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The p-n Junction D1 Head of Experiment: Sergei Popov The following experiment guide is NOT intended to be a step-by-step manual for the experiment but rather provides an overall introduction to the experiment and outlines the important tasks that need to be performed in order to complete the experiment. Additional sources of documentation may need to be researched and consulted during the experiment as well as for the completion of the report. This additional documentation must be cited in the references of the report. RISK ASSESSMENT AND STANDARD OPERATING PROCEDURE 1. PERSON CARRYING OUT ASSESSMENT Name Geoff Green Position Chf Lab Tech Date 18/09/08 2. DESCRIPTION OF ACTIVITY D1 Experiments with P-N Diodes 3. LOCATION Campus SK Building Huxley Room 403 4. HAZARD SUMMARY Accessibility X Mechanical Manual Handling X Hazardous Substances X Electrical X Other X Lone Working Permitted? Yes No Permit-to- Work Required? Yes No 5. PROCEDURE PRECAUTIONS Use of 240v Mains Powered Equipment Isolate Socket using Mains Switch before unplugging or plugging in equipment Accessibility All bags/coats to be kept out of aisles and walkways. Use of Liquid Nitrogen & Vacuum Flask See attached Scheme of Work Use of Hot Plate and Hot Water Avoid direct contact; protect hands and feet; avoid spills and upsets 6. EMERGENCY ACTIONS All present must be aware of the available escape routes and follow instructions in the event of an evacuation LIQUEFIED GAS AND CRYOGENIC SAFETY The main hazards associated with handling cryogenic liquids are – (i) Cold burns. Avoid skin contact with liquid or cold metal. Take sensible precautions such as wearing gloves and eye protection while handling liquids. The skin may be frozen on to coJd surfaces and injury is likely when the skin is pulled away. (ii) Explosion due to overpressure or implosion due to mechanical failure or breakage. Glass dewars must be surrounded by plastic to guard against flying glass. Any closed system must incorporate a pressure relief valve. Blockages can occur in the necks of dewar vessels because of ice or air in a helium dewar. If it is suspected that a high pressure has developed in a piece of apparatus, great care must be taken in venting it as the exhausting gas may still be very cold. (iii) Condensation. Condensed water running down inside cryostats, particularly those with glass dewars, can cause the dewar to crack. Ensure that you can check that the dewars are dry. (iv) Structural problems. Spillage of liquid nitrogen may cause cracking in plastic insulation and the cooling of structural steel may well result in brittle fracture. Pouring liquid nitrogen steadi ly over a single point on the lip of a glass dewar can cause the dewar to shatter. The dewar should be moved from side-to-side all the time the nitrogen is being filled or poured. The evaporation of large quantities of liquid nitrogen or liquid helium or the sublimation of large quantities of carbon dioxide in confined areas may result in displacement of oxygen and the risk of asphyxiation. (v) Chemical explosions due to presence of oxygen. Oxygen from the atmosphere will dissolve in liquid nitrogen up to a concentration of 55%. Therefore "old" liquid nitrogen can contain hazardous concentrations of oxygen. Liquid nitrogen storage and transfer vessels should be loosely stoppered and not left open. Never use rotary pumps to reduce pressure over 'old' nitrogen as the oxygen dissolved has been known to combine explosively with the pump oil. The handling of liquid helium (projects only) requires special techniques and advice should be sought before any experiments are attempted. Third Year Laboratory Diode Experiments Aims The aim of this experiment is to study the technologically important p-n junction, to see if the theory of the device can be verified in practice, and to learn how the diode’s behaviour makes the p-n junction useful in a wide range of device applications. The experiment consists of three parts. In the first part you will study the so-called forward bias behaviour at room temperature and liquid nitrogen temperature of three p-n diodes and three light emitting diodes (LEDs) made from different band-gap type semiconductors. The aim will be to see which diodes obey the Shockley equation, over what bias ranges and at what temperatures. Once you have established the influence of the band-gap energy on the forward current of a p-n junction you can then study how the band-gap affects the wavelength of the LEDs emission. In the second part you will measure the capacitance of two rectifier diodes in reverse bias and, under specific assumptions, measure the "built-in potential difference" and doping level. In the third part you will measure the reverse bias behaviour of two voltage regulator diodes at room temperature and liquid nitrogen temperature to determine the mechanism responsible for breakdown in each particular case. Theory The experiment provides a good opportunity to revise the theory of the p-n junction. The textbook "Hook and Hall" has much of the required theory in Chapters 5 and 6. The more advanced textbook "Sze" goes into the theory in more detail in a chapter devoted to the p-n junction and has a particularly useful summary of the voltage regions in which the Shockley equation breaks down in Fig. 21 on page 