Optical and electronic properties of heavily boron-doped homo-epitaxial diamond

phys. stat. sol. (a) 199, No. 1, 9–18 (2003) / DOI 10.1002/pssa.200303819

© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Editor’s Choice

Optical and electronic properties

of heavily boron-doped homo-epitaxial diamond

E. Bustarret*, 1

, E. Gheeraert1, and K. Watanabe

2

1 Laboratoire d’études des propriétés électroniques des solides, LEPES-CNRS, BP166X,

38042 Grenoble 9, France 2 National Institute for Materials Science, NIMS/STA, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

Received 14 April 2003, accepted 26 May 2003

Published online 15 September 2003

PACS 61.72.Ww, 72.80.Cw, 78.30.Am

At room temperature, the optical, transport and magnetotransport properties of homo-epitaxial MPCVD

diamond layers with boron contents in the 2 × 1020 to 2 × 1021 cm–3 range are expected to be governed by

the characteristics of the boron impurity band. A comparison of room temperature infrared transmittance,

reflectance and visible ellipsometry spectra to temperature-dependent Hall effect and conductivity meas-

urements allows a quantitative determination of optical constants and of transport parameters. The results

are discussed in reference to the metallic– insulator transition in heavily doped semiconductors.

This description enables us to discuss the Raman spectra of p+ monocrystalline diamond, focussing

on the polarization dependence of the low energy tail, of the unassigned broad peak observed around

500 cm–1 and of the optical phonon frequency range where the Fano interference occurs. On the basis of

the observed scattering selection rules, we propose that these features result from electronic scattering in

the impurity band and from the electron–phonon coupling on the boron center.


1 Introduction Since boron was identified [1] as the acceptor responsible for the poor insulating prop-

erties of natural IIb crystals [2], the transport properties of boron-doped monocrystalline diamond have

been the subject of a number of investigations. Crystals [3, 5] synthesized under High Pressure and

at High Temperature (HPHT) as well as Microwave Plasma-assisted Chemical Vapour Deposited

(MPCVD) epitaxial layers [6, 9] were doped in-situ and their electrical properties were studied at high

[3, 4, 6–9] and low [4, 5] temperatures. The results have been interpreted in terms of thermal activation,

Variable Range Hopping [4, 5] and compensation effects [3–5, 9] for Boron contents lower than

2 × 1019 cm–3. Compensation-independent Nearest Neighbour Hopping [8] and the less specific hopping

[9] and “impurity band” conduction [3] were proposed to describe the dominant charge transport mecha-

nisms in the intermediate range 2 × 1019 < [B] < 2 × 1020 cm–3. At still higher Boron concentrations

where the average distance between boron acceptors becomes comparable to the acceptor Bohr radius

aH, “metallic” conduction was reported [3, 5, 7, 9], with room-temperature conductivities of a few

102 Ω–1 cm–1 [7–9].

Comparison between the more popular p-type polycrystalline thin films grown by MPCVD on silicon

and monocrystalline layers disclosed systematic differences in the transport properties [10] as expected

from the finite grain sizes as well as from the presence of grain boundaries or additional defects. How-

ever, in the 1020–1021 cm–3 Boron contents range on which the present paper will focus, polycrystalline

* Corresponding author: e-mail: [email protected], Phone: 33(0)476887468, Fax: 33(0)476887988

10 E. Bustarret et al.: Optical and electronic properties of heavily boron-doped homo-epitaxial diamond


p+ thin films were found to have electrical properties [11–13] similar to those of their monocrystalline

counterparts. Such p+ layers have various potential industrial applications, among which electrical ohmic

contacts to more resistive diamond layers as well as chemically inert electrodes for advanced electro-

chemical sensing or processing devices [14–16]. In a less expected direction, recent theoretical calcula-

tions [17] have shown that diamond with a free hole density of 3.5 × 1020 cm–3 in which a concentration

of 2.5% of magnetic atoms such as Mn had been introduced would be the ideal semiconductor for high

temperature ferromagnetism, thanks to the small spin-orbit splitting and the predicted strong hole-

mediated exchange interactions.

