Meyer-Neldel Rule in Deep-Level-Transient-Spectroscopy and its Ramifications
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Meyer-Neldel Rule in Deep-Level-Transient-Spectroscopy and its Ramifications Richard S. Crandall National Renewable Energy Laboratory, Golden, Colorado 80401 ABSTRACT This paper presents data showing a Meyer-Neldel rule (MNR) in InGaAsN alloys. It is shown that without this knowledge, significant errors will be made using Deep-Level Transient-Spectroscopy (DLTS) emission data to determine capture cross sections. By correctly accounting for the MNR in analyzing the DLTS data the correct value of the cross section is obtained. INTRODUCTION Meyer Neldel Rule The large body of literature amassed since its discovery in 1937 attests to the widespread applicability of the Meyer-Neldel rule. This rule connects the activation energy (Eact) in a family of thermally activated processes with the prefactor in the expression: r = ν0e
−
E act k BT
,
(1)
where r is some variable that is activated, T the temperature, and kB is the Boltzmann constant. The Meyer-Neldel-Rule (MNR) connects ν0 and Eact: ln(ν 0 ) = ln(ν 00 ) +
E act , k B TISO
(2)
with ν00 and TISO positive constants. In these equations ν0 is an attempt-to-escape frequency. Equation (2) shows that ν0 can vary by many orders-of-magnitude if Eact varies over a significant range. The MNR is obeyed in many transport processes in solids and liquids. It has been observed in systems as diverse as liquid semiconductors [1] and protein denaturation.[2] In many instances where the MNR is obeyed the activation energy is much greater than the highest system excitation (phonons) energy. Perhaps the first systematic observation of this rule was in diffusion in crystalline solids where it was given the name the “compensation law”.[3] The term “compensation” certainly represents the essential physics since the law means that the increase in ν0 with Eact compensates for the Boltzmann factor in reaction (1). There have been various attempts to explain Eq. (2). See Ref. ([4]) for a discussion of the different approaches. Perhaps the most satisfying approaches are the models based on the realization that there is considerable entropy associated with the assembly of a large number of system excitations (phonons) together at a particular site to make a thermally activated jump over a barrier. [4-7]
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Consequences of the Meyer-Neldel rule The consequences of the MNR can be seen by substituting Eq. (2) into Eq. (1) to give r = ν 00e
E act k B T ISO
e
−
E act k BT
.
(3)
This equation shows the two key features of the MNR. The prefactor, ν0 appearing in Eq. (1) should vary with the activation energy and r is independent of Eact at T=TISO. The former is seen in all cases. However, the later is rare and only observed in a few cases.[8,9] As T approaches close to TISO the emission rate for the different Eact vary significantly l
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