Hi, to derive the equation of the current across a diode or ideal diode equation, william shockley argues that the total voltage drop across the diode or pn junction can be divided into three parts. At thermal equilibrium 1 number of carriers in the. Imax and imelt specify the pn junction explosion current expli which is used in the following equations. Pn junction diode 2 diode introduction a diode is formed by joining an ntype semiconductor with a ptype semiconductor. Calculation of the ideal diode current in a graded n diode poses a special problem since ap gradient of the bandedge exists within the quasineutral region. For a diode with a graded doping concentration this implies an exponential doping profile as can be found in an ionimplanted base of a silicon bipolar junction transistor. In this lecture, we derive the steadystate currentvoltage relationship aka iv characteristic of a pn junction diode based on ideal assumptions. A small increase in the drift current is experienced due to the small increase in the width of the depletion region. It works on the principle of photoelectric effect the operating principle of the photodiode is such that when the junction of this twoterminal semiconductor device is illuminated then the electric current starts flowing through it. Diode characteristics dynamic resistance, transition time. The basis for derivation of the equation of the depletion region vi characteristic are the boundary.
Solve minority carrier diffusion equation in quasineutral regions determine minority carrier currents from continuity equation evaluate currents at the depletion region edges add these together and multiply by ar ea to determine the total current through the device. Most semiconductor devices involve regions with two different kinds of doping, so a pn junction is present in all of them. It is well known that semiconductor diodes exhibit shot noise. First,the poisson equation describing the band bending in the depletion. Uniti diode current equation vi characteristics of pn junction. Furthermore, an equivalent circuit for pnjunctions will be presented. The diode equation the reason for calling the proportionality constant isat will become obvious when we consider reverse bias. Band diagrams and builtin voltage of the pn junction.
However, at times the inverse relation may be more useful. Pn junction diode is widely known for passing the electric current solely in one direction. Forward current derivation through diode this is the derivation of current through the diode considering minority charge carriers concentration in n. Is the law of junction still valid under bias voltage applied. There is also a difference in the reverse bias region due to both material characteristics and fabrication of the diode junction. Derivation of vi characteristics of pn junction diode. Alan doolittle pn junction iv characteristics electron diffusion current electron drift current hole diffusion. May 16, 2015 for the love of physics walter lewin may 16, 2011 duration. In this lecture, the educator has discussed how to derive a diode current equation in forward bias and reverse bias. The pand ntype regions are referred to as anode and cathode respectively.
If model parameter allowscaling is set to yes, the diode geometry parameters periph, width, and length are multiplied by scale, while area is multiplied by scale scale for level 11 only. To see how it can be derived, we must examine the various reasons for current. The shockley diode equation, is a mathematical model of the forward and reverse biased characteristic of a diode. Concentration linearly increases from scr edge to ohmic contact. Lecture 6 biased pn junction diodes and current flow. What is usually done is to measure the diode current and forward voltage over several orders of magnitude of current.
A pn junction diode is twoterminal or twoelectrode semiconductor device, which allows the electric current in only one direction while blocks the electric current in opposite or reverse direction. Shockley derives an equation for the voltage across a pn junction in a long article published in 1949. Feb 20, 2018 diode current equation diode equation thermal voltage and ideality factor diode duration. As in forward bias, the drift current is limited by the number of minority carriers on either side of the pn junction and is relatively unchanged by the increased electric field. Lecture 15 the pn junction diode i iv characteristics november. However it doesnt model the breakdown region and ignores the minority change carriers. A physical switch that has this property is a pn junction diode. Of course, we can just give you the equation to figure it out, but what good will that do. Current hole diffusion current negligible due to large energy barrier hole drift current current flow is constant due to thermally generated carriers swept out by efields in the depletion region current flow is dominated by minority carriers flowing across the junction and becoming majority carriers quicktime movie. Characteristics of junction diodes technical articles. The pn junction is the fundamental building block of the electronic age. Lets now get back to the equilibrium condition and start to analyze the junction quantitatively.