91. Since there are multiple editions of Sze’s textbook, the Fig. 21 is also duplicated in the Appendix A of this script. It should be noted, that here we refer to the 2nd edition of Sze’s book published by Wiley. The interactive models can be looked at and would allow to improve understanding of the p-n junction operation; please refer to http://pveducation.org/pvcdrom/ and https://nanohub.org/tools/pntoy Si and Ge are typical semiconductors widely used in electronic devices. Si at room temperature typically has approximately one carrier per 1010 atoms which determines high resistivity of the material. Such a semiconductor is known as intrinsic. Additional elements, dopants, can be introduced to increase conductivity. The doped semiconductor is known as extrinsic. The dopant element creates energy level close to the bandgap edge of the intrinsic material. For n-type dopants, the energy level is very close to the bottom of the intrinsic conduction band and can be typically activated by thermal energy (check the energy needed; can this condition be satisfied at liquid nitrogen temperatures?). The same is true for p-type dopants. However, the dopant levels are typically not included expressly in the band diagrams and just assumed to be parts of the conduction and valence bands. Of particular importance is the boundary between the n-type and p-type regions that form a p-n junction (check the ways the p-n junction can be fabricated). The rectifying behaviour of the p-n junction results from the effect on the electrons energy levels in the junction region as shown in Fig. 1 below. There, the energy levels are shown as a function of position alcross the junction. The relative positions of the levels on the both sides of the junction are determined by the necessity of maintaining a uniform chemical potential ( ). The equilibrium is achieved by a low rate transfer of electrons from the n side to the p side, whereas recombination results in the region with a very few free carriers at the position of the junction known as a depletion layer. Due to the absence of free carriers, unscreened positively and negatively charged ions located in n and p regions respectively create an internal electric field in the depletion layer (Fig. 1a). This in turn results in lowering the electron energy levels on the n side and rising on the p side, as shown in Fig. 1b. The energy difference between the two conduction bands or the two valence bands is known as a potential difference or potential barrier. It prevents electrons’ flow from the n side to the p side and, similarly, holes’ flow from the p side to the n side. An application of the external bias across the p-n junction results in the potential difference and electric current through the junction. If the positive side of the voltage potential is applied to the p region, the junction is said to be forward biased and the potential difference reduces. If the positive side is attached to the n region then the junction is reverse biased and the potential difference increases (How do the band diagrams look like in both these cases?) Figure 1. The electric field in the depletion region (a) and the energy band diagram of a p-n junction in thermal equilibrium. Part 1. It is important to revise the physical assumptions made in deriving the Shockley ideal equation (1) Here the reverse-bias saturation current ( ) is given in terms of the diffusion constant ( ) and diffusion length ( ) of the minority carrier electrons on the p-side with the doping density ( ), and the diffusion constant ( ) and diffusion length ( ) of the minority carrier holes on the n-side with the doping density ( ) by (2) where is the junction area normal to the current and is the intrinsic carrier density. (a) (b) Equation (2) is derived by considering minority carriers diffusing away from the edges of the depletion region. Hence the current which obeys the Shockley equation is often called the diffusion current. It is important to be able to show that the temperature and band-gap dependence of can be substituted from p. 141-3, Hook and Hall, so that the saturation current becomes (3) where the constant is only weakly dependent on temperature (in the experiment you can assess this small extra dependence). In practice the in the Shockley equation can be ignored (check for what voltages and explain why). To allow for the fact that diffusion is not always the dominant mechanism the equation is often written as (4) where is the ideality factor which equals if diffusion dominates. As discussed in Hook and Hall (p 179) and in more detail in Sze (p 90 - 92), if another mechanism dominates, namely generation-recombination of carriers in the depletion region, then . If the forward bias current-voltage characteristic follows equation (4) then and can be found from the slope and intercept respectively of a versus plot. Part 2. It is extremely important to know how to apply the Gauss' Law to determine the "built-in" potential difference ( ) across the p-n junction in terms of , and the depletion region widths on the p-side ( ) and n-side ( ) as in Hook and Hall p 172 - 173, giving (5) It is also important to be able to use this result for finding the incremental capacitance ( ) of the junction as a function of the applied bias ( ) (6) Note that in the "one-sided" case (i.e. one side of the junction is much more