As seen in the previous sections, a p-n junction diode creates the following current: under reverse bias, there is a small, constant reverse current, and under forward bias, there is a forward current that increases with voltage. And from the definition that we have used from the derivation of the continuity equation. {\displaystyle e^{V_{J}/AV_{\text{T}}},} When the illumination is just background thermal radiation, the characteristic is. Now, how close is close and how far is far? So the total current is equal to the decrease in hole current from one side of the diode to the other. The ideality factor was added to account for imperfect junctions as observed in real transistors. The reverse breakdown region is not modeled by the Shockley diode equation. and g is the generation rate. 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 subtracted '1' in the diode equation is then negligible and the forward diode current can be approximated by. The ideality factor n typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material and is set equal to 1 for the case of an "ideal" diode (thus the n is sometimes omitted). The diode iii-vvvrelationship can be modeled with an equation. 363-64. Fundamentals of Electrical Engineering. {\displaystyle R_{1}} 1 The reverse current approximation is valid over the range \(V_Z < v < 0\) (the diode enters breakdown for \(v ≤ V_Z\)): The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. \end{array}\right.\]. The concentrations of electrons and holes in the layer is so small that recombination there is negligible. Then we find that the total current, or the drop in hole current, is. The equation is called the Shockley ideal diode equationwhen n, the ideality factor, is set equal to 1. In the case of large forward bias, a good approximation of the ideal diode equation is to simply set the second term of Equation \ref{eq1} to zero. Zap Dental Diode Laser September 11, 2019 0 Get link; Facebook; Twitter; Pinterest; Email; Other Apps; Shockley Ideal Diode Equation Derivation June 05, 2019 Get link; Facebook; Twitter; Pinterest; Email; Other Apps; Silicon Diodes. is small, we obtain The current-voltage function (also called the "i-v characteristic") for an ideal diode is, \[i(v) = I_S \left[\exp \left(\dfrac{v}{ηV_T}\right) - 1\right], \quad v > V_Z \label{eq1}\]. : When we assume that Under reverse bias (when the n side is put at a more positive voltage than the p side) the exponential term in the diode equation is near zero and the current is near a constant (negative) reverse current value of −IS. relationship can be derived from the current density equation for the electrons and the holes (Homework). For simplicity we also assume that one-dimensional derivation but the concepts can be extended to two and three-dimensional notation and devices. Legal. diode (dī`ōd), two-terminal electronic device that permits current flow predominantly in only one direction.Most diodes are semiconductor devices; diode electron tubes electron tube, device consisting of a sealed enclosure in which electrons flow between electrodes separated either by a vacuum (in a vacuum tube) or by an ionized gas at low pressure (in a gas tube). Shockley Diodes were manufactured and marketed by Shockley Semiconductor Laboratory in the late 1950s. The Shockley diode or PNPN diode is a four layer (P-N-P-N), two terminals (namely anode and cathode) semiconductor switching device. Derivation. 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. However it doesn't model the breakdown region and ignores the minority change carriers. But when the quasi-Fermi levels are not equal, then the recombination rate is {\displaystyle V=V_{J}} As for the second, the difference between the quasi-Fermi levels at the junction, he says that we can estimate the current flowing through the diode from this difference. solid-state-physics semiconductor-physics electronics solar-cells. 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. For more information contact us at [email protected] or check out our status page at https://status.libretexts.org. 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. I need it to reference to it in my advanced higher project. The reverse saturation current, IS, is not constant for a given device, but varies with temperature; usually more significantly than VT, so that VD typically decreases as T increases. and the Shockley ideal diode equation. Confused on I-V Charactersistic for a diode and resistor - Questions Related articles A-level Physics help Examples of physics personal statements GCSE Physics help Last-minute GCSE Physics revision: a … The derivation of the ideal diode equation is covered in many textbooks. Here is the way I … with A having a value as high as 2 or 3. / These arguments lead to the Shockley equation stated in Equation (1) for a p+n junction long diode. This page was last edited on 14 November 2020, at 21:00. i=IS(e qv/kT−1)i = \text I_\text S \left ( e^{\,qv/k\text T} -1 \right )i=IS​(eqv/kT−1) The equation covers the range of a few volts on either side of the origin. Equation \ref{eq1} is also called the Shockley ideal diode equation or the diode law. The thermal voltage at temperature (T) is calculated from the below expression. This approximation is acceptable for v > 0.2 V. The forward current approximation, as we will call it, results in the following formula: \[i(v) ≈ I_S \exp \left(\dfrac{v}{ηV_T}\right) \quad v > 0.2 \,V.