p-GaSe:Gd schottky barrier diodes

ARTICLE IN PRESS Physica E 42 (2010) 1958–1962

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Electrical characterization of Ag/p-GaSe:Gd schottky barrier diodes ¨ S. Duman n, B. Gurbulak, S. Dog˘an, T. Bahtiyari Tekle Department of Physics, Faculty of Sciences, Atat¨ urk University, 25240 Erzurum, Turkey

a r t i c l e in f o

a b s t r a c t

Article history: Received 21 October 2009 Received in revised form 8 February 2010 Accepted 10 February 2010 Available online 19 February 2010

Some parameters of Ag/p-GaSe:Gd Schottky barrier diodes have been investigated by means of current–voltage and capacitance–voltage measurements at room temperature. Schottky barrier height and ideality factor values were determined from current–voltage characteristics of identically prepared twenty Ag/p-GaSe:Gd Schottky barrier diodes. By applying thermionic emission theory, the obtained barrier height and ideality factor values varied from 0.69 to 0.85 eV, and from 1.13 to 1.74, respectively. The homogeneous barrier height of Schottky barrier diodes was found to be 0.83 eV from the linear relationship between barrier height and ideality factor values. & 2010 Elsevier B.V. All rights reserved.

Keywords: GaSe Schottky diodes Current–Voltage characteristic Barrier height Ideality factor

1. Introduction Gallium selenide (GaSe) and indium selenide (InSe) belong to a vast class of layered semiconductors. They have a significant anisotropy of chemical bonds within layers and, because of their layered structures, natural and clean surfaces with high optical quality are easily obtained by cleaving the layers [1]. GaSe crystals have potential applications as light emitting diodes [2,3], Schottky barrier diodes (SBDs) [4–6], radiation detectors operated at room temperature [7,8] and a photoelectric analyzer for polarized light [9]. It has been reported that high resistivity SBDs were used as nuclear detectors [10]. SBDs are among the simplest metal– semiconductor (MS) devices due to technological importance [11,12]. Several parameters of SBDs, such as ideality factor (n), Schottky barrier height (Fb) and series resistance (Rs), play an important role on the electrical characteristics of rectifying contacts or junctions. These parameters give useful information concerned with the nature of the diode. There are quite few reports describing metal contacts of GaSe in the literature. Both the electrical and material characteristics of Ag/p-GaSe SBD were studied and Fb was determined to be 0.99 eV [4]. Microscopic-scale lateral inhomogeneties of the Schottky-barrier-formation was indicated [13] by photoemission–spectromicroscopy studies of Au on p-GaSe and the value of Fb was reported to be 0.4 eV [13]. The aim of this paper is to calculate some characteristic parameters of Ag/p-GaSe:Gd SBDs such as n, Fb, and Rs obtained from current to voltage (I–V)

n

Corresponding author. E-mail address: [email protected] (S. Duman).

1386-9477/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2010.02.017

measurements and to determine laterally homogeneous BHs obtained from the linear relationship between experimental Fb values and n values for the diode [14] at room temperature and under dark conditions. Since I–V characteristics showed series resistance effects in the forward bias region, Cheung functions have also been used to determine some contact parameters such as n, Fb, and Rs values. To our knowledge, the statistical distribution of the characteristics parameters of the devices was made firstly by means of the Gaussian function.

2. Experimental procedure p-GaSe:Gd crystal used in this work was grown by the modified Bridgman–Stockbarger method using our homemade crystal growth system and then it was freshly and gently cleaved with a razor blade from the grown ingot. Sample having the thickness of 0.2 mm was prepared by cleaving the ingot along a surface that was approximately perpendicular to the c-axis. Further polishing or cleaning was not required because of the natural mirror-like cleavage faces of the sample. Ohmic contact was obtained by vapor deposition of high purity (5N) indium (In) on one surface of GaSe:Gd and annealed at 300 1C for 3 min in N2 atmosphere. Twenty Schottky diodes were formed by vapor deposition of silver (Ag) as dots with diameter of 1 mm on the other surface of the p-GaSe:Gd to form Ag/p-GaSe:Gd SBD. All vapor deposition processes were carried out in a vacuum coating unit at about 10  6 Torr. The I–V and C-V measurements of the diodes were performed using a Keithley 487 picoammeter/voltage source and a HP 4192A LF impedance analyzer, respectively, at room temperature and under dark conditions.

ARTICLE IN PRESS S. Duman et al. / Physica E 42 (2010) 1958–1962

3. Results and discussion

1.00

where   qFb ; I0 ¼ AA T 2 exp  kT

ð2Þ

I0 is the saturation current derived from the straight line intercept of ln(I)–V at V =0, where k is the Boltzmann’s constant, T is temperature in Kelvin, A is diode contact area, An is Richardson’s constant, q is electron charge, V is applied voltage, and Fb is Schottky barrier height at zero bias. The latter can be obtained from the following equation.   2 AA T ð3Þ qFb ¼ kT ln I0 n is the ideality factor, which is determined from the slope of the linear region (indicating that the effect of series resistance in this region was not important) [15] of the forward bias ln(I)–V characteristics through the relation: n¼

q dV kT dðln IÞ

ð4Þ

Consequently, n depends on the current flow at the interface, although it is equal to one for an ideal diode. Experimentally obtained n values usually have a value greater than one. The high values of n can be attributed to the presence of a wide distribution of low-Schottky barrier height patches caused by lateral barrier inhomogeneity. Also, image-force effects, recombination– generation, and tunneling mechanisms may be responsible for n values greater than one [12,16]. Fig. 1 shows the experimental forward- and reverse-bias ln(I)–V characteristic of one of the Ag/p-GaSe:Gd SBDs at the room temperature, which exhibits a rectifying behavior. In identically prepared Ag/p-GaSe:Gd SBDs, the experimental values of Fb and n were determined at room temperature from the current axis intercept using Eq. (3) and the slope of the linear region of the

Ag/p-GaSe:Gd

10-3

10

-4

Current (A)

10-5

10

-6

10-7 10-8

Exp. Fit TE

TE

10

-1.00

-0.50

-9

0.00 Voltage (V)

0.50

1.00

Fig. 1. Forward- and reverse-bias ln(I)–V characteristics of one of the Ag/p-aSe:Gd Schottky barrier diodes at room temperature. The full square symbols are fitted assuming thermionic emission theory across the Schottky barrier.

Ag/p-GaSe:Gd

0.95

Y=-0.16x+0.99 Φhom = 0.83 eV

0.90 Barrier height (eV)

According to thermionic emission (TE) theory, the current in SBDs can be expressed as [12]     qV I ¼ I0 exp 1 ; ð1Þ nkT

1959

0.85 0.80 0.75 0.70 0.65 0.60 0.55

0.80

1.20

1.60 2.00 Ideality factor

2.40

Fig. 2. Experimental barrier height versus ideality factor plot for Ag/p-GaSe:Gd Schottky barrier diodes at room temperature.

forward bias ln(I)–V characteristics using Eq. (4). Fig. 2 shows the plot of the experimental Fb versus n values of twenty identically prepared Ag/p-GaSe:Gd SBDs at room temperature. The Fb values for the Ag/p-GaSe:Gd SBDs calculated from the voltage characteristics varied from 0.69 to 0.85 eV, and the n values ranged between 1.13 and 1.74. Experimental Fb and n ideality factors obtained from the ln(I)–V characteristics differ from diode to diode even if they are identically prepared on the same sample [14,16]. The Fb values decrease while the n values increase. There is also a linear relationship between experimental Fb and n of Schottky contacts that can be explained by the lateral inhomogeneities of the BHs in SBDs [14,15–30]. The inhomogeneity model is based on small local regions or patches assumed to exist at the junction, with lower Fb values than the junction’s mean Fb values. The reason for low Fb values and high n values may be explained by the patch density. Briefly, inhomogeneous metal–semiconductor contacts are thought as to consist of separate diodes with different barrier heights and areas in parallel. Such models are correct as long as the dimensions of the patches are large enough compared to the Debye length of the semiconductor. That is, if the sizes of the patches embedded in have much larger areas and, higher and uniform barrier height which are comparable to or smaller than the Debye length, then saddlepoint barriers exist in front of the patches. If the barrier height at the saddle point is intermediate between the values of the patch itself and of the surrounding homogeneous contact area, the saddlepoint barrier depends on the applied voltage. This results in a ‘‘pinch-off’’ of the patches as the bias increases and can be seen in detail [16,19,30]. This finding and the assumption that patches have smaller Fb values than the homogeneous contact explain the experimentally observed reduction of the Fb values with increasing n values. The homogeneous Fb values rather than mean values or effective Fb values of individual contacts should be used to discuss theories of physical mechanisms that determine the Fb values of MS contacts [19]. A laterally homogeneous Fb value of approximately 0.83 eV from extrapolation to n=1 for the Ag/p-GaSe:Gd SBDs was obtained from the linear relationship between experimental effective Fb and n values in Fig. 2. A histogram showing the distribution of the observed Fb and n values has been constructed. Fig. 3a and b shows the histograms of the effective Fb and n values for identically prepared twenty Ag/p-GaSe:Gd SBDs. Gaussian distribution function was used to obtain best fits and the statistical analysis of the histograms yielded the mean n = 1.3870.206 (the mean

ARTICLE IN PRESS 1960

S. Duman et al. / Physica E 42 (2010) 1958–1962

6

8

Ag/p-GaSe:Gd

=1.38 σ=0.206

7

<Φ>= 0.78 σ= 0.04

6 Number of diodes

Number of diodes

5

Ag/p-GaSe:Gd

4 3 2

5 4 3 2

1 0 0.60

1

0.90

1.20 1.50 Ideality factor

1.80

2.10

0 0.60

0.65

0.70 0.75 0.80 0.85 Barrier height (eV)

0.90

Fig. 3. Gaussian distributions of ideality factors and effective barrier heights obtained from the forward bias current–voltage characteristics of Ag/p-GaSe:Gd SBDs at room temperature. The Gaussian fit yields (a) n= 1.38 and s = 0.206 for the ideality factors and (b) Fbp = 0.78 eV and s = 0.04 for the barrier heights.

ideality factor exceeds unity) and the mean Fb = 0.7870.04 eV for the Ag/p-GaSe:Gd SBDs. If a semiconductor is covered with a thin oxide layer during sample preparation, chemical treatment, metal vapor deposition, or thermal annealing, this interface oxide layer may have a strong influence on the diode characteristics and increases the Rs. This can be clearly observed in the nonlinear region of the forward ln(I)–V curve. As can be seen in Fig. 1, the concavity of the forward bias I–V characteristics increases with increasing series resistance [31]. The forward bias ln(I)–V characteristics of a SBD with series resistance can be expressed as [12]   qðVIRs Þ ð5Þ I ¼ I0 exp nkT where IRs is the voltage drop across the device. The Fb, n and Rs can be calculated by means of a method developed by Cheung [32]. The Cheung’s functions can be written as follows:

H(I) (Volt)

dV/d(lnI) (V)

1.60

0.00 Y= 2.29x+1.15 Φ= 0.66 eV

-0.40

0x10

0

10

-1

-1

2x10

1.20 -1

3x10

I (mA) Fig. 4. Experimental H(I)  I and dV=d lnðIÞI curves of Ag/p-GaSe:Gd SBD at room temperature.

-4

2

2.0x10

1.0x10

ð6Þ 500 kHz

9.0x101

-4

1.6x10

ð7Þ 8.0x101

and HðIÞ ¼ nFb þIRs

2.00

0.40

ð8Þ

where Fb is the BH obtained from data of the downward curvature region in the forward bias ln(I)–V characteristics. When dV=dðln IÞ versus I is plotted using Eq. (6), this plot is a straight line. The slope and y-axis intercept of this plot will give Rs and nkT/q, respectively. Using the n value determined from Eq. (6) and the data of the downward curvature region in the forward bias ln(I)–V characteristics in Eq. (7), a plot of H(I) versus I will also give a straight line according to Eq. (8). The slope of this plot provides a second determination of Rs, and the value of Fb can be obtained from the y-axis intercept, since the intercept is equal to nFb. The plots given in Fig. 4 are drawn using the data of the downward concave curvature region in the forward bias ln(I)–V characteristics demonstrated for only one diode in Fig. 1. Using Eq. (6), the values of n and Rs were determineted as 1.74 and 2.21 kO, respectively, and using Eq. (8), the values of Fb and Rs were determined as 0.66 eV and 2.29 kO, respectively, at room

-4

1.2x10

7.0x101

C (pF)

    nkT I ln HðIÞ ¼ V  2 q AA T

2.40

Y = 2.21x+0.045 n = 1.74

C-2(pF)-2

dV nkT ¼ þ IRs dðln IÞ q

0.80

8.0x10-5 6.0x101 4.0x10-5

0.0x100

-1.0

5.0x101

-0.5

0.0

0.5

1.0

1.5

4.0x101

2.0

V (Volt) Fig. 5. Forward- and reverse-bias C–V and the reverse bias C  2–V characteristics of one of the Ag/p-GaSe:Gd Schottky diodes at 500 kHz.

temperature. It is seen that these two values of Rs obtained from two Cheung plots are in good agreement. The capacitance–voltage (C–V) characteristic is one of the fundamental properties of the Ag/p-GaSe:Gd SBD as well.

ARTICLE IN PRESS S. Duman et al. / Physica E 42 (2010) 1958–1962

2.5x102

2.5x102

2.0x102

ΔV=0.05 V 0.20 V

1.0x102

0.00 V

Capacitance (pF)

Capacitance (pF)

2.0x102 1.5x102

1961

1.5x102

0.20 V

1.0x102

5.0x101

5.0x101

0

0

0.70 V 0.0x10

102

104 Frequency (Hz)

106

0.0x10

102

104 Frequency (Hz)

106

Fig. 6. Experimental forward bias capacitance plots as a function of the frequency with bias voltage as a parameter of Ag/p-GaSe:Gd SBD in the range (a) 0.00–0.20 V and (b) 0.25–0.7 V at room temperature.

By plotting C  2–V for reverse bias, the Fb and the carrier concentration of the semiconductor for the SBD can be easily determined [10]. For that purpose, the C–V measurements for Ag/p-GaSe:Gd SBD were performed at 500 kHz and room temperature in the dark. Fig. 5 shows, for one diode, the forward- and reverse-bias C–V characteristics and the reverse bias C  2–V characteristics. Fb obtained from the reverse bias C  2–V characteristics at 500 kHz for Ag/p-GaSe:Gd SBD shown in Fig. 5 has been calculated to be 1.78 eV, which is higher than that obtained from ln(I)–V measurements. The net acceptor density based on C–V measurements has been calculated as 3.75  1022 m  3. As expected, the C–V curves give SBH values higher than those derived from the ln(I)–V measurements. The difference between BHs obtained from ln(I)–V and C–V measurements may be explained as due to trap states in the substrate, the effect of the image-force, and barrier inhomogeneities [10]. Fig. 6 shows the experimental capacitance curves as a function of frequency for Ag/p-GaSe:Gd SBD at various bias voltages. The bias dependent capacitance data in Fig. 6 seem to be consistent with those in Fig.5 showing a peak with increasing bias. The value of capacitance increased with bias voltage to 0.20 V (Fig.6a) and then decreased between 0.25 and 0.70 V (Fig.6b). As can be seen in Figs. 5 and 6, the value of capacitance gives a peak near 0.2 V. Such a behavior shows that there are various kinds of interface states with different lifetimes and they can follow an ac signal at low and intermediate frequencies, but cannot follow at high frequencies [33]. Relatively high values of capacitance are obtained at low frequencies, resulting from interface states. As the frequency increases, the capacitance becomes constant over a wide frequency range before it starts to decrease again due to the influence of the high series resistance value of the device fabricated from the p-GaSe:Gd with high resistivity [34,35].

4. Conclusion In this study, some characteristics for Ag/p-GaSe:Gd SBD have been presented. They indicate inhomogeneities of these SBDs and they are statistically described by a Gaussian distribution. The I–V characteristics of Ag/p-GaSe:Gd SBDs were investigated by taking into account TE theory. The linear relationship between experimental effective Fb and n values of SBDs were explained by means of lateral inhomogeneities of the Fb values in diodes. The laterally homogeneous Fb value of approximately 0.83 eV was obtained for

the Ag/p-GaSe:Gd SBD from the linear relationship between experimental effective Fb values and n values. Statistical analysis yielded the mean Fb =0.7870.04 eV and the mean n=1.3870.206 from the ln(I)–V characteristics for the Ag/p-GaSe:Gd SBDs.

Acknowledgements ¨ This work was supported by the Ataturk University Research Fund, Project nos. 2009/90 and 2009/253. S. Dog˘an would like to thank the Turkish Academy of Sciences (TUBA) for the support through the Distinguished Young Scientist Award Program (GEBIP).

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