When electric field applied between the electrodes is very high of the order of 10,000 V/cm, then charges are injected from electrodes and a space charge is created in the insulators or semiconductors having small concentration of thermally generated charge carriers

Hi,

in the space-charge limited current (SCLC) regime, the current is dominated by charge carriers injected from the contacts and the current-voltage characteristics becomes quadratic (I ~ V2). The current is then only dependent on the mobility and no more on the charge carrier density, hence, the mobility can be estimated from a simple current-voltage measurement. This is in contrast to Ohmic conduction, where the current is mainly driven by the mobile charge carriers being intrinsically present in your material, so that the charge carrier density need to be known to say something about the mobility.

If you want to extract the mobility from SCLC measurements, it is important to make sure that you are really in the SCLC regime. Therefore, the scaling exponent in a log-log representation has to be analyzed (and should have a value of 2). However, the situation becomes more complex when traps are involved, where also higer exponents than 2 can be observed. 

Further reading: Mott–Gurney law

The below paper by Poplavskyy describes transient and steady state methods for determining space charge limited current with reference to the work of Murgatroyd.

The quoted definition is "When the injecting contact is ohmic, the steady-state current is limited by the space-charge in the sample and is proportional to the mobility of carriers...in the absence of traps, the steady-state current density as function of applied voltage is given by Murgatoryd's equation."

"Bipolar charge transport, injection, and trapping studies in a model green-emitting polyfluorene copolymer"

http://scitation.aip.org/content/aip/journal/jap/98/1/10.1063/1.1941482

Cont'd from previous answer

Due to space charge created at high fields, current becomes super ohmic. In the trap free material current increases as squire of Voltage. However, when traps are present, current- voltage behaviour depends on the energy distribution of trap in the band gap of the material. For detailed expression, go through the book on Current Injection in Solids by Lampert and Mark. I have done SCLC measurements on amorphous silicon and chalcogenide glasses. Go through my research gate profile for reference.

Thank you all for your responses.

Just making sure if I got this right. If it is really in the space charge limited current region, then the JV characteristics would have J proportional to V^2 rather than any other relationship ( in the trap free case)? Can we use this test to verify the SCLC region?

@Sebastian, you have mentioned that when traps are involved, that scaling exponent of a log-log plot is greater than 2. What about the electric field dependent mobility? would this also cause same kind of effect?

@Waranatha: Indeed, field-dependence makes the problem more complicated... Here is one paper discussing this topic:

http://www.elp.uji.es/recursos/paper16.pdf

Congratulations Sebastian and Waranatha,

That's the fastest start up in SCLC that I have seen ever!

Some tips for identification of SCLC.

J~V^2/d^3 is the classic relation (Mott-Gurney law) valid for constant (and low) mobility at sufficiently high (but not very high) bias.

J~V^(2+n)/d^(3+n) is SCLC with trap filling. Waranantha is right, n>0 is often regarded as mobility enchantment factor. n is constant in the case of exponential distribution of traps. It might be surprising, but both band conduction and charge hopping conduction lead to the same value of n. The value of n is larger at low temperature, n+2=2To/T, where To is characteristic temperature for exponential DOS~exp(-E/kTo), where k is Boltzmann constant. n~0 for T>To.

O. Marinov, M. J. Deen, R. Datars, "Compact Modeling of Charge Carrier Mobility in Organic Thin-Film Transistors", Journal of Applied Physics, 106(6), 064501-1 to -13, 2009; DOI: 10.1063/1.3212539

n is often denoted with Greek letter gamma in the literature on thin-film transistors.

Note the exponential term in eq. (26) in the paper from Murgatroyd. Elaborations in 1990's and early 2000 introduced the so-called Gaussian Disorder Model and deduced variable value for n at assumption of normally-distributed DOS. Note also that at low bias SCLC results in linear J~V.

It might be useful to know that for thin-film structures

I/W ~ V^2/L^2, where W is the width of the contacts and L is the distance between the contacts.

J. A. Geurst, "Theory of Space-Charge-Limited Currents in Thin Semiconductor Layers", Physica Status Solidi (b), Vol. 15, Iss. 1, pp. 107-118, 1966

Best,

Dr. O. Marinov

Hi,

first of all, thanks for your kind words, Ognian! :)

Oh, I just realized that there were two mistakes in my orginial answer where I unintentionally wrote "charge carrier mobility" instead of "charge carrier density". I corrected this now and feel sorry for any confusion!

