n-Si (MIS) Schottky diodes

Solid-State Electronics 51 (2007) 941–949 www.elsevier.com/locate/sse

Temperature dependence of characteristic parameters of the Au/SnO2/n-Si (MIS) Schottky diodes ¨ zer, D.E. Yıldız, S M. O ß . Altındal *, M.M. Bu¨lbu¨l Department of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey Received 17 November 2006; received in revised form 30 March 2007; accepted 23 April 2007

The review of this paper was arranged by Prof. E. Calleja

Abstract The variation in electrical characteristics of Au/SnO2/n-Si (MIS) Schottky diodes have been systematically investigated as a function of temperature by using forward bias current–voltage (I–V) measurements. The main diode parameters, ideality factor n and zero-bias barrier height UB0, were found strongly temperature dependent and while the zero-bias barrier height UB0(I–V) increases, the n decreases with increasing temperature. This behavior has been interpreted by the assumption of a Gaussian distribution of barrier heights due to barrier inhomogenities that prevail at the metal–semiconductor interface. The zero-bias barrier height UB0 vs q/(2kT) plot has been drawn to obtain evidence of a Gaussian distribution of the barrier heights, and values of UB0 ¼ 1:101 eV and r0 = 0.158 V for the mean barrier height and zero-bias standard deviation have been obtained from this plot, respectively. Thus a modified ln(I0/T2)  (q2 r20 Þ/2k2T2 vs q/(kT) plot has given mean barrier height UB0 and Richardson constant (A*) as 1.116 eV and 127.86 A cm2 K2, respectively. The A* value 127.86 A cm2 K2 obtained from this plot is in very close agreement with the theoretical value of 120 A cm2 K2for n-type Si. Hence, it has been concluded that the temperature dependence of the forward bias I–V characteristics of the Au/SnO2/n-Si (MIS) Schottky diode can be successfully explained on the basis of a thermionic emission (TE) mechanism with a Gaussian distribution of the Schottky barrier heights (SBHs). In addition, we have reported a modification by the inclusion of both n and av0.5d in the expression of I0 to explain the positive temperature dependence of UB0 against that of energy band-gap of Si. Thus, the values of temperature coefficient of the effective barrier height UBef(3.64 · 104 eV/K) is very close agreement with the temperature coefficient of Si band-gap (4.73 · 104 eV/K).  2007 Elsevier Ltd. All rights reserved. PACS: 73.30.+y; 73.40.Qv; 73.40.Ns Keywords: Temperature dependence; Insulator layer SnO2; I–V measurements; MIS Schottky diodes; Barrier inhomogeneities

1. Introduction The performance and reliability of metal–insulator– semiconductor (MIS) Shottky diodes especially depend on the formation of an insulator layer, active metal/semiconductor interface, the interface states distribution at the semiconductor, insulator interface, series resistance and inhomogeneous barrier heights [1–12]. The interface *

Corresponding author. Fax: +90 312 212 2279. E-mail address: [email protected] (S ß . Altındal).

0038-1101/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2007.04.013

properties, carrier transport mechanisms and the same structural parameters of type SBDs have been studied both experimentally and theoretically in past decades [9–23]. The popularity of such studies does not assure uniformity of the results or of interpretation. The electrical characteristics of a Schottky barrier diode (SBD) with an interfacial insulator layer, such as SiO2, SnO2 and Si3N4, does not obey the ideal thermionic emission (TE) theory. The insulator layer (SnO2) is a material of growing importance for a wide variety of novel and special applications [24,25]. Especially, the formation and characterization of SnO2 insulator layer

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¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