Beside such a technological drive, the open questions of the nature of the Metal-to-Insulator Transi-

tion (MIT) and in particular of the value of the critical concentration in a material where the Bohr radius

of the acceptor ground state aH is of the order of the lattice parameter are of fundamental interest and

provide ample motivation for the preliminary experimental investigation of transport properties to be

presented below. The tremendous difficulty to control with the necessary precision the boron concentra-

tion in diamond crystals may explain why the MIT critical concentration Nc has not been yet determined

in the C:B system. On the basis of the criterion first proposed by Mott [18] for metal–non metal transi-

tions, which in its final form (Nc1/3aH = 0.26) has been verified in a wide variety of condensed media

[19], the critical concentration in p-type diamond is expected to be about two orders of magnitude greater

than that of Si :B which is around 4 × 1018cm–3 [20]. Such considerations led various authors to propose

Nc = 1.2 × 1020 [6] or 2 × 1020 cm–3 [3] while another less adapted formula yielded 9 × 1021 cm–3 [5].

Limitations to this approach arise from the discrepancies in the value of aH proposed in the literature, in

line with other inconsistencies about the valence band parameters. From an experimental point of view,

RX diffraction [21] or Raman [22] studies as well as extrapolations [7, 9] of the Pearson–Bardeen model

[23] have led to values ranging from 1.7 to 3.0 × 1020 cm–3, while different transport measurements have

prompted other authors to propose that Nc lies between 7 and 10 × 1020 [11], or even near 4 × 1021 B/cm3

[24].

In parallel to these transport studies, optical spectroscopy in the infrared has been extensively used on

B-doped diamond, first on natural and HPHT crystals [1, 25–26] and then on homo-epitaxial MPCVD

layers [27, 28] with the main purpose of estimating the concentration of neutral boron atoms. As detailed

elsewhere [28–31], the four main features of the absorption spectra are a single phonon absorption

around 1280 cm–1, a set of three or even four [30] lines around 2450, 2800, 2930 and 3015 cm–1 corre-

sponding to the excitation spectrum of bound holes, a photo-ionization continuum with a threshold at

3080 cm–1, and finally various phonon replica [29] of these electronic transitions. Temperature- and

concentration-dependent measurements have yielded additional energy values, at 525 and 1760 cm–1 for

thermal transitions [31] and an estimate of the impurity band width below the MIT, around 250 cm–1

[28]. For comparison, the spin–orbit splitting of the 1s ground state of the acceptor has been measured

around 16 cm–1 [32] against almost 50 cm–1 as estimated [33] for the states at the top of the valence band.

Among these studies, only a few deal with the highly doped ([B] > 1020 cm–3) material of interest here,

either monocrystalline [28] or polycrystalline [13, 34], probably because the layers become opaque and

weakly photoconductive in this concentration range. This difficulty can be circumvented by growing

much thinner films or by using reflection geometries as described below. In a previous work [35], it was

established that the reflectance spectra of monocrystalline p+ diamond layers in the mid-infrared yielded

the typical plasmon edge associated to the collective excitation of free holes in the semiconductor.

Another specific feature of p+ diamond is a particularly complex Raman response with a shifted zone-

center Raman peak, a wide band at lower frequencies with two broad features around 1230 and 500 cm–1,

a Fano deformation and a low-frequency tail, as reported a few years ago by various groups [13, 36–38]

on polycrystalline films and confirmed more recently on isolated micro-crystals [39, 40] and monocrys-

talline layers [22, 41]. While the low-energy tail and the line shape deformation around the optical pho-

non frequency can be easily ascribed to scattering processes by electronic excitations associated to the

free holes similar to the case of Si :B [42, 43], we are of the opinion that the details of the Fano interfer-

ence (between a vibrational discrete level and a continuum of electronic excitations) in p+ diamond re-

main not completely understood [13, 22, 34, 41]. As for the broad peaks at 500 and 1230 cm–1 already

phys. stat. sol. (a) 199, No. 1 (2003) / www.physica-status-solidi.com 11


0 100

5 10-4

1 10-3

1.5 10-3

2 10-3

0 5 10 15 20 25 30 35 40

co

rre

cte

ds

tra

ind

a/a

Boron concentration [ B ] (1020

cm-3

)

calibrated SIMS

Vegard's law

Dp

> 0 Dp

< 0

monocrystallineB-doped diamond

Fig. 1 Average solid state boron contents of various

heavily B-doped monocrystalline MPCVD layers as a

function of the boron-to-carbon atomic concentration

ratio in the gas phase. Full symbols: calibrated SIMS

experimental data, with the linear interpolation fit

(broken line). Open symbols: B concentrations (either

measured or extrapolated) previously published

(Ref. [31]).

