Charge Extraction
Lecture 9 – 10/06/2011
MIT Fundamentals of Photovoltaics
2.626/2.627 – Fall 2011
Prof. Tonio Buonassisi
Buonassisi (MIT) 2011
2.626/2.627 Roadmap
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Buonassisi (MIT) 2011
2.626/2.627: Fundamentals
Every photovoltaic device must obey:
Output Energy
Conversion Efficiency  
Input Energy

For most solar cells, this breaks down into:
Inputs
Solar Spectrum
Light
Absorption
Charge
Excitation
Charge
Drift/Diff
usion
Outputs
Charge
Separation
Charge
Collection
total  absorption  excitation  drift/diffusion  separation  collection
Buonassisi (MIT) 2011
Liebig’s Law of the Minimum
S. Glunz, Advances in
Optoelectronics 97370
(2007)
Image by S. W. Glunz. License: CC-BY. Source: “High-Efficiency Crystalline
Silicon Solar Cells.” Advances in OptoElectronics (2007).
total  absorption  excitation  drift/diffusion  separation  collection
Buonassisi (MIT) 2011
Learning Objectives: Charge Extraction
1.
2.
3.
4.
5.
6.
Describe the purpose of contacts, and their most common types.
Describe the impact of good and poor contacts on IV characteristics.
Sketch the IV characteristics of Schottky and Ohmic contacts.
Describe what fundamental material parameters determine the IV
characteristics of a contact/semiconductor junction.
Sketch common band alignments (Types 1, 2, 3 junctions).
Sketch common solar cell device architectures.
Buonassisi (MIT) 2011
Contacts
• …extract carriers from device.
• …prevent back-diffusion of carriers into device.
• …are studied extensively in the semiconductor industry
(several good review papers) for “common” semiconductors.
• …are semiconductor-specific: While fundamentals generally
apply universally, the devil is in the details, and each material
system requires individual optimization.
• … are influenced heavily by surface states (i.e., repeatable
surface preparation is a must!)
Buonassisi (MIT) 2011
Materials Commonly Used for Contacts
• Metals
– Optically opaque.
– Electrically conductive.
• Transparent Conducting Oxides (TCOs)
– Optically transparent.
– Electrically conductive.
Buonassisi (MIT) 2011
Properties of TCOs
Transparency
Conductivity ()
Quartz
Transparency
Visible
1
Insulator
-18
0
0
1
2
3
Energy of light (eV)
 Transmittance: > 80% (Films)
 Range: 400 ~ 700 nm
 Band gap > 3.1eV
Glass
-14
-10
Si
Ge
ITO Ag
Semi
conductor
-6
-2
log  (S/cm)
Metal
2
6
=ne
n - carrier conc. (cm-3)
 - mobility (cm2/Vs)
e - charge per carrier
Buonassisi (MIT) 2011
How TCOs Work
CB
E1 = Large
E
E3 = very small
EF
E2 = Large
VB
x
Buonassisi (MIT) 2011
Learning Objectives: Charge Extraction
1.
2.
3.
4.
5.
6.
Describe the purpose of contacts, and their most common types.
Describe the impact of good and poor contacts on IV characteristics.
Sketch the IV characteristics of Schottky and Ohmic contacts.
Describe what fundamental material parameters determine the IV
characteristics of a contact/semiconductor junction.
Sketch common band alignments (Types 1, 2, 3 junctions).
Sketch common solar cell device architectures.
Buonassisi (MIT) 2011
Equivalent Circuit: Simple Case
J0
Vja
V
Current Density (mA/cm2)
Lin Scale
I-V Curve
1.E+00
8.E-01
6.E-01
4.E-01
2.E-01
0.E+00
 qV  
J  J0exp  1 JL
 kT  
Current Density (mA/cm2)
0
0.2
0.4
0.6
Voltage (V)
0.8
Log Scale
I-V Curve
1.E+00
1.E-02
1.E-04
1.E-06
1.E-08
1.E-10
0
0.2
0.4
0.6
Voltage (V)
0.8
Buonassisi (MIT) 2011
J0
Vja
Rs
V
Current Density (mA/cm2)
Equivalent Circuit: Simple Case
I-V Curve
5.E-02
4.E-02
3.E-02
2.E-02
1.E-02
0.E+00
 qV  JR  
s


