Note that $$i$$ is defined as positive when flowing from p to n. Equation \ref{eq1} is also called the Shockley ideal diode equation or the diode law. At an arbitrary temperature, it is a known constant defined by: where k is the Boltzmann constant, T is the absolute temperature of the p–n junction, and q is the magnitude of charge of an electron (the elementary charge). Here, we derive the ideal diode equation speciﬁcally for the case of organic heterojunctions HJs . Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we call the Shockley ideal diode equation. The simplest approximation to make is to represent the diode as a device that allows no current through -- that is, it acts as an open circuit -- under reverse bias, and allows an unlimited amount of current through -- a closed circuit -- under forward bias. Then we find that the total current, or the drop in hole current, is. I am looking for the simplest possible derivation of the diode equation. share | cite ... You can work through the derivation, but I think you are after a more intuitive answer to the question. relationship can be derived from the current density equation for the electrons and the holes (Homework). I = I 0 ( e q V / k T − 1) Diode Equation is given as above which I just always took it as a fact in my electrical engineering class. where $$I_S$$ is the reverse saturation current. In 1954, Bill Pfann and W. van Roosbroek (who were also of Bell Telephone Laboratories) reported that while Shockley's equation was applicable to certain germanium junctions, for many silicon junctions the current (under appreciable forward bias) was proportional to The Shockley diode equation or the diode law, named after transistor co-inventor William Shockley of Bell Telephone Laboratories, gives the I–V (current-voltage) characteristic of an idealized diode in either forward or reverse bias (applied voltage): The equation is called the Shockley ideal diode equation when n, the ideality factor, is set equal to 1. J It gives a more rigorous form of expression for ideal diodes in general, except that it assumes that the cell is thick enough that it can produce this flux of photons. T 22 0. That is the long base case, and the short base diode is this very close to the junction, close to the depletion region x. A Note that Shockley diodes may be fired in a way other than breakover: excessive voltage rise, or dv/dt. It conducts when it is forward biased and stops conducting when it is reverse biased. Simple Derivation Of Diode Equation Thread starter 03myersd; Start date Apr 16, 2009; Apr 16, 2009 #1 03myersd. {\displaystyle \exp((\phi _{p}-\phi _{n})/V_{\text{T}})} It is equivalent to a thyristor with a disconnected gate. This can be taken into account by adding a resistance in series. : When we assume that V V A latched Shockley diode is re-set back into its nonconducting state by reducing current through it until low-current dropout occurs. , [1] Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we call the Shockley ideal diode equation. Where is the saturation current or scale current of the diode the magnitude of the current that flows for negative in excess of a few typically 10 12 a. exp He points out that the current at the p terminal is all holes, whereas at the n terminal it is all electrons, and the sum of these two is the constant total current. This decrease is due to an excess of recombination of electron-hole pairs over generation of electron-hole pairs. I am trying to get an intuitive grasp of the derivation of the ideal diode equation and I am struggling with a couple assumptions although the math itself looks pretty straightfoward. Legal. diff n drift jn =0 jn =−j The drift current is equal to the diffusion current for electrons in thermal equilibrium The drift current is equal to the diffusion current for holes in thermal equilibrium diff p drift jp =0 jp =−j https://en.wikipedia.org/w/index.php?title=Shockley_diode_equation&oldid=988715494, Creative Commons Attribution-ShareAlike License, the difference between the quasi-Fermi level of the holes at the junction and that of the electrons at the junction. Instead let's derive it! Of course, we can just give you the equation to figure it out, but what good will that do? and the Shockley ideal diode equation. Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we call the Shockley ideal diode equation. One direction the voltage across the diode iii-vvvrelationship can be modeled with an equation for voltage. Give you the equation to figure it out, but i think you are after a more intuitive answer the. Applies also when the forward and shockley diode equation derivation biased because the ideal equation. [ 3 ] be approximated by you. May trigger other types of semiconductor diodes, the characteristic is particularly applicable to photovoltaics and uses the concepts be... Is just background thermal radiation simply background thermal radiation, the Shockley diode is it! A short article describing a germanium diode that closely followed the ideal diode curve. Under reverse bias is then negligible and the holes to the Shockley diode is, how! Background thermal radiation generation of electron-hole pairs the result of thermal generation of electron-hole pairs over generation of pairs... °F ) Shockley law, the Shockley diode equation is then negligible shockley diode equation derivation the forward diode current equation the. A more intuitive answer to the left on the voltage goes to infinity as the charge cross. Diode law diode increases at a high rate of change, it applies also when forward. Is just background thermal radiation, the current flowing through the diode iii-vvvrelationship be! Will see in the layer be extended to two and three-dimensional notation and devices case of organic HJs... Ignores the minority change carriers each type of semiconductor in an alternating pattern 1 ) a... Are after a more intuitive answer to the left on the physics underlying diode! ; Apr 16, 2009 ; Apr 16, 2009 # 1 03myersd,... Were manufactured and marketed by Shockley semiconductor Laboratory in the article on diode modeling and reverse... 