Synthesis, structure, and properties of the electron-poor II-V semiconductor ZnAs

Article abstract of DOI:10.1021/ic501308q

ZnAs was synthesized at 6 GPa and 1273 K utilizing multianvil high-pressure techniques and structurally characterized by single-crystal and powder X-ray diffraction (space group Pbca (No. 61), a = 5.6768(2) A, b = 7.2796(2) A, c = 7.5593(2) A, Z = 8). The compound is isostructural to ZnSb (CdSb type) and displays multicenter bonded rhomboid rings Zn₂As ₂, which are connected to each other by classical two-center, two-electron bonds. At ambient pressure ZnAs is metastable with respect to Zn₃As₂ and ZnAs₂. When heating at a rate of 10 K/min decomposition takes place at ～700 K. Diffuse reflectance measurements reveal a band gap of 0.9 eV. Electrical resistivity, thermopower, and thermal conductivity were measured in the temperature range of 2-400 K and compared to thermoelectric ZnSb. The room temperature values of the resistivity and thermopower are ～1 ω cm and +27 μV/K, respectively. These values are considerably higher and lower, respectively, compared to ZnSb. Above 150 K the thermal conductivity attains low values, around 2 W/m·K, which is similar to that of ZnSb. The heat capacity of ZnAs was measured between 2 and 300 K and partitioned into a Debye and two Einstein contributions with temperatures of θ_D = 234 K, θ_E1 = 95 K, and θ_E2 = 353 K. Heat capacity and thermal conductivity of ZnSb and ZnAs show very similar features, which possibly relates to their common electron-poor bonding properties.

Full text of DOI:10.1021/ic501308q

Article
pubs.acs.org/IC
Synthesis, Structure, and Properties of the Electron-Poor II−V
Semiconductor ZnAs
Andreas Fischer,† Daniel Eklof,‡ Daryn E. Benson,§ Yang Wu,∥,⊥ Ernst-Wilhelm Scheidt,†
̈
Wolfgang Scherer,† and Ulrich Haussermann*,‡
̈
†Department of Physics, Augsburg University, D-86135 Augsburg, Germany
‡Department of Materials and Environmental Chemistry, Stockholm University, S-10691 Stockholm, Sweden
§Department of Physics and Department of Chemistry & Biochemistry, Arizona State University, Tempe, Arizona 85287, United
∥
States
S
* Supporting Information
ABSTRACT: ZnAs was synthesized at 6 GPa and 1273 K utilizing multianvil high-
pressure techniques and structurally characterized by single-crystal and powder X-ray
diffraction (space group Pbca (No. 61), a = 5.6768(2) Å, b = 7.2796(2) Å, c = 7.5593(2) Å,
Z = 8). The compound is isostructural to ZnSb (CdSb type) and displays multicenter
bonded rhomboid rings Zn2As2, which are connected to each other by classical two-center,
two-electron bonds. At ambient pressure ZnAs is metastable with respect to Zn3As2 and
ZnAs2. When heating at a rate of 10 K/min decomposition takes place at ∼700 K. Diffuse
reflectance measurements reveal a band gap of 0.9 eV. Electrical resistivity, thermopower,
and thermal conductivity were measured in the temperature range of 2−400 K and
compared to thermoelectric ZnSb. The room temperature values of the resistivity and
thermopower are ∼1 Ω cm and +27 μV/K, respectively. These values are considerably
higher and lower, respectively, compared to ZnSb. Above 150 K the thermal conductivity
attains low values, around 2 W/m·K, which is similar to that of ZnSb. The heat capacity of
ZnAs was measured between 2 and 300 K and partitioned into a Debye and two Einstein contributions with temperatures of θD =
234 K, θE1 = 95 K, and θE2 = 353 K. Heat capacity and thermal conductivity of ZnSb and ZnAs show very similar features, which
possibly relates to their common electron-poor bonding properties.
on synthesis, structure, and physical properties of isostructural
ZnAs.
1. INTRODUCTION
The binary Zn−Sb system has a peculiar phase diagram where
three fields of phases are located in the narrow range between
50 and 60 atom % Zn (ZnSb, Zn4Sb3, and Zn3Sb2).1,2 Zn4Sb3
exhibits one of the highest thermoelectric figures of merit
known for a binary compound and has been intensely
investigated.3−5 Lately also ZnSb has been recognized as a
high-performance thermoelectric material.6−8 Zn3Sb2 is meta-
stable at room temperature, and its properties are not well-
characterized. Moving from the Zn−Sb to the Zn−As system
there are remarkable changes: in the ambient-pressure Zn−As
phase diagram ZnAs and Zn4As3 are absent, and congruently
melting ZnAs2 and Zn3As2 represent the only phases.2
According to earlier reports equiatomic ZnAs is accessible
either from the pressure-induced decomposition of ZnAs2 or
Zn3As2 or from the direct reaction of the elements at high-
pressure, high-temperature conditions.9,10 Earlier work did not
address the physical properties of ZnAs. Recently we
investigated the bonding properties and electronic structure
of ZnAs in a computational study.11 Similar to ZnSb, ZnAs
possesses an indirect band gap, but its size remains uncertain.