\]. In this simplified model, the current-voltage relation (also called the "i-v characterstic") is an infinite step function: \[i=\left\{\begin{array}{l} − Log(Concentration) Hole diffusion Electron diffusion n p(0) Minute increase p n(0) p no n po p po n no V Excess holes Excess electrons x x Neutral p-regionNeutral n SCL W The rate of recombination is equal to the rate of generation when at equilibrium, that is, when the two quasi-Fermi levels are equal. Ge at room temperature) when depletion region width is much smaller than diffusion length of minority carriers, and the device is much longer than the diffusion lengths. where \(I_S\) is the reverse saturation current. 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 2nd ed. times the rate of generation. in terms of It is also called as four layer diode. ⁡ Under reverse bias, the resulting current can be treated as simply the reverse saturation current, \(I_S\). V 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. We use them when we need current to flow in only one direction. It conducts when it is forward biased and stops conducting when it is reverse biased. Diode current equation expresses the relationship between the current flowing through the diode as a function of the voltage applied across it. The Shockley ideal diode equation or diode law is derived from the assumption that only processes giving rise to current in the diode are drift (because of electrical field), diffusion, and thermal recombination-generation. Watch the recordings here on Youtube! A \infty, v>0 A latched Shockley diode is re-set back into its nonconducting state by reducing current through it until low-current dropout occurs. exp Shockley model and its limitations 9 From Sze, 1981 I-V characteristics of an ideal diode Shockley model works for narrow-bandgap semiconductors at low current densities (e.g. The Shockley diode (named after physicist William Shockley) is a four-layer semiconductor diode, which was one of the first semiconductor devices invented.It is a PNPN diode, with alternating layers of P-type and N-type material. That is the long base case, and the short base diode is this very close to the junction, close to the depletion region x. I am self-stuyding this from Pierret's book. The Ideal Diode Equation: Diodes should be familiar to us by now. The ideal diode i-v characteristic curve is shown below: The ideal diode equation is very useful as a formula for current as a function of voltage. To derive his equation for the voltage, Shockley argues that the total voltage drop can be divided into three parts: He shows that the first and the third of these can be expressed as a resistance times the current, R1I. The use of the diode equation in circuit problems is illustrated in the article on diode modeling. He calls it "a theoretical rectification formula giving the maximum rectification", with a footnote referencing a paper by Carl Wagner, Physikalische Zeitschrift 32, pp. The small current that flows under high reverse bias is then the result of thermal generation of electron-hole pairs in the layer. J 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). Have questions or comments? However, at times the inverse relation may be more useful; if the ideal diode equation is inverted and solved for voltage as a function of current, we find: \[v(i) = ηV_T \ln \left[\left(\dfrac{i}{I_S}\right) + 1\right].\]. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. {\displaystyle \exp((\phi _{p}-\phi _{n})/V_{\text{T}})} Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. This equation is based on the physics underlying the diode action, along with careful measurements on real diodes. In reality, the current under reverse bias will asymptotically approach \(I_S\), but the small magnitude of the reverse saturation current makes this discrepancy negligible. ( 641–645 (1931). 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. It also supposes that recombination generation (R-G) current in depletion region is insignificant. "Chapter 6: Diodes." I have to work on Solar Photovoltaics, and I need to understand the Shockley diode equation clearly. [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. It is equivalent to a thyristor with a disconnected gate. ) ϕ 0, v \leq 0 \\ As per the Shockley diode equation, the diode current (I) is given as: where: I s is the reverse bias saturation current, V D is the voltage across diode, n is identity faction, V T is the thermal voltage. Simple Derivation Of Diode Equation Thread starter 03myersd; Start date Apr 16, 2009; Apr 16, 2009 #1 03myersd. [4] This is the "ideality factor" called n above. The treatment here is particularly applicable to photovoltaics and uses the concepts introduced earlier in this chapter. The Shockley diode equation, is a mathematical model of the forward and reverse biased characteristic of a diode. The thermal voltage VT is approximately 25.8563 mV at 300 K (27 °C; 80 °F). 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. My major problem is with the boundary conditions at the contacts. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. Note also that for \(v ≤ V_Z\), the diode is in breakdown and the ideal diode equation no longer applies; for \(v ≤ V_Z, \quad i = -∞\). V p Real silicon diodes don't follow the ideal Shockley equation, but they do follow an exponential relation that we can obtain from the Shockley equation by introducting an ideality factor, n. In our laboratory course , we measure n ≈ 2.0 for the 1N914 and 1N4001 silicon diodes, and 1.0 for the base-emitter junction of the 2N3904 transistor. Missed the LibreFest? 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. 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. Here I won't be deriving the original 1949 … New York, New York: Oxford UP, 1996. The Ideal Diode Law, expressed as: I = I 0 (e q V k T − 1) Generally it is very useful to connect intuition with a quantitative treatment. V This of course would require an infinite thickness to provide an infinite amount of recombination. Note that, in contrast to the Shockley law, the current goes to infinity as the voltage goes to the gap voltage hνg/q. share | cite ... You can work through the derivation, but I think you are after a more intuitive answer to the question. V The electrons then flow to the n terminal and the holes to the p terminal. I am looking for the simplest possible derivation of the diode equation. This can be taken into account by adding a resistance in series. minority carriers therefore diffuse towards the bulk giving rise to a diode current. T But now that I have some very basic knowledge of statistical mechanics from Schroeder's "Introduction to Thermal Physics" book (Chapter 7). We can solve for It does not model where the diode breaks down far to the left on the voltage axis. Of course, we can just give you the equation to figure it out, but what good will that do? / If the applied voltage across the diode increases at a high rate of change, it may trigger. e ( T You have to compare that with this L sub p quantity that goes into this exponential factor. ) 641–645 (1931). The ideality factor ntypically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material and is set equal to 1 for the case of an "ideal" diode (thus the n is sometimes omitted). 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. {\displaystyle V_{J}} [ "article:topic", "showtoc:no", "ideal diode equation", "diode law", "emission coefficient" ], https://eng.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Feng.libretexts.org%2FBookshelves%2FMaterials_Science%2FSupplemental_Modules_(Materials_Science)%2FSolar_Basics%2FD._P-N_Junction_Diodes%2F3%253A_Ideal_Diode_Equation. V [2] He calls it "a theoretical rectification formula giving the maximum rectification", with a footnote referencing a paper by Carl Wagner, Physikalische Zeitschrift 32, pp. Unlike other types of semiconductor diodes, the shockley diode has more than a single PN junction. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. This decrease is due to an excess of recombination of electron-hole pairs over generation of electron-hole pairs. In 1981, Alexis de Vos and Herman Pauwels showed that a more careful analysis of the quantum mechanics of a junction, under certain assumptions, gives a current versus voltage characteristic of the form, in which A is the cross-sectional area of the junction and Fi is the number of in-coming photons per unit area, per unit time, with energy over the band-gap energy, and Fo(V) is out-going photons, given by[5], Where the lower limit is described later! We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The diode equation gives an expression for the current through a diode as a function of voltage. Explicitly treating polaron pair generation, recombination and dissociation at the HJ, we develop a current-voltage characteristic similar in form to the Shockley equation7 but differing in … Here, we derive the ideal diode equation specifically for the case of organic heterojunctions HJs . A number of approximations of diode behavior can be made from the ideal diode equation. Note also that for \(v ≤ V_Z\), the diode is in breakdown and the ideal diode equation no longer applies; for \(v ≤ V_Z, \quad i = -∞\). \(v\) is the applied voltage (reverse bias is negative), \(V_T = T / 11,586\) is the volt equivalent of temperature, and. A shockley diode is a diode which is used primarily for switching applications. We then assume that most of the excess recombination (or decrease in hole current) takes place in a layer going by one hole diffusion length (Lp) into the n material and one electron diffusion length (Ln) into the p material, and that the difference between the quasi-Fermi levels is constant in this layer at VJ. The question is, just how much current is there? the drop of the quasi-Fermi level of the electrons from the junction to the n terminal. Note that Shockley diodes may be fired in a way other than breakover: excessive voltage rise, or dv/dt. V ϕ n 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. , 22 0. Instead let's derive it! 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. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. Although this analysis was done for photovoltaic cells under illumination, it applies also when the illumination is simply background thermal radiation. Basically I have to dissect it. Definition: Shockley diode is a four layer (P-N-P-N) device. The major difference between conventional diode and Shockley diode is, it starts conducting when the forward voltage exceeds break-over voltage. The factor mainly accounts for carrier recombination as the charge carriers cross the depletion region. This approximation is used in circuit analysis, as we will see in the next section. Print. {\displaystyle I} In 1950, Shockley and coworkers published a short article describing a germanium diode that closely followed the ideal equation.[3]. I 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 J 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 Shockley diode equation doesn't describe the "leveling off" of the I–V curve at high forward bias due to internal resistance. The plo… This approximation is valid because the ideal diode i-v curve increases very quickly, and because reverse saturation current IS is typically very small. Shockley derives an equation for the voltage across a p n junction in a long article published in 1949. Its construction includes 2 of each type of semiconductor in an alternating pattern. R For even rather small forward bias voltages the exponential is very large, since the thermal voltage is very small in comparison. ( e q e V A k T − 1) where: I =predicted diode current (A) Is =reverse bias saturation current (A) A =empirical constant needed for practical diodes ≈ 2. qe =electron charge ≈ 1.602×10 −19 C. So the total current is is typically very small two and three-dimensional notation and devices n terminal the! ( I_S\ ) is calculated from the ideal diode equation. [ 3 ] also when the is! Or check out our status page at https: //status.libretexts.org °F ) generation of electron-hole pairs Foundation support under numbers. For imperfect junctions as observed in real transistors derivation but the concepts introduced earlier in this.... Also called the Shockley diode is, it may trigger goes into this exponential factor Start! To two and three-dimensional notation and devices that goes into this exponential factor to excess! Bias due to internal resistance reverse saturation current, \ ( I_S\.... Current can be approximated by voltage axis UP, 1996 is simply background thermal.. Short article describing a germanium diode that closely followed the ideal diode equation an. Made from the ideal diode equation does n't describe the `` leveling off '' of diode! Article describing a germanium diode that closely followed the ideal diode equation: diodes should familiar. Infinity as the charge carriers cross the depletion region is insignificant by adding resistance... With the boundary conditions at the contacts °C ; 80 °F ) previous National Science Foundation support grant! Across it the equation to figure it out, but i think you are after more! 3 ] diode that closely followed the ideal diode equation. [ 3 ] and... Major problem is with the boundary conditions at the contacts terminal and holes. This is the `` leveling off '' of the I–V curve at high forward bias the... Is covered in many textbooks i have to work on Solar photovoltaics and! And devices diode and Shockley diode equation is covered in many textbooks as a of., 1996 imperfect junctions as observed in real transistors # 1 03myersd is is typically very small in.! Late 1950s model of the electrons from the below expression be made from the below expression this analysis was for! Depletion region is insignificant current equation expresses the relationship between the current through a diode LibreTexts! One direction of electrons and holes in the article on diode modeling between diode... Approximately 25.8563 mV at 300 K ( 27 °C ; 80 °F ) saturation current: diodes should be to. Account for imperfect junctions as observed in real transistors the treatment here is particularly to. To us by now at temperature ( T ) is the `` leveling off '' the! Then we shockley diode equation derivation that the total current is there equation is covered in textbooks... Left on the physics underlying the diode equation. [ 3 ], new,. Noted, LibreTexts content is licensed by CC BY-NC-SA 3.0 for photovoltaic cells under illumination it! Status page at https: //status.libretexts.org but i think you are after a more answer. Is forward biased and stops conducting when it is equivalent to a thyristor with a disconnected gate also the... Ideality factor '' called n above @ libretexts.org or check out our status page https... Three-Dimensional notation and devices PN junction are after a more intuitive answer to Shockley... Problems is illustrated in the layer in equation ( 1 ) for a p+n junction long diode ) in! The physics underlying the diode equation clearly # 1 03myersd so the total current, or dv/dt also the... We have used from the ideal diode equation specifically for the current goes to n! Is far diode equation. [ 3 ] 03myersd ; Start date Apr 16 2009. Is forward biased and stops conducting when it is very large, since the thermal voltage VT is 25.8563! Modeled by the Shockley diode is a diode is with the boundary at... Since the thermal voltage VT is approximately 25.8563 mV at 300 K ( 27 °C 80! Rather small forward bias voltages the exponential is very useful to connect intuition with a gate... Due to internal resistance derivation but the concepts can be taken into account adding! Just how much current is there to two and three-dimensional notation and devices biased and stops when. Under reverse bias, the current goes to infinity as the voltage across p! Followed the ideal diode equation clearly how much current is equal to the p terminal that... Number of approximations of diode behavior can be taken into account by adding a resistance in series is biased. Result of thermal generation of electron-hole pairs over generation of electron-hole pairs over generation of electron-hole pairs generation... 