Charge Extraction by Linearly Increasing Voltage (CELIV)

Introduction

CELIV is powerful method allowing the charge transport and recombination to be studied in various semiconductors. It is a complimentary technique in the sense that it allows to study materials when other techniques such as Time-of-Flight are inapplicable.
Advantages:

• Strongly dispersive transport in disordered semiconductors can be probed, where in TOF featureless exponential decay is seen.
• Extraction time t_max is still visible in strongly dispersive transport (in TOF the position of the kink is not so obvious even in log-log scale).
• Films with high intrinsic conductivity can be studied, whereas in TOF only films with low conductivity can be measured.
• Recombination processes can be studied.

Disadvantages:

• Requires blocking contacts to prevent injection current.
• Current transients are strongly dependent on photogeneration profile and carrier concentration.
• Electric field mobility measurements are unreliable since the applied field is linearly increasing.

History of CELIV

First application of carrier extraction with linearly increasing (or rising) voltage technique was published in Russian language by D. Petravichyus, G. B. Yushka, and R. V. Baubinas in journal Sov. Phys. -Semicond. (you can download PDFs of all references from the list below).[1]
The equation to calculate charge carrier mobility in case of surface photogenerated small charge was derived:

Hole mobility was measured in p-CdSe. Soon after, Moore applied this technique to measure the electron and hole drift mobilities in amorphous silicon and called this new technique PYB taking the first letters of the authors of original paper.[2]
Organic electronic devices, such as solar cells and light emitting diodes are typically very thin, on the order of hundreds of nanometers, therefore, charge carrier are photogenerated in the volume of the films, according to Beer-Lambert law. Also, charge carrier distribution due to doping is typically homogeneous throughout the film. Analytical theory to calculate the mobility of charge carriers extracted from the volume of the film (not from the interface through the film) for any film conductivity (carrier concentration) was published in 2000 PRL by Juska et al.[3] The case of low conductivity and volume carrier distribution:

The case of high conductivity, carrier extraction from the volume:

A correction factor to estimate the carrier mobility for intermediate film conductivities again in case of carrier extraction from the volume of the film was published later as determined from numerical calculations.

Further works by other groups, namely Deibel and Bange showed that the correction factor shall be slightly different, which would only change the results much less that the experimental error itself. They also demonstrated, that CELIV transients and the extraction time itself are dependent carrier bimolecular recombination and carrier concentration, which must be considered and accounted for in mobility calculations.[4,5] We have extended this work further to account for all possible experimental parameters, namely light absorption profile, charge carrier concentration, and bimolecular recombination all together. How to calculate the charge carrier mobility in CELIV experiment correctly accounting for all these experimental conditions is discussed below.

Schematic experimental setup and typical CELIV transients

Typical CELIV setup is not different than TOF, except that when TOF can be (though usually is not) measured with large load resistances (integral mode TOF), CELIV can only be done in differential mode when the load resistance is low (RC < t_tr).

Triangle-shaped increasing voltage pulse is applied and the current response is measured as change in voltage on the load resistance of the oscilloscope.

Two types CELIV experiments can be done:

1. Extraction of equilibrium generated (due to doping) carriers.
2. Extraction of photogenerated carriers, photo-CELIV. This mode is used for undoped films, when no thermally generated (equilibrium) carriers exist.

Typically, Photo-CELIV is used to measure the charge carrier mobility in organic semiconductors since they are large bandgap (2 eV or so) and not much thermally generated carriers are present for extraction in the dark.
The essence of this technique to measure the charge carrier mobility is very simple. The charge carrier mobility is defined as carrier drift velocity v in a given electric field E:
v = μ × E.
From classical mechanics, the constant speed of moving object is defined as the time required to travel the given distance d:
v = d / t.
In our case, the given distance is the film thickness and time is the transit time:
μ = v / (t_trE) = d² / (t_trU).

The transit time is the time required to extract the small amount of charge carriers (less than CU) from the surface through the film. While carriers are being extracted by applied electric field, the current is observed in the external circuit and recorded in the oscilloscope. When all carriers reach the opposite electrode, extraction current drops to zero and the extraction time is recorded from which carrier mobility is calculated. However, in CELIV, the electric field is non-constant, carrier generation might be not at the surface and the time at the extraction maximum current is taken for mobility calculations, which require complex analysis.

1. D. Petravichyus, G. B. Yushka, and R. V. Baubinas, Sov. Phys. -Semicond. 9, 1530 (1976).
2. A. R. Moore, Applied Physics Letters 31, 762 (1977).
3. G. Juska, K. Arlauskas, M. Viliunas, and J. Kocka, Physical Review Letters 84, 4946 (2000).
4. C. Deibel et al, xxx.
5. S. Bange, M. Schubert, and D. Neher, Phys. Rev. B 81, 035209 (2010).