4. For a silicon linearly graded junction with an impurity gradient of 5 x 10'/cm“, (a) calculate built-in potential (b) calculate depletion width Hint: Use iteration method using Eqs. 31 and 32, p. 93) given in example 3, p. 94 or Lecture 10 (Slide 25)

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For a silicon linearly graded junction with an impurity gradient of 1020 cm“, calculate the depletion-layer width
and the maximum field and built-in voltage (T= 300 K).
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SOLUTION To solve the transcendental equation of Eq. 32, we can use a simple numeric method to find the built-i
potential Vi and the depletion layer width W simultaneously. We start with a reasonable V value, e.g., 0.3 V, to
calculate W by Eq. 31. W is 0.619 µm. Then, W and a are substituted in Eq. 32 to obtain V Vi, is 0.657 V. This
Vi value is substituted in Eq. 31 to obtain a new W, and in turn to calculate a new Vi- After several trials as show
in the following table, we obtain the final V of 0.671 V and W of 0.809 µm.
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bi.
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trial
1
3
4
bi (V)
W (um)
0.3
0.657
0.670
0.671
0.671
0.619
0.804
0.809
0.809
0.809
qaW²
E =
1.6×10-19 ×10²0 ×(0.809×10*)²
= 1.24×10* V / cm
8E s
8×11.9×8.85×10-14
1/3
12ɛ,V.
(aW / 2)(aW / 2)
aW \ Eq (32)
kT
Eq (31) V¼=
2kT
In
2n,
W =
s' bi
In
qa
bi
2
Semiconductor Devices, 2/E by S. M. Sze
Copyright © 2002 John Wiley & Sons. Inc. All rights reserved.
Bhaskar L Mantha, SJSU, EE 221
25
5:57 AM
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25-Mar-22
Transcribed Image Text:PowerPoint Presentation - Adobe Reader File Edit View Window Help 25 / 35 Tools Fill & Sign Comment Оpen 113% IT Sign In • Export PDF Example 3 (p. 94) • Create PDF v Edit PDF For a silicon linearly graded junction with an impurity gradient of 1020 cm“, calculate the depletion-layer width and the maximum field and built-in voltage (T= 300 K). Adobe Acrobat Pro Easily edit text and images in PDF documents Start Now SOLUTION To solve the transcendental equation of Eq. 32, we can use a simple numeric method to find the built-i potential Vi and the depletion layer width W simultaneously. We start with a reasonable V value, e.g., 0.3 V, to calculate W by Eq. 31. W is 0.619 µm. Then, W and a are substituted in Eq. 32 to obtain V Vi, is 0.657 V. This Vi value is substituted in Eq. 31 to obtain a new W, and in turn to calculate a new Vi- After several trials as show in the following table, we obtain the final V of 0.671 V and W of 0.809 µm. • Combine PDF • Send Files bi. • Store Files trial 1 3 4 bi (V) W (um) 0.3 0.657 0.670 0.671 0.671 0.619 0.804 0.809 0.809 0.809 qaW² E = 1.6×10-19 ×10²0 ×(0.809×10*)² = 1.24×10* V / cm 8E s 8×11.9×8.85×10-14 1/3 12ɛ,V. (aW / 2)(aW / 2) aW \ Eq (32) kT Eq (31) V¼= 2kT In 2n, W = s' bi In qa bi 2 Semiconductor Devices, 2/E by S. M. Sze Copyright © 2002 John Wiley & Sons. Inc. All rights reserved. Bhaskar L Mantha, SJSU, EE 221 25 5:57 AM Type here to search 26°C 25-Mar-22
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For a silicon linearly graded junction with an
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impurity gradient of 5 x 101/cm“,
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(a) calculate built-in potential
(b) calculate depletion width
Hint: Use iteration method using Eqs. 31 and 32,
p. 93) given in example 3, p. 94 or
Lecture 10 (Slide 25)
9:28 AM
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---
II
Transcribed Image Text:A Homework 6b 03182022.docx.pdf - Adobe Reader File Edit View Window Help Tools Fill & Sign Comment Оpen 3 176% IT Sign In • Export PDF • Create PDF v Edit PDF A. Adobe Acrobat Pro Easily edit text and images in PDF documents Start Now For a silicon linearly graded junction with an • Combine PDF impurity gradient of 5 x 101/cm“, • Send Files • Store Files (a) calculate built-in potential (b) calculate depletion width Hint: Use iteration method using Eqs. 31 and 32, p. 93) given in example 3, p. 94 or Lecture 10 (Slide 25) 9:28 AM Type here to search 28°C 24-Mar-22 --- II
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