on the Si and Schottky barrier formation between metal and semiconductor interface on a fundamental basis still remains a challenging problem. Various models have been proposed to describe the behavior of the Si/SnO2 interface and carrier transport across it [1,5,8,26]. The SnO2 interfacial insulator layer plays a more significant role than serving as a contact and is likely to influence the current– voltage (I–V) characteristics of the Si/SnO2 interface. Until now, the literature has contained numerous reports on the current transport mechanism of MIS diodes [1,3– 9,15–18,26–31]. Card and Rhoderick [3] and Strikha [27] estimated the surface state density located at the insulator–silicon interface and examined effects of the surface states on the ideality factor of the forward bias I–V characteristics. Some studies [5–7,17,22,27–29] inspected the effects of surface states on the behavior of Schottky diodes and extracted the density distribution of surface states in the semiconductor band gap from the forward bias I–V characteristics. In generally, analysis of the I–V characteristics of SBDs based on TE theory usually reveal an abnormal decrease in the barrier height and increase in the n with decrease in the temperature [7,18,23,30–32]. The decrease in the BH at low temperatures leads to a non-linearity in the activation energy ln(I0/T2) vs 1/T plot. Yu and Snow [33] observed that n for Schottky diodes depends on the forward bias voltage. Levine [34] also suggested that both UB and n should depend on the bias voltage. Hackam and Harrop [18] proposed that the ideality factor n should be included in the expression for the reverse saturation current I0. The analysis of the current–voltage (I–V) characteristics of the Shottky barrier diodes (SBDs) only at room temperature or narrow range of temperature, do not give detailed information about their current-transport mechanisms or the nature of barrier formation at the metal–semiconductor (MS) interface. On the other hand, the temperature dependence of forward bias I–V measurements allows us to understand different aspects of current-transport mechanism. For this purpose the current–voltage (I–V) characteristics of Au/SnO2/n-Si (MIS) Schottky diodes have been systematically investigated at wide temperature range (200–350 K) by using forward bias current–voltage (I–V) measurements. In this study, for the first time, we report the forwardbias current–voltage characteristics and barrier parameters in Au/SnO2/n-Si diodes in the temperature range 200– 350 K. The temperature dependence of barrier height (SBHs) characteristics of Au/SnO2/n-Si (MIS) diodes were interpreted on the basis of the existence of Gaussian distribution of the BHs around a mean value due to barrier height inhomogeneities prevailing at the metal–semiconductor interface. Also, we have reported a modification which is includes the ideality factor n and tunneling parameter av0.5d in the expression of reverse saturation current I0.

wafer with h1 1 1i surface orientation, 280 mm thick, 200 diameter and 4 X cm resistivity. The Si wafer was degreased for 5 min in boiling trichloroethylene, acetone and ethanol consecutively and then etched in a sequence of H2SO4 and H2O2, 20% HF, a solution of 6HNO3: 1HF:35H2O, 20%HF. Preceding each cleaning step, the wafer was rinsed thoroughly in deionised water of resistivity of 16 MX cm. Immediately after surface cleaning, high ˚ purity Au metal (99.999%) with a thickness of 2500 A was thermally evaporated from the tungsten filament onto the whole back surface of the wafer in the pressure of 1 · 106 Torr. Sintering the evaporated Au, the ohmic back contact was formed under vacuum. Immediately after ohmic contact, a thin layer of SnO2 was grown on the Si substrate by spraying a solution consisting of 32.21 wt% of ethyl alcohol (C2H5OH), 40.35 wt% of deionised water (H2O) and 27.44 wt% of stannic chloride (SnCl4 Æ 5H2O) on the substrate, which was maintained at a constant temperature of 400 C. The temperature of the substrates was monitored by chromel–calomel thermocouple fixed on top surface of the substrate. The variation of the substrate temperature during spray was maintained within ±2 C with the help of a temperature controller. The rate of spraying was kept at about 30 cc min1 by controlling the carrier gas flowmeter. Dry nitrogen (N2) was used as the carrier gas. SnO2 dots were 4 mm in diameter. After spraying pro˚ thick cess, circular dots of 2 mm in diameter and 2500 A Au rectifying contacts were deposited onto the SnO2 surface of the wafer through a metal shadow mask in liquid nitrogen trapped oil-free ultrahigh vacuum system in the pressure of 1 · 106 Torr. Metal layer thickness as well as deposition rates were monitored with the help of a digital quartz crystal thickness monitor. The deposition rates were ˚ s1. about 1–3 A The temperature dependent current–voltage (I–V) characteristics of the Au/SnO2/n-Si Schottky diodes were measured in the temperature range of 200–350 K using a temperature controlled Janes vpf-475 cryostat, which enables us to make measurements in the temperature range of 77–450 K, and a Keithley 220 programmable constant current source and a Keithley 614 electrometer in dark conditions. The sample temperature was always monitored by using a copper-constantan thermocouple and a Lakeshore 321 auto-tuning temperature controller with sensitivity better than ±0.1 K. All measurements were carried out with the help of a microcomputer through an IEEE-488 ac/dc converter card.

