UNIVERSITY OF CALIFORNIA
College of Engineering
Department of Electrical Engineering and Computer Sciences
EE 130
Spring 2007
Discussion Section 102
Frank Liao
Worksheet 2A
Identify the source of non-idealities (A, B, C, D, and E) in the I-V characteristic of a
room temperature Si diode. Notice the forward bias region is on a semi-log plot and the
reverse bias region is on a linear scale.
log I
E
D
Ideal
-VA
C
VA
B
A
-I
A2, B3, C1, D5, E4
1. Thermal recombination in the
depletion region
2. Avalanching and/or Zener process
3. Thermal generation in the depletion
region
4. Series resistance
5. High level injection
Consider an ideal pn+ step-junction narrow-base Si diode maintained at 300K with crosssectional area A = 10-4 cm2. The doping concentration on the p-type side is NA = 1016 cm-3
(uncompensated). (The n-type side is degenerately doped.) The electron recombination
lifetime in the p-type region is n = 10-6 s. The width of the p-type region is 1 μm.
a) For VA = 0.7 V, calculate the magnitude of the minority-carrier charge stored in the
quasi-neutral p-type region.
The stored charge is the area underneath the carrier concentration profile.
WP
QN  qA  n p ( x)dx
0
np(x”)
QN [=] Area under curve
x”
np0[e(qVA/kT)-1]
0
WP’
First we calculate the width of the quasi neutral region
 1016 cm 3 
EG kT  N A 
  0.56V  0.026V ln  10 3   0.92V
Vbi 

ln 
2q q  ni 
 10 cm 
W  xp 
2 Si (Vbi  V A )

qN A
2  1.04  10 12 F / cm(0.92V  0.7V )
 0.17 m
1.6  10 19 C (1016 cm 3 )
 WP  WP  x p  1m  0.17 m  0.83m
'
Now find the stored charge using the area of a triangle:
2
QN


n
1
1
'
'
  qAn p ( x"  0)WP   qA i e ( qVA / kT )  1 WP
2
2
NA
 (0.5)(1.6  10 19 C )(10 4 cm 2 )( 4.9 1015 cm 3 )(0.98 10 4 cm)  3.8  10 12 C
b) How would the current change if the width of the p-type region is reduced? Explain
briefly.
The current would increase since the slope of the minority carrier concentration will
increase.
c) How would your answers to part (a) and (b) change if NA decreases?
The peak minority carrier concentration will increase so there will be more charge
stored in the diode. There will be more current since
-Vbi decreases
-the min. carrier concentration gradient will increase
-higher mobility and diffusion length
d) If I decrease τn to 10-7 s, will there be more or less charge be stored? What if this was
a long-base diode?
If τn decreases to 10-7 s, Ln will still be greater than W (see below), so there will be no
change in the amount of stored charge since this is a short-base diode. However, if
this was a long-base diode then less charge stored in the diode.
DN   n
kT
 801cm 2 V 1 s 1  0.026V  20.8 cm 2 / s
q
 LN  DN  n  20.8  10 7 cm 2  14.4 m
 LN  14.4m  WP  1m  W ' P  WP  xn
e) Which one switches faster: a long base or short base diode?
The short base diode because less charge is stored.