# Charge transport in high mobility single crystal diamond

Miloš Nesladek, Anna Bogdan, Wim Deferme, Nicolas Tranchant, Philippe Bergonzo

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## To cite this version:

Miloš Nesladek, Anna Bogdan, Wim Deferme, Nicolas Tranchant, Philippe Bergonzo. Charge transport in high mobility single crystal diamond. Diamond and Related Materials, 2008, 17 (7-10), pp.1235-1240. 10.1016/j.diamond.2008.03.015. cea-05469487v2

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Submitted on 12 Feb 2026

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Charge transport in high mobility single crystal diamond

Miloš Nesladek<sup>a,b, □</sup>, Anna Bogdan<sup>b</sup>, Wim Deferme<sup>b</sup>, Nicolas Tranchant<sup>a</sup>, Philippe Bergonzo<sup>a</sup>

<sup>a</sup> CEA-LIST, Diamond Sensor Laboratory, CEA-Saclay, 91191 Gif sur Yvette, France

<sup>b</sup> Institute for Materials Research (IMO) University of Hasselt, Weteneschapspark 1; B 3590 Diepenbeek, Belgium

ABSTRACT

Time of Flight (TOF) measurements using conventional laser TOF and α-particle TOF setups have been carried out on high quality CVD diamond samples to study the electron and drift mobility and to compare them with the mobility data for IIA diamond. The measured mobilities for all samples investigated are in the range 2000–2250 cm²/Vs for holes and 2200–2750 cm²/Vs for electrons, thus close to the theoretical prediction as well as to IIa diamond mobility values. The charge transient profile measured in the laser TOF measurements is influenced by the electric field profile in the sample, which might be changed based on the charge trapping at low electric fields applied, depending on the surface atomic termination. The temperature dependence of the drift mobility indicates that at room temperature the scattering on acoustic phonons is the main dominant scattering mechanism and the contribution of other types of carrier scattering mechanism is negligible.

Keywords: Single crystal CVD diamond, Electrical transport properties, Electrical charge mobility, Defects

1. Introduction

Optimisation of CVD diamond for electronic and detector applications requires a precise knowledge
about the charge carrier drift mobilities. Because high purity undoped CVD diamond is highly
resistive, Hall measurements are not straightforward and cannot be easily applied. Alternatively, drift
mobilities can be measured for example using conventional Time-of-Flight (TOF) method, relying on
photocarriers generated by strongly absorbed UV photons or alternatively α-particles [1–3]. In both
methods the generated carriers drift through the sample under an applied electric field. The laser
TOF data, published in ref. [1] have suggested the charge mobility as high as 3800 cm²/Vs and 4500
cm²/Vs for holes and electrons respectively [1]. These values were determined at low electric fields
using the “Space Charge Current-Limited (SCLC) TOF mode. In SCLC-TOF the photogenerated charge
is higher than the C□U product, where the C is the sample capacity and the U the voltage applied on
the sample. The measured values of 3800 cm²/Vs and 4500 cm²/Vs for holes and electrons
respectively in ref. [1] exceed significantly the values experimentally measured by the TOF technique
for IIa diamond where values in the range of about 1800–2800 cm²/Vs [2–6] for the electrons and
holes are reported. It was suggested that these high mobilities were enabled due to the superior
quality of the CVD diamond films as compared with standard IIa diamond [1]. To discuss in detail this
controversy we have carried out laser and α-particle TOF measurements on commercial as well on
laboratory grown single crystal CVD diamonds in order to compare the mobility data from the both
methods and to study the charge carrier transport and the charge scattering in the temperature
range 300–500 K. For conventional laser TOF method we have studied the phototransients in so
called small signal TOF (Q<CU) and SCLC TOF (Q>CU) modes.