Because of the increasing interest in ZnSb as a thermoelectric
material we deemed it important to obtain more information
Generally II−V semiconductors (II = Zn, Cd; V = P, As, Sb)
display interesting, often anisotropic transport properties.12−15
Compared to the well-investigated tetrahedrally bonded II−VI
and III−V compound semiconductors, crystal structures and
bonding properties are far more complex and less understood.
It is not immediately apparent why band gaps should actually
should occur given the fact that the average electron
concentration of many II−V systems is lower than four.16
Other peculiarities include a very low lattice thermal
conductivity, which is especially observed for Zn4Sb3 and
ZnSb and is a major reason for the favorable thermoelectric
performance of these materials. The origin of the low lattice
thermal conductivity of Zn4Sb3 and ZnSb is still debated,4−6
and the study of ZnAs may provide new insight.
2. EXPERIMENTAL METHODS
Synthesis. Zn (shot, 99.99%) and As (pieces, 99.999%) from
Sigma-Aldrich were weighed in atomic ratios between 0.45:0.55 and
0.55:0.45 and pressed into pellets in an argon-filled glovebox. Pellets
were then placed in a threaded BN capsule (0.8 mm wall thickness, 4.5
Received: June 5, 2014
Published: July 28, 2014
© 2014 American Chemical Society
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Table 1. Summary of Crystallographic Data and Structural Analysis for ZnAs
ZnAs 100 K
ZnAs 300 K
formula
ZnAs
crystal system
space group
a, Å
orthorhombic
Pbca, No. 61 ITC
5.6607(3)
7.2774(4)
7.5605(5)
311.43(3)
5.9827
5.6730(1)
7.2754(2)
7.5572(2)
311.916(13)
5.9735
b, Å
c, Å
V, Å3
ρ (g/cm3)
Z
8
504
F000
crystal size
0.041 × 0.072 × 0.074
μ(Ag Kα), mm−1
19.009
100(2)
18.979
300(2)
T, K
radiation
Ag Kα
θ range (deg)
sin θ/λmax
4.18 < θ < 30.54
4.18 < θ < 30.60
0.906
0.908
data collected (h, k, l)
no. of reflns measured
no. of unique reflns
no. of observed reflns, I > 3σ(I)
no. of refined parameters
extinction
−9 < h < 10, −12 < k < 12, −13 < l < 13
−10 < h <10, −12 < k <13, −13 < l < 13
13 833
15 257
928
930
874
843
20
type 2 isotropic
ρiso
0.08(2)
4.24
0.06(2)
4.17
Rint
R1 I > 3σ(I)
wR1 I > 3σ(I)
GOF on F
1.52
1.58
2.25
2.18
1.43
1.36
largest peak/hole e/Å3
absorption correction
transmission min, max
+1.08/−0.76
+0.75/−0.69
numerical, face-indexed
0.3649, 0.6278
0.3671, 0.6212
mm inner diameter), which was closed by screwing on a BN lid. The
threading provided a reasonable airtight seal for the reaction mixture.
Subsequently capsules were transferred outside the glovebox. High-
pressure syntheses were performed in a 6−8 multianvil high-pressure
device using an 18/12 assembly developed by Stoyanov et al.17 BN
sample capsules were positioned in a graphite furnace that, in turn, was
placed together with a zirconia thermal insulating sleeve (0.57 mm wall
thickness, 7.77 mm OD, 10.80 mm length) in a magnesia octahedron
with 18 mm edge length. Samples were pressurized at a rate of about
0.5 GPa/h with 25 mm tungsten carbide cubes truncated to 12 mm
edge length. After reaching the target pressure (between 4 and 6 GPa)
the samples were heated. Deviations from the target pressure are
estimated as 0.3 GPa. The temperature was measured close to the
sample using a thermocouple type C (W5%Re − W26%Re wire) in an
Al2O3 sleeve.
To prevent blowouts, heating was done very carefully. The
following protocol was established: (i) temperature was raised to
673 K at a rate of 10 K/min and kept there for 15 min, (ii)
temperature was raised to 873 K at a rate of 5 K/min and kept there
for 30 min, (iii) temperature was raised to 1073 K at a rate of 5 K/min
and kept there for 15 min, (iv) temperature was raised to 1273 K at a
rate of 5 K/min. After a dwell time of 15 min, the samples were
quenched at approximately constant pressure by turning off the power
to the furnace (initial quench rate ≈ 50 °C/s). Afterward, the pressure
was released at a rate of approximately 0.5 GPa/h, and samples were
recovered. A variety of reaction parameters (temperature, pressure,
dwell time, Zn/As ratio) were explored. Phase-pure samples of ZnAs
resulted from a starting mixture of 51.5 atom % As and 48.5 atom %
Zn being reacted at 6 GPa and 1273 K. Products were obtained as
dense cylinders with approximate dimensions of 4.5 mm o.d. and 4.2
mm height. Cylinders were partially crushed and ground for
subsequent sample analysis.
