– Transient response: turn-on
– Summary of important concepts
– Diode applications
• Varactor diodes
• Tunnel diodes
• Optoelectronic diodes
Reading: Pierret 9; Hu 4.12-4.15

Consider a p + n diode (Q p
D p n
(x)
>> Q n
):
i(t) x x n
For t > 0: dp n dx x
 x n
  i qAD p

0
EE130/230A Fall 2013 Lecture 14, Slide 2 v
A
(t) t t

dQ p dt
 i

Q p
τ p

I
F

Q p for t
τ p

0

• By separation of variables and integration, we have
Q p
( t )

I
F
τ p
1

 e
 t /
τ p

• If we assume that the build-up of stored charge occurs quasi-statically so that
Q p
( t )

I diffusion
τ p

I
0
 e qv
A
/ kT 
1

τ p then v
A
t
 kT


 q
I
F
I
0

 e
 t / τ p
 

EE130/230A Fall 2013 Lecture 14, Slide 3

• If t p is large, then the time required to turn on the diode is approximately
D
Q/I
F
D
Q
 D
Q p
 D
Q j
EE130/230A Fall 2013 Lecture 14, Slide 4

• Under forward bias, minority carriers are injected into the quasi-neutral regions of the diode.
• The current flowing across the junction is comprised of hole and electron components.
– If the junction is asymmetrically doped (i.e. it is “one-sided”) then one of these components will be dominant.
• In a long-base diode, the injected minority carriers recombine with majority carriers within the quasineutral regions.
EE130/230A Fall 2013 Lecture 14, Slide 5

• The ideal diode equation stipulates the relationship between J
N
(-x p
) and J
P
(x n
):
J
N
(
 x p
)

J
P
( x n
)
D n
L p
N
D
D p
L n
N
A

 n i
2 p
 side n i
2 n
 side


 For example, if holes are forced to flow across a forward-biased junction, then electrons must also be injected across the junction.
EE130/230A Fall 2013 Lecture 14, Slide 6

• Under reverse bias, minority carriers are collected into the quasi-neutral regions of the diode.
– Minority carriers generated within a diffusion length of the depletion region diffuse into the depletion region and then are swept across the junction by the electric field.

The negative current flowing in a reverse-biased diode depends on the rate at which minority carriers are supplied from the quasi-neutral regions.
• Electron-hole pair generation within the depletion region also contributes negative diode current.
EE130/230A Fall 2013 Lecture 14, Slide 7

EE130/230A Fall 2013
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-21
Lecture 14, Slide 8

• Voltage-controlled capacitance
– Used in oscillators and detectors
(e.g. FM demodulation circuits in your radios)
– Response changes by tailoring doping profile:
C j

V r
 n
V for r

V bi n
 m
1

2
EE130/230A Fall 2013 Lecture 14, Slide 9

I
I
L


I
0 q V
( e A kT
 qA ( L
P

1

W
)


I
L
L
N
) G
L
EE130/230A Fall 2013 Lecture 14, Slide 10 R.F. Pierret, Semiconductor Fundamentals, Figure 9.2

OC
V oc

V
A
I

0
 kT q ln





L p t p
L p

W

L n

 p n
 L n t n n p
G
L

1



EE130/230A Fall 2013 Lecture 14, Slide 11 C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-25(b)

Cyferz at en.wikipedia
EE130/230A Fall 2013 Lecture 14, Slide 12

• Achieved by anisotropic wet etching (e.g. in KOH)
P. Papet et al ., Solar Energy Materials and Solar Cells, Vol. 90, p. 2319, 2006
EE130/230A Fall 2013
Lecture 14, Slide 13
M. A. Green et al., IEEE Trans. Electron Devices, Vol. 37, pp. 331-336, 1990

• W

W i-region
, so most carriers are generated in the depletion region
 faster response time (~10 GHz operation)
• Operate near avalanche to amplify signal
EE130/230A Fall 2013 Lecture 14, Slide 14
R.F. Pierret, Semiconductor Fundamentals, Figure 9.5

• LEDs are made with compound semiconductors (direct bandgap)
R.F. Pierret, Semiconductor Fundamentals, Figure 9.13
R.F. Pierret, Semiconductor Fundamentals, Figure 9.15
EE130/230A Fall 2013 Lecture 14, Slide 15

Question 1 (re: Slide 12): Why are the contacts to the back
(non-illuminated) side of a solar cell made only at certain points (rather than across the entire back surface)?
Answer: To increase energy conversion efficiency i) The absorption depth (average distance a photon travels before transferring its energy to an electron) for longwavelength photons is greater than the Si thickness.
 The bottom surface oxide and metal layer effectively form a mirror that reflects light back into the silicon.
ii)There is more recombination in heavily doped contacts than at a good Si/SiO
2 interface; most of the back surface should be covered by SiO
2 so that generated carriers have a high probability of diffusing to the depletion region before they recombine.
EE130/230A Fall 2013 Lecture 14, Slide 16

Question 2 (re: Slide 15): What limits the lifetime of an LED?
Answer: i) LED lifetime is defined to be the duration of operation after which the light output falls to only 70% of original.
(Even afterwards, the LED will continue to function.) ii) The power density of an LED can be high (up to 10 W/cm 2 , comparable to an electric stove top), causing significant heating which can degrade the light output through various mechanisms:
1.Degradation of epoxy package causing partial absorption of light
2.Mechanical stress weakening the wire bond (electrical connection)
3.Formation/growth of crystalline defects, or diffusion of metal into the semiconductor, resulting in increased recombination via midgap states
EE130/230A Fall 2013 Lecture 14, Slide 17