J  J0
exp
1
  kT
 JL
 
 
Current Density (mA/cm2)
0
0.2
0.4
0.6
Voltage (V)
0.8
I-V Curve
1.E+00
1.E-02
1.E-04
1.E-06
1.E-08
1.E-10
0
0.2
0.4
0.6
Voltage (V)
0.8
Buonassisi (MIT) 2011
Vja
Rsh
 qV  JR   V  JR
s
s



J  J0
exp
1
 JL




kT
R
sh
 
 
V
Current Density (mA/cm2)
J0
Rs
Current Density (mA/cm2)
Equivalent Circuit: Simple Case
I-V Curve
5.E-02
4.E-02
3.E-02
2.E-02
1.E-02
0.E+00
0
0.5
Voltage (V)
1
I-V Curve
1.E+00
1.E-02
1.E-04
1.E-06
1.E-08
1.E-10
0
0.5
Voltage (V)
1
Buonassisi (MIT) 2011
Equivalent Circuit: Simple Case
J0
Vja
Rs
Rsh
V
Courtesy of PVCDROM. Used with permission.
 qV  JR   V  JR
s
s



1
J  J0
exp
 JL




kT
R
sh
 
 
Firing contacts? Three possibilities:
1. Contact just right: low Rs, large Rsh.
2. “Underfired” contact: Poor contact with
Si, large Rs.
3. “Overfired” contact: Metal drives too
deep into Si, low Rsh.
Buonassisi (MIT) 2011
Learning Objectives: Charge Extraction
1.
2.
3.
4.
5.
6.
Describe the purpose of contacts, and their most common types.
Describe the impact of good and poor contacts on IV characteristics.
Sketch the IV characteristics of Schottky and Ohmic contacts.
Describe what fundamental material parameters determine the IV
characteristics of a contact/semiconductor junction.
Sketch common band alignments (Type 1, 2, 3, and 4 junctions).
Sketch common solar cell device architectures.
Buonassisi (MIT) 2011
Classes of Contacts
Ohmic and Schottky Contacts
• Ohmic:
• Schottky:
– Exponential I-V curve.
– Used when charge
separation is desired.
+
Current (a.u.)
– Linear I-V curve.
– Typically used when
charge separation is not
a goal for metallization.
0
Schottky
Ohmic
-
0
+
Voltage (a.u.)
Buonassisi (MIT) 2011
Learning Objectives: Charge Extraction
1.
2.
3.
4.
5.
6.
Describe the purpose of contacts, and their most common types.
Describe the impact of good and poor contacts on IV characteristics.
Sketch the IV characteristics of Schottky and Ohmic contacts.
Describe what fundamental material parameters determine the IV
characteristics of a contact/semiconductor junction.
Sketch common band alignments (Types 1, 2, 3 junctions).
Sketch common solar cell device architectures.
Buonassisi (MIT) 2011
Step #1: Schottky Theory
(the ideal case)
Buonassisi (MIT) 2011
Contacts: Schottky Model
E
Vacuum
qc
q fM
EC
EF
EV
Semiconductor
Metal
x
Buonassisi (MIT) 2011
Contacts: Schottky Model
E
Vacuum
qc
q fM
EC
EF
EV
Semiconductor
Metal
x
Buonassisi (MIT) 2011
Contacts: Schottky Model
• For Ohmic contact: fm > fs
• Barrier Height: fb = fm - c
• Contact Potential: Vbi = fm - fs
• Space-charge region width:
W 