Fig. 2 Boron concentration dependence of the relative

lattice expansion corrected for biaxial strain. Open cir-

cles refer to earlier B contents values (Ref. [31]), while

full symbols correspond to updated B concentration

values using the linear interpolation fit proposed in

Fig. 1.

mentioned in the earliest report [36], they remain unassigned. In the present work we shall endeavour

to shed some light on the matter by reporting among others the polarization dependence of these spectral

features for well characterized monocrystalline p+ layers, putting in perspective the microscopic transport

parameters deduced from the electrical and optical measurements mentioned above with the line shape

parameters of the polarized Raman spectra of the same or very similar samples. Similar correlations

between either transport properties and Raman unpolarized spectra or infrared and Raman temperature

dependence measured on the same polycrystalline films have already been proposed in the literature [13,

34]. More generally, we aim here at opening the way for a more detailed and quantitative description and

understanding of the specific Raman scattering spectral signature of boron-doped p+-type diamond, in

order to learn more about the details of the band structure and the nature of the states near the top of the

valence band or the impurity band in a concentration range close to the metal-non metal transition.

2 Experimental The diamond films were prepared by microwave plasma-assisted Chemical Vapor

Deposition of mixtures containing 96% H2/4% CH4 and B2H6. The B/C ratio in the gas phase was varied

from 200 to 2800 ppm. Boron-doped films with thickness ranging from 0.1 to 5 µm were deposited at

820 °C on the (001) surface of Ib synthetic crystals after growth of a typically 0.5 µm-thick non-

intentionally doped buffer layer. Simple four-point probe d.c. conductivity were performed along the

diagonal of these 3 × 3 mm2 samples at room temperature. Ag or Pt pads were sputtered on some sam-

ples through Van der Pauw mechanical masks and the contacted samples were inserted in the local heat-

ing vertical stage (anti-cryostat) of a superconducting coil system working at liquid He temperature and

ensuring an homogeneous horizontal magnetic field up to 6 T. For Hall measurements, the injected d.c.

current was 0.1 mA and the Hall voltage was measured with lock-in amplifier at 19 Hz. Optical reflect-

ance at 20° incidence and normal incidence transmittance were measured at room temperature without

polarisation analysis in the 500 to 12000 cm–1 range in a FTS-60A FTIR spectrophotometer and at higher

wavenumbers in a Lambda 900 dual beam spectrometer. The depth profiles of boron and carbon were

measured in a Cameca ims 4f Secondary Ion Mass Spectroscopy (SIMS) apparatus using a Cs+ primary

ion beam and monitoring the negative 11B–, 12C–, and 12C11B– ions. Polarized micro-Raman backscat-

0

5

10

15

20

0 1000 2000 3000

Bo

ron

ato

mic

co

nte

nt

(102

0 cm

-3)

(B/C)gas

(ppm)

(B/C)sol

= (B/C)gas

homo-epitaxial

p+ diamond



Fig. 3 Relative variation of the resistance of two B-

doped homo-epitaxial films as a function of the am-

plitude of the d.c. magnetic field for two opposite

relative orientations (0° and 180°) of the sample with

respect to the field axis. The parasitic magnetoresi-

stance (MR) signal is given by the average of the two

contributions of opposite signs.

Fig. 4 Temperature dependence of the normalized a.c.

(19 Hz) conductivity σ (left-hand scale) and of the Hall

voltage VH

in a 5 T magnetic field for two p+-type dia-

mond epilayers.

tering measurements were performed at ×100 magnification with two different commercial systems with

exciting cw laser lines at 633 and 514.5 nm.