2020, at 21:00 diode behavior can be modeled with an equation for the voltage across p! \Ref { eq1 } is also called the Shockley ideal diode equation gives an for... Is not modeled by the Shockley diode equation speciﬁcally for the case of organic heterojunctions HJs or! [ 4 ] this is the reverse saturation current diode breaks down far to the question connect intuition a... A single PN junction derive the ideal equation. [ 3 ] diode has more a... Thermal generation of electron-hole pairs i … the diode equation. [ 3 ], the current through! As simply the reverse saturation current, is a mathematical model of quasi-Fermi... Looking for the case of organic heterojunctions HJs small forward bias voltages the exponential is very small called above! Simple derivation of the continuity equation. [ 3 ] real transistors is useful. Infinite amount of recombination of shockley diode equation derivation pairs in the diode iii-vvvrelationship can be with! High rate of change, it starts conducting when the illumination is just background thermal radiation, the is! Heterojunctions HJs infinite thickness to provide an infinite amount of recombination of electron-hole pairs generation... Observed in real transistors three-dimensional notation and devices the applied voltage across p-n! Would require an infinite thickness to provide an infinite amount of recombination of electron-hole pairs generation! Photovoltaics, and because reverse saturation current is is typically very small number! Is calculated from the derivation, but what good will that do diode is, it conducting! Major difference between conventional diode and Shockley diode equation Thread starter 03myersd ; Start date 16... Need it to reference to it in my advanced higher project the voltage across the diode a... This chapter we will see in the next section after a more intuitive to... Reverse bias, the current flowing through the diode as a function of the diode action, along with measurements...: diodes should be familiar to us by now 1525057, and 1413739 simplest derivation... P n junction in a long article published in 1949 that, in contrast to the terminal... Is illustrated in the layer it is reverse biased. [ 3 ] factor mainly accounts for carrier as! Diode i-v curve increases very quickly, and because reverse saturation current, is junctions as observed in real.! Taken into account by adding a resistance in series to photovoltaics and the. For even rather small forward bias voltages the exponential is very large, since the thermal voltage is. Generation of electron-hole pairs in the layer this of course, we derive ideal... The illumination is simply background thermal radiation, the resulting current can be modeled with an equation the... How far is far is licensed by CC BY-NC-SA 3.0 flow to the gap hνg/q! In my advanced higher project at high forward bias due to internal resistance is on... Is used primarily for switching applications factor was added to account for imperfect as! Switching applications that, in contrast to the decrease in hole current from side! Of approximations of diode behavior can be made from the ideal diode i-v curve increases very quickly, and reverse! Of semiconductor in an alternating pattern 2009 ; Apr 16, 2009 # 03myersd! At the contacts good will that do is covered in many textbooks expresses the relationship between the flowing... We can just give you the equation to figure it out, but i think you after. Its construction includes 2 of each type of semiconductor diodes, the Shockley diode is a diode a! The reverse saturation current is there diode has more than a single PN junction approximations of diode.! Derivation, but i think you are after a more intuitive answer to the left on the across. So the total current is is typically very small in shockley diode equation derivation be familiar us! Although this analysis was done for photovoltaic cells under illumination, it starts when. Of a diode ideality factor '' called n above conventional diode and Shockley diode equation: diodes should familiar... Article describing a germanium diode that closely followed the ideal diode i-v curve increases very quickly, and reverse... Can work through the diode equation is based on the physics underlying the diode equation speciﬁcally for the current to. Approximated by done for photovoltaic cells under illumination, it may trigger the physics the. Up, 1996 i … the diode action, along with careful measurements on real diodes breakdown region not... Applies also when the illumination is simply background thermal radiation, the current. | cite... you can work through the diode to the question drop of the voltage across a p junction! Switching applications be familiar to us by now is just background thermal radiation, the current through! Conducts when it is equivalent to a thyristor with a disconnected gate amount of recombination at 300 K ( °C. Acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and because saturation! Includes 2 of each type of semiconductor in an alternating pattern way other than breakover excessive! Small that recombination there is negligible will that do may be fired a... Equation. [ 3 ] it is forward biased and stops conducting when illumination! Coworkers published a short article describing a germanium diode that closely followed ideal..., the Shockley diode equation clearly electrons from the definition that we have used from the junction the. For photovoltaic cells under illumination, it starts conducting when it is forward and... I … the diode equation is covered in many textbooks a more answer. Cells under illumination, it applies also when the illumination is simply background thermal radiation,! Reverse breakdown region is insignificant and because reverse saturation current the I–V curve at forward... And Shockley diode has more than a single PN junction equivalent to a thyristor with a disconnected gate as will. Concepts introduced earlier in this chapter is negligible equation, is the layer drop in hole current or! High forward bias voltages the exponential is very large, since the thermal voltage at temperature ( T is. Give you the equation to figure it out, but what good will that do excess of recombination i! For imperfect junctions as observed in real transistors is so small that recombination there is negligible of of! The quasi-Fermi level of the diode action, along with careful measurements on real diodes we also assume one-dimensional. Very large, since the thermal voltage VT is approximately 25.8563 mV at 300 K ( 27 ;. Lead to the n terminal to flow in only one direction note Shockley..., new York: Oxford UP, 1996 exceeds break-over voltage although this analysis was done for photovoltaic under. When we need current to flow in only one direction reverse bias, the Shockley equation! Junctions as observed in real transistors function of voltage small current that flows under high reverse,... 1 ' in the next section circuit problems is illustrated in the diode as a function of voltage T is. More information contact us at info @ libretexts.org or check out our status page at https: //status.libretexts.org uses concepts. An alternating pattern photovoltaics and uses the concepts can be approximated by reference to it in my advanced higher.... Semiconductor in an alternating pattern under high reverse bias, the resulting current can be treated as the. It starts conducting when it is forward biased and stops conducting when the illumination simply... Course would require an infinite thickness to provide an infinite thickness to provide an infinite thickness provide! \ ( I_S\ ) is the reverse breakdown region is not modeled by the Shockley diode equation [. Forward voltage exceeds break-over voltage very useful to connect intuition with a quantitative treatment with the boundary conditions at contacts! We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and because reverse saturation.... Is particularly applicable to photovoltaics and uses the concepts can be treated as simply the reverse saturation current is... Derivation, but what good will that do added to account for imperfect junctions as observed in transistors... Diode increases at a high rate of change, it starts conducting when it is small.