The p-n Junction D1. Head of Experiment: Sergei Popov

Transcription

1 The p-n Junction D 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. dditional 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.

2 RISK SSESSMENT ND STNDRD OPERTING PROCEDURE. PERSON CRRYING OUT SSESSMENT Name Geoff Green Position Chf Lab Tech Date 8/9/8. DESCRIPTION OF CTIVITY D Experiments with P-N Diodes 3. LOCTION Campus SK Building Huxley Room HZRD SUMMRY ccessibility 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 PRECUTIONS Use of 4v Mains Powered Equipment ccessibility Use of Liquid Nitrogen & Vacuum Flask Use of Hot Plate and Hot Water Isolate Socket using Mains Switch before unplugging or plugging in equipment ll bags/coats to be kept out of aisles and walkways. See attached Scheme of Work void direct contact; protect hands and feet; avoid spills and upsets 6. EMERGENCY CTIONS ll present must be aware of the available escape routes and follow instructions in the event of an evacuation

3 LIQUEFIED GS ND CRYOGENIC SFETY The main hazards associated with handling cryogenic liquids are (i) (ii) (iii) (iv) (v) Cold burns. void 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. Explosion due to overpressure or implosion due to mechanical failure or breakage. Glass dewars must be surrounded by plastic to guard against flying glass. ny 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. 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. 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 steadily 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. 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 a n y experiments are attempted.

4 Third Year Laboratory Diode Experiments ims The aim of this experiment is to study the technologically important p-n junction, to see if the theory of the device works in practice, and to see how the diode behaviour makes the p-n junction useful in a wide range of device applications. The experiment is in three parts. In the first part you will study the 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 semiconductors. The aim will be to see which diodes obey the Shockley Equation, over which bias ranges and at what temperature. Once you have established the influence of the band-gap on the forward current of a p-n junction you can then study how the band-gap effects the wavelength of the light from the LEDs. In the second part you will measure the capacitance of two rectifier diodes in reverse bias and, under certain assumptions, measure the "built-in voltage" 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 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 Chapter and has a particularly useful summary of the voltage regions in which the Shockley Equation breaks down in Fig. on page 9. Part. It is important to revise the assumptions made in deriving the Shockley equation I ev k B T I e () where the reverse-bias saturation current (I ) is given in terms of the diffusion constant (D e ) and diffusion length (L e ) of the minority carrier electrons on the p-side where the doping density is P and the diffusion constant (D h ) and diffusion length (L h ) of the minority carrier holes on the n-side where the doping density is N by I en i De L P e Dh L N h ()

5 where is the junction area normal to the current and n; is the intrinsic carrier density. The expression in eqn. () is derived by considering minority carriers diffusing away from the edges of the depletion region. Hence the current which obeys the Shockley eqn. is often called the diffusion current. It is important to be able to show that the temperature and band-gap dependence of n s can be substituted from p 4-3, Hook and Hall, so that the saturation current becomes I CT 3 e E g kbt (3) where the constant C is only weakly dependent on temperature. (If you do experiment B.8you will estimate this small extra T dependence). In practice the (-) in the Shockley eqn. can be ignored (for what voltages). To allow for the fact that diffusion is not always the dominant mechanism the equation is often written as I I e ev nk T where n is the ideality factor which equals if diffusion dominates. s discussed in Hook and Hall (p 79) and in more detail in Sze (p 9-9), if another mechanism dominates, namely generation-recombination of carriers in the depletion region, then n =. If the forward bias current-voltage characteristic follows eqn. 4 then n and I can be found from the slope and intercept respectively of a lni versus V plot. B (4) Part. It is extremely important to know how to use Gauss' Law to determine the "built-in" potential difference (V t ) across a p-n junction in terms of P, N and the depletion region widths on the p-side (d p ) and n-side (d n ) as in Eqn. 4.4 of second year notes and Hook and Hall p 7-73, giving V t Nd Pd e n p r It is also important to be able to use this result to find the incremental capacitance of the junction as a function of applied bias V C dq dv e rnp ( N P)( V V ) t Note that in the "one-sided" case (i.e. one side of the junction is much more heavily doped than the other) then this simplifies to