3 Chemical and structural properties The average solid state boron concentrations [B] reported in

Fig. 1 correspond to SIMS profiles very similar to those already published [35] except for a 25% upward

correction of the absolute value resulting from a more recent calibration specific to samples where [B] >

1020 cm–3 and for which a Ib 100-oriented substrate has been implanted off-axis with 1015 cm–2 B ions

at 90 keV. As seen on Fig. 1, for atomic concentration ratios in the gas phase [B]/[C]gas higher than

1500 ppm the gas-to-solid incorporation rate increases markedly, departing from the 1:1 ratio (continu-

ous line in Fig. 1) usually observed at lower Boron contents. For the highest gas ratio used here, the

boron concentration reaches 1.9 × 1021 cm–3, corresponding to an average Boron-to-Boron distance of

roughly 0.8 nm. Such values lead to a sizable expansion of the lattice parameter as a result of the larger

covalent radius of boron (rB = 0.088 nm) with respect to that of carbon (rC = 0.077 nm). This has been

verified by X-ray diffraction experiments on homoepitaxial films very similar to the present samples

[21]. However, the clear uptake of the gas-to-solid incorporation described by the interpolated linear fit

of the SIMS data presented in Fig. 1 leads us to re-evaluate the boron concentrations extrapolated in

Ref. [21] and to re-examine the variations of the “relaxed” expansion coefficient (i.e. corrected for bi-

axial strain) deduced from the experimental diffraction patterns. As depicted in Fig. 2, we now find that

the internal strain introduced by substitutional boron atoms is smaller than that expected from Vegard’s

law [44]. The sign of the deformation potential Vp resulting from the contribution of the free holes to the

lattice distortion seems therefore to be negative, in agreement with theoretical calculations on such

p+-type semiconductors [45].

4 Electrical properties Preliminary results on the magnetic field dependence of the film resistance in

the Van der Pauw geometry at liquid He temperature are given in Fig. 3 for one thin and one thick

p+-type epilayers doped in the lower 1021 cm–3 range. The difference between the two curves obtained for

two opposite orientations of the same sample with respect to the magnetic field result from the positive

Hall effect on the free holes, while the average of these two measurements correspond to the magnetore-

0

1

2

3

4

4 10-7

6 10-7

10-6

3 10-6

5 10-6

7 10-6

0 50 100 150 200

VHall

(V)

Temperature (K)

Co

nd

uc

tiv

ity

rati

o 1.9 1021

B/cm3

9.1 1020

B/cm3

B = 5TI = 0.1 mA

σ (Τ )/σ (4Κ )σ (Τ )/σ (4Κ )σ (Τ )/σ (4Κ )σ (Τ )/σ (4Κ )

VH

VH

p+

diamond

-0.005

0

0.005

0.02

0 1 2 3 4 5 6 7

dR

/R

magnetic field (T)

0°

180°

MR >0

Hall

effectMR

1.9 1021

B/cm3

9.1 1020

B/cm3

T = 4.2 K

homo-epitaxial

p+

diamond

0



0.1

0.3

0.5

0.7

0.9

0 2000 4000 6000 8000

Drude

Exp

RE

FL

EC

TA

NC

Eo

rT

RA

NS

MIT

TA

NC

E

Wavenumber (cm-1

)

R T (x3)

9.1 1020

B/cm3

3 µm-thick

1.9 1021

B/cm3

0.14 µm -thick

homo-epitaxial p+ diamond

Fig. 5 Specular reflectance (R) and real (n) or

imaginary (k) part of the optical refractive index of a

typical 3 µm-thick p+-type diamond epilayer.

Fig. 6 FTIR reflectance (R) and transmittance (T)

experimental spectra of two monocrystalline B-doped

layers grown on Ib diamond substrates. The grey lines

result from a fit by a Drude model.

sistance (MR) of p+-type diamond detected here because of the imperfections of our Van der Pauw pat-

tern. The MR was found to be always positive, even at higher temperatures, as observed in p-type Si and

Ge [46, 47].

For the same two samples, as the temperature was raised from 4 to about 230 K, the Hall voltage de-

creased slightly (see Fig. 4), indicating that the ratio of the free carrier density p to the Hall coefficient

rH changed very little, especially between 20 and 230 K. The relative increase of the conductivity with T

also represented in Fig. 4 was more marked but remained weak. It did not seem to follow any of the laws

associated with carrier hopping mechanisms [4, 5, 48] but rather a σ(0) + αTν dependence with α > 0

and 0.3 < ν < 1 typical of the metallic side of the MIT usually studied at lower temperatures in doped

semiconductors [24, 49–51]. Here, in the absence of transport measurements at temperatures lower than

4K, the extrapolated σ(0) values greater than 100 Ω–1 cm–1 and the σ(300 K)/σ(4 K) ratios lower than 4

also suggest that both diamond films are metallic.

