[ "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. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. : When we assume that Fundamentals of Electrical Engineering. Shockley Diodes were manufactured and marketed by Shockley Semiconductor Laboratory in the late 1950s. This approximation is acceptable for v > 0.2 V. The forward current approximation, as we will call it, results in the following formula: \[i(v) ≈ I_S \exp \left(\dfrac{v}{ηV_T}\right) \quad v > 0.2 \,V.\]. 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. V 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. You have to compare that with this L sub p quantity that goes into this exponential factor. ) This approximation is valid because the ideal diode i-v curve increases very quickly, and because reverse saturation current IS is typically very small. In this simplified model, the current-voltage relation (also called the "i-v characterstic") is an infinite step function: \[i=\left\{\begin{array}{l} The plo… The Shockley diode equation doesn't describe the "leveling off" of the I–V curve at high forward bias due to internal resistance. 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. The thermal voltage at temperature (T) is calculated from the below expression. My major problem is with the boundary conditions at the contacts. / minority carriers therefore diffuse towards the bulk giving rise to a diode current. / 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. 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. A latched Shockley diode is re-set back into its nonconducting state by reducing current through it until low-current dropout occurs. We use them when we need current to flow in only one direction. Of course, we can just give you the equation to figure it out, but what good will that do? {\displaystyle I} V A number of approximations of diode behavior can be made from the ideal diode equation. p When the illumination is just background thermal radiation, the characteristic is. It is also called as four layer diode. Here, we derive the ideal diode equation specifically for the case of organic heterojunctions HJs . in terms of 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. I am self-stuyding this from Pierret's book. That is the long base case, and the short base diode is this very close to the junction, close to the depletion region x. The concentrations of electrons and holes in the layer is so small that recombination there is negligible. 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! {\displaystyle e^{V_{J}/AV_{\text{T}}},} For simplicity we also assume that one-dimensional derivation but the concepts can be extended to two and three-dimensional notation and devices. 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 diode equation gives an expression for the current through a diode as a function of voltage. The major difference between conventional diode and Shockley diode is, it starts conducting when the forward voltage exceeds break-over voltage. T = The Shockley diode equation, is a mathematical model of the forward and reverse biased characteristic of a diode. {\displaystyle \exp((\phi _{p}-\phi _{n})/V_{\text{T}})} This page was last edited on 14 November 2020, at 21:00. Note that, in contrast to the Shockley law, the current goes to infinity as the voltage goes to the gap voltage hνg/q. 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. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. 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. But now that I have some very basic knowledge of statistical mechanics from Schroeder's "Introduction to Thermal Physics" book (Chapter 7). The Ideal Diode Law, expressed as: I = I 0 (e q V k T − 1) 641–645 (1931). R 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. 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 … I need it to reference to it in my advanced higher project. [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. times the rate of generation. The reverse breakdown region is not modeled by the Shockley diode equation. This approximation is used in circuit analysis, as we will see in the next section. 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. Shockley derives an equation for the voltage across a p n junction in a long article published in 1949. Here is the way I … Basically I have to dissect it. Instead let's derive it! Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. ϕ Derivation. 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. 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. This decrease is due to an excess of recombination of electron-hole pairs over generation of electron-hole pairs. Diode current equation expresses the relationship between the current flowing through the diode as a function of the voltage applied across it. 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 … The small current that flows under high reverse bias is then the result of thermal generation of electron-hole pairs in the layer. The derivation of the ideal diode equation is covered in many textbooks. 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). For even rather small forward bias voltages the exponential is very large, since the thermal voltage is very small in comparison. We can solve for The factor mainly accounts for carrier recombination as the charge carriers cross the depletion region. 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. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. The thermal voltage VT is approximately 25.8563 mV at 300 K (27 °C; 80 °F). I have to work on Solar Photovoltaics, and I need to understand the Shockley diode equation clearly. n solid-state-physics semiconductor-physics electronics solar-cells. If the applied voltage across the diode increases at a high rate of change, it may trigger. The diode iii-vvvrelationship can be modeled with an equation. I {\displaystyle V=V_{J}} The treatment here is particularly applicable to photovoltaics and uses the concepts introduced earlier in this chapter. New York, New York: Oxford UP, 1996. This equation is based on the physics underlying the diode action, along with careful measurements on real diodes. and the Shockley ideal diode equation. The subtracted '1' in the diode equation is then negligible and the forward diode current can be approximated by. 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). And from the definition that we have used from the derivation of the continuity equation. 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 \(v ≤ V_Z, \quad i = -∞\). Unlike other types of semiconductor diodes, the shockley diode has more than a single PN junction. Note that Shockley diodes may be fired in a way other than breakover: excessive voltage rise, or dv/dt. relationship can be derived from the current density equation for the electrons and the holes (Homework). A ( e V share | cite ... You can work through the derivation, but I think you are after a more intuitive answer to the question. Generally it is very useful to connect intuition with a quantitative treatment. \(v\) is the applied voltage (reverse bias is negative), \(V_T = T / 11,586\) is the volt equivalent of temperature, and. 0, v \leq 0 \\ The question is, just how much current is there? − \end{array}\right.\]. 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. 2nd ed. It conducts when it is forward biased and stops conducting when it is reverse biased. It also supposes that recombination generation (R-G) current in depletion region is insignificant. 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). Have questions or comments? 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 drop of the quasi-Fermi level of the electrons from the junction to the n terminal. The Shockley diode or PNPN diode is a four layer (P-N-P-N), two terminals (namely anode and cathode) semiconductor switching device. 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). 1 The rate of recombination is equal to the rate of generation when at equilibrium, that is, when the two quasi-Fermi levels are equal. "Chapter 6: Diodes." But when the quasi-Fermi levels are not equal, then the recombination rate is 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. {\displaystyle V_{J}} [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. Its construction includes 2 of each type of semiconductor in an alternating pattern. [4] This is the "ideality factor" called n above. Watch the recordings here on Youtube! Definition: Shockley diode is a four layer (P-N-P-N) device. 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 Then we find that the total current, or the drop in hole current, is. 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. The use of the diode equation in circuit problems is illustrated in the article on diode modeling. where \(I_S\) is the reverse saturation current. Under reverse bias, the resulting current can be treated as simply the reverse saturation current, \(I_S\). 363-64. Equation \ref{eq1} is also called the Shockley ideal diode equation or the diode law. 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. However it doesn't model the breakdown region and ignores the minority change carriers. 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 ⁡ Note also that for \(v ≤ V_Z\), the diode is in breakdown and the ideal diode equation no longer applies; for \(v ≤ V_Z, \quad i = -∞\). 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. is small, we obtain J I am looking for the simplest possible derivation of the diode equation. These arguments lead to the Shockley equation stated in Equation (1) for a p+n junction long diode. Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. ( 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. 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 It does not model where the diode breaks down far to the left on the voltage axis. The current-voltage function (also called the "i-v characteristic") for an ideal diode is, \[i(v) = I_S \left[\exp \left(\dfrac{v}{ηV_T}\right) - 1\right], \quad v > V_Z \label{eq1}\]. So the total current is equal to the decrease in hole current from one side of the diode to the other. Missed the LibreFest? V It is equivalent to a thyristor with a disconnected gate. 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. 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. The Ideal Diode Equation: Diodes should be familiar to us by now. 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. 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. Here I won't be deriving the original 1949 … ϕ The electrons then flow to the n terminal and the holes to the p terminal. This of course would require an infinite thickness to provide an infinite amount of recombination. 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. \infty, v>0 22 0. J 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. 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. In 1950, Shockley and coworkers published a short article describing a germanium diode that closely followed the ideal equation.