Effects of Mn, Al and Lattice Defects on the
Thermoelectric Properties of CrSi2
CrSi2 の熱電特性における Mn, Al 及び格子欠陥が与える影響

Takahiro ORITA

Kazuhiro ICHINO

折田 昂優

一野 和寛

Keywords； CrSi2, thermoelectric material, power factor, band structure, density functional theory
キーワード；CrSi2，熱電材料，パワーファクター，バンド構造， 密度汎関数理論
Abstract
Chromium disilicide (CrSi2) is a p-type degenerate semiconductor, and its thermoelectric properties
can be controlled by the substitution of Al or Mn. However, it has not been clarified why holes are themajority carriers in pure CrSi2. In this study, Cr1−xMnxSi2 and CrSi2−yAly samples with x and y ranging
from 0.00 to 0.20 were prepared and their thermoelectric properties were evaluated. The electronic
density of states calculated by first-principles calculation based on density functional theory revealed
that the atomic vacancies in the Si sites can supply holes.
二珪ケイ化クロム(CrSi2)は一般に p 型縮退半導体として知られており，その熱電特性は
Al や Mn の置換によってコントロールできることが知られている．しかしながら，不純物を含まない純粋な CrSi2 において正孔が多数キャリアを示す理由は明らかにされていなかった．本報告では，Cr1-xMnxSi2 及び CrSi2-yAly 試料の x 及び y を 0.00 から 0.20 の範囲で変化させて作製し，その熱電特性を評価した．また，格子欠陥を考慮して密度汎関数法に基づく第一原理計算により電子状態密度を求めることにより，WDX により存在が示唆された Si サイト上の原子空孔が正孔を供給できることを明らかにした．

Nippon Tungsten Review Vol.42 (2024)- 32 -

1. Introduction
Transition metal disilicides exhibit high power factors (PFs) at high temperatures. In addition, theabundance of constituent elements, large electrical conductivity, high-temperature stability, andcorrosion resistance make them excellent thermoelectric material candidates［1］. Among the transition
metal disilicides, CrSi2 has attracted much attention because of its semiconducting properties［2］–［4］and excellent oxidation resistance in the high-temperature range of 700–1000 °C［5］. CrSi2 is ahexagonal C40 crystal with space group P6222, and it is a p-type degenerate semiconductor with aforbidden band width of 0.32 eV, but it has not been clarified what the carrier holes are derived fromwhen CrSi2 is undoped［6］–［9］. The PF of CrSi2 is the highest at approximately 300 °C. However, at
higher temperatures, the PF decreases as the Seebeck coefficient decreases owing to the bipolar effect,
making it impossible to effectively regenerate waste heat from steel mills and nonferrous metal plants,
where waste heat at 400–500 °C is common. Replacing the Si site with Al in the degenerate compound
semiconductor CrSi2 improves the PF by reducing the resistivity owing to the increased acceptor
concentration, which changes the Fermi level to a lower position relative to the upper end of thevalence band［9］–［12］. In the same way, substitution of Mn for Cr sites increases the concentration ofelectrons, which are minor carriers, generating an n-type semiconductor. We previously reported
CrSi2−yAly (y = 0.00, 0.04, 0.08, 0.12, 0.16, 0.20)［13］.
In this study, we investigated the electrical properties of Cr1−xMnxSi2 (x = 0.00, 0.04, 0.08, 0.12, 0.16,0.20) and the crystal lattice changes before and after sintering, and we discuss the origin of the holes
in undoped CrSi2.

