# What is the difference between contact-limited and space-charge-limited charge transport?

I am reading a paper ("Tunable Electrical Conductivity of Individual Graphene Oxide Sheets Reduced at 'Low' Temperatures," Jung, et al. Nano Lett. 2008, 8, 4283-4287) about electrical conductivity in graphene oxide. In this paper, the authors plot a variety of current-potential ($I-V$) curves to determine how the electrical conductivity of graphene oxide relates to the extent of reduction. The authors find that "the $I-V$ curves are independent of the contact area or length of the electrode edges...." From this, they conclude:

Charge transport in graphene oxide is thus not contact-limited; instead, it is space-charge-limited, and the injected carriers significantly alter the local electric field created by the electrode potentials. [page 4284]

My question is, what is the difference between contact-limited and space-charge-limited charge transport?

I understand (I think) why the injected carriers (electrons supplied by the battery to which graphene oxide is attached?) would alter the local electric field. Does the authors' assertion that charge transport in graphene oxide is not contact-limited perhaps refer to the extended pi network in graphene and even in graphene oxide (where oxygen-containing functionalities disrupt in patches the pi network)?

Later in the paper, the authors bring up a seemingly related point about the mode of charge transport. They find that, upon heating (which removes some of the oxygen-containing functionalities which disrupt the pi network), the n-type conductivity becomes more pronounced: "Small n-type dominated conductivity at room temperature is transformed upon heating to a much larger electron-doped conductivity with significantly reduced gate dependence." By plots of resistance versus temperature and resistance versus gate voltage, the authors conclude:

In this case, the overall charge transport is controlled by thermal activation instead of carrier injection. [page 4286]

Are the terms contact-limited charge transport and space-charge-limited charge transport somehow related to whether the charge transport is controlled by thermal activation or carrier injection?

Thanks for your time. I am not looking for a detailed first-principles explanation; I am just looking for a "freshman physics"-level explanation of the different modes of charge transport. Thanks!

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