No problem. Actually, your "typo" just reminds me to mention that the mobility enhancement is normally given as function of charge concentration in organic semiconductors, e.g., in

R. Coehoorn, W. Pasveer, P. Bobbert, M. Michels, "Charge-carrier Concentration Dependence of the Hopping Mobility in Organic Materials with Gaussian Disorder", Physical Review B, 72(15), 155206-1 to -20, 2005; DOI: 10.1103/PhysRevB.72.155206

Hi, In the case SCLC, you may not really get I = V2 relation. You might end up getting various values for exponent in different regions of electric field. in my measurements, i do get series of values to exponents between 1 and 2. Some time even higher than2, up to 5 or 6. So you cannot generalize SCLC as have I=V2 relation.

Is there a reason why the space charge limited current region would disappear in a p-i-n junction ... possibly because the band offsets in the i- layer are altered  ?

I got value of exponent in-between 0-1 at low voltages ..is this SCLC region , plz explain

Mohd Hanief Najar , no it is not a SCLC region , for m=1 it as an ohmic region

for SCLC i got slope in the range 1-2, for schottky emission in the range 0-0.7 and for poole-frenkel in the range 0-0.8. is the slope range is right for the conduction mechanism.

For SCLC the current density is proportionel to V (Voltage) exposant m where m is the slope fit of Log-Log scale , for m=1 is ohmic region, for m=2 SCLC ,m=3 TFL

Hi,

You could check this paper http://pubs.acs.org/doi/abs/10.1021/am5050136

for a real case of what will happen for an orgainc semiconductor or insulator.

Usually, different conducting mechanisms are involved, including SCLC, Pool-Frenkel, 

and Schottky emission, which dominates depending on lots of factors including the band structure, the thickness scale, and defects types.

Hi,

I just came across this post. If you are still looking for the answer, you may read the attached publication. It is having an in-depth analysis of space charge behavior.

Hope it will help you.

Article On the Uniqueness of Ideality Factor and Voltage Exponent of...

hello Mohd Hanief najar, if your m is greater than or is equal to 2 then only that is SCLC. If m is in between 1-2, it indicates ohmic conduction mechanism dominates the conduction.

Doubt:

What could be the reason for increasing in SCL current with increase in temperature?

Hello everyone.

I just wanted to add a few important points to this rather old discussion.

Regarding the transition from linear to quadratic behaviour at low voltages, this is actually not due to a transition from Ohmic to SCLC, but rather a transition from an Ohmic-like current to SCLC. There's a subtle difference here, but important none-the-less:

http://iopscience.iop.org/article/10.1088/1361-648X/aa66cc/meta

An observed slope larger than two does not have to be due to traps. This could also be caused by the presence of a built-in voltage. It is important to measured your I-V curves both in forward and reverse directions. If those two curves are asymmetric, then you have a built-in voltage in your device. If they are symmetric but you still have a slope larger than 2, then you probably have traps. However, the nature of said traps can be vary and the curves will vary accordingly. Simply saying that m>2 are due to traps is not entirely correct. An increase in the current with an increase in temperature, could simply be arising from the presence of injection barriers between your contacts and your semiconductor. An increase in the current could also arise from the presence of traps where charge carriers have a higher probability of escaping said traps when the temperature increases.

Article Charge Transport in Spiro-OMeTAD Investigated through Space-...

Also, one has to be careful when measuring very thin devices and/or devices with large injection barriers. In those cases you will never reach a "true" space-charge-limited regime, but you will rather quickly transition into an injection limited regime. For that reason, you might never see a slope of 2, or you might see a slope or 2 (or greater than 2 for that matter), even though you are not a true space-charge-limited regime. Basically, you can overlapping regimes depending on how you construct your device, and that can have a profound effect on the analysis of said device.

http://iopscience.iop.org/article/10.1088/1361-648X/aaabad/meta

I hope this is useful.

Jason

Jason Rohr is right: Always inspect possibilities for other charge transport phenomena before attributing experimental data to only one charge transport. Two "remainders": at low voltage bias and current, the space charge limit is insignificant and voltage and current are proportional. At high current, the temperature elevates, and if tail states are present near the charge transport band edge, then the mobility changes (increases). Accordingly, the current is super-quadratic SCLC. Other possibilities are thoroughly elaborated in the publication, which Jason Rohr referred to. Indeed, there are cross-overs between different charge transports at different regimes even in one sample. Thus, Jason Rohr is right: Always inspect possibilities for other charge transport phenomena before attributing experimental data to only one charge transport.

Hi everyone,

I just wanted to say that I recently derived an expression for easy determination of the built-in voltage (Vbi) in case your single-carrier device is asymmetric (different current density between forward and reverse bias):

Article Direct Determination of Built-in Voltages in Asymmetric Sing...

To determine the Vbi you do not need to know the charge-carrier mobility. The preprint can be found on my profile. Let me know if you have any questions. Enjoy!

Jason

Hi everyone,

Article Analytical Description of Mixed Ohmic and Space-Charge-Limit...