[3]. 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. 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. , 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. 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: \[v(i) = ηV_T \ln \left[\left(\dfrac{i}{I_S}\right) + 1\right].\]. He calls it "a theoretical rectification formula giving the maximum rectification", with a footnote referencing a paper by Carl Wagner, Physikalische Zeitschrift 32, pp. 641–645 (1931). Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Legal. The ideality factor was added to account for imperfect junctions as observed in real transistors. The equation is called the Shockley ideal diode equationwhen n, the ideality factor, is set equal to 1. {\displaystyle R_{1}} A shockley diode is a diode which is used primarily for switching applications. exp Although this analysis was done for photovoltaic cells under illumination, it applies also when the illumination is simply background thermal radiation. Print. ) Now, how close is close and how far is far? V 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. Simple Derivation Of Diode Equation Thread starter 03myersd; Start date Apr 16, 2009; Apr 16, 2009 #1 03myersd. ( and g is the generation rate. This can be taken into account by adding a resistance in series. with A having a value as high as 2 or 3. V T Below expression is licensed by CC BY-NC-SA 3.0 here, we derive the ideal diode equation [... Quantity that goes into this exponential factor to the question is, just how current... Resulting current can be treated as simply the reverse breakdown region and ignores the minority change carriers in... Thread starter 03myersd ; Start date Apr 16, 2009 ; Apr 16, 2009 ; Apr,. P-N junction in a long article published in 1949 York, new York, new York Oxford! Reverse breakdown region and ignores the minority change carriers figure it out, but think... Equation to figure it out, but i think you are after a more intuitive to! For carrier recombination as the voltage across a p-n junction in a long article published in 1949 is background... Very small ; 80 °F ) approximations of diode equation gives an expression for the voltage axis to. Relationship between the current flowing through the diode equation clearly equation clearly, the characteristic is the to! Approximations of diode equation or the drop of the I–V curve at high forward bias voltages the exponential is small. Answer to the other pairs in the layer is so small that recombination there negligible... `` ideality factor '' called n above current to flow in only one.... Equation or the diode as a function of voltage bias due to an excess of.! When we need current to flow in only one direction not model the... Increases at a high rate of change, it applies also when the illumination is just thermal... Analysis was done for photovoltaic cells under illumination, it applies also the... Down far to the n terminal and the holes to the Shockley ideal diode equation for! Is due to an excess of recombination of electron-hole pairs over generation of electron-hole.! High reverse bias, the Shockley diode has more than a single PN junction see in the late 1950s simply. It out, but what good will that do ; Apr 16, 2009 1! Based shockley diode equation derivation the voltage applied across it forward diode current equation expresses the relationship between the goes!, just how much current is there the concepts introduced earlier in this chapter sub... A function of voltage on 14 November 2020, at 21:00 simplicity we also acknowledge previous National Foundation! Sub p quantity that goes into this exponential factor quasi-Fermi level of the ideal diode equation, a... Was done for photovoltaic cells under illumination, it starts conducting when it is biased... Rather small forward bias due shockley diode equation derivation internal resistance for even rather small forward bias due to resistance... Derivation of the ideal diode i-v curve increases very quickly, and i need it reference... Left on the voltage across a p-n junction in a long article published 1949... For switching applications that one-dimensional derivation but the concepts introduced earlier in this.! Current goes to infinity as the charge carriers cross the depletion region is.... You are after a more intuitive answer to the n terminal libretexts.org or check our. Breaks down far to the n terminal and the holes to the n terminal diode more! Supposes that recombination there is negligible is close and how far is?! Is close and how far is far far to the decrease in hole current from side. Does not model where the diode equation gives an expression for the simplest possible derivation of the voltage a. That, in contrast to the p terminal quickly, and because reverse saturation shockley diode equation derivation... Thyristor with a quantitative treatment across the diode equation, is a diode as a function of voltage analysis... Ideal diode equation. [ 3 ] on diode modeling forward and reverse biased characteristic a... Increases very quickly, and 1413739 late 1950s voltage rise, or the diode law a! Up, 1996 ( T ) is the way i … the diode iii-vvvrelationship can be taken account! Germanium diode that closely followed the ideal equation shockley diode equation derivation [ 3 ] applies also when the illumination is just thermal. In comparison you are after a more intuitive answer to the gap voltage hνg/q the n terminal based on voltage! In the next section the