2. Experimental procedure

The current through a Schottky barrier diode (SBD) with the series resistance (Rs) at a forward bias, based on the thermionic emission (TE) theory, is given by the relation [1,2]

The Au/SnO2/n-Si (MIS) diodes used in this work were fabricated using n-type (P-doped) single crystal silicon

3. Results and discussions 3.1. Temperature dependence of the forward bias I–V characteristics

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

I ¼ I 0 exp

    qðV  IRs Þ qðV  IRs Þ 1  exp nkT kT

ð1Þ

where V is the applied voltage, the term IRs is the voltage drop across the Rs of diode, n is an ideality factor, T is the absolute temperature, k is the Boltzmann constant and q is the electronic charge and I0 is the reverse saturation current and expressed as   qUB0 I 0 ¼ AA T 2 exp  ð2Þ kT where UB0 is the zero-bias barrier height, A is the diode area, A* is the effective Richardson constant and equals to 120 A/cm2 K2 for n-type Si. Fig. 1 shows the experimental semi-logarithmic forward bias current–voltage (I–V) characteristics of the Au/SnO2/n-Si (MIS) Schottky diode in the temperature range of 200–350 K. As can be seen in Fig. 1, the downward curvature in the I–V characteristics at high forward bias values is attributed to a continuum of surface states (NSS), which are in equilibrium with the semiconductor, apart from the effect of Rs. While the Rs is significant especially in the downward curvature of the forward bias I–V characteristics, the NSS is effective in both -0.8

-0.6

-0.4

-0.2

943

inversion and depletion range and their distribution profile changes from region to region in the band gap. The I0 values were obtained by extrapolating the linear portion semi-logarithmic forward bias I–V plot to the intercept point on the current axis at zero bias (V = 0) and the UB0 values were calculated by using Eq. (2). The values of ideality factor n were calculated from the slope of the ln I–V plot in the linear region and can be written using Eq. (1) as   q dðV  IRs Þ n¼ ð3Þ kT dðlnðIÞÞ The experimental values of UB0 and n were determined from Eq. (2) and (3), respectively, at each temperature and are given in Table 1. As seen in Table 1, the experimental values of UB0 and n for the Au/SnO2/n-Si (MIS) Schottky diode ranged from 0.396 eV and 5.14 (at 200 K) to 0.708 eV and 2.49 (at 350 K), respectively. Such behavior of ideality factor has been attributed to particular distribution of interface states and insulator layer (SnO2) between metal and semiconductor [3–7,17,19,30]. These values of UB0 calculated from forward bias I–V characteristics have shown an abnormal behavior that it increases with increasing temperature. Such temperature dependence is 0

0.2

0.4

0.6

0.8

1.E-03

1.E-04 200 K 250 K

I(A)

295 K 315 K

1.E-05

335 K 350 K

1.E-06

1.E-07 V(V)

Fig. 1. Experimental semi-logarithmic forward bias I–V plots of the Au/SnO2/n-Si (MIS) Schottky diode at various temperatures.

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

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Table 1 Temperature dependent values of various parameters obtained from forward bias I–V characteristics of the Au/SnO2/n-Si (MIS) Schottky diode T (K)

I0 (A)

n

UB0 (eV)

UBef (eV)

Rs(dV/dln I) (X)

NSS (eV1 cm2)

200 250 295 315 335 350

1.65 · 105 2.37 · 105 2.41 · 105 2.55 · 105 2.65 · 105 3.05 · 105

5.14 3.92 3.10 2.84 2.61 2.49

0.396 0.496 0.594 0.636 0.679 0.708

0.615 0.593 0.578 0.572 0.565 0.559

140.35 94.27 71.43 60.96 29.77 9.80

4.56 · 1012 3.20 · 1012 2.28 · 1012 1.99 · 1012 1.73 · 1012 1.60 · 1012

an obvious disagreement with the reported negative temperature coefficient of the Schottky barrier height. Also, the values of ideality factor n was found to increase, while the UB0 decrease with decreasing temperature, as can be seen in Fig. 2. As explained in the references [6,7,10– 12,31,35], since the current transport across the metal– semiconductor interface is a temperature activated process, electrons at low temperatures are able to surmount the lower barriers. In other words, more and more electrons have sufficient energy to overcome the higher barrier build up with increasing temperature and bias voltage. Therefore, the current transport will be dominated by the current flowing through the patches of lower SBH, leading to a larger ideality factor. An apparent increase in the ideality factor and a decrease in the barrier height at low temperatures are caused possibly by other effects such as inhomogeneities of thickness and non-uniformity of the interfacial charges. Also, the change in ideality factor n was found to change linearly (Fig. 3) with the inverse temperature (1/T) as nðT Þ ¼ a þ T 0 =T

ð4Þ

where the a and T0 are constants which were found to be 1.122 and 1253 K, respectively. Depending on conditions