2. Experimental setup

The laser-TOF setup, used in this study is outlined in Fig. 1. The UV laser source is based onto the
third harmonics of a Nd:YAG laser, used to pump an OPO crystal and further doubled, tuneable from
210 till 350 nm. The pulses are 2.7 ns long. The samples are free standing IIa as well as CVD diamond
plates of several hundreds micrometers thick. Each sample is equipped with two electrical contacts
(on the top and on the bottom surfaces). The laser pulse trigger is delayed by ~50 µs with respect to
the ~1 ms long DC voltage pulse bias. This sufficiently short time prevents any dielectric relaxation
which is characterised by a time constant τε (tε~pε, where ρ is the diamond specific resistivity and ε the dielectric permittivity respectively). The electrical current transients are recorded, using a 1 GHz digital Tektronix oscilloscope, by averaging over 25 single shot measurements to reduce the electrical noise. The typical UV light absorption depth at 218 nm is about 8 µm. Therefore one polarity of carriers can be directly collected by the upper electrode, while the other polarity carriers are transiting through the bulk of the sample towards the back electrode. The electric field is varied in the range from 0.1 V/µm to 1.5 V/µm.

Samples measured are (100) oriented natural Ila diamonds as well as commercial and laboratory fabricated CVD diamond plates [7–9], grown using microwave CVD systems in two independent laboratories (CEA-LIST Paris and IMO Belgium). The typical CVD growth conditions are: gas pressures ~100–200 Torr, CH4 concentration 4–10%, substrate temperature 700–900 °C and MW power densities of about 1000 W/cm³, for details see [8,9]. After growth, the epitaxial layers are removed from the substrate by laser cutting, then polished, and their surface oxidised using a solution of H₂SO₄ +KNO₃ at 300 °C during 30 min and rinsed in deionised ultra-pure water. Then, the top semitransparent or back nontransparent Al or Au contacts are prepared by evaporation from thermal Al and Au sources.

Alternatively, we also used a second type of the diamond surface that is hydrogen terminated, obtained using standard hydrogenation treatment and leading to a 2×1 H reconstructed surfaces [9,10]. The samples are further annealed in UHV at 300 °C and after Al or Au contacts are also evaporated. After contact preparation, the samples are then exposed to RF oxygen plasma at ~1 mbar, 200 W and during 30 s to oxidise the sample surface between the top and bottom contacts. This treatment converts the H termination to an oxygen termination, in order to reduce any surface parasitic electrical conductivity between the top and the bottom contact surfaces. The contacts are sufficiently blocking to satisfy the TOF requirements. The light transmittance of the Al/Au semitransparent contact is about 20–30% at 220 nm and their resistance remains below 1 kΩ.

# 3. Results and discussion

## 3.1. Time of flight data

Two modes of TOF operation were used. Firstly, in the small signal TOF mode, the photo generated charge Qph is kept well below Q0, where Q0=CU, as above. On the other hand, the so called SCLC mode is obtained when Qph>> Q0. A typical value for the C is <0.5 pF for a 2 mm diameter contact size and a thickness of the diamond layer of 500 µm. The RC constant of the detection system is much lower than the transit time. This is achieved by matching the detection circuit using 50 Ω high frequency detection electronics, specially designed for the TOF experiments. The transit time tt is calculated as the time of arrival of the main charge packet to the electrode, on the basis of which the drift mobility μ can be calculated (μ=L²/U tᵣ), where L is the sample thickness (Table 1).

Fig. 2 shows TOF data for the high purity sample IMO1 grown at IMO in Belgium, as a function of the laser intensity expressed in the power of the IR (1024 µm) YAG beam. By increasing the laser intensity the SCLC conditions are reached as indicated by a dotted line in Fig. 2. Upon increasing the laser intensity the shape of the transient changes significantly and a “cusp”, characteristic for the SCLC mode, appears. This feature is known as so-called extraction time [11,12], which is related to the transit time by the following equation:

$$tE \frac{1}{2} b tT \delta t = 1$$

with the β coefficient given at ~0.787 [1]. The experimentally measured values of the extraction time yield for data in Fig. 2 β value of ~0.85. This suggests that the mechanism of the electric field relaxation at the contacts deviates slightly from the theory presented in ref. [11,12]. This is believed to be due to charge trapping at the contacts, which can change the electric field profile, as discussed below. In order to determine the charge carrier mobility at low electric field the experimental data are fitted with the formula (2). The parameters μ0 and saturation velocity vS were adjusted to match the experimental data.