heavily doped than the other) this simplifies to (7) Hence (8) where is the doping level on the more lightly doped side. If the p-n junction is abruptly doped, with one side more heavily doped than the other, then equation (8) suggests that, if the capacitance is measured as a function of applied bias , then the plot of 1/C2 against should be a straight line. The built-in potential difference (sometimes called the built-in voltage or barrier height - be careful of the units) will be given by the intercept of this plot. The slope gives the doping density on the least doped side: (9) The metal semi-conductor contact or Schottky type junction is also important in semiconductor devices. It behaves very much like a one-sided p-n junction because the metal can be thought of as a semiconductor with very high impurity doping. It is useful to think about the energy band diagram for the metal-semiconductor contact and understand in which cases this junction exhibits Ohmic or diode behaviour. The expressions in equations (8) and (9) can be used to determine the semiconductor doping and barrier height in the Schottky junction device. Furthermore, the dopant‘s concentration as a function of position can be determined from the slope of the plot of 1/C2 versus reverse-bias voltage: (10) where is the depletion-region width that corresponds to the applied reverse bias . Sze p. 81 - 82 shows that, if the p-n junction is not abruptly doped but has a linear doping density proportional to a constant , then the incremental capacitance per unit area is (11) and a plot of ( ) against is a straight line in this case. Note that Sze also explains a correction to these capacitance expressions because the charge distributions are not abrupt at the edges of the depletion region (Is this correction important for your results?). Part 3. There are two main methods by which a diode breaks down in reverse bias. Both can be used to construct a voltage limiting device. One is the tunnelling (or Zener) breakdown and the other avalanche breakdown. These are explained on p. 181 Hook and Hall or Sze p. 113. The temperature dependencies of the breakdown voltages are different which makes it possible to distinguish which mechanism dominates. It is important to understand the explanations of why these temperature dependencies differ. The Experiment Hints  Do not forget to identify the diode devices you use (make notes of the serial/manufacturer part number). If available, check the device’s data sheet. The devices are available in the workshop area opposite to the entrance to the technicians’ offices.  Make sure that you analyse the data while conducting/during the experiment. This is particularly important for the Part 1 where the right regime of operation and range of voltages should be identified prior to measuring characteristics of various diodes. Part. 1 i) Devise a simple circuit to measure the forward I-V characteristics of the Ge, Si, and GaAs diodes at room temperature and at liquid nitrogen temperature (check the exact liquid nitrogen temperature value). Since an excessive current can permanently damage low power diodes it is important to have a series resistor which should limit the current to no more than 300mA. In fact, you will mainly be interested in currents much less than this and certainly voltages less than, or of the order of, the band-gap voltage. (check the band-gap in eV of the known diodes from Sze). ii) Determine and from your plots. Take care to see if there are any devices, bias ranges or temperatures over which the behaviour follows n=1 or n=2. If you can find a region where n is approximately a unity, within the error, the value of I0 can be found from equation (2). iii) Do your I0 values for the n = 1 regions vary depending on the band-gap and temperature as you might expect from equation (3)? Try to be as quantitative as possible in your interpretation. iv) At high forward bias the resistance of the metal contacts with the semiconductor may become important particularly at 77 K. Why are such contact resistances only important at high forward bias? Can you think of the way of demonstrating that any change of the slope of versus V plot is due to the series resistance effect rather than the "high injection" region as shown in Sze Fig. 21 (Appendix A)? v) Now choose three LEDs which emit three different colours. The aim will be to try to work out what semiconductor each is made from and approximately what the band gap energy is. You can make at least a preliminary first estimate of the band-gap from the colour/wavelength of the LED. vi) Try to make another estimate of the LEDs’ band-gaps by using the electrical measurements. Analyse equations (3) and (4) to adapt them for the band gap measurements. This shows that there are three main parameters that can vary: the electrical current , the applied voltage and the temperature of the device . To simplify the problem, you can fix either the current or voltage. Please, assess the suitable temperature range to limit the measurement uncertainties due to the temperature variation of the band gap (see Sze for more details). A hot plate can also be used for these measurements. Are any of the LEDs likely to be constructed of Si or Ge? Is the energy of the photons emitted by the LEDs always equal to the band gap energy? How to make light emission a more efficient