6 C e r N V V t Hence V C e N r V t (5) where N 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 eqn. (5) suggests that, if the capacitance is measured as a function of applied bias V, then a plot of (/C ) against V should be a straight line. The built-in potential difference V t ( some times called the built-in voltage or barrier height - be careful of the units!) will be given by the V = intercept of this plot. The slope gives the doping density N on the least doped side. d C dv e N r (6) The metal semi-conductor contact or Schottky Junction is 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. Hence the expressions in eqns. (5) and (6) can be used to determine the semiconductor doping and barrier height in a Schottky junction device. Sze p. 8-8 shows how if the p-n junction is not abruptly doped but has a linear doping density, proportional to a constant a, then the incremental capacitance per unit area is C r ea ( V V ) t 3 (7) and a plot of (/C 3 ) against V is a straight line in this case. Note that Sze also explains how there is 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 8 Hook and Hall or Sze p 3. 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 for why these temperature dependencies differ.

7 Experiment Part. i) Devise a simple circuit to measure the forward I-V characteristics of the Ge, Si, and Gas diodes at room temperature and at liquid nitrogen temperature. Since excess current can permanently damage a diode it is important to have a series resistor which will limit the current to less than 3 m. 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 p5). ii) iii) iv) Determine n and I from your plots. Take care to see if there are any devices, bias ranges or temperatures over which the behaviour follows n = or n =. If you can find a region where n is approximately unity, within errors, the value of Io should be given by eqn.. Do your I values for the n = regions vary with band-gap and temperature as you might expect from eqn. (3)? Try to be as quantitative as possible in your interpretation. t high forward bias the resistance of the metal contacts to the semiconductor may become important particularly at 77 K. Why are such contact resistances only important at high forward bias? Can you think of a way to demonstrate that any change in slope on your Inl versus V plot is due to series resistance rather than the "high injection" region shown in Sze Fig.? v) Now choose three LEDs which radiate with three different colours. The aim will be to try to work out what semi-conductor each is made from and approximately what the band gap is. You can make one estimate of the band-gap from the colour of the LED. vi) vii) Try to make another estimate from the I band gap dependence as you did for the known diodes with n =. re any of the LEDs likely to be constructed of silicon or germanium? Is the energy of the light emitted light by an LED always equal to the band gap energy? Note the biases at which the LED starts glowing and qualitatively compare the light output of the LEDs at room temperature and 77K. Can you think of reasons for any differences? Part. 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, using the computer controlled LCR bridge. The bridge has a port for applying an external bias. Check first that the bridge gives a sensible results for a standard capacitor. It is important to consider the implications of the high diode resistance in reverse bias. ii) Use eqns. (5) and (7) above to establish whether these power diodes more closely approximate to the abrupt junction or linear graded doping behaviour.

8 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. (6). To estimate the doping density you will need the area of the device. Both diodes have junction area ~ mm. If you need to know this area more accurately you could file down a diode in the workshop. Part 3 i) Measure the reverse bias I-V characteristics of the two regulator diodes BZX (.7 V) and BZX (9.V) at room temperature and 77K with a series resistor which limits the current in the reverse direction to less than m. 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 the breakdown mechanism in the two cases. If time permits you could devise a way to measure the breakdown voltage as the device warms up from 77K to room temperature. Hints for the Write-up s the Laboratory handout indicates, the report should be between 6 and pages of hand-written 4 (or the equivalent word-processed), excluding diagrams and graphs. Marks will be deducted if the report, including appendices, is outside these limits. There is no need to include tables of raw measurements, graphs will suffice. One partner can use a good Xerox copy of these. However, each partner must have their own text and their own tables summarising results derived from the graphs. Do not reproduce chunks of this script. Though it will be important revision for you to work through the derivations described in the "Theory" section, they are all standard and need not 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 assumptions behind any formula you are using. good write-up is one which uses tables and graphs to summarise the results and for which thought has been given to the best section headings to use. These will vary from experiment to experiment. However, all reports should have "bstract", "Introduction" and "Conclusions" sections. The "bstract" is a one paragraph section summarising what was done and giving the main numerical results with errors. The "Conclusions" section is very important. The answers to many of the questions raised here in the script probably belong in this section. You should summarise your main numerical results there also (with errors) and compare with expectations from Sze or the specification in the device catalogue. Do not forget to identify the devices you used. Bibliography "Solid State Physics" J.R.Hook and H.E.Hall, (Wiley, Sec.Ed. 99). "Physics of Semiconductor Devices", S.M.Sze, (Wiley, Sec.Ed. 98).