Find the breakdown voltage? Please give the answer with details.

The breakdown voltage of an insulator is the minimum voltage that causes a portion of an insulator to become electrically conductive.For diodes, the breakdown voltage is the minimum reverse voltage that makes the diode conduct appreciably in reverse. Some devices (such as TRIACs) also have a forward breakdown voltage.Solids EditBreakdown voltage is a characteristic of an insulator that defines the maximum voltage difference that can be applied across the material before the insulator conducts. In solid insulating materials, this usually[citation needed] creates a weakened path within the material by creating permanent molecular or physical changes by the sudden current. Within rarefied gases found in certain types of lamps, breakdown voltage is also sometimes called the "striking voltage".[1]The breakdown voltage of a material is not a definite value because it is a form of failure and there is a statistical probability whether the material will fail at a given voltage. When a value is given it is usually the mean breakdown voltage of a large sample. Another term is also withstand voltage, where the probability of failure at a given voltage is so low it is considered, when designing insulation, that the material will not fail at this voltage.Two different breakdown voltage measurements of a material are the AC and impulse breakdown voltages. The AC voltage is the line frequency of the mains. The impulse breakdown voltage is simulating lightning strikes, and usually uses a 1.2 microsecond rise for the wave to reach 90% amplitude, then drops back down to 50% amplitude after 50 microseconds.[2]Two technical standards governing performing these tests are ASTM D1816 and ASTM D3300 published by ASTM.[3]Gases and vacuum EditMain article: Gas dischargeIn standard conditions at atmospheric pressure, air serves as an excellent insulator, requiring the application of a significant voltage of 30 kV/cm before breaking down (e.g., lightning). In partial vacuum, this breakdown potential may decrease to an extent that two uninsulated surfaces with different potentials might induce the electrical breakdown of the surrounding gas. This may damage an apparatus, as breakdown is analogous to a short circuit.In a gas, the breakdown voltage can be determined by Paschen`s law.The breakdown voltage in a partial vacuum is represented as[4][5][6]{\displaystyle V_{\mathrm {b} }={\frac {B\,p\,d}{\ln \left(A\,p\,d\right)-\ln \left[\ln \left(1+{\frac {1}{\gamma _{\mathrm {se} }}}\right)\right]}}} {\displaystyle V_{\mathrm {b} }={\frac {B\,p\,d}{\ln \left(A\,p\,d\right)-\ln \left[\ln \left(1+{\frac {1}{\gamma _{\mathrm {se} }}}\right)\right]}}}where {\displaystyle V_{\mathrm {b} }} V_{{\mathrm {b}}} is the breakdown potential in volts DC, {\displaystyle A} A and {\displaystyle B} B are constants that depend on the surrounding gas, {\displaystyle p} p represents the pressure of the surrounding gas, {\displaystyle d} d represents the distance in centimetres between the electrodes,[clarification needed] and {\displaystyle \gamma _{\mathrm {se} }} \gamma _{{\mathrm {se}}} represents the Secondary Electron Emission Coefficient.A detailed derivation and some background information is given in the article about Paschen`s law.Diodes and other semiconductors EditDiode I-V diagramBreakdown voltage is a parameter of a diode that defines the largest reverse voltage that can be applied without causing an exponential increase in the leakage current in the diode. As long as the current is limited, exceeding the breakdown voltage of a diode does no harm to the diode. In fact, Zener diodes are essentially just heavily doped normal diodes that exploit the breakdown voltage of a diode to provide regulation of voltage levels.Rectifier diodes (semiconductor or tube/valve) may have several voltage ratings, such as the Peak Inverse Voltage (PIV) across the diode, and the maximum RMS input voltage to the rectifier circuit (which will be much less).Many small-signal transistors need to have any breakdown currents limited to much lower values to avoid excessive heating. To avoid damage to the device, and to limit the effects excessive leakage current may have on the surrounding circuit, the following bipolar transistor Maximum Ratings are often specified:VCEO (sometimes written BVCEO or V(BR)CEO – the maximum voltage between collector and emitter that can be safely applied (and with no more than some specified leakage current, often) when no circuit at the base of the transistor is there to remove collector-base leakage. Typical values: 20 Volts to as high as 700 Volts; very early Germanium point-contact transistors such as the OC10 had values around 5 Volts or less.VCBO – the maximum collector-to-base voltage, with emitter open-circuit. Typical values 25 to 1200 Volts.VCER – the maximum voltage rating between collector and emitter with some specified resistance (or less) between base and emitter. A more realistic rating for real-world circuits than the open-base or open-emitter scenarios above.VEBO – the maximum reverse voltage on the base with respect to the emitter.VCES – collector to emitter rating when base is shorted to emitter; equivalent to VCER when R = 0;Field Effect transistors have similar maximum ratings, the most important one for Junction FETs is the gate-drain rating.Some devices may also have a maximum rate of change of voltage specified.