Modeling novel effects in transient current measurements of single-crystal CVD diamond with carrier excitation by MeV α-particles

Abstract

Temperature- and electric field-dependent transient current measurements with 4.6 MeV high-energy α-particle excitation were reported recently in commercially available CVD diamonds and were used to extract drift velocities and drift mobilities of electrons and holes [1–3]. These data showed unexpected characteristic temperature-dependent pulse current profiles which remained unexplained as well as other novel observations. Here we interpret all experimental findings by a detailed physical model. It demonstrates that the measured electron or hole currents consist of two components one of which is constant in intensity whereas the other is temperature-dependent due to thermal activation of carriers out of a low-temperature storage state shown to consist of electron-hole droplets (EHDs); this is a condensed phase of electrons and holes. EHDs form in regions with electrons and holes embedded between adjacent regions with electrons or holes alone. This local separation is caused by the electric field during carrier relaxation from the highly excited states. The model describes all experimental findings very satisfactorily, some of them quantitatively. Maxima in the transit time as a function of temperature were experimentally reported [2, 3] which successively become more pronounced at decreasing electric fields while shifting to lower temperatures. This observation is modeled by temperature-controlled re-population of the “slow” and “fast” conduction band valleys split apart by the applied electric field upon lifting the sixfold valley orientational degeneracy. The model suggests that the novel effects are characteristic of the very high excitation energy of the free excess carriers and would not be observable for near-band gap excitation.

Introduction

In transient current measurements – often referred to as time-of-flight measurements – time resolved currents are recorded due to electrons or holes which are pulse generated in excess of their thermal equilibrium-densities and drift in an external electric field. When the drift distance is known, drift velocities and mobilities can be extracted from the transit times of the measured current pulses.

There is a great body of experimental data from single-crystal chemical vapor deposition (CVD) diamond obtained by the transient current technique (TCT) since knowledge of such basic electrical data is important for characterizing the material for research and applications.

This paper aims at explaining novel effects in transient current measurements performed in the group of H. Pernegger at CERN (Geneva, Switzerland) with excitation of free carriers by 4.6 MeV α-particles. The data published in three papers (Refs. [1–3]) are unique with regard to three aspects:

• The measurements were performed in a wide temperature range reaching from 295 K to 60 K [1] extended later to the range from 295 K to 2 K [2,3]. To the knowledge of the author no other investigations have been made at temperature as low as 2 K. These measurements showed remarkable features of both electron and hole current pulse shapes (cf. Fig. 1) hinting to a storage and releasing mechanism at around 80 K to 140 K related by the authors vaguely with excitons without further discussion.

• It is also remarkable that electron and hole current pulses have generically the same pulse shapes for all temperatures and electric fields being at very low and high temperatures rectangular-like and distinguished only quantitatively by virtue of different drift velocities. Naively, this seems not to be surprising but actually the pulse shapes are often very different for the two species deviating from the present rectangular shapes. Examples are found in [4] where at room temperature electron and hole spectra differ widely. Strongly fading amplitudes for holes across the pulse length have in this case been attributed to trapping of the holes by a negative space charge in the bulk related with a non-uniform effective electric field. Reversely, again at room temperature, generically identical pulse spectra were observed for electrons and holes at widely varied electric field strengths in [5]. Also, virtually rectangular-like hole pulse shapes have been reported in [6] at electric bias values of 70 V and 40 V though only at room temperature. In contrast, largely differing pulse shapes were reported in [7] changing in character from low to high excitation. In some TCT investigations mobilities of carriers are shown versus temperature but no pulse spectra are reported at all. Summarizing these few examples, the experimental manifestation of current pulses is manifold and the present pulses are singular in their straight regularity.

• The new data were obtained from three samples prepared from nominally identical commercially grown CVD single-crystal diamonds but processed in different laboratories. Values for electron drift velocities and mobilities are well comparable to those of published data from other samples. The data look very reliable and sound having been obtained in a laboratory with great pertinent expertise.

These statements conspire to suggest that in spite of the small experimental basis of only three samples the novel effects are real and the samples are - for the purpose of TCT - of outstanding quality. Hence, it appears worth to provide here a comprehensive model of the observed effects which has not been given so far. The original model was developed by the author in 2012 aiming at explaining the data in [[1], [2], [3]]. This turned out to be successful for several observations and the model was widely used in [3]. Other observations required amendments and led to the present final version which differs from the primary version in many decisive parts not yet published and mentioned in detail below.