Connect currents across scl to get total junction current, id. Likewise, we can find the voltage across the diode. Diodes are electronic check valves which allow current to flow freely in one direction, but block current flow in the opposite direction. Enee 3, spr 09 midterm ii solution part idrift and diffusion, 30 pts 1. The semiideal diode had a leakage current across the junction the reverse saturation current, shown by i. How to derive the equation of the current across a diode. Depending on the polarity of the voltage vd the diode is said to be. As long as the light is on, there is a current flowing through the pn junction. The potential barrier in the pn junction diode is the barrier in which the charge requires additional force for crossing the region. Electrostatics of pn junction in equilibrium a spacecharge region surrounded by two quasineutral regions formed. We have solved for the current densities in the quasineutral region to obtain the current density in the depletion region, but what were looking for is current through the diode.
Apply basic semiconductor drift diffusion equations to determine current flow in semiconductor devices. Applying the basic equations to a pn junction pveducation. Jan 28, 2017 i is current flowing through the diode. Outline 1 overview 2 qualitative derivation of the ideal diode. As we said,i is a very small current, and so trying to do the reverse test is probably not going to be successful. Lecture 5lecture 5 pn junction diodes quantitative. Simple derivation of diode equation physics forums. The applied electric field nowadds in the same direction to the builtin field. Semiconductor energy bands and fermi energy concept free electrons free holes valence band. This recombination can occur within the quasineutral regions, within the depletion region or at the metalsemiconductor ohmic contacts. I 0 dark saturation current, the diode leakage current density in the absence of light.
I unfortunately dont know how to derive it and i cant find one simple enough to use. Assume that the forward current is determined by the shockley equation minority carrier diffusion. The behaviour of the pn junction with regards to the potential barriers width produces an asymmetrical conducting two terminal device, better known as the pn junction diode. The ideal diode equation is very useful as a formula for current as a function of voltage. The current in a pn diode is due to carrier recombination or generation somewhere within the pn diode structure. Uniti diode current equation vi characteristics of pn junction diodeapplication half wave rectifier and full wave rectifiers with and without filters derivation of ripple factor rectification of efficiency and tufzener diode and its application, clippers,clampers,voltage multiplier.
Minority carriers flow from contacts to scr and are swept across the junction. Pn junction diodes quantitative analysis math, math and more math georgia tech ece 4833. The junction can be formed by the implantation or diffusion of dopants in an wafer. This pn junction can be used to operate and implement the functions of a diode because it can conduct considerable current in the forward direction and roughly no current in the reverse direction.
The amount of current flowing through the pn junction diode greatly depends on the type of material used and also depends on the concentration of doping in the fabrication of pn diode. Under forward bias, the diode current is due to recombination. When the diode is forwardbiased, it can be used in led lighting applications. Lecture 5lecture 5 pn junction diodes quantitative analysis. For the derivation of the ideal diode equation we will again. The derivation below can be applied to a pn diode with a graded doping density as well as one with a graded bandgap provided that the gradient is constant.
This is because the builtin potential across the depletion layer of the pn junction is high enough to prevent the majority carriers from returning once they cross the junction. The short circuit current, i sc, is the current at zero voltage which equals i. The diode equation gives an expression for the current through a diode as a function of voltage. Ee105 fall 2014 microelectronic devices and circuits. From the analysis of both forward bias and reverse bias, we can arrive at one fact a pn junction diode conducts current only in one direction i. For the love of physics walter lewin may 16, 2011 duration. I need it to reference to it in my advanced higher project. Mathematically it is given as where, i is the current flowing through the diode i0 is the dark saturation current, q is the charge on the electron, v. The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Theory of pn junction diode, diode current equation. To conclude about pn junction characteristics, we need to get an answer to the first question we have raised what is the use of pn junction. Module 2 essentially, they serve the same function in circuits, as the valves in your heart and. The main characteristic of a pnjunction or a diode is that for positive voltages forward bias the diode is conduction, whereas for negative voltages reverse bias the current flow is blocked. Diodes and diode circuits tlt8016 basic analog circuits 20052006 20 3. What are the leading dependences of the saturation current. It will not pass current as readily as a conductor nor will it block. Consider the heavily doped pn junction shown to the left. Application of the current continuity equation dx o p n n n. The boltzmann approximation is to say that the resulting current being small compared with the components of this current, we consider that we are still in quasi equilibrium and therefore that the currents equation is still valid by replacing v bi by v.
