback resistor in your radiometer circuit. The op-amp in this type of configuration is called a current-to-voltage converter, which it is indeed; it s also sometimes referred to as a transimpedance amplifier, where the gain is proportional to R 1. Figure 25 Op-amp with a feedback resistor connected from (-) input to the output. This configuration produces (negative) gain. 8 PHOTODIODES AND AMPLIFIERS There s a whole class of applications in which this configuration is quite useful and important. An important case is when you need an op-amp to amplify the signal from a sensor, such as a photodiode. In the op-amp example of Figure 25 we generated current by applying an input voltage (V in ) across R 2. Remember Ohms Law states I = V/R. We now can use our photodiode in place of R 2 to generate current proportional to incident flux (see Figure 26). Figure 26 Op-amp configuration that converts current into voltage. This is what a resistor does, but an opamp does it better. 14

15 If you just let the photodiode dump its current out into a resistor, there are two problems. You may be able to achieve large gain but you will have a slow responding device. Similarly, if you want a fast responding device, you will have to suffer with low gain. To avoid this terrible compromise, it's a good idea to feed the photodiode's output current directly into a transimpedance amplifier or current-to-voltage converter, as previously discussed (see Figure 26). In Figure 26 we have not biased the diode itself with an external source, say a battery. That is, one end of the diode is grounded. Again, this is called the photovoltaic mode or zero bias mode of operation. This configuration is preferred when a photodiode is used in low frequency applications (under 350 Hz) and ultra low light level applications. The radiometer constructed in your laboratory will be of this configureation. The photodiode is also sometimes operated with an applied reverse bias. This can greatly improve the speed or response of the device. This configuration is sometimes referred to as the photoconductive mode. The overall frequency improvement is due to an increase in the depletion region width and consequently decrease in junction capacitance. Applying a reverse bias, however, will increase the dark noise. 9 SPECTRAL RESPONSE / RESPONSIVITY AND QUANTUM EFFICIENCY < Future notes > By controlling the thickness of the outer p-layer, substrate n-layer and bottom n + -layer as well as the doping concentration, the spectral response and frequency response can be controlled. 15

16 10 QUESTIONS There is no formal write-up for this lab; however, you are required to provide a detailed explanation of each of the following questions. These will be graded. 1. Why is un-doped silicon not a good conductor? 2. Why don t all the electrons (in n-type material), for example, diffuse into the p-type material when n- and p- type semiconductors are placed together? 3. What is the depletion region in a pn-junction device and why is it important in imaging? 4. Name the two types of current flow in a semiconductor. 5. What are the majority carriers in a P-type semiconductor? 6. What are two types of current flow in semiconductor? 7. In reference to the schematic symbol for a diode, under forward bias, do electrons flow toward or away from the arrow? 8. In order to reverse bias in a PN junction, what terminal of a battery is connected to the P material? 9. What type of bias opposes (weakens) the PN junction barrier? 10. What is the photo-voltaic effect? 11. When a photon enters the depletions region, with no bias applied, and with energy greater than the bandgap, why do the electrons go to the n-region? 12. Why doesn t the electron-hole pair that is generated in the depletion under no-bias, region re-combine? 13. Why do they (e-h pair) separate in the first place? 16