Sample Analysis. Powder X-ray diffraction (PXRD) patterns were
collected on a Panalytical X’Pert PRO diffractometer operated with Cu
Kα1 radiation and in θ−2θ diffraction geometry. Powdered samples
were applied to a zero diffraction plate and diffraction patterns
measured in a 2θ range of 20−80°.
Rietveld refinement using the Jana2006 package18 was performed to
determine the phase fraction of impurities. A summary of the
refinement results is given as Supporting Information (Table S1).
Scanning electron microscopy (SEM) investigations were performed
on a JEOL JSM-7000F instrument to examine the microstructure and
compositional homogeneity of ZnAs specimens. Samples were first
polished mechanically and then with an Ar+-ion beam in a Cross
Section Polisher SM-09011 instrument from JEOL. Backscattered
electron images were recorded with an acceleration voltage of 8 kV.
According to a simulation of electron trajectory (program CASINO)19
this voltage yields an information depth of 75−100 nm. For energy-
disperse X-ray spectrometry (EDX) an X-ray detector from Oxford
instruments, INCA X-sight, was used. The density of samples was
determined by measuring their volume with a gas (He) expansion
pycnometer (AccuPyc 1330 from Micromeretics). The instrument was
calibrated, and its accuracy was confirmed with pieces of crystalline Si
of similar volume as the ZnAs samples. Errors in determined densities
are estimated to be less than 0.2%.
Thermal Analysis. 10.03 mg of ZnAs was sealed in an aluminum
pan. Differential scanning calorimetry (DSC) was performed using a
PerkinElmer Pyris 1 “heat flux” calorimeter under a nitrogen gas flow
of ∼20 mL/min. The scanning range was from 473 to 773 K with a
heating/cooling rate of 10 K/min. A baseline calibration was
performed to compensate for the cell heat flow imbalance between
reference and sample positions. Temperature and heat flow were
calibrated using indium (Tm = 429.8 K, ΔHfus = 28.4 J/g) and tin (Tm
= 505.1 K). DSC curves and enthalpy of transitions were accessed with
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Figure 1. (a) Photograph of an as-synthesized cylindrical ZnAs specimen. SEM backscattered electron images of a cross-section polished surface at a
magnification of ×100 (b) and of ×1000 (c). Black areas correspond to cracks and pores.
the PerkinElmer Instruments software, Pyris Software for Windows
3.51, and Pyris Thermal Analysis System Version 3.51.
k-point grid was used for integration, and a 2 × 2 × 2 q-grid was used
for calculations of the dynamical matrix elements. A planewave energy
cutoff of 35 hartree (∼950 eV) was employed. Prior to the phonon
dispersion calculations ZnAs was structurally relaxed with respect to
lattice parameters and atomic positions with forces converged to better
than 1 × 10−3 eV/Å. From the phonon density of states (PDOS) it is
possible to obtain the thermodynamic functions of a material.30 Within
the harmonic approximation the constant-volume specific heat CV at
temperature T is calculated as
Crystal Structure Characterization. A gray, dull, and irregularly
shaped crystal (dimensions of 0.041 × 0.072 × 0.074 mm) was
selected from a crushed part of a sample cylinder. Data were collected
using a Bruker SMART-APEX diffractometer equipped with a D8
goniometer and an INCOATEC IμS Ag microsource (λ = 0.560 87 Å)
employing Helios mirror optics. The crystal was measured at room
temperature (300(2) K) and at 100(2) K with an Oxford cryostream
cooling unit. The frames were integrated with the Bruker SAINT
software package20 using a narrow-frame algorithm. A numerical
absorption correction was applied using SADABS.21 Structure
refinements were performed by using the JANA2006 package.18 The
assignment of Zn and As atoms having very similar X-ray scattering
factors was based on the structure model of ZnSb. Table 1 lists a
summary of the refinement results. Additional crystallographic
information can be found in the Supporting Information.
2
ωL ⎛
⎜
⎞
⎟
⎠
⎛
⎜
⎝
⎞
⎟
⎠
ℏω
B
ℏω
B
2
Cv = 3nkB
csch
g(ω)dω
∫
0
2k T
2k T
⎝
(1)
where kB is the Boltzmann constant, ω is the phonon frequency, ωL is
the highest frequency, n is the number of atoms in the unit cell, and
g(ω) is the PDOS.