5 Microscopic transport parameters Turning now to the room-temperature optical properties of such

materials, one sees on Fig. 5 that the good surface quality of thick opaque epilayers allowed reliable

visible spectroscopic ellipsometry and specular reflectance experiments to be performed, leading to the

determination of the real (n) and imaginary (k) part of the refractive index. The typical spectral shapes of

n and k in the near-infrared suggest the onset of free carrier absorption as confirmed by the obvious plas-

mon edge present at lower frequencies in the unpolarized FTIR reflectance spectrum also shown in

Fig. 5. A previous publication [35] has detailed how this absorption edge shifted to higher energies as the

boron contents of the films was increased and how this optical response could be easily reproduced

above 1350 cm–1 by that of a Drude metal, as illustrated in Fig. 6 by the reflectance and transmittance

spectra of the respectively thick and thin B-doped films already described in the previous section. Sys-

tematic fitting to such a simple model yielded plasmon frequencies ωp and damping coefficients γ [35]

which could be in turn related to the microscopic mobility µopt and to the density p of the free holes,

provided that an appropriate value of the optical effective mass m* be chosen. In particular, for the value

m* = 0.74m0 known to give the best fit to the optical excitation spectrum of the boron acceptor [30], and

assuming a single conduction channel with rH = 1, free carrier concentrations p deduced respectively

from our optical and Hall effect measurements are compared in Fig. 7 to the Hall effect values reported

for B-doped polycrystalline films in the literature [7, 11, 12]. Independent of the poly- or monocrystal-

line nature of the p+ diamond layers, in most cases p is significantly higher than [B], suggesting either a

0

0.5

1

1.5

2

2.5

0 1 104 2 104 3 104 4 104

Re

fle

cta

nc

eo

rre

fra

cti

ve

ind

ex

Wavenumber (cm-1

)

R

n

k

1.2 1021 B/cm-3

3 µm-thickhomo-epitaxial diamond

300 K



0.1

1

10

100

0.1 1 10 100

this work (m* = 0.74 m0)

this work (rH

= 1)

ref. 11

ref. 7

ref. 12

Ho

lec

on

ce

ntr

ati

on

p(1

020

cm

-3)

Boron concentration [B] (1020

cm-3

)

p = [B] 300 K

0

200

400

600

800

1000

1200

1400

0 5 10 15 20

co

nd

uc

tivi

ty(

-1c

m-1

)

Boron contents [B] (1020

cm-3

)

300 K

homo-epitaxial p+

diamond

ΩΩ ΩΩ

Fig. 7 Free carrier concentrations at room temperature

deduced from optical (full circles) and Hall effect (full

diamonds) on our monocrystalline p+ epilayers com-

pared to the Hall effect values reported for B-doped

polycrystalline films in the literature.

Fig. 8 Optically (open circles) and electrically (full

circles) determined conductivities vs. boron contents.

The broken line is a fit to a ([B]-Nc)1/2 dependence with

Nc = 2.1 × 1020 cm–3.

much heavier effective mass for the holes (i.e. an impurity band much flatter that the valence band) or

additional conduction channels.

An interesting feature of the optical conductivity σopt(ω) associated to the Drude model is that that it

admits a low frequency limit σopt(0) = ε0ωp2/γ independent of the choice on m*. Such microscopic opti-

cal conductivities deduced from fitting the FTIR reflectance spectra are shown in Fig. 8 to be as expected

always higher than the macroscopic d.c. values measured in a four-point probe apparatus on the same

layers. Moreover, the Boron contents dependence of these room-temperature conductivities is similar to

the classical square-root variation of the extrapolated zero-temperature conductivity σ(0) with the doping

atom density observed in most heavily doped silicon-based crystalline semiconductors on the metallic

side of the MIT [48, 50], and suggest a critical acceptor concentration around 2 × 1020 B/cm3, in line with

previous estimates [3].