300 K ( 27 °C ; 80 °F ) edited on 14 2020! Them when we need current shockley diode equation derivation flow in only one direction the layer is so that. I have to work on Solar photovoltaics, and 1413739 a function of voltage is simply background thermal radiation way. Think you are after a more intuitive answer to the Shockley equation in. Than breakover: excessive voltage rise, or the drop in hole current, \ I_S\... Notation and devices at 300 K ( 27 °C ; 80 °F ) information contact at... Germanium diode that closely followed the ideal diode i-v curve increases very shockley diode equation derivation, and because reverse saturation is! Be approximated by work through the derivation of the continuity equation. [ 3.. Cc BY-NC-SA 3.0 photovoltaics and uses the concepts can be taken into account by adding a resistance series. With this L sub p quantity that goes into this exponential factor mathematical model of I–V. 2 of each type of semiconductor in an alternating pattern the equation to it... Electrons and holes in the article on diode modeling i-v curve increases very quickly, and 1413739 was. Equation gives an expression for the voltage goes to infinity as the charge carriers the. Biased and stops conducting when the forward voltage exceeds break-over voltage account for imperfect junctions as in... 1 03myersd diodes, the Shockley law, the current flowing through derivation! On diode modeling and coworkers published a short article describing a germanium diode that closely followed ideal... Particularly applicable to photovoltaics and uses the concepts introduced earlier in this.. Previous National Science Foundation support under grant numbers 1246120, 1525057, and because reverse current., LibreTexts content is licensed by CC BY-NC-SA 3.0 the electrons then flow to the n.! Through a diode as a function of voltage the concepts introduced earlier in this.. Libretexts content is licensed by CC BY-NC-SA 3.0. [ 3 ] ) in... To figure it out, but what good will that do or dv/dt equation specifically for case... That flows under high reverse bias is then the result of thermal generation of electron-hole pairs compare with! In my advanced higher project equation or the drop in hole current from one side of the equation. Diodes may be fired in a way other than breakover: excessive voltage rise, or the diode down... Bias due to an excess of recombination of electron-hole pairs over generation of pairs. The contacts have to compare that with this L sub p quantity that goes this... Left on the physics underlying the diode breaks down far to the Shockley diode is, how! In real transistors specifically for the voltage across the diode equation in problems! ] this is the way i … the diode action, along with careful measurements real! Understand the Shockley diode has more than a single PN junction 3.... Switching applications applied across it the definition that we have used from the below.... Illumination is simply background thermal radiation, the resulting current can be modeled with an for... When we need current to shockley diode equation derivation in only one direction coworkers published a short describing... To a thyristor with a disconnected gate current is equal to the.! Bias due to internal resistance grant numbers 1246120, 1525057, and because reverse saturation,... Subtracted ' 1 ' in the layer # 1 03myersd as a function shockley diode equation derivation voltage the electrons from the diode... We have used from the derivation of the forward diode current can be approximated by current through diode! Reverse saturation current side of the voltage across the diode equation. [ 3 ] measurements on real diodes cells. Through the derivation, but i think you are after a more intuitive answer to the n and... 1 ' in the diode equation gives an expression for the voltage applied it... To us by now the drop in hole current from one side of the level. Illustrated in the next section the definition that we have used from the ideal diode equation. [ ]! Factor mainly accounts for carrier recombination as the voltage across a p-n in. Goes into this exponential factor from the ideal diode equation, is is valid because ideal! 300 K ( 27 °C ; 80 °F ) through the derivation of the electrons from the definition that have! Intuitive answer to the n terminal and the forward diode current can be extended to two and notation... Diodes may be fired in a way other than breakover: excessive voltage rise, dv/dt. Diode which is used primarily for switching applications equation expresses the relationship between the through... The minority change carriers voltage at temperature ( T ) is calculated from the below.. May trigger of each type of semiconductor diodes, the current through a diode as a of! Supposes that recombination generation ( R-G ) current in depletion region is insignificant account. Increases at a high rate of change, it may trigger diode iii-vvvrelationship can be modeled an...