Property Measurements. A bar-shaped specimen with approx-
imate dimensions of 4 × 1 × 1 mm was cut from a cleaned and
polished ZnAs cylinder (from the multianvil synthesis) using a wire
saw. On this bar four gold-coated copper leads were connected via
silver-filled epoxy (Epotek H31E) and silver paint in a four-probe
setup. Seebeck coefficient, thermal conductivity, and electric resistivity
were measured using the Thermal Transport Option (TTO) of the
Physical Property Measurement System (PPMS) from Quantum
Design. These measurements were done in vacuum (10−6 bar) in the
temperature range of 2−400 K. Radiation heat loss was automatically
corrected with the incorporated functions of the software for
measurements using the TTO option. Heat capacity was measured
between 300 and 2 K (50 points distributed logarithmically) using a
quasi-adiabatic step heating technique as implemented in the PPMS.
For heat capacity measurements a piece of a crushed cylinder (39.7
mg) was thermally connected to the platform of the sample-holder via
a small amount of Apiezon-N grease (0.1 mg). The uncertainty for this
measurement technique is estimated to be lower than 5%.
Spectroscopy Measurements. Optical diffuse reflectance meas-
urements were performed with finely ground samples of ZnAs at room
temperature. The spectrum was recorded in the region of 3200−
10 500 cm−1 with a Bruker Equinox 55 FT-IR spectrometer equipped
with a diffuse reflectance accessory (Harrick). Raman spectra of ZnAs
and elemental As were measured using a Labram HR 800
spectrometer. The instrument is equipped with an 800 mm focal
length spectrograph and an air-cooled (−70 °C), back-thinned CCD
detector. Samples were excited using an air-cooled double frequency
Nd:YAG laser (532 nm) and an input laser power of 5.6 mW (ZnAs)
and 14 mW (As). Raman spectra were collected with an exposure time
of 60 s, accumulation number of 10, and using an 1800 grooves/mm
grating.
3. RESULTS AND DISCUSSION
Synthesis and Phase Relations. ZnAs was prepared from
the elements by using high-pressure, high-temperature
conditions. This is in accord with the finding of Clark and
Range who employed a pressure of 4 GPa and a temperature of
1273 K in their synthesis.9,10 However, when applying these
conditions we obtained products containing substantial
fractions of Zn3As2. The formation of Zn3As2 could be
suppressed when applying higher pressures (around 6 GPa).
We note that reactions were difficult to control and terminated
frequently with blowouts when heating was performed at rates
higher than 5 K/min and without intermediate holding steps.
Figure 1a shows a photograph of an as-obtained ZnAs
specimen. The density was determined as 5.82 g/cm3, which
corresponds to 97.6% of the crystallographic density of ZnAs.
SEM backscattered electron images of a polished surface are
depicted in Figure 1b,c. These images reveal the presence of
broad, micrometer-wide, cracks that extend 1 mm in length, as
well as micrometer-sized pores. In addition, there is a large
concentration of fine cracks (Figure 1c). Cylinder specimens
obtained from high-pressure reactions could be easily crushed
and disintegrated into a fine powder. EDX analysis of the area
indicated in Figure 1c yielded 48.5 atom % Zn and 51.5 atom %
As. This is in close agreement with the composition of the
employed synthesis mixture, where a small excess of As was
found to be advantageous for achieving products void of ZnAs2
and Zn3As2. Figure 2 shows the PXRD pattern of this sample.
The major impurity is As with about 2.5 wt %, which again
reflects very well the starting composition. Binary oxides are
barely detectable. However, it is possible that small amounts
(<1 wt %) of other, not identifiable, impurities are present.
At ambient pressure ZnAs is metastable with respect to
decomposition into Zn3As2 and ZnAs2, which are the stable
phases according to the Zn−As phase diagram.2 Figure 3
Computation. The phonon dispersion relations and thermody-
namic functions of ZnAs were calculated via the Abinit program
package22−24 and employing the generalized gradient approximation
(GGA) with the Perdew−Burke−Ernzerhof (PBE) parametriza-
tion.25−27 GGA-PBE pseudopotentials were provided by the Abinit
Web site. These pseudopotentials are norm-conserving and were
generated using the fhi98PP package.28 A 6 × 6 × 6 Monkhorst Pack29
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Figure 4. Molar volumes of zinc arsenide and antimonide phases (red
and blue symbols, respectively) as compared to the weighted sum of
atomic volumes with respect to the elemental structures (red and blue
lines, respectively). Pn = As, Sb. Zn13Sb10 is the idealized
crystallographic composition of Zn4Sb3.3,16
Figure 2. Rietveld fit to the PXRD pattern (Cu Kα1) of as-synthesized
ZnAs. Black circles and the red line represent measured and calculated
diffraction patterns, respectively. The blue line corresponds to their
difference. Refined wt % phase fractions: ZnAs−96.6(2), As−2.3(1),
As2O3 − 0.3(1), ZnO − 0.7(1).
will be somewhat reduced at high pressures due to the rather
high compressibility of As,31 it can be safely stated that the pV
term of the enthalpy is not favoring the formation of ZnAs from
the elements. However, when instead referring to Zn3As2 and
ZnAs2the thermodynamically stable compounds in the Zn−
As systema different result emerges. As shown in Figure 4
the molar volume of both stable compounds exceeds the sum of
atomic volumes to an even larger extent than ZnAs.
Consequently, the reaction Zn3As2 + ZnAs2 = 4 ZnAs is
actually accompanied by a volume reduction of almost 10%
(172.4 Å3 vs 156.2 Å3). Therefore, it may be argued that ZnAs
is obtained at high-pressure conditions because (i) compound/
phase formation in the Zn−As system is generally strongly
favored through the internal energy term of the enthalpy (e.g.,
we note that the melting point of Zn3As2 is considerably higher
than that of Zn3Sb2, 1290 vs 840 K)2 and (ii) compared to
stable Zn3As2 and ZnAs2 the molar volume of ZnAs shows a
much smaller volume expansion with respect to the volumes of
the elements (cf. Figure 4). It can be expected that ZnAs will
decompose at pressures above 10 GPa. This is known for
isostructural ZnSb, which undergoes pressure-induced decom-
position into Zn and an alloy with an approximate composition
of Zn40Sb60 at 7 GPa and room temperature.32
The phenomenon of volume increase upon compound
formation is also observed for Zn−Sb phases, although less
pronounced. It is in stark contrast to compound semi-
conductors exhibiting a larger degree of ionicity (e.g., Zintl
phases), which typically show a pronounced volume decrease.
The volume increase is in line with the covalent bonding
scenario pursued earlier for ZnSb and ZnAs.11 It is interesting
to speculate whether Zn4As3, analogous to Zn4Sb3, can also be
prepared at high pressures. Our synthesis efforts from the
elements do not give any evidence. On the other hand Clark
and Range reported the formation of a further quenchable Zn−
As high-pressure phase when subjecting ZnAs2 or mixtures of
Zn3As2 and As to 4 GPa and 1473 K.9,10 The composition and
structure of this phase could not be characterized.
Figure 3. DSC heating (red line) and cooling trace (blue line) of
ZnAs. The exothermic event corresponds to decomposition into
ZnAs2 and Zn3As2. The area of integration considered for enthalpy
determination is indicated. The associated enthalpy is −3.6 J/g.
depicts DSC heating and cooling traces. Upon heating, a broad
endothermic event occurs above 600 K, which is followed by a
sharper exothermic one with an onset at 700 K and a maximum
around 718 K. The latter event corresponds to decomposition
of ZnAs with an enthalpy around −3.6 J/g. The PXRD pattern
(see Supporting Information, Figure S1) of the decomposed
sample after a DSC heating and cooling cycle fits approximately
the expectation of an equimolar mixture; 4 ZnAs = ZnAs2 +
Zn3As2. The temperature of the exothermic decomposition
depends on the heating rate or thermal history of the sample.
Clark and Range reported a partial decomposition of ZnAs
when performing annealing experiments for 17 h in a
temperature range of 473−623 K, and complete decomposition
occurred at higher temperatures.9 The first thermal event in
Figure 3 occurs reproducibly, but its origin is not clear. We
attribute it to the presence of As in the sample, which
segregates (“sweats”) from the inside to the surface, and
perhaps even oxidizes there. The sublimation temperature of
As2O3 would fall in the temperature range of this event.
Crystal Structure Analysis. The previous structure
determination of ZnAs was performed in 1976 and based on
Guinier PXRD data.10 In this work we succeeded to collect and
refine high-resolution X-ray intensity data from a single crystal.
Additionally Rietveld refinement of PXRD data was performed
(for details see Supporting Information, Table S1). Tables 2
We conclude this section by recognizing that the synthesis of
ZnAs by high-pressure conditions appears peculiar. At ambient
pressure the molar volume of ZnAs exceeds the sum of atomic
volumes of Zn and As (with respect to the elemental
structures) by more than 6% (cf. Figure 4). Although this
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and 3 compare obtained structure parameters and interatomic
distances, respectively.
Table 2. Lattice Parameters in Å, Unit Cell Volume in Å3,
Fractional Atomic Coordinates and Equivalent Atomic
Displacement Parameters in Å2 for ZnAs (space group Pbca)
with Estimated Standard Deviations in Parentheses
SCXRD
100 K
SCXRD
300 K
parameter
Rietveld
ref 10
a
b
c
5.6607(3)
7.2774(4)
7.5599(5)
311.43(3)
0.54016(3)
0.61934(3)
0.63509(2)
0.00610(5)
0.13827(3)
0.07273(2)
0.10086(2)
0.00448(5)
5.6731(1)
7.2754(2)
7.5572(2)
311.92(1)
0.54145(3)
0.62021(3)
0.63546(3)
0.01443(6)
0.13820(3)
0.07269(2)
0.10084(2)
0.00920(5)
5.6768(2)
7.2796 (2)
7.5593(2)
312.39(1)
0.5409(7)
0.6191(5)
0.6360(5)
0.036(2)
5.679(2)
7.277(4)
7.559(4)
312.4
V
x (Zn)
y (Zn)
z (Zn)
0.530
0.614
0.639
U
iso/Ueq (Zn)
Figure 5. Crystal structure of ZnAs. (a) The quasi-tetrahedral
coordination of Zn atoms by As is emphasized. (b) Edge-sharing
arrangement of ZnAs4 tetrahedra and five-coordination of Zn and As
atoms. The rhomboid ring motif Zn2As2 is highlighted by bold bonds.
(c) Rhomboid ring and its connectivity in the structure of ZnAs. The
two different Zn−As distances within the ring (r1 and r2) and
connecting rings (c1 and c2) are marked (cf. Table 3). The center of
the ring corresponds to a center of inversion. Ellipsoids represent the
experimentally determined thermal displacement parameters and are
drawn at the 99.9% probability level (left for 300 K, right for 100 K).
Zn atoms−cyan circles; As atoms−red circles.
x (As)
y (As)
z (As)
0.13096(6)
0.0714(4)
0.1007(4)
0.027(1)
0.141
0.076
0.100
U
iso/Ueq (As)
Table 3. Selected Interatomic Distances in Å for ZnAs.
Standard Deviations Are Given in Parentheses. Labeling of
Zn−As Distances Refers to Figure 5c
atom pairs
SCXRD 100 K SCXRD 300 K
Rietveld
ref 10
Zn−Zn
2.7195(3)
2.4716(3)
2.4994(3)
2.5711(3)
2.6826(3)
2.4282(3)
2.7336(3)
2.4697(3)
2.4985(3)
2.5712(3)
2.6966(3)
2.4290(2)
2.729(5)
2.489(5)
2.490(5)
2.571(5)
2.680(5)
2.431(5)
2.70
2.47
2.49
2.61
2.62
2.47
Zn−As (c1)
Zn−As (c2)
Zn−As (r1)
Zn−As (r2)
As−As
on a covalent description. The different bonding motifs
(rhomboid ring multicenter and connecting 2c2e) are well-
reflected in the distribution of involved interatomic distances:
Zn−As interatomic distances within a ring are about 0.1 Å
larger than the ring connecting ones (cf. Table 3). The
peculiarly short Zn−Zn distance (around 2.73 Å) is part of the
multicenter bonding motif. The short As−As distance of
around 2.43 Å corresponds to a ring-linking 2e2c bond. These
nearest-neighbor distances associated with bonding interactions
are well-separated from the next nearest ones, starting off above
3.5 Å.
We finally note that the results from the refinement of the
single-crystal and PXRD room-temperature data are in close
agreement. There is also a remarkable agreement between the
previous refinement from Guinier powder data10 and today’s
considerably more accurate ones. Significant deviations are only
present for the Zn positional parameters.
ZnAs crystallizes in an orthorhombic Pbca structure (CdSb
type) which contains eight formula units in the unit cell. Both
kinds of atoms are situated on Wyckoff sites 8c. The structure
consists of edge-sharing ZnAs4 tetrahedra that, in turn, are
connected via common corners (Figure 5a,b). Each atom in the
ZnAs structure attains a peculiar 5-fold coordination by one like
and four unlike neighbors. At the same time each atom is also
part of planar rhomboid rings Zn2As2. These rings contain a
short Zn−Zn contact, which is a consequence of edge-sharing
ZnAs4 tetrahedra. A ring and its linkage to neighboring ones is
shown in Figure 5c. This figure also compares the thermal
ellipsoids at room temperature and 100 K. It is seen that the
displacement parameters for Zn are larger and considerably
more anisotropic than for As. This is especially the case at room
temperature, whereas differences diminish at 100 K. When
comparing further structure parameters at room temperature
and 100 K one realizes only very small differences, which are
virtually restricted to slight changes in the Zn positional
parameters and the a lattice parameter. As a consequence the
unit cell volume at 100 K is by only 0.2% smaller than at room
temperature.
Band Gap. Electronic band structure calculations predicted
an indirect band gap with a size of 0.3 eV for ZnAs.11 The
measured diffuse reflectance R was transformed into the
Kubelka−Munk remission function FKM = (1 − R2)/2R.33
FKM(hν) for R of ZnAs is shown in Figure 6, together with
FKM1/2(hν), which is the transform characteristic for describing
indirect allowed transitions along the absorption edge. Ideally
FKM is flat and has low values in the low-absorbance region at
small photon energies.34 This is not the case here, perhaps
because of strong free carrier absorption or a high value of the
refractory index. The band gap was estimated as the
intersection of the straight-line extrapolations below and
There are six distinct nearest-neighbor distances in the ZnAs
structure, which are all captured within the rhomboid ring and
its connectivity. According to Benson et al. the rhomboid ring
represents a four-center, four-electron (4c4e) bonded entity
that is connected via 2c2e bonds to neighboring rings.11 This
bonding model has also been applied to isostructural CdSb and
ZnSb and provides an electron-precise situation for ZnAs based
above the knee of the FKM curve.34 The value is around
1/2
0.9 eV, which is substantially higher than the one obtained from
first-principles calculations. It is also higher than the
spectroscopically determined band gap for ZnSb (around 0.5
eV at room temperature).35
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resistivity attains values around 1 Ω cm. Because of cracks
present in the samples, resistivity values may not be correct on
an absolute scale, and generally the results for the transport
properties are to be regarded critically.
The Seebeck coefficient of ZnAs has a positive sign−
implying holes as the major type of charge carriers−and
exhibits an almost linear temperature dependence (also Figure
7a). This is similar to ZnSb; however, the value of +27 μV/K
attained at room temperature is roughly an order of magnitude
36
lower. The Goldsmid relation Eg ≈ 2eSmaxTmax
,
which links
the band gap and the Seebeck coefficient, holds roughly for
ZnSb and would suggest a much higher Seebeck coefficient for
ZnAs than the experimentally determined value. Again, sample
imperfection (cracks, impurity phases) may lead to lower values
than expected; however, the Seebeck coefficient may also be
diminished by the presence of minority carriers from impurity
bands. Figure 7b shows the thermal conductivity of ZnAs
together with ZnSb (according to ref 37). In a highly crystalline
semiconductor material the change between defect/boundary
scattering and Umklapp scattering leads typically to a
pronounced maximum upon heating.38 Compared to ZnSb
this maximum (seen at around 50 K for ZnAs) is not well-
developed. This indicates that the ZnAs sample possesses
highly fractured grains. Although absolute values are obscured
by the presence of micrometer-sized cracks and impurities it
appears that the thermal conductivity of ZnAs above 150 K
(with values around 2 W/K·m) is very similar to ZnSb, which is
composed of the heavier element Sb.37
Figure 6. Spectral dependence of the Kubelka−Munk function (FKM
,
black line) and the transform FKM1/2, red line). Straight broken lines fit
the slopes of FKM1/2. The broken vertical line indicates the band gap at
around 0.9 eV.
Transport Properties. The electrical resistivity of ZnAs
decreases with increasing temperature as expected for a
semiconductor (Figure 7a). However, instead of an exponential
behavior, the decrease occurs rather linearly. Therefore, it was
not possible to determine the band gap from resistivity data. In
the region from 75 to 100 K an anomaly occurs, which is
reproducibly observed upon temperature cycling and for other
measured sample specimens. At room temperature the
Vibrational Properties. Figure 8a shows first-principles
calculated phonon dispersion curves and the PDOS for ZnAs.
The four modes at highest wavenumbers (at around 240 cm−1)
are only very weakly dispersed, which gives rise to a
pronounced peak in the PDOS. These modes correspond to
stretches within pairs of As atoms (“dumbbells”). There are
four As2 pairs in the unit cell. Modes that can be associated with
inter-ring (c1 and c2) Zn−As atom pair stretches are
distributed in the ranges from 200 to 230 cm−1 (8 modes)
and from 170 to 200 cm−1 (8 modes). At lower wavenumbers
inter-ring bends and vibrations within rhombohedral ring units
mix. The PDOS shows that the contribution of As atoms to the
displacements of modes with wavenumber below 170 cm−1 is
significantly diminished. The phonon dispersion curves of ZnAs
do not indicate peculiarities, like soft modes or a tendency to
dynamical instability.
The Raman spectrum of ZnAs is shown in Figure 9 and is
compared to elemental As. The complex ZnAs structure gives
rise to 24 Raman active modes. Their analysis was attempted
for CdSb,39 but clear assignments proved difficult for other II−
V compounds.40 Seven bands can be discerned in our spectrum.
The most intense one at 250 cm−1 is clearly attributed to the
As−As stretches (calculated values are 240 cm−1 (B2g), 239
cm−1 (B1g), 237 cm−1 (Ag), 234 cm−1 (Ag)). The wavenumbers
associated with these bands relate well to the Ag mode in
elemental As. The rhombohedral structure of gray arsenic
comprising puckered hexagon layers has two Raman active
modes: the Ag mode where atoms displace along the C3 axis,
and the degenerate Eg mode where atoms displace
perpendicular. Those are seen at 256 and 194 cm−1,
respectively. The bands observed at 72, 87, and 104 cm−1 for
ZnAs (i.e., peaks 1−3 in Figure 9) can be associated with the
weakly dispersed low-energy modes accumulating at the Γ
point in the range of 70−100 cm−1 in Figure 8.
Figure 7. (a) Electrical resistivity, Seebeck coefficient, and (b) thermal
conductivity of ZnAs. The thermal conductivity of ZnSb is shown for
comparison (data from ref 37).