6 Raman scattering Taking the x and y propagation directions to lie along the first two principal axis

of the cubic crystal and the x ′ and y ′ directions to correspond to the 110 and –110 crystallographic

axis respectively (see Fig. 9), in the polished edge view configuration with the backscattering optical axis

along x ′ the inelastic scattering spectrum of a typical p+-type diamond monocrystal is shown in Fig. 9 to

depend strongly on the relative orientations of the electric fields of the linearly polarized incident and

scattered light with respect to one another as well as to the crystal axis.

Using the well-known Porto notation, we observe a scattering tail at low frequencies extending in

some cases above 2000 cm–1 in the x ′(y ′z)-x ′ and x ′(y ′y ′)-x ′ geometries which coincide with the allowed

selection rules of the optical zone-center phonon of undoped diamond. The well-defined broad peak at

500 cm–1 which we have observed in heavily B-doped samples down to liquid helium temperatures is

clearly parallel polarized, although it does sometimes show up on top of the tail in some depolarized

geometries. The spectral feature around 1230 cm–1 is readily observed in all polarization configurations,

and a comparison of the experimental planar view spectra shown in Figs. 10 and 11 obtained on another

heavily B-doped sample shows that it becomes more asymmetric when the low energy tail is present, in

contrast to the broadened zone-center optical phonon peak at 1330 cm–1 which is seen in Fig. 9 to be

more symmetric and intense in the x ′(y ′z)-x ′ configuration. This suggests a Γ25, symmetry for the low

energy tail as in p-type Si [43] where such a tail has been attributed to intraband hole scattering resulting

from the deviations of the valence band structure from isotropy and parabolicity, although some inter-



0

0.5

1

1.5

2

2.5

3

3.5

4

500 1000 1500 2000

Sc

att

ere

din

ten

sit

y(a

rb.

un

its

)

Raman shift (cm-1

)

homo-epitaxial p+

diamond

X'(Y'Z)-X'

X'(Y'Y')-X'

Z

XX'

Y

Y'growthaxis

band transitions may have the same symmetry [43]. The symmetry of the 1230 cm–1 feature appears to be

Γ12, also distinct from that of the polarized peak around 500 cm–1.

While there is to our view no question about the purely electronic character of the low energy scatter-

ing tail which we tentatively attribute to intra-impurity band hole scattering, the origin of the peak

around 500 cm–1 remains unclear. Recent Raman results to be published separately indicate that the fre-

quency of this parallel-polarized feature remains unaltered upon isotopic 13C substitution. This fact, to-

gether with the absence of any phonon density of states (PDOS) maximum below the TA (L) frequency,

lead us to favour an electronic origin for this band. The energy value (close to 65 meV) matches well that

[30] of parallel-polarized Raman-active electronic transitions between the 2P (Γ ′2) and 4P (Γ ′12) excited

states of the boron acceptors, and which may explain the thermal energy value deduced recently from

T-dependent infrared spectroscopy of diamond samples with lower B contents [31]. However, in view of

the above mentioned transport properties of diamond films in the boron concentration range considered

here, we believe that a better knowledge of the electronic density of states in the boron impurity band is

needed before we can assign the 500 cm–1 peak to any particular interband transition.

1000 1500

Z(X'Y')Z

(1)(2)R

aman

Inte

nsi

ty(a

.u.)

Raman shift (cm-1)

1000 1500

Ram

anIn

ten

sity

(a.u

.)

Raman shift (cm-1)

Z(X'X')ZCalculated

Fig. 10 Room temperature micro-Raman depolarized

spectrum excited at 632.8 nm of an epitaxial diamond

layer (planar view) prepared with a boron-to-carbon

ratio in the gas phase of 1850 ppm, with the two spec-

tral components resulting from the decomposition dis-

cussed in the text.

Fig. 11 Room temperature micro-Raman polarized

spectrum excited at 632.8 nm of an epitaxial diamond

layer prepared with a boron-to-carbon ratio in the gas

phase of 1850 ppm. The broken line is the spectrum

resulting from a convolution of component (1) of

Fig. 10 with the Fano expression given in the text, added

to component (2) and to a low energy scattering tail.

Fig. 9 Room temperature micro-Raman spectra obtained

with a 514.5 nm excitation on the 110 polished surface

(edge view) of a MPCVD monocrystal deposited with a

boron-to-carbon ratio in the gas phase of 970 ppm.



As described elsewhere, 13C isotope substitution leads to a decrease in the frequency of the peak usu-

ally detected at 1230 cm–1. This result and the weak polarization dependence led us to attribute this spec-

tral feature to a broad band of disorder-activated carbon-related vibrational states, for example to opti-

cal lattice phonons at the Brillouin zone boundary, or to TO modes in the Σ region where the PDOS

maximum of diamond lies [52, 53], or even to C–B local modes. Although it has been widely recog-

nized that the optical phonons region of the Raman spectrum of heavily B-doped diamond displayed

a Fano-type deformation [13, 22, 34, 36–41] the few attempts at a quantitative analysis [34, 41]

dealt so far with experiments where the scattered light was not analyzed for polarization and led to simu-

lated line shapes where the fitting range was restricted to a typically 100 cm–1-wide region around

the frequency of the zone-center phonon (discrete level) assumed to be involved in the Fano interference

[54, 55].

Because of the contrast between the relative sharpness and symmetry of the optical phonon peak in the

x′(y′z)-x′ spectrum of Fig. 9 and the intense tail corresponding to the continuum of electronic excitations

that dominates the same spectrum, we decided to explore the possibility of a Fano interference between

the continuum and the broader phonon band leading to the 1230 cm–1 feature. Starting with the depolar-

ized spectrum of Fig. 10 which was taken on another sample, we assume that to first order there is no

interference in this case and that between 800 and 1800 cm–1 the signal results from a sum of two com-

ponents at 1230 and 1330 cm–1. We now convolute the 1230 cm–1 component taken as an estimate of the

broad level DOS with the classical Fano line shape I(E) ~ (q + ε)/(1+ ε 2) where q is a dimensionless

number measuring the departure from antiresonance behaviour and ε is a normalized frequency shift [54,

55]. Finally, we add the resulting Fano line shape (q = –3) first to the depolarised 1330 cm–1 signal of

Fig. 10 and then to a broad tail background taken from the polarized spectrum of Fig. 11. The resulting

calculated sum spectrum is compared in Fig. 11 to the experimental polarized micro-Raman response of

the same scattering volume. To our view, the good agreement obtained on a wide spectral range indicate

that the observed signal deformation results from the interference between the 1230 cm–1 line and the

broad scattering tail due to free carriers. When observed at all, the broadening and shifting of the

1330 cm–1 peak may have another origin and would anyway correspond to a much weaker coupling. In a

more speculative view, the strong electron–phonon coupling deduced from the present Fano parameters

may indicate that the 1230 cm–1 band is related to the boron center.

7 Conclusion In summary, we have shown that p+-type diamond monocrystalline layers with 2 1020 <

[B] < 2 1021 cm–3 had electronic properties (positive magnetoresistance and Hall tension, high d.c. and

optical conductivities in excess of 100 Ω–1 cm–1) which vary very little over the 4 K to 350 K temperature

range, suggesting that at these concentrations diamond is already metallic. We have given new evidence

that free holes reduce the lattice expansion as compared to Vegard’s law and demonstrated the strong

polarization dependence of the Raman response of such epitaxial films. Finally, we have assigned in this

work the 500 cm–1 Raman peak to electronic interband transitions and emphasized the role of the

1230 cm–1 band in analyzing the Fano-distorted spectral line shapes around the optical phonon fre-

quency. We believe that the present study opens the way to a more quantitative understanding of Raman

processes in such heavily B-doped diamond crystals.

Acknowledgements Thanks are due to A. Deneuville who insisted in the first place that many samples be pre-

pared around 2000 ppm, and to F. Pruvost and M. Bernard who grew the epilayers. We are also indebted to

C. Cytermann (Technion, Haifa) and to F. Bertin (CEA-LETI, Grenoble) who measured respectively the SIMS

profiles and the ellipsometry spectra. The invaluable help of J. Marcus with the low-temperature magneto-transport

set-up is also gratefully acknowledged. Finally, we thank heartily Dr H. Kanda who provided the 13C-substituted

HPHT crystal.

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Documents

Optical and electronic properties of heavily boron-doped homo-epitaxial diamond