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