process? vii) Note the biases at which the LED starts emitting and qualitatively compare the light emission of the LEDs at room temperature and 77K. Can you think of reasons for any differences? Part 2. i) Devise a circuit to measure the capacitance voltage (C-V) characteristics of the silicon power rectifier diode and silicon Schottky power rectifier diode provided by using the microprocessor controlled commercial LCR bridge. The bridge has a port for applying an external bias. Before proceeding with the diodes measurements, check that the bridge provides a sensible result for a standard capacitor of the known value. It is important to consider the implications of the high diode resistance in reverse bias and the frequency the LCR bridge conducts the measurements at. ii) Use equations (8) and (11) to establish whether the structure of these power rectifier diodes can more closely be approximated by the abrupt or linear graded junction doping geometry. iii) Determine the built-in voltages and doping density in the two cases and compare with expectations from Sze, in particular for the barrier height. If one or other of the diodes does not follow the abrupt behaviour closely you might wish to try to estimate the doping profile with eqn. (10). To estimate the doping density you will need the area of the device. Both diodes have junction area ~ 2 mm2. If you need to know this area more accurately you could file down a diode in the workshop and assess the junction area value. Part 3 i) Measure the reverse bias I-V characteristics of the two regulator diodes BZX (2.7 V) and BZX (9.1V) at room and liquid nitrogen temperatures with a series resistor which limits the current in the reverse direction to less than 20 mA. Plot the I-V characteristics and decide on a consistent way to determine the breakdown voltages at the two temperatures. ii) Calculate the temperature coefficients of the breakdown voltage and check against the specifications for these devices in the catalogue. Hence decide on the breakdown mechanisms in the two cases. If time permits, you could devise a way to measure the breakdown voltage as the diode warms up from liquid nitrogen temperature to room temperature. What semiconductor parameter determines the prevailing breakdown mechanism? Hints for the Write-up As the Laboratory lecture handouts indicate, the report should be between 2,000 and 3,000 words excluding diagrams, graphs, tables, formulae, bibliography and figures captions. Marks will be deducted if the report, including appendices, is outside these limits. There is no need to include tables of raw measurements, well presented, clear graphs will suffice. While graphs can be shared, each partner must have their own analysis text and their own tables summarising results derived from the graphs. Do not reproduce parts of this script. Use appropriate references whenever you use expressions from known bibliography sources. Though it will be important revision for you to work through the derivations described in the "Theory" section, they are all standard and do not need to be reproduced. However, you should include any non-standard derivations relevant to your analysis, possibly in an appendix. It is also very important that you make clear the physical assumptions behind any formula you are using and expressly assess associated error values. It is important to demonstrate a deep understanding of the devices’ operation in various regimes. Therefore, it is advisable to include illustrations like a band diagram of the device, a schematic of the connections and to discuss the major physical processes under forward and reverse bias conditions. A good write-up is one which uses tables and graphs to summarise and analyse the results and for which a thought has been given as to what best section headings to use. These will vary from experiment to experiment. However, all reports should have "Abstract", "Introduction" and "Conclusions" sections. The "Abstract" is a one paragraph section summarising what was done in terms of aims and objectives, and it should list the major numerical results with errors. The “Introduction” should briefly outline the aims and objectives of the experiment within the scope of general physics and also briefly outline the structure of the report. The "Conclusions" section is also very important. The answers to key physical questions raised in this script probably belong in this section. You should summarise your main numerical results (with errors) in the Conclusion and compare with expected values from literature or the specifications of the devices. Do not forget to identify the devices you used. Bibliography "Solid State Physics" J.R. Hook and H.E. Hall, (Wiley, Sec.Ed. 1991). "Physics of Semiconductor Devices", S.M. Sze, (Wiley, Sec.Ed. 1981). “Principles of Semiconductor Devices”, Bart Van Zeghbroeck (2004). Accessible online via http://ece-www.colorado.edu/~bart/book/book/contents.htm the most relevant Chapters are 4 and 5. Appendix A Figure 21. Current-voltage characteristics of a practical Si diode, where is the Boltzmann constant and corresponds to in this laboratory script. (a) Generation-recombination current region, (b) Diffusion current region, (c) High-injection region, (d) Series resistance effect, (e) Reverse leakage current due to generation-recombination and surface effects [Sze, 1981].