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Piezoelectric effect in AuCdS Schottky barrier
Surface. Science 64 (1977) 793-796 0 North-Holland Publishing Company
PIEZOELECTRIC Received
9 November
EFFECT IN Au-WI 1976; manuscript
SCHOTTKY BARRIER
received in final form 14 February
1977
Recently it has been shown that the piezoelectric effect causes various macroscopic phenomena in a depleted surface layer of polar semiconductors [l-6]. In this paper the piezoelectric effect is reported, whereby mechanical bending of CdS wafers causes remarkable changes in the current-voltage characteristics of AuCdS diodes. This effect was attributed to the polarization induced in the depletion layer by the mechanical stress. Sample wafers were cut from undoped ultra high quality n-type CdS single crystals with a carrier density of about 101’/cm3. They have two polar surfaces, (0001)Cd and (OOOl)S, which were identified by etch figures. Their surfaces were mechanically polished and chemically etched in a solution of 0.5 M KZCr207 in 16 H$04 at a temperature of 95’C for 20 min and then they were rinsed thoroughly with deionized distilled water. Immediately after this process, they were placed in a vacuum system. By evaporating gold on these surfaces at a pressure of less than 5 X lo-* Torr, two kinds of diodes were fabricated. One is diode A where gold was evaporated on the (0001)Cd surface and the other is diode B where gold was evaporated on the (0OOi)S surface. Ohmic contacts were prepared by InGa alloy. The wafers, whose thickness was about 0.4 mm, were attached on the cantilever which was constructed of steel. Cadmium sulfide wafers were bent about the [ 1201 axis by bending a cantilever which loaded down with the weight at the end. Tensile
/’
-LOAD
SAMPLE ORIENTATION Fig. 1. Schematic representation of the cantilever and the sample orientation. Ty@cal samples dimension is 5 X 10 X 0.4 mm and surface strain is about 1 X 10V4 for (l/R) = 2 X 10p3/cm. 793
794
M. Kusaka et al. /Piezoelectric
effect in Au-CdS
Schottky barrier
DiodeB
y
UNB .L
t f UNB B I LJNBENDlNGb 4 3.0mm
B
"Y
t BENDING
Fig. 2. Typical change of the stress-induced tension; (b) S surface under compression.
timecurrents
during
the
time:
(a) S surface
under
or compressive stress perpendicular to the c-axis could be introduced into the sample wafer. The bending apparatus and sample orientation are shown in fig. 1. The current-voltage characteristics of the Au-CdS diodes without bending agreed with the previously reported one [7]. When the sample wafer was bent at a constant applied forward or backward bias voltage, it was found that the currents of diode A increased under the compressive stress and decreased under the tensile stress. The changes in the currents were opposite for diodes B. As shown in fig. 2, a typical change of the stress-induced currents is caused by bending. Significant transient phenomena are not observed and the stress-induced currents are measured
SURFACE
O-4 5 Cd
STRAINdXl64)
-8
A-A-A \ \,\ \$
12 0.1 Bias
0.2
o-3
Voltage
Fig. 3. Dependence of the ratio tension: (o) l/R = 2 X 10e3/cm; Pig. 4Changes surface strain:
.0.4
:lO -a -6 -4-2
(V)
(l/R)
2
4
6
B 10
X lo3 (l/cm)
iY/I on the forward bias voltage for diode B(6-S-3) under the (X) 4 X 10W3/cm; (a) 6 X 10e3/cm; (o) 8 X 10e3/cm.
in barrier height as a function of the radius (o) diode A (3Cd-3); (X) diode B (2-S-l).
of bending.
and the corresponding
M. Kusaka et al. / Piezoelectric effect in Au-CdS Schottky bawier
195
at the stationary interval. In fig. 3, typical values of AI/I for diode B are plotted as a function of forward bias voltage under the constant load in tension; where AZis the change in current and I the current without bending. Under the constant load the values of AZ/Z are nearly constant for small bias voltage and decrease gradually with increasing of forward bias voltage. In the constant region of AI/i, typical plots of AI/I versus (l/R), in which R is the radius of bending, are shown in fig. 4 for both diode A and diode B. It is found that the values of AI/I are proportional to (1 /R) and the slopes (&/Z)/( 1/R) h ave opposite sign between diode A and diode B. If the AZ is caused by the change of the barrier height and its change occurs in the depletion layer, AZ/Z can be obtained from the current-voltage characteristics of the Schottky diode. As in fig. 4, the corresponding potential value to the change 4% in AI/Z can be determined to have the value of 1 mV. On the other hand, the change of diffusion potential in depletion layer can be calculated using the following basic equations from mechanical and electrical boundary conditions: = P,
>
aD3/ax3
SI = S,E, TI + dxE3
,
p=W,
S2
+ &Es
,
E3=Q,
+ d33E3
,
T2 = T, = 0 ,
03
= d31 TI
= S1Ez7-1
S3 = S,E37-1
+ eT3E3
-dV,dx3=E,
V=0
in the bulk,
where D3 is the electric displacement, E3 is the electric field, Sr and S2 are the mechanical strain components, T1, T2 and Ts are the mechanical stress components, d31 is the piezoelectric strain constant, SF, and Sy2 are the elastic compliances, eT3 is the permittivity, p is the density change, V is the diffusion potential, N is the donor concentration in CdS and R is the radius of curvature of the cantilever. The origin of the coordinate is taken at the neutral layer. From the above equations we obtain
A#, = 3
(d2-d,f)-;&-;,
(1)
G3
where A$, is the change in barrier height, d is the width of depletion layer in stress and do is the width in no external stress. If we assume that the width of the depletion layer does not depend on the strain of the wafer, eq. (1) becomes
1 41
A@, = i 2i73R
d2
where the t sign refers to the S surface and the - sign to the Cd surface, and R is taken as a positive value in tension. The values of eq. (2) agree fairly well with those obtained from experiments.
M. Kusaka et al. /Pie.zoelectric
796
effect in Au-CdS
This work is partially supported by the Grant-in-Aid “Surface Electronics” from the Ministry of Education.
Schottky barrier
for Scientific
Research on
M. KUSAKA, M. KANAKURA and S. OKAZAKI
Laboratory for Surface Science, Faculty of Science, Okayama University, Okayama, Japan
References [l] [2] [3] [4] [5] [6] [7]
1. Lagowski and H.C. Gatos, Surface Sci. 45 (1974) 353. J. Lagowski, A. Morawski and H.C. Gatos, Surface Sci. 45 (1974) 325. J. Lagowski, I. Baltov and H.C. Gatos, Surface Sci. 40 (1973) 216. J. Lagowski and H.C. Gatos, Surface Sci. 30 (1972) 491. J. Lagowski and H.C. Gatos, Appl. Phys. Letters 20 (1972) 14. D.L. White, IRE Intern. Convention Record 1 (1967) 304. M. Kusaka, T. Matui and S. Okazaki, Surface Sci. 41 (1974) 607.
PIEZOELECTRIC Received
9 November
EFFECT IN Au-WI 1976; manuscript
SCHOTTKY BARRIER
received in final form 14 February
1977
Recently it has been shown that the piezoelectric effect causes various macroscopic phenomena in a depleted surface layer of polar semiconductors [l-6]. In this paper the piezoelectric effect is reported, whereby mechanical bending of CdS wafers causes remarkable changes in the current-voltage characteristics of AuCdS diodes. This effect was attributed to the polarization induced in the depletion layer by the mechanical stress. Sample wafers were cut from undoped ultra high quality n-type CdS single crystals with a carrier density of about 101’/cm3. They have two polar surfaces, (0001)Cd and (OOOl)S, which were identified by etch figures. Their surfaces were mechanically polished and chemically etched in a solution of 0.5 M KZCr207 in 16 H$04 at a temperature of 95’C for 20 min and then they were rinsed thoroughly with deionized distilled water. Immediately after this process, they were placed in a vacuum system. By evaporating gold on these surfaces at a pressure of less than 5 X lo-* Torr, two kinds of diodes were fabricated. One is diode A where gold was evaporated on the (0001)Cd surface and the other is diode B where gold was evaporated on the (0OOi)S surface. Ohmic contacts were prepared by InGa alloy. The wafers, whose thickness was about 0.4 mm, were attached on the cantilever which was constructed of steel. Cadmium sulfide wafers were bent about the [ 1201 axis by bending a cantilever which loaded down with the weight at the end. Tensile
/’
-LOAD
SAMPLE ORIENTATION Fig. 1. Schematic representation of the cantilever and the sample orientation. Ty@cal samples dimension is 5 X 10 X 0.4 mm and surface strain is about 1 X 10V4 for (l/R) = 2 X 10p3/cm. 793
794
M. Kusaka et al. /Piezoelectric
effect in Au-CdS
Schottky barrier
DiodeB
y
UNB .L
t f UNB B I LJNBENDlNGb 4 3.0mm
B
"Y
t BENDING
Fig. 2. Typical change of the stress-induced tension; (b) S surface under compression.
timecurrents
during
the
time:
(a) S surface
under
or compressive stress perpendicular to the c-axis could be introduced into the sample wafer. The bending apparatus and sample orientation are shown in fig. 1. The current-voltage characteristics of the Au-CdS diodes without bending agreed with the previously reported one [7]. When the sample wafer was bent at a constant applied forward or backward bias voltage, it was found that the currents of diode A increased under the compressive stress and decreased under the tensile stress. The changes in the currents were opposite for diodes B. As shown in fig. 2, a typical change of the stress-induced currents is caused by bending. Significant transient phenomena are not observed and the stress-induced currents are measured
SURFACE
O-4 5 Cd
STRAINdXl64)
-8
A-A-A \ \,\ \$
12 0.1 Bias
0.2
o-3
Voltage
Fig. 3. Dependence of the ratio tension: (o) l/R = 2 X 10e3/cm; Pig. 4Changes surface strain:
.0.4
:lO -a -6 -4-2
(V)
(l/R)
2
4
6
B 10
X lo3 (l/cm)
iY/I on the forward bias voltage for diode B(6-S-3) under the (X) 4 X 10W3/cm; (a) 6 X 10e3/cm; (o) 8 X 10e3/cm.
in barrier height as a function of the radius (o) diode A (3Cd-3); (X) diode B (2-S-l).
of bending.
and the corresponding
M. Kusaka et al. / Piezoelectric effect in Au-CdS Schottky bawier
195
at the stationary interval. In fig. 3, typical values of AI/I for diode B are plotted as a function of forward bias voltage under the constant load in tension; where AZis the change in current and I the current without bending. Under the constant load the values of AZ/Z are nearly constant for small bias voltage and decrease gradually with increasing of forward bias voltage. In the constant region of AI/i, typical plots of AI/I versus (l/R), in which R is the radius of bending, are shown in fig. 4 for both diode A and diode B. It is found that the values of AI/I are proportional to (1 /R) and the slopes (&/Z)/( 1/R) h ave opposite sign between diode A and diode B. If the AZ is caused by the change of the barrier height and its change occurs in the depletion layer, AZ/Z can be obtained from the current-voltage characteristics of the Schottky diode. As in fig. 4, the corresponding potential value to the change 4% in AI/Z can be determined to have the value of 1 mV. On the other hand, the change of diffusion potential in depletion layer can be calculated using the following basic equations from mechanical and electrical boundary conditions: = P,
>
aD3/ax3
SI = S,E, TI + dxE3
,
p=W,
S2
+ &Es
,
E3=Q,
+ d33E3
,
T2 = T, = 0 ,
03
= d31 TI
= S1Ez7-1
S3 = S,E37-1
+ eT3E3
-dV,dx3=E,
V=0
in the bulk,
where D3 is the electric displacement, E3 is the electric field, Sr and S2 are the mechanical strain components, T1, T2 and Ts are the mechanical stress components, d31 is the piezoelectric strain constant, SF, and Sy2 are the elastic compliances, eT3 is the permittivity, p is the density change, V is the diffusion potential, N is the donor concentration in CdS and R is the radius of curvature of the cantilever. The origin of the coordinate is taken at the neutral layer. From the above equations we obtain
A#, = 3
(d2-d,f)-;&-;,
(1)
G3
where A$, is the change in barrier height, d is the width of depletion layer in stress and do is the width in no external stress. If we assume that the width of the depletion layer does not depend on the strain of the wafer, eq. (1) becomes
1 41
A@, = i 2i73R
d2
where the t sign refers to the S surface and the - sign to the Cd surface, and R is taken as a positive value in tension. The values of eq. (2) agree fairly well with those obtained from experiments.
M. Kusaka et al. /Pie.zoelectric
796
effect in Au-CdS
This work is partially supported by the Grant-in-Aid “Surface Electronics” from the Ministry of Education.
Schottky barrier
for Scientific
Research on
M. KUSAKA, M. KANAKURA and S. OKAZAKI
Laboratory for Surface Science, Faculty of Science, Okayama University, Okayama, Japan
References [l] [2] [3] [4] [5] [6] [7]
1. Lagowski and H.C. Gatos, Surface Sci. 45 (1974) 353. J. Lagowski, A. Morawski and H.C. Gatos, Surface Sci. 45 (1974) 325. J. Lagowski, I. Baltov and H.C. Gatos, Surface Sci. 40 (1973) 216. J. Lagowski and H.C. Gatos, Surface Sci. 30 (1972) 491. J. Lagowski and H.C. Gatos, Appl. Phys. Letters 20 (1972) 14. D.L. White, IRE Intern. Convention Record 1 (1967) 304. M. Kusaka, T. Matui and S. Okazaki, Surface Sci. 41 (1974) 607.