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Material Type: Notes; Professor: Schubert; Class: MICROELECTRONICS TECHNOLOGY; Subject: Electrical & Comp. Sys. Engr.; University: Rensselaer Polytechnic Institute; Term: Spring 2006;
Typology: Study notes
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1
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.
2
n p
D n
A p
s 0
where d
d
x x x x
N x x
q
N x x
q
x
ε
ε
ε= ε ε
p n
− x p 0 x n
E max = − q N A x p /ε = − q N D x n/ε
p n
n n
D
p p
A
x x x x
x x x x
qN
x x x x
qN x
ε
ε
3
E max = − q N A x p / ε = − q N D x n / ε
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
A D
D p A
A n D N N
x W N N
x W
If N A >> N D, then W ≈ x n and if N A << N D, then W ≈ x p
4
V x x x
V x x
or ( )d d
d (^) n
p
V bi = − {area under E versus x curve}
= − (1/2) [ W (– q N D x n / ε) ]
= [ q / (2ε)] N D x n W
A D
A n A D
A D^2 since 2
W x W N N
q N N
ε +
bi A D
q
7
8
9
N D = 2 × 10 16 cm–3^ N A = 3 × 10 17 cm– N A = 1× 10 16 cm–3^ N D = 2 × 10 17 cm–
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?
10
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?