2. Materials and Methods
2.1 Material synthesis
Cr powder of 99.9% purity, Mn pellets of 99.9% purity, Si pellets of 99.999% purity, and Al pellets
of 99.9% purity were weighed to obtain Cr1−xMnxSi2 (x = 0.00, 0.04, 0.08, 0.12, 0.16, 0.20) andCrSi2−yAly (y = 0.00, 0.04, 0.08, 0.12, 0.16, 0.20) in stoichiometric ratio. Each mixture was placed ina BN-coated alumina crucible and melted at 1500 °C in an Ar atmosphere of 4.0 atm using a multipurpose high-temperature furnace (Fuji Dempa Kogyo Co., Ltd.) to synthesize polycrystalline ingots.
The ingots were ground in an alumina mortar and sieved into powder using a 75 µm mesh. The powder
was sintered by uniaxial hot pressing (HP) at 1175 °C and 39.2 MPa (400 kgf cm−2) for 120 min in an
Ar atmosphere of 4.0 atm. The lattice parameters were identified by X-ray diffraction (XRD)
measurement of a portion of the sintered compact and the powder before sintering using a Cu Kα line
at Rigaku Co. The detailed composition of the sintered compact was determined by scanning electron
microscopy/wavelength dispersive X-ray analysis (SEM-WDX, JXA-8230, JEOL Ltd.).
2.2 Fabrication and characterization of the devices
After each sample was cut to a size of approximately 5 mm × 1.5 mm × 12 mm, the Seebeckcoefficient S and specific resistance ρ were measured from room temperature to 500 °C under reducedpressure with a rotary pump. S was calculated by heating both ends of the sample with a heater andmeasuring the temperature and potential difference V at both ends of the sample using the equation- 33 -

Nippon Tungsten Review Vol.42 (2024)

S = V/(TH − TL)(1)where TH is the temperature at the high-temperature side of the sample and TL is the temperature at
the low-temperature side of the sample, set to a difference of 20 °C. The specific resistance ρ was
calculated by the following equation using the four-terminal resistance measurement method:ρ = V t w I−1 l−1(2)where t is the thickness and w is the width of the sample. I is the value of the current flowing in thelongitudinal direction of the sample, and it was set to 0.1 or 0.4 A. l is the distance between theterminals for measuring the potential difference in the longitudinal direction of the sample, which was
8 mm. V is the voltage.
The PF was obtained from the measured Seebeck coefficient S and specific resistance ρ using.
PF = S2 ρ−1(3)

2.3 Electronic structure analysis by first-principles calculations
The electronic structures of CrSi2, CrSi1.96□0.04 with atomic vacancies at the Si site, and Al-substituted
CrSi1.926Al0.074 and CrSi1.8Al0.2 were calculated from first principles using 2×2×3 supercells. For CrSi2,
the Cr and Si sites were completely occupied by Cr and Si, and atomic vacancies and Al atoms werepartially introduced into the silicon sites. The calculations were performed with the cooperation ofProfessor Munetoh of Kyushu University.

3. Results and Discussion
3.1 Crystal structure analysis
The lattice constants a and c versus the Mn composition obtained from XRD measurements areshown in Figs. 1 and 2. For the Cr1−xMnxSi2 sample (Fig. 1), the lattice constants a and c decreased
with sintering, and the decrease rate of the lattice constants increased with increasing amount of Mn
substitution. This suggests that the substitution of Mn in Cr sites was further promoted by HP sintering.
The lattice parameters also decreased with increasing Mn substitution after HP sintering. Conversely,
for CrSi2−yAly (Fig. 2), the lattice constants did not significantly change with HP sintering. Thissuggests that the substitution of Al in Si sites was complete at the end of melting. As the y value
increased, a monotonically decreased, and c reached a maximum at y = 0.04 and decreased with afurther increase in y (Fig. 2b). This is the same trend as that observed for samples prepared by HP in
the range y = 0–0.1［11］.

Nippon Tungsten Review Vol.42 (2024)- 34 -

(a)

(b)
6.374

4.47

6.372

4.46

6.370

After sintering
sintered
After

6.368

c (Å)

a (Å)

4.45

BeforeBefore sintering
sintered

4.44

6.366
6.364

4.43
4.42

6.362

Before sinteredsintering
Before6.360

After sinteredsintering

6.358

4.41
0

0.04

0.08 0.12 0.16
Composition, x

0

0.2

0.04

0.08 0.12 0.16
Composition, x

0.2

Fig. 1 Lattice parameters (a) a and (b) c of Cr1−xMnxSi2 versus the Mn preparation composition(x = 0.00–0.20).
(a)

(b)

4.47

6.374
6.372

4.46

6.370
6.368

c (Å)

a (Å)

4.45
4.44

6.366
6.364

4.43

BeforeBefore sintering
sinteredsintered
After sintering

4.42

BeforeBefore sintering
sintered

6.362

sintered
After sintering

6.360

4.41

6.358
0

0.04

0.08 0.12 0.16
Composition, y

0.2

0

0.04

0.08 0.12 0.16
Composition, y0.2

Fig. 2 Lattice parameters (a) a and (b) c of CrSi2−yAly versus the Al preparation composition(y = 0.00–0.20).
3.2 Seebeck coefficient and resistivity measurement
The temperature dependence of the Seebeck coefficient and resistivity for each sample is shown in
Figs. 3 and 4, in which the average temperature at both ends of the sample and the temperature at thecenter of the sample are the x axis, respectively. For the Cr1−xMnxSi2 sample, the Seebeck coefficientwas positive for x ≤ 0.08, indicating that it is a p-type semiconductor. The sample with x = 0.20 showednegative values over the entire temperature range, indicating that it is an n-type semiconductor. The
Seebeck coefficients of the samples with x = 0.12 and 0.16 were negative at room temperature,indicating n-type behavior, whereas the absolute values of the Seebeck coefficients decreased withincreasing sample temperature, and the sign reversed above 200–300 °C, indicating p-typesemiconductor behavior. From these results, it can be inferred that the number of electrons increased
as the amount of Mn substitution increased. The samples with x = 0.12 and 0.16 showed very large- 35 -

Nippon Tungsten Review Vol.42 (2024)

resistivity (Fig. 4), suggesting that they are intrinsic semiconductors with approximately the same
number of electrons and holes. As the sample temperature increased, the number of holes increased
more than the number of electrons, which possibly caused the p-type behavior of the Seebeckcoefficient. The samples with x = 0.00 and 0.04 exhibited very small resistivity values (Fig. 4). The
values tended to increase similarly with increasing temperature. For normal semiconductors, theresistivity decreases as the carrier concentration increases with increasing temperature. In contrast, theresistivity of degenerate semiconductors with high carrier concentration increases with increasing
temperature because the effect of the lattice vibration is dominant, as in metals. From this fact, thesamples with x = 0.00 and 0.04 are considered to be degenerate semiconductors. The sample with x =0.08 exhibited the highest resistivity. This indicates that the sample with x = 0.08 had the lowest carrier
concentration, and it is considered to be an intrinsic semiconductor. This is consistent with the large
Seebeck coefficient. For x ≥ 0.12, the resistivity tended to decrease with increasing amount of Mn
substitution. This is due to the contribution of Mn as a donor, which is consistent with the Seebeckcoefficient measurements.

Seebeck coefficient (μV K−1)

150

100

50

0

-50

-100

-150
0

100

200

300

400

500

Temperature (°C)
xx=0.00xx=0.12xx=0.04xx=0.16xx=0.08xx=0.20Fig. 3 Temperature dependence of the Seebeck coefficient for the Cr1−xMnxSi2 samples(x = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).

Nippon Tungsten Review Vol.42 (2024)- 36 -

110

4.0

100

x
x=0.08xx=0.12xx=0.16xx=0.20

90

3.5

Resistivity (mΩ cm)

Resistivity (mΩ cm)

4.5

3.0
2.5
2.0
1.5
xx=0.00
xx=0.04

1.0
0.5

80
70
60
50
40
30
20
10

0.0

0
0

100

200

300

400

500

0

Temperature (°C)

100

200

300

400

Temperature (°C)

500

Fig. 4 Temperature dependence of the resistivity for the Cr1−xMnxSi2 samples(x = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).
The Seebeck coefficients of the CrSi2−yAly samples were all positive, confirming that these samples
are p-type semiconductors. The Seebeck coefficient was the highest for the sample with y = 0.00 anddecreased with increasing Al substitution. This suggests that the carrier concentration increased withincreasing Al substitution. For some of the samples, the Seebeck coefficient decreased in the hightemperature range above 400 °C. This may be due to the bipolar effect. In particular, the Al-substituted
samples with y = 0.08 or lower still exhibited a large Seebeck coefficient above 400 °C owing to the
low carrier concentration, while the Al-substituted samples with y ≥ 0.12 showed a decrease in the
Fermi level, and they are thus less susceptible to the bipolar effect. The higher carrier concentrationof the Al-substituted samples results in a smaller Seebeck coefficient. The resistivity decreased withincreasing Al substitution amount y (Fig. 6). As for the Seebeck coefficient results (Fig. 5), this may
be due to the increase in the carrier concentration. For all of the samples, the resistivity increased withincreasing temperature, suggesting that all of the CrSi2−xAlx samples are degenerate p-typesemiconductors with high carrier concentration.

Seebeck coefficient (μV K−1)

140
120
100
80
60
40
20
0
0

100

y
y=0.00yy=0.12

200

300

400

Temperature (°C)
yy=0.04yy=0.16500
yy=0.08yy=0.20Fig. 5 Temperature dependence of the Seebeck coefficient for the CrSi2−yAly samples(y = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).

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Nippon Tungsten Review Vol.42 (2024)

3.0

1.2

Resistivity (mΩ cm)

2.5

Resistivity (mΩ cm)

yy=0.00yy=0.04

2.0
1.5
1.0

1.0

y
y=0.08yy=0.12yy=0.160.8

yy=0.20

0.6
0.4
0.2

0.5

0.0

0.0
0

100

200

300

400

0

500

100

Temperature (°C)

200

300

400

500

Temperature (°C)

Fig. 6 Temperature dependence of the resistivity for the CrSi2−yAly samples(y = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).
The correlation between the PF and temperature calculated using the electrical properties of eachsample is shown in Fig. 7. The sample with x, y = 0.00, which had no elemental substitution, exhibitedthe best PF of 0.776 mW m−1 K−2 at 250 °C. The sample with y = 0.04 exhibited the highest PF in thehigh-temperature range above 400 °C. This is because of the more pronounced decrease in the Seebeckcoefficient with increasing temperature for the x, y = 0.00 sample and the approximately 1.5 times
higher specific resistance of the x, y = 0.00 sample when comparing the electrical properties of the x,
y = 0.00 and y = 0.04 samples in the high-temperature range. Conversely, for the Cr1−xMnxSi2 samples,
the PF value decreased with increasing Mn substitution. This is considered to be largely because thespecific resistivity significantly decreased with decreasing carrier concentration and approached that

1.0

1.0

0.9

0.9

0.8

0.8

PF(mW m−1 K−2)

PF(mW m−1 K−2))of a true semiconductor.

0.7
0.6
0.5
0.4
0.3

0.7
0.6
0.5
0.4
0.3

0.2

0.2

0.1

0.1

0.0

0.0
0

100

200

300

400

500

0

x
x=0.04xx=0.16

200

300

400

500

Temperature (°C)

Temperature (°C)
xx=0.00
xx=0.12100

xx=0.08xx=0.20yy=0.00yy=0.12yy=0.04yy=0.16yy=0.08yy=0.20Fig. 7 Temperature dependence of the power factor for the Cr1−xMnxSi2 and CrSi2−yAly samples(x, y = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).

Nippon Tungsten Review Vol.42 (2024)- 38 -

3.3 Origin of the carriers
A more accurate composition of the matrix phase in CrSi2−yAly was obtained by WDX. The
abundance ratio of each element and the stoichiometric ratios calculated so that Cr = 1 are given in
Table 1. The abundance ratio of each element was determined by measuring five locations in thematrix and using the average of the three points excluding the maximum and minimum values. No
elements other than Cr, Si, and Mn were detected in any of the Cr1−xMnxSi2 samples, and similarly noelements other than Cr, Si, and Al were detected in all of the CrSi2−yAly samples. For CrSi2−yAlysamples, the sums of the stoichiometric ratios of Si and Al were less than 2 when the stoichiometricratio of Cr was 1. This reduction is denoted □Si. Therefore, it is suggested that atomic vacancies may
exist at the Si site, including in the undoped samples (x, y = 0.00).

Table 1 WDX results of samples prepared with compositions of CrSi2−yAly(y = 0.00, 0.04, 0.08, 0.12, 0.16, and 0.20).
y in CrSi2−yAly
0.00
0.04
0.08
0.12
0.16
0.20

Chemical composition (%)
Cr
Si
Al
34.5
65.5
N/A
34.1
64.5
1.4
33.9
63.1
2.9
34.2
61.7
4.1
34.4
60.3
5.4
33.8
59.2
7.0

Cr
1.00
1.00
1.00
1.00
1.00
1.00

Stoichiometric ratio
Si
Al
1.90
0.00
1.89
0.04
1.86
0.09
1.81
0.12
1.75
0.16
1.75
0.21

□Si
0.10
0.07
0.05
0.07
0.09
0.04

From the results obtained from this experiment, the mechanism of the carrier generation in CrSi2 isdiscussed. To computationally confirm that the carrier concentration increases with increasing Al
substitution y in CrSi2−yAly and that the p-type behavior is also observed at y = 0, the electronic densityof states were determined for three compositions, y = 0.00, 0.074, and 0.20, by first-principles
calculations. WDX measurements suggested the presence of atomic vacancies at the Si site of the
CrSi2 crystal, suggesting that the stoichiometry was deficient. For larger Al substitution, the Fermi
level is located at lower energy with respect to the upper end of the valence band, and the apparent
band gap increases (Fig. 8a, c, and d). The apparent band gap, which is the difference between thelower end of the conduction band and the Fermi level in the valence band, increases with increasing
Al substitution (Fig. 8a, c, and d). This suggests that the hole concentration increases with increasing
Al substitution and the bipolar effect is suppressed, which is consistent with the results of the Seebeckcoefficient (Fig. 5) and resistivity (Fig. 6) measurements. However, the calculated result for y = 0.00
(Fig. 8a) suggests that it is a true semiconductor, which is inconsistent with the measured result thatsuggested degeneracy. Conversely, the Fermi level of CrSi1.96□0.04 is located in the valence band (Fig.
8b). This suggests that the reason why pure CrSi2 becomes a degenerate p-type semiconductor is theexistence of atomic vacancies at the Si site, which contribute to the formation of holes.

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Nippon Tungsten Review Vol.42 (2024)

(a) CrSi2(b) CrSi1.96□0.04(c) CrSi1.926Al0.074(d) CrSi1.8Al0.2

Fig. 8 Comparison of the density of states (DOS) near the Fermi level of CrSi2 and its relatives
obtained by first-principles calculations: (a) CrSi2, (b) CrSi1.96□0.04, (c) CrSi1.926Al0.074, and(c) CrSi1.8Al0.2

4. Conclusions
The thermoelectric properties of Cr1−xMnxSi2 (0.00 ≤ x ≤ 0.20) and CrSi2−yAly (0.00 ≤ y ≤ 0.20) havebeen evaluated. The results showed that Mn functions as a donor and Al functions as an acceptor. The
electronic density of states of crystals with and without atomic vacancies at the Si site, and for each of
the Al-doped crystal models were determined by first-principles calculations. The results of thesecalculations and the measurements described above confirmed that Al doping increases the holedensity. In the case of the CrSi2 crystal without atomic vacancies, the Fermi level exists in theforbidden band, while in the case of CrSi1.96□0.04 crystal with atomic vacancies, the Fermi level exists
in the valence band, suggesting degeneracy. These results indicate that the reason why CrSi2 is adegenerate p-type semiconductor even if undoped is the presence of atomic vacancies at the Si site,which act as acceptors.

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[6] Mattheiss, L. F., Physical Review B, 43(2), (1991), 1863.
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