$$c \frac{1}{2} c0 1 \beta c0E vS ; \delta t = 2$$
The mobility determined from the small signal TOF is calculated using a numerical fitting based on Eq. (2). This fitting yields a value of 2050 cm²/Vs for electrons and 2250 cm²/Vs for holes at room temperature for IMO1 sample. These values correspond to the data obtained for IIa diamond with a difference of ±200 cm²/Vs. However this sample shows higher mobility for holes than electrons which might be caused by a residual presence of boron ~1 ppb) in this samples. The fitting of the saturation velocity gives ~1 × 10⁷ cm/s for holes and about 1.2 × 10⁷ cm/s for electrons.

The transit time is determined from data in Fig. 2. As discussed in the literature, several definitions of $t_T$ time can be found, one of them is that $tT$ is defined as a time during which the photocurrent drops to 50% of its value after the laser shot charge generation [13,14]. This definition of the transit time $t_T$ is related to a movement of the main weight of the laser generated charge parcel, transported through the sample. However, this definition is generally used in the case of non-dispersive transport i.e. in the absence of the charge trapping which delays by trapping and remission events the arrival of the charge to the collecting electrode. If a part of the charge is trapped just after the laser pulse, the change in the slope in the $log(I)-log(t)$ plot indicates the arrival of the fastest carriers to the collecting electrode which can be used as a definition of the $tT$. Such definition of the transit time is directly related to the microscopic drift mobility, defined as the time required for the fastest carriers to move through the entire samples from the front to the back electrode without any trapping. This definition of $tT$ is used throughout this work. As shown below, the main influence on the determination of the electron and drift mobilities comes from the changes in the electric field profiles in the sample, due to the charge built-up. Our previously measured data [15] had compared IIa diamond with CVD diamond samples and almost identical mobility values were found.

## 3.2. Effects of the surface termination

The surface density of states, related to the atomic surface termination of diamond, is an important parameter from the point of view of electrical charge transport. The possible charge trapping at the interface is a consequence of the presence of these surface states that can influence the electrical contact properties. In this work (100)-oriented CVD diamond films are terminated by hydrogen or oxygen atoms. XPS and UPS carried out on such samples [9], indicate the differences in the work function for specific atomic surface terminations. We have concluded [9] that in agreement with published data [16–18], the oxygen-related states are generating defect states in the surface band gap at about 1.2–1.6 eV above the Ev, these states lead to charge trapping effects at the interface. On the other hand, little is known about the surface defect states after hydrogen treatment. On H-terminated surface, STM and STS measurements are not easily possible if surface adsorbates are desorbed by annealing at UHV conditions, decreasing the surface electrical conductivity. The high resistivity of clean H terminated surfaces suggests low surface density of states (i.e. no tunnelling to the surface states is possible). From this study one can assume that the H-terminated diamond surface will exhibit a reduced charge trapping which might be an advantage for the TOF measurements and for the determination of the drift mobility.

Using the TOF technique a comparison is made between oxidised and hydrogenated diamond surfaces. In these measurements one has to be careful about the blocking properties of the contacts as Al makes a blocking contact on H-terminated surface whilst Au on H-terminated surface makes an injecting contact. In our experiments we have used only Al/Au or Al/Al contact structures, i.e. one of the top or bottom contacts was always Al to reduce the charge injection. For Al/Al structures the hydrogen terminated surfaces lead to clearly better electrical blocking properties, due to the reduced tunnelling through the surface states. Corresponding I–V characteristics are shown Fig. 3A. At the same time, interestingly we observed electroluminescence from the CVD diamond, visible at high electric fields 1 V/µm, depending on the surface termination. In the case of oxidised surfaces the luminescence is dominated by a blue band A, while for the H surface, the intensity of the band A luminescence is decreased with a simultaneous increase of the free exciton luminescence. We attribute this phenomena to an enhanced tunnelling current through the surface states and the surface state pining [17]. Fig. 3B compares luminescence spectra for both cases. It confirms that the presence of surface states, leading to tunnelling can be significant for O-terminated surfaces.
Photoelectric transients I(t) can be described by formula I(t)~μE(t,x), where E(t,x) is the time and coordinate (x) dependent electric field in the sample. If a time dependent space charge progressively builds up, due to trapping, the electric field across the samples evolves, leading to changes from the ideal theoretical rectangular profile and affecting the tt. Figs. 4 and 5 show the experimental plot for the drift mobility, calculated from the TOF — transit time data using both the laser TOF and α-particle TOF setups respectively. The data in Fig. 4 for laser TOF are related to the different surface termination and Al/Au contacts for commercial sample COM1. Data in Fig. 4 shows the extrapolated mobility for electrons and holes ~2500 ±300 ~cm²/Vs and 2250±300 cm²/Vs respectively. From the data shown in Fig. 4, obtained at low electric fields, the calculated mobility depends strongly on the type of contacts and on the atomic termination used. For oxygen terminated surfaces using Al contacts the apparent transit time for lower electric fields for electrons is shorter as suggested by the numerical fitting using the asymptotic dependence from Eq. (2). This can only be possible if the charge trapped does induce electric field with the same polarity on the contact as the applied field. By reversing the polarity and illuminating the sample again through the top contact a reduction of the drift mobility for the holes can be observed. The existence of the electric field due to surface charge trapping can be verified easily by zeroing the external electric field applied to the sample: in this case for the electrons the TOF signal is still detectable with the same polarity, and it slowly decreases with time with tt shifting to lower time scale. The signal can be measured clearly for prolonged time period ~200 laser shots, confirming a slow and progressive removal of the trapped charge. Fig. 5 shows the data using α-particle TOF setup for the sample grown at CEA-LIST in Paris, using an oxidised surface and with Al contacts. The TOF data show no significant trapping and can be well fitted leading to a mobility of 2730 cm²/Vs and 2370 cm²/Vs for electrons and holes respectively. Based on the numerical fitting we can additionally estimate the error due to the saturation velocity fitting ~10%. Therefore, taking into the account the tt definition, which measures the arrival of the fastest carriers the mobility values calculated can be determined with a precision of ~20%. To explain differences in low-field behaviour between the laser and α-particle TOF we have however to consider the differences in charge density profiles, induced by the α-particle or the laser irradiation. In the first case the charge induced by α-particle is much lower (each particle provides 5.5 MeV thus only ~4.2×10⁵ generated electron-hole pairs) and also the absorption profile is deeper and spreads across the first 14 µm. On the other hand for laser TOF, the absorption profile is exponentially decreasing in the first 8 µm. From our experience this seems to be important. Additionally if coupled with the different number of carriers generated (and therefore trapped), it influences significantly the current transients and low electric fields. It is thus obvious that not only the traps at the surface but also the sample characteristics, specifically background impurities and trap levels, do influence the photoelectrical current transients. The CEA-LIST sample clearly behaves better, showing reduced trapping. However by comparing measurements on samples of different origins, nearly the same mobilities are obtained by fitting the mobility data in the full range of applied electric fields.

### 3.3. The temperature dependence of the drift mobility

Fig. 6 shows the temperature dependence of the drift mobility comparing the commercial samples COM1 and laboratory sample CEA-LIST (see also Figs. 4 and 5) with data from the literature on IIA diamond [4–6] and Isberg data on CVD diamond [1]. At room temperature the slope of μ(T), is expressed in the form.

