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Ch 42: Molecules and Condensed Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
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Capitolo 42, Problema 31a

A forward-bias voltage of 15.015.0 mV produces a positive current of 9.259.25 mA through a p−np-n junction at 300300 K. What does the positive current become if the forward-bias voltage is reduced to 10.010.0 mV?

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Understand the relationship between the current and voltage in a p-n junction diode. The current through a diode is given by the Shockley diode equation: I = I_s (e^(qV / kT) - 1), where I is the current, I_s is the reverse saturation current, q is the charge of an electron, V is the forward-bias voltage, k is Boltzmann's constant, and T is the temperature in kelvins.
Recognize that the temperature T is constant at 300 K, and the reverse saturation current I_s does not change. The relationship between the current and voltage is exponential, so a small change in voltage will result in a significant change in current.
Use the Shockley diode equation to express the ratio of the currents at the two voltages. Let I_1 and I_2 be the currents at voltages V_1 = 15.0 \, \(\text{mV}\) and V_2 = 10.0 \, \(\text{mV}\), respectively. The ratio is given by: \(\frac{I_2}{I_1}\) = e^{q(V_2 - V_1) / kT}.
Substitute the known values into the ratio equation. Use q = 1.6 \(\times\) 10^{-19} \, \(\text{C}\), k = 1.38 \(\times\) 10^{-23} \, \(\text{J/K}\), and T = 300 \, \(\text{K}\). The voltage difference is V_2 - V_1 = 10.0 \, \(\text{mV}\) - 15.0 \, \(\text{mV}\) = -5.0 \, \(\text{mV}\), or -5.0 \(\times\) 10^{-3} \, \(\text{V}\).
Calculate the exponential factor e^{q(V_2 - V_1) / kT} to find the ratio \(\frac{I_2}{I_1}\). Multiply this ratio by the given current I_1 = 9.25 \, \(\text{mA}\) to determine the new current I_2.

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p-n Junction

A p-n junction is formed by joining p-type and n-type semiconductors, creating a diode that allows current to flow primarily in one direction. The p-type material has an abundance of holes (positive charge carriers), while the n-type has excess electrons (negative charge carriers). This structure is fundamental in understanding how diodes operate under different voltage conditions.
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Kirchhoff's Junction Rule

Forward Bias

Forward bias occurs when the positive terminal of a voltage source is connected to the p-type material and the negative terminal to the n-type material of a diode. This reduces the barrier potential at the junction, allowing charge carriers to recombine and resulting in a flow of current. The amount of current is dependent on the applied voltage and the characteristics of the diode.
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Shockley Diode Equation

The Shockley diode equation describes the current flowing through a diode as a function of the applied voltage. It is given by I = I0 (e^(qV/kT) - 1), where I0 is the reverse saturation current, q is the charge of an electron, V is the voltage across the diode, k is Boltzmann's constant, and T is the absolute temperature. This equation illustrates how current changes exponentially with small variations in forward-bias voltage.
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