2 s
Vo
qN D
Courtesy of Tesfaye Ayalew. Used with permission.
http://www.iue.tuwien.ac.at/phd/ayalew/node56.html
Buonassisi (MIT) 2011
Classes of Contacts
• Ohmic:
• Schottky:
– Electron barrier
height > 0 (for p-type)
– Exponential I-V curve.
– Used when charge
separation is desired.
Ohmic and Schottky Contacts
+
Current (a.u.)
– Electron barrier
height ≤ 0 (for n-type)
– Linear I-V curve.
– Typically used when
charge separation is
not a goal for
metallization.
0
Schottky
Ohmic
-
0
+
Voltage (a.u.)
Buonassisi (MIT) 2011
Evaluating Metals for Contacts - Schottky Model
Courtesy of Tesfaye Ayalew. Used with permission.
http://www.iue.tuwien.ac.at/phd/ayalew/node56.html
Buonassisi (MIT) 2011
Reality: Deviations from Schottky theory
• Substantial deviations from Schottky theory are possible, due
to interface effects including:
– Orientation-dependent surface states.
– Elemental nature of surface termination in binary compounds (e.g., A
or B element?).
– Interface dipoles.
– and more…
Courtesy of Tesfaye Ayalew. Used with permission.
http://www.iue.tuwien.ac.at/phd/ayalew/node56.html
Buonassisi (MIT) 2011
Role of Surface States
For related visuals, please see the lecture 9 video or the reference below.
D.K. Schroder, IEEE Trans. Electron Dev. 31, 637 (1984)
Buonassisi (MIT) 2011
Contacts: Schottky Model
• For Ohmic contact: fm > fs
• Barrier Height: fb = fm - c
• Contact Potential: Vbi = fm - fs
• Space-charge region width:
W 

2 s
Vo
qN D
Courtesy of Tesfaye Ayalew. Used with permission.
http://www.iue.tuwien.ac.at/phd/ayalew/node56.html
Buonassisi (MIT) 2011
Thermionic Emission & Field Emission Effects
For related visuals, please see the lecture 9 video or the reference below.
D.K. Schroder, IEEE Trans. Electron Dev. 31, 637 (1984)
Buonassisi (MIT) 2011
Evaluating Metals for Contacts - Practical
• Sources:
–
–
–
–
Reference books
Review articles
Scientific articles
Trusted websites
https://web.archive.org/web/20130818214213/
http://www.siliconfareast.com/ohmic_table.htm
• NB:
– Surface states
matter!! Be sure
you have
repeatable surface
preparation.
Buonassisi (MIT) 2011
Learning Objectives: Charge Extraction
1.
2.
3.
4.
5.
6.
Describe the purpose of contacts, and their most common types.
Describe the impact of good and poor contacts on IV characteristics.
Sketch the IV characteristics of Schottky and Ohmic contacts.
Describe what fundamental material parameters determine the IV
characteristics of a contact/semiconductor junction.
Sketch common band alignments (Types 1, 2, 3 junctions).
Sketch common solar cell device architectures.
Buonassisi (MIT) 2011
Evaluating Heterojunctions
Not always possible to dope a material both n- and p-type. Not always
possible to find the perfect contact material. Need: heterojunction.
(At least) three types of heterojunction:
What junction will separate charge?
Buonassisi (MIT) 2011
Evaluating Heterojunctions
Simplest case (analogy to Schottky band alignment for metalsemiconductor contacts):
1- Set chemical potential equal across entire device.
2- Then, align vacuum levels.
3- Note that VB and CB must follow vacuum levels.
E
x
Buonassisi (MIT) 2011
Evaluating Heterojunctions
Simplest case (analogy to Schottky band alignment for metalsemiconductor contacts):
1- Set chemical potential equal across entire device.
2- Then, align vacuum levels.
3- Note that VB and CB must follow vacuum levels.
Buonassisi (MIT) 2011
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