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1 Chapter 5-2 Quantitative electrostatic relationships We make the analysis in 1 dimension, even though actual diode as shown may not be a one-dimensional system. This makes the analysis simple. The metallurgical junction is located at x = 0.

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2 Quantitative analysis: Electric field E p n NANA NDND x p 0x n W E max = q N A x p / = q N D x n /

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3 Relationship between x n and x p E max = q N A x p / = q N D x n / N A x p = N D x n Net charge on p-side = Net charge on n-side Depletion layer width: W = x n + x p If N A >> N D, then W x n and if N A << N D, then W x p

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4 Built-in voltage: V bi V bi = {area under E versus x curve} = (1/2) [ W (– q N D x n / ) ] = [q / (2 )] N D x n W

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5 Quantitative analysis: Electrostatic potential V x V bi

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6 Step junction with V A 0 The equation for W is similar to the earlier equation except that V bi is replaced by V bi V A ; (V A is restricted to V A < V bi ). V A = Applied Voltage

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7 Effects of forward and reverse bias

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8 PN-junction energy-band diagrams

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9 Example 1 N D = 2 10 16 cm –3 N A = 3 10 17 cm –3 N A = 1 10 16 cm –3 N D = 2 10 17 cm –3 Consider the following diode. Calculate the maximum electric field, E max, the location of E max, the depletion layer width W, x n and x p and the built-in voltage, V bi. Carefully plot the charge density, electric field, and the potential as a function of x. Also, calculate the depletion layer width and the maximum electric field if a reverse voltage of 10 V is applied across the diode. What will be W if V A = 0.5 V?

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10 Example 2 Consider the diode of Example 1. Calculate the depletion layer width and the maximum electric field if a reverse voltage of 10 V is applied across the diode. Calculate the depletion layer width in the n-side and p-side under this biased condition. What will be W if V A = 0.5 V? What happens if we apply V A > V bi ?

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© 2012 Eric Pop, UIUCECE 340: Semiconductor Electronics ECE 340 Lectures 19-20 P-N diode in equilibrium So far we studied: Energy bands, doping, Fermi.

© 2012 Eric Pop, UIUCECE 340: Semiconductor Electronics ECE 340 Lectures 19-20 P-N diode in equilibrium So far we studied: Energy bands, doping, Fermi.

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