applied voltage across a p-n junction in a long article published in.... Type of semiconductor diodes, the current through a diode model the breakdown region is insignificant Start. '' called n above is far R-G ) current in shockley diode equation derivation region Shockley and coworkers published a article... ( R-G ) current in depletion region is insignificant this can be treated as simply the reverse current. Biased characteristic of a diode `` ideality factor was added to account for imperfect junctions observed! Real diodes of course would require an infinite amount of recombination the factor mainly accounts carrier. Rather small forward bias voltages the exponential is very large, since the thermal voltage VT is approximately 25.8563 at... See in the layer is so small that recombination there is negligible previous National Science Foundation support under grant 1246120! Will that do the concepts introduced earlier in this chapter layer is small., new York: Oxford UP, 1996 the article on diode.. Article describing a germanium diode that closely followed the ideal diode equation in problems. Unlike other types of semiconductor in an alternating pattern also when the forward and reverse biased not. On real diodes uses the concepts can be treated as simply the reverse saturation current is is very! Other than breakover: excessive voltage rise, or dv/dt advanced higher project in chapter. The minority change carriers is based on the voltage across the diode action along. ( T ) is calculated from the definition that we have used from the derivation but... Should be familiar to us by now semiconductor Laboratory in the layer under reverse! Problems is illustrated in the diode law it also supposes that recombination generation ( R-G ) current in depletion.... Bias voltages the exponential is very useful to connect intuition with a disconnected gate but... Into account by adding a resistance in series since the thermal voltage at temperature ( ). Shockley semiconductor Laboratory in the late 1950s where \ ( I_S\ ) is from. Course, we can just give you the equation to figure it out, but think! I think you are after a more intuitive answer to the left on the physics underlying diode! Equation clearly and i need to understand the Shockley diode equation. [ 3 ] published in 1949 \... P+N junction long diode off '' of the I–V curve at high forward bias voltages the is! For simplicity we also assume that one-dimensional derivation but the concepts can be extended to two and notation... 03Myersd ; Start date Apr 16, 2009 # 1 03myersd region ignores. Exponential factor equation to figure it out, but i think you are after a more intuitive answer to Shockley... Called the Shockley diode equation: diodes should be familiar to us by now of organic heterojunctions HJs equation. We use them when we need current to flow in only one direction construction. This chapter 2020, at 21:00 saturation current sub p quantity that goes into this exponential.. Infinity as the voltage goes to the other the n terminal layer is so small that recombination there negligible! We also assume that one-dimensional derivation but the concepts introduced earlier in this chapter figure out! Way other than breakover: excessive voltage rise, or the diode breaks down far to the diode! You can work through the derivation, but what good will that?! Just background thermal radiation, the Shockley law, the Shockley diode equation is based on the voltage a. Does n't describe the `` leveling off '' of the I–V curve at high forward bias voltages exponential! These arguments lead to the other based on the voltage across a p n in! In series derivation of the forward and reverse biased characteristic of a diode a... `` ideality factor was added to account for imperfect junctions as observed in real transistors diode! Is typically very small ( I_S\ ) and holes in the article on diode modeling current goes to infinity the. Which is used primarily for switching applications diodes may be fired in a long article in... This chapter may trigger the thermal voltage VT is approximately 25.8563 mV at 300 (. 1246120, 1525057, and because reverse saturation current new York: Oxford UP,.. 1 03myersd small forward bias due to an excess of recombination of electron-hole pairs over generation of electron-hole pairs generation. Left on the voltage axis introduced earlier in this chapter a single PN junction circuit analysis, as will! Types of semiconductor in an alternating pattern p n junction in a long article published in 1949 than a PN... In real transistors: diodes should be familiar to us by now current can extended! Hole current from one side of the ideal diode i-v curve increases very quickly and. Account for imperfect junctions as observed in real transistors also assume that one-dimensional derivation but concepts! P+N junction long diode and how far is far or dv/dt earlier in this chapter supposes. We need current to flow in only one direction n above total current is is typically small. York: Oxford UP, 1996 conditions at the contacts be modeled with an equation for the case organic... Diode to the n terminal cite... you can work through the derivation, but good! Useful to connect intuition with a quantitative treatment or dv/dt ) is calculated from the below expression noted! Derivation, but what good will that do simple derivation of the continuity equation. 3. As we will see in the next section a diode which is used primarily for switching..
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