#### AeTa ð3þ

Fitting the data in Fig. 6 yields to a value for α of about -1.5 for holes and -1.4 for electrons, in the temperature range of 300–340 K. Above 340 K, the slope is changing to value -3.2 for holes and -2.5 for electrons. These values compare very well with theoretical ones for Ila diamond with α ~1.5 for acoustic phonon scattering and due to optical (holes) or intervalley (electrons) phonon scattering mechanism at higher temperatures. The comparison with Fig. 6 shows that for high quality laboratory and commercial samples, the mobilities are well in agreement with theoretical and experimental data known for Ila diamond.
## 4. Discussion

The mobility data can be calculated based on the electron and hole effective masses $m_e^\square, m_h^\square$ and the acoustic/optical deformation potential tensor E1. In high quality nearly atomically flat B-doped samples with low B-concentration in the range of ~1016 $cm^{-3}$, room temperature mobilities of 1800 $cm^2/Vs$ were measured [19]; close to the expected theoretical values. To compare with the TOF data one has to consider the Hall-coefficient value. Despite the fact that the Hallcoefficient is usually taken as about unity, Regianni at al [4] suggested that it can be as low as 0.65 at 300 K. This would place the maximal hole mobility values at 300 K closer to the value of 2600 ~$cm^2/Vs$. However this value is still significantly lower than the drift mobility data published by Isberg at al [1]. For the electron transport this situation is still more complicated because of the lack of experimental data for (100) oriented n-type diamond. This, together with the uncertainty for the Hall-coefficient rH value, renders difficult the appreciation of the upper value for the room temperature mobility. However taking into the account the values for the effective masses for electrons and for the acoustic deformation potential tensor E1, the calculated values get very close to the ones obtained for IIa diamond and are in the range of 2000–2500 $cm^2/Vs$ [4,5].

Interestingly, a parameter not taken into account for these calculations yet is the acoustic velocity $s$, although it appears in the expression of $\sigma$, which dominate the acoustic scattering mechanism at RT: $r \frac{1}{4} 25=2 p1=2e\hbar 4qs2 3K3=2 B 1 \beta mh=ml \delta \beta 1=2 E02 1 m5=2 l 1 \beta mh=ml \delta \beta 3=2 h i2 \delta 4\beta$

where other parameters are the density $\rho$, kB the Boltzmann constant and $\hbar$ the Planck constant. Several studies using isotopically purified diamond [20] showed that diamond can be synthesised with higher RT thermal conductivity values than IIa diamond. In the simple Debye model, the thermal conductivity is proportional to the acoustic velocity. This ~25% difference between the thermal conductivity could account for the increase of the acoustic velocity $s$ ($\sigma \sim s^2$). However no electrical measurement data are yet available. Additionally, no values for acoustic deformation potential for isotopically purified CVD diamond are available to date. This will have to be further studied to confirm a possibility to increase the drift mobility for such material. However based on our model we predict that isotopically purified diamond can possess higher carrier mobility. To conclude for all CVD samples, the measured mobility was matching the upper limit of the theoretical calculations and measurements on IIa diamond, best values yielding to ~2700 $cm^2/Vs$ for electrons and ~2250 $cm^2/Vs$ for holes.

## 5. Conclusions

High quality CVD diamond samples prepared in different laboratories were studied using TOF and compared with data obtained on commercial samples and in the literature, and with theoretical data for IIa diamond. The measured mobilities of all samples investigated are in the range 2000–2250 $cm^2/Vs$ for holes and 2200–2750 $cm^2/Vs$ for electrons, thus close to the theoretical prediction as well as to IIa diamond mobility values. The charge transient profile measured in the laser TOF measurements is influenced by the electric field in the sample, which might be changed based on the charge trapping. This can be especially important for low electric fields applied. It should be noted that the study in ref. [1] was also using such low electric fields in SCLC mode to calculate the mobilities. The charge trapping at the surface depends on the surface termination and the sample quality. We have shown that H-terminated surfaces lead to lower charge trapping compared to oxidised diamond surfaces.

The temperature dependence of the drift mobility indicates that at room temperatures the scattering on acoustic phonons is the main dominant scattering mechanism. Also, the contribution of scattering on optical phonons for holes and on intervalley phonons for electrons is increasing with the temperature, thus in agreement with published data on IIa diamond as well as on n-type diamond [21]. All data presented confirm that for the samples measured here, the contribution of other types of carrier scattering mechanism is negligible and that we have effectively reached phonon scattering limits.
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