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Figure 8. (a) Phonon dispersion (left) and phonon density of states (PDOS) of ZnAs (right). The As contribution to the PDOS is indicated by the
cyan area. (b) PDOS model based on the Debye and Einstein temperatures as extracted from the measured heat capacity (cf. Figure 10). The height
of the Einstein lines is arbitrary, but scaled to their respective contributions.
Figure 9. Raman spectrum of ZnAs and As recorded with an excitation
wavelength of 532 nm. The values (in cm−1) for the labeled bands 1−7
for ZnAs and A−B for As are as follows: 1:72, 2:87, 3:104, 4:120,
5:151, 6:186, 7:250, A:194 and B:256.
Figure 10. Specific heat Cp of ZnAs. Experimental data is shown as
black squares, to which a Debye-Einstein fit was applied (red line, for
details see text). Experimental data of ZnSb was added for comparison
(connected green squares). The blue line is the computed constant
volume specific heat Cv as obtained from the PDOS according to eq 1.
(inset) C/T.
The heat capacity measurement, shown in Figure 10, does
not indicate a phase transition at low temperatures for ZnAs.
The room-temperature value of the specific heat, Cp, is about
48 J/mol·K and approaches the Dulong−Petit limit of 3R J/
mol·atom·K (49.9 J/mol·K). The experimental data can be
accurately modeled by a simple Debye−Einstein model, which
assumes a Debye-type behavior for the three acoustic phonon
branches and an Einstein (k-independent oscillator) behavior
for the contributions from the optical branches.41 Because of
the presence of low-lying optical branches at least two different
Einstein functions are necessary to model the phonon
contributions to the specific heat. To be consistent with the
lattice degrees of freedom the coefficient of the Debye
contribution was kept at 3 R, while the coefficients of the
Einstein functions were freely refined. The best fit was obtained
with a Debye temperature ΘD of 234 K, and the two Einstein
temperatures ΘE1 = 95 K (66 cm−1; 8.2 meV) and ΘE2 = 281 K
(245 cm−1; 30.4 meV) with coefficients 0.90 and 2.16 R,
respectively. This fitted Debye temperature is lower than the
one obtained in the low-temperature regime between 1.86 and
3.15 K, ΘD,LT = 328 K. From this low-temperature region also a
γ-value of 0.44 mJ/mol·K2 could be estimated, which was kept
constant during the fitting procedure. Both Einstein temper-
atures are well-reflected in the theoretical PDOS (cf. Figure 8a)
by the presence of low-lying optical modes (ΘE1) and the
characteristic As−As stretches (ΘE2). The model PDOS based
on ΘD, ΘE1, and ΘE2 is shown as Figure 8b. The sum of the
coefficients of the Debye and Einstein modes in our fitting
model exceeds the ideal value of 6 R by 1%, which might be
attributed to the presence of small As impurities, thermal lattice
expansion, or experimental errors.
The specific heat capacity of ZnAs is also strikingly similar to
isostructural ZnSb whose heat capacity is also shown in Figure
10. The heat capacity of ZnSb can be modeled in the same
fashion with a related fitting model assuming a Debye
temperature ΘD of 188 K and the two Einstein temperatures
ΘE1 = 72 K (50 cm−1, 6.2 meV) and ΘE2 = 353 K (195 cm−1,
25.4 meV) with coefficients of 0.96 and 2.10 R, respectively.
With knowledge of the PDOS the vibrational heat capacity at
constant volume (Cv) can be calculated according to eq 1. The
result is compared in Figure 10 with the measured heat capacity
(Cp) of ZnAs. Above 150 K there is good agreement between
experiment and theory. This phenomenon is due to the
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underestimation of calculated wavenumbers, which is about 5%
(cf. calculated As−As stretches at 240 cm−1 and corresponding
Raman band at 250 cm−1). At low temperatures underestimated
phonon frequencies will lead to an overestimation of the heat
capacity. At high temperatures, when the Dulong-Petit limit is
approached, there must be agreement again, provided that
contributions due to volume change and anharmonicity are
small. The volume dependence of the heat capacity of ZnAs is
considered negligible in the investigated temperature range
because the crystallographic data suggest that thermal
expansion is very small (cf. Table 2). The good agreement
between calculated Cv and measured Cp above 150 K indicates
further that the vibrational properties of ZnAs are essentially
harmonic up to 300 K.
ACKNOWLEDGMENTS
■
This work was supported by the U.S. National Science
Foundation (NSF-DMR-1007557), the Swedish Research
Council (2010-4827 and 2013-4690), and the Deutsche
Forschungsgemeinschaft (DFG, SCHE 478/12-1). We are
grateful to Prof. U. Halenius (Swedish Museum of Natural
̊
History, Stockholm) for assistance with the optical diffuse
reflectance measurements.
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