Apr 16, 2009 i am looking for the simplest possible derivation of the diode equation. To first order, carrier concentrations in spacecharge region are much smaller than the doping level. Why does the pn junction diode exhibit current rec tification. The equation for the diode current of a planeparallel junction diode 2 is i is exp 1 kt where is is the saturation current of the diode, q is the electronic charge, k is boltzmanns constant, and t is the junction temperature in k. How to derive forward current equation for pn junction. In other words, the barrier in which the charge carrier stopped by the obstructive force is known as the potential barrier. Module 1 semiconductor pnjunction diodes what are they and what is their purpose. V applied voltage across the terminals of the diode. The conventional voltage polarity across the diode terminals and the current direction through the diode are also indicated on figure 1.
This expression only includes the ideal diode current of the diode, thereby ignoring recombination in the depletion region. Reverse saturation current in a silicon pn junction diode nearly doubles for very a. By exploring the electrical properties of silicon, it is possible to acquire an understanding of the inner workings of the pn junction. There are a few basic concepts to be introduced, such as energy bands, drift and diffusion currents, etc. Connect currents across scl to get total junction current, i d features and limitations of the model engineering the minority carrier injection across a junction deviations at low and high current levels deviations at large reverse bias 6. Forward biased, vd 0, anode voltage is greater than the cathode voltage, or. Device physics i pn junctions diode equation neudeck p. In this equation, two parameters require to be discussed in quite detail. Use our free online app pn junction diode calculators to determine all important calculations with parameters and constants.
Pn junction diode 1 ee105 fall 2014 microelectronic devices and circuits prof. The shockley ideal diode equation characterizes the current across a pn junction as a function of external voltage and ambient conditions temperature, choice of semiconductor, etc. Forward current derivation through diode this is the derivation of current through the diode considering minority charge carriers concentration in n region that is holes and minority charge. A diode is a simple device, which can be implemented by a pn junction, as well as other hetero junction structures. Diode current equation expresses the relationship between the current flowing through the diode as a function of the voltage applied across it. If the diode is forward biased, it allows the electric current flow. Kasap, 1990 2001 an ebooklet 4 d what is the reverse current at 27 c when the diode voltage is. Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we. Gilbert ece 340 lecture 27 102912 zener breakdown last time we talked about zener breakdown the zener effect is the breakdown mechanism if the reverse bias required to force breakdown occurs at low voltages. Diode current equation vi characteristics of pn junction diodeapplication half wave rectifier and full wave rectifiers with and without filters derivation of ripple.
If i short terminals of pn junction diode, does current flow on the outside circuit. The figure below shows the symbolic representation of a photodiode. The equation 2 can be written for open circuited unbiased pn junction diode by putting v 0 as, where p n0 is the concentration of holes on nside just near the junction when diode is open circuited i. One of the most common applications of the diode is the pn junction. A pn junction diode is one of the simplest semiconductor devices around, and which has the characteristic of passing current in only one direction only. This means the barrier will increase instead of decrease, and so we have what is shown in figure 1. I0 dark saturation current, the diode leakage current density in the absence of light. Silicon a single silicon atom consists of fourteen negatively. A pn junction diode in thermal equilibrium you have already seen a pn junction diode in thermal equilibrium. Jul 30, 2018 diode current equation expresses the relationship between the current flowing through the diode as a function of the voltage applied across it. Reverse diode leakage is related to offstate leakage of an ic current proportional to the diode junction area and inversely proportional to doping why you want lightly doped substrates reverse current dependent on the. Pn junction underbiasing 14 boltzmanns approximation.
If you recall, current is charge crossing an area, therefore we multiply you can do this the current density j by the area a to obtain the ideal diode equation. The derivation below can be applied to a pn diode with a graded doping concentration as well as one with a graded bandgap provided that the gradient is constant. I am looking for the simplest possible derivation of the diode equation. Lets consider the bandbending and carrier densities at equilibrium. The iv characteristics of the ideal diode are modeled by the ideal diode equation qualitative and quantitative derivation. Derivation of vi characteristics of pn junction diode 4.
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