If you want to measure lightly-doped semiconductors with SCLC, the above article might be helpful to you. The full article can be found on my profile. Enjoy!

Best,

Jason

thank you sebastian wiken i have no more to add to your answer

Simply from dark current voltage curve you can calculate SCLC information, namely carrier mobilities, Child region, trap-filled region, ohmic region, etc.

The following references may help.

1. http://dx.doi.org/10.1016/j.solener.2020.07.034

2. https://doi.org/10.1016/j.solener.2019.07.081.

Nasir Ali I would be very careful with how you interpret SCLC in perovskites. The presence of mobile ions makes it quite difficult to extract meaningful information. I know it's common to use this method, but it's really not as straight forward as people pretend it is.

In fact, it's been shown that the apparent "trap-filled" region is most likely not due to traps at all, but rather due to the mobile ions inducing built-in voltages across the device. It's also not that clear whether the Mott-Gurney law is even a good model for perovskites, even though it's being heavily used. Calling it the "Child" region is also odd (but common) as we're not dealing with SCLC i vacuum. Also, calling it Ohmic is also quite questionable as will be apparent from reading the other comments in this thread.

I would check out the work by Duijnstee and Le Corre:

https://scholar.google.com/citations?user=b3iUwQgAAAAJ&hl=en&oi=ao

https://scholar.google.com/citations?user=NWwTmU0AAAAJ&hl=en&oi=sra

They've done a great job sheading some light on some of the issues pertaining with SCLC in perovskites. Keep in mind that there is still a lot of work to do before we know for sure whether it's meaningful or not.

Jason Alexander Röhr

Yes, I second you. It is indeed a very rough method to estimate carriers mobility and concentration of the carriers (holes and electron) for PVK film, which is full of traps. However, frequently utilized; I will go through the literature provided by you. Thank you so much.

Query:

How to convert SCLC (J=9με0εr E^2 / 8 d) equation in form of y=mx + c theoretically?

Pankaj Solanki I'm not sure what you mean. The MG law is not a linear equation? It will also never intersect with the y-axis, so the constant c here is meaningless.

Your best bet might be to plot your J-V curve as J vs. V^2? What are you trying to do?

1. If all you want to know is whether the current is space-charge limited or not, you can do impedance spectroscopy and look at the Cole-Cole plot in Modulus. (Impedance is also fine.)

If it is SCLC, a distorted semi-circle will be observed. At the same time, if you look at the frequency dependence of capacitance, you can observe a negative dip that shifts with voltage.

In SCLC, the carriers injected by the electric field have a high density near the injection electrode, resulting in non-uniform conductivity within the layer, which causes a distribution in the relaxation time and a distortion of the semi-circle in the Cole-Cole plot.

Under the presence of an appropriate injection layer, the Cole-Cole plot of a single-layer single-charge device using a "high-purity small-molecule compound" shows a good semi-circle in the low-voltage region, and at the same time, Shockley eq. is established, which shows that the current is injection limited. Above a certain voltage, the distortion of the Cole-Cole plot appears and it is observed that the device turns into SCLC.

2. If what you are looking for is mobility evaluation using SCLC, then you can look at the relaxation frequency. The relaxation time obtained by impedance spectroscopy is the reciprocal of the transit time in the layer and therefore the relaxation time is the transit time itself (aside from some numerical factor) in the case of SCLC. If a proper Cole-Cole plot is obtained, the evaluation is free from the injection problem. These are superior to the Mott-Gurney eq., which requires the good injection and the assumption that the mobility is constant with respect to the electric field. However, the impedance method has a fatal flaw that the meaning of the electric field strength is ambiguous because the electric field is not uniform in the device. But it seems to be working well.

Please read

DOI: 10.35848/1347-4065/ab9a89

or

https://www.researchgate.net/publication/342022776_In-situ_evaluation_of_the_carrier_mobility_using_Mott-Schottky-equivalent_analysis_in_organic_light_emitting_diodes

Jason Alexander Röhr I'm trying to fit SCLC equation in linear form, i know about final plot ( it mean what is the value of V and J is applicable at X and Y axis). But thing is that how get this values theoretically?

Pankaj Solanki ,

I would recommend that you plot your data on a log-log scale and then fit the Mott-Gurney law to that plot if you're trying to use that particular model. You might see that it won't give a good fit, and then you will have to rely on some other model that reflect the underlying physics better. The Mott-Gurney law is rarely a good model. That might be evident from plotting your data on a log-log scale and also by looking at the power law dependence of your data by calculating:

m = d log J / d log V

and then plotting m as a function of voltage. If you don't see m approaching 2 for high voltages, then you're not in the Mott-Gurney regime.