0.80 0.75

200

250

295 o *

315

335

350

of experiment one of them plays a prevailing role. The increase in the ideality factor with decreasing temperature is known as T0 effect [36]. Explanations of the possible origin of such case have been proposed taking into account the interface state density distribution, quantum mechanical tunneling and image force lowering [2,37,38]. To determine the barrier height in another way, Eq. (2) can be rewritten as  ln

I0 T2



¼ ln ðAA Þ 



qUB0 kT

 ð5Þ

Also, a plot of ln(I0/T2) vs 1/T shows a non-linear behavior in a certain temperature range, the reason being the decrease in barrier height and increase in the ideality factor with fall in temperature. In contrary to ln(I0/T2) vs 1/T, the ln(I0/T2) vs 1/nT gives a straight line (Fig. 4). As explained in Ref. [7–11,17,20–22,39], the non-linearity of the conventional ln(I0/T2) vs 1/T plot is caused by the temperature dependence of the barrier height and ideality factor. This shows that the reverse saturation current I0 can be described by 

2

I 0 ¼ AA T expðav

1=2



qUBef dÞ exp  nkT

 ð6Þ

6.0 5.5

Bo

5.5 Bef.

0.70

5.0

5.0

0.50

Bef. (T)

-4

4.0

= (0.686 -3.64x10 T ) eV 3.5

0.45

Ideality factor, n

Bef .

0.55

n

4.5

0.60

Bo ,

(eV)

0.65

4.5 4.0 3.5 n(T) = -1.122+1253 T

3.0

3.0

2.5

2.5

2.0

2.0 0.0025

-1

0.40 0.35 0.30

T (K) Fig. 2. Temperature dependence of UB0, UBef and n obtained from forward bias I–V Characteristics for Au/SnO2/n-Si (MIS) Schottky diode at various temperatures.

0.003

0.0035

0.004

0.0045

0.005

0.0055

T-1 (K-1) Fig. 3. Plots of n vs T1 of Au/SnO2/n-Si (MIS) Schottky diode obtained from I–V characteristics.

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O -21.5

-21.9

y = -3273,3x - 18,402

-22.1

-22.3 0.0009 0.00095 0.001 0.00105 0.0011 0.00115 0.0012

1/nT (K-1) Fig. 4. The Richardson plot of the ln(I0/T2) vs 1/nT for Au/SnO2/n-Si (MIS) Schottky diode.

where A is the diode area, A* is the effective Richardson constant, UBef is the flat-band barrier height, a = (4p/ h)(2m*)1/2 is a constant that depends on the tunnelling effective mass m* and Planck’s constant h, v is the mean tunnelling barrier presented by the interfacial insulator layer, d is the thickness of the interfacial film through which the carriers tunnel and av1/2d is the hole tunnelling factor. Thus, the values of modified barrier height (UBef) can be obtained from Eq. (6) as    nkT I0  1=2 lnðAA Þ  av d  ln UBef ¼ ð7Þ q T2 Furthermore, the temperature dependence of the effective barrier height can be described as UBef ¼ UBef ðT ¼ 0Þ þ aT

should give a straight line for the data of downward curvature region in the forward bias I–V characteristics. The term IRs is the voltage drop across series resistance of diode. The voltage Vd = V  IRs across the diode can be expressed in terms of the total voltage drop V across the series combination of the diode and the series resistance. In Fig. 5, experimental dV/d(ln I) vs I plot is presented at different temperatures for Au/SnO2/n-Si (MIS) Schottky diode. Eq. (9) should give straight line for the data of downward curvature region in the forward bias I–V characteristics. Thus, a plot of dV/dln(I) vs I will give Rs as the slope and nkT/q as the y-axis intercept. As a function of temperature, the values of Rs derived from Fig. 5 are given in Table 1 and Fig. 6. As shown in Fig. 6, the values of Rs decrease strongly with increasing temperature. The decrease of Rs with the increasing of temperature is believed to appear from the factors responsible for increase of ideality factor n and lack of free carrier concentration at low temperatures [9]. For a real metal–semiconductor (MS) or metal–insulator–semiconductor (MIS) type Schottky diode, the density distribution curves of the interface state NSS in equilibrium with the semiconductor can be determined from the forward bias I–V characteristics at each temperature. The effective barrier height Ue(V) is assumed to be bias dependent due to the presence of an interfacial insulator layer and interface states located between interfacial layer and semiconductor interface, and is given by [5,15]   1 Ue ðV Þ ¼ UB0 þ 1  ð10Þ ðV  IRