# Presentation: 138315

## Device Physics of Nanocrystalline(and Amorphous) Silicon Solar Cells

- Eric Schiff
*Syracuse University*

- Forschungszentrum Jülich: Thorsten Dylla, Friedhelm Finger
- NREL: Howard Branz, Dick Crandall, Paul Stradins, Qi Wang, Kai Zhu
- Penn State: Joshua Pearce, Chris Wronski
- United Solar: Gautam Ganguly, Subhendu Guha, Baojie Yan, Jeff Yang
- Syracuse: Steluta Dinca, Jianjun Liang

- NREL Amorphous Silicon Team Meeting, April 17, 2006, San Francisco.

## Themes

- VOC: mainly bandtail recombination
- a-Si:H, probably nc-Si:H too.
- Fill-factors: mainly hole mobilities
- a-Si:H, possibly nc-Si:H too.
- Bandtails affect both *V**OC** *and *FF *- but differently
- Metastability in a-Si:H (J. Liang talk, Tuesday morn)
- Apparently driven by bandtail recombination
- Apparently consistent with H-collision
- “Self limiting:”Saturation occurs at 300K when defect recombination traffic becomes comparable to bandtail recombination traffic

**Notes:**
Logic of presentation
Review of a-Si:H.
As-deposited Voc(T,d): consistent with bandtail recombination recombination measurements.
As deposited P(T,d): consistent with hole drift-mobility measurements
Light-soaked Voc, P: consistent with dangling bond perturbation of recombination & trapping processes at AM1.5 .
Nanocrystalline silicon:
Drift-mobilities more or less known for Juelich material (give properties)

## Toy Model for a Low-mobility pin Solar Cell

- E. A. Schiff, *J. Non-Cryst. Solids*, *in press *(ICANS 2005)*. *[_[.](http://physics.syr.edu/~schiff/Publications/SchiffJNCS06.pdf)__[pdf](http://physics.syr.edu/~schiff/Publications/SchiffJNCS06.pdf)_]
- E. A. Schiff, *Solar Cells and Solar Energy Materials ***78**, 567-595 (2003).[_[.pdf](http://physics.syr.edu/~schiff/Publications/Low-mobility_Solar_Cells.pdf)_]

**Notes:**
Photocurrent density & fill-factor depend only very weakly on recombination.
They depend strongly on the smaller mobility, and basically not at all on the larger one.

## Hole Drift-Mobilities in Disordered Silicons

- E. A. Schiff, *J. Non-Cryst. Solids*, *in press *(ICANS 2005)*.*[_[.pdf](http://physics.syr.edu/~schiff/Publications/SchiffJNCS06.pdf)_]
- nc-Si:H *- *T. Dylla, F. Finger, and E. A. Schiff,* Appl. Phys. Lett. ***87**, 032103 (2006) [_[.](http://physics.syr.edu/~schiff/Publications/DyllaAPL05.pdf)__[pdf](http://physics.syr.edu/~schiff/Publications/DyllaAPL05.pdf)_].
- E. A. Schiff, *J. Phys.: Condens. Matter* **16**, S5265-5275 (2004) [_[.](http://physics.syr.edu/~schiff/Publications/SchiffJPCM04.pdf)__[pdf](http://physics.syr.edu/~schiff/Publications/SchiffJPCM04.pdf)_].

**Notes:**
Orange – SU measurements.
Here we show a range of hole drift mobilities reported for various experiments in the last decade or so.

## Bandtail Multiple-Trapping Model for Hole Drift Mobility

| Bandtail Parameters |  |
| --- | --- |
| EV | Valence Bandtail Width |
| h | Hole Band Mobility |
| NVbT | Attempt Frequency |
|  |  |

## Power Density vs. Temperature: A Test for Mobility Limitation

| AMPS Model Parameters |  |
| --- | --- |
| p  | 0.3 cm2/Vs  |
| Ev  | 0.040 eV  |
| Nv,NC  | 41020 cm-3  |
| bT | 1.310-9 cm3s-1  |
| Eg  | 1.74 eV  |
| bR  | 1.010-9 cm3s-1  |

- L. Jiang, E. A. Schiff, S. Guha, B. Yan, and J. Yang, Appl. Phys. Lett. 88 063512 (2006).[_[.pdf](http://physics.syr.edu/~schiff/Publications/LiangAPL06.pdf)_]

**Notes:**
Show Jianjun’s as-deposited data. Idea is to establish that the temperature-dependence is predicted by the valence bandtail model.

Walk-thru of data: Voc mostly reflects recombination and quasi-Fermi level splitting in the “bulk material.” Hence the thickness-independence.
Walk-thru of modeling: corrected by dEg/dT from electroabsorption. \alpha(T) also corrected.
Bandtail parameters: previously published. Mainly from hole TOF. One parameter fitted to yield Voc(T).

P/Jsat : we use normalized power because \alpha is changing with T, and measurements were done at constant F. Probably better to do measurements at constant Jsat, but we didn’t do that. As you can see, most of the experimental features are pretty well accounted for by the 

## VOC in Amorphous and Nanocrystalline Silicon

**Notes:**
Note: Not a straight line; bandtail model is quadratic form in kT.
Note: This Graph is NOT corrected for Eg(T).

Note: TOF determines “free mobility,” bandtail width, and the product Nvbt . For nc-Si:H, I used the standard values for Nv and Nc.
Klein et al (Juelich) published Voc in range 500-600 mV, good efficiencies.

## Hole Drift-Mobilities in Disordered Silicons

| Parameters | nc-Si:H | a-Si:H |
| --- | --- | --- |
| p (cm2/Vs ) | 2.0 | 0.7 |
| Ev (eV) | 0.032 | 0.045 |
|  (s-1) | 5109  | 11012 |

- Detailed balance:= *N**v**b**t*

**Notes:**
Orange – SU measurements.
Here we show a range of hole drift mobilities reported for various experiments in the last decade or so.

## VOC in Nanocrystalline Silicon: Bandtail Recombination

| Parameters | nc-Si:H | a-Si:H |
| --- | --- | --- |
| p (cm2/Vs ) | 2.0 | 0.7 |
| Ev (eV) | 0.032 | 0.045 |
| Nv (cm-3)NC (cm-3) | 1.01019 2.81019 | 51020 51020 |
| bT (cm3s-1) | 510-10 | 210-9 |
| Eg (eV) | 1.12  | 1.74  |
| bR (cm3s-1) | 110-9 | 110-9 |

**Notes:**
Note: Not a straight line; bandtail model is quadratic form in kT.
Note: This Graph is NOT corrected for Eg(T).

Note: TOF determines “free mobility,” bandtail width, and the product Nvbt . For nc-Si:H, I used the standard values for Nv and Nc.
Klein et al (Juelich) published Voc in range 500-600 mV, good efficiencies.

## Fill-Factor in Nanocrystalline Silicon Solar Cells

**Notes:**
Fill-factor behavior is roughly correct, but simulation results are larger than expected.
Hole drift-mobilities from thick Juelich cells used. Possible that thick cells have mobilities that are larger than for thin cells. Our measurements used light absorbed near the top of the cells, and are mostly sensitive to the top 2/3 of the film.
Of course defects could also play a role: who knows. Again, this would require a coincidence (similar to self-limitation).

## Modeling Issues in Nanocrystalline Silicon Solar Cells

*V**OC*: Bandtail recombination predictions look about right
- T-dependence to confirm?
*FF*: Mobility-based predictions are somewhat too large
- Mobility parameters from expt. not representative of current optimized solar cells?
*Jsc*: Do amorphous regions “sensitize” nanocrystalline cells?

**Notes:**
Fill-factor behavior is roughly correct, but simulation results are larger than expected.
Hole drift-mobilities from thick Juelich cells used. Possible that thick cells have mobilities that are larger than for thin cells. Our measurements used light absorbed near the top of the cells, and are mostly sensitive to the top 2/3 of the film.
Of course defects could also play a role: who knows. Again, this would require a coincidence (similar to self-limitation).

## How Low-Mobility Solar Cells Work

*Electron-Hole**Recombination*

- Quasi-FermiLevels

***V******OC***

*Hole**Drift Mobility*

- Space-Charge

- Photocurrent
-  Density

*Photogeneration*

- Power

**Notes:**
Valediction

## United Solar Ovonic Cells: Temperature Effects

- United Solar Ovonic cells
- 685 nm laser illumination
- Lines are computer calculations
- As-deposited: only bandtails significant
- Light-soaked: bandtail+defect
- Defect density about 2x1016 cm-3
- Defect parameter values from Street’s deep-trapping measurements

- L. Jiang, E. A. Schiff, S. Guha, B. Yan, and J. Yang, Appl. Phys. Lett. 88 063512 (2006).

## What if – hole mobility increases?

- E. A. Schiff, unpublished

## Power Density: Hole Mobility Model

| Model Parameters |  |
| --- | --- |
| p  | 0.3 cm2/Vs  |
| Ev  | 0.040 eV  |
| Nv,NC  | 41020 cm-3  |
| bT | 1.310-9 cm3s-1  |
| Eg  | 1.74 eV  |
| bR  | 1.010-9 cm3s-1  |
| (Optimized for AMPS) |  |

- _[http://](http://physics.syr.edu/~schiff/AMPS/SU Parameter Suggestions.html)__[physics.syr.edu/~schiff/AMPS](http://physics.syr.edu/~schiff/AMPS/SU Parameter Suggestions.html)__[/](http://physics.syr.edu/~schiff/AMPS/SU Parameter Suggestions.html)_
- K. Zhu, *et al.*, in *Amorphous and Nanocrystalline Silicon Based Films – 2003*, edited by J.R. Abelson, *et al. *(Materials Research Society Symp. Proc. Vol. 762, Pittsburgh, 2003), pp. 297--302.[_[.pdf](http://physics.syr.edu/~schiff/Publications/MRS_S03_Bandtail_Limits.pdf)_]

**Notes:**
Calculations done w. AMPS

## Temperature-depedent Bandgap of c-Si

## Low-mobility pin Solar Cells: “Toy” Model and Analytical Solution

- E. A. Schiff, *Solar Cells and Solar Energy Materials ***78**, 567-595 (2003).[_[.pdf](http://physics.syr.edu/~schiff/Publications/Low-mobility_Solar_Cells.pdf)__]_

**Notes:**
Electron mobility much larger than hole mobility.
Lower bound to bR (but not an upper bound!). Comment on Langevin: bR is actually smaller than expected.
New concept: Think of Pmax as Jmax x (Delta V). Jmax = (\mu \epsilon e^3 G^3 {\Delta V}^2)^1/4
In this model, J_sc can be computed from Voc, etc.. 
Dimensionless units: divide Voc by kT/e. Then the quantity inside the 1⁄4 power becomes ((kT)^2G/e)^3 .

## Mobility Is Power: Computer and Analytical Calculations

- E. A. Schiff, *J. Non-Cryst. Solids*, *in press *(ICANS 2005)*.*

## Toy Model for a Low-mobility pin Solar Cell