I would be helpful understanding what materials you're working with and seeing your data. Feel free to PM me if you need any help.

Jason

Dear Pankaj Solanki , space charge limited current (J) in general follows V^n. Here, usually is greater than 1. You may want to read about Child's law and Langmuir's work on space charge limited current in vacuum tubes in addition to Mott-Gurney's relation to better understand the physics behind space charge limited current. In the nutshell, space charge limited current is due to fixed charges in the material space which varies quadratically in most of the cases with potential and hence the space charge limited current. In some special cases, the relationship may not be parabolic and you may observe exponent value other than 2. Therefore, theoretically, a linear relationship between current and voltage may not indicate space charge limited current but ohmic current.

If as a mathematical exercise you want to fit a linear equation on a JV curve, then you may do so by using the least mean square method. However, in this case, you have to be careful with the meaning of different parameters that you obtain and their physical significance.

I hope that clarifies your doubt.

Your suggestions cleared the some of my doubts and I will go trough this again.

Thank You, Jason Alexander Röhr and Sumanshu Agarwal

Hi everybody,

Do you consider the meaning of the V^2 term in the Mott-Gurney and Margatroyd equation?

Let's rewrite the Mott-Gurney equation as J=(9/8)(εSV/SL)/Lμ(V/L). ...(1)

Pay attention that εVS/L is the stored charge in a capacitor of the dielectric material.

J can be written as J=enpμE, where enp=(9/8)(εSV/L)/L is the "volumetric density of carriers with an extrinsic origin".

The differential conductivity measured by the impedance spectroscopy is σd=∂(JL)/∂V=2πεf. ... (2)

When the relaxation comes from the transit time effect, the relaxation frequency is f=(L/μE)^-1.

If μ is a constant and E is rewritten by the averaged electric field, eq. 2 ∂(JL)/∂V=2πεμV/L^2 can be integrated over V.

Then you will obtain the Mott-Gurney equation (1). Of course, the assumption of E is too strong, but will be acceptable within a numerical factor. The 0.891 in the Murgatroyd equation will be the correction due to the replacement of the internal electric field by the averaged one.

Compare the dielectric relaxation time td and the transit time tt, td/tt=CR/(L/μE)=(ε/enμ)/(L/μE)=(εV/L)/(enL)=Qp/Qc, where Qp is the stored space charge density and Qc is the internal carrier density.

Those equations show the competition between the internal carrier and the extrinsically stored space charge.

Have you had the image of SCLC?

The space charge with the extrinsic origin plays the dominat role in the carrier dynamics of small molecule organic electronics. If you are interested in it, please read my article.

https://www.researchgate.net/publication/349526160_Carrier_accumulation_in_organic_heterojunctions_controlled_by_polarization

Finally, keep in mind that you must not use J∝V^2 as a criterion of SCLC. If you adopt it, you must explain why the electric field dependence of mobility disappears. It's another physics.

Hi everybody,

I have a homework assignment for you.

On the wikipedia page of the space charge, there are examples of the linear J-V equation and I want you to think of simple explanations for them.

Hi Jun-Ichi Takahashi ,

You might find the following articles helpful:

Article Transport of ions of one kind through thin membranes - II. N...

Article Space‐charge‐limited current and capacitance in double‐junction diodes

Article Ohmic current in organic metal-insulator-metal diodes revisited

Article On the correct interpretation of the low voltage region in i...

Article Analytical Description of Mixed Ohmic and Space-Charge-Limit...

The latter two are mine.

Best,

Jason

Thanks all for the informative discussion

Hi all,

If you're interested in applying SCLC to perovskite materials, I would recommend checking out or new paper on this topic (and the cited papers within).

It can currently be found on arXiv:

Preprint The Validity Window of Space-Charge-Limited Current Measurem...

and here on Researchgate:

Preprint The Validity Window of Space-Charge-Limited Current Measurem...

Enjoy!

Edit: Our paper complements the previous work by Duijnstee, Le Corre, and Wetzelaer quite nicely. For a complete picture, I would check out their work too.

Dear all,

I have recently published a theory paper on carrier dynamincs in dielectrics.

It discusses SCLC, impedance spectroscopy, quasiconductor concept, and operating dyanamics of OFET.

I hope that it would be helpful to you.

https://www.researchgate.net/publication/361606156_Category_Theory_and_Organic_Electronics

https://www.sciencedirect.com/science/article/pii/S2666032623000133?via%3Dihub

the relation of current with voltage in the SCLC zone is not according to Ohm's law, i.e. the current increases quadratically with the applied voltage. see this link

https://www.researchgate.net/figure/Space-charge-limited-current-SCLC-measurements-of-the-electron-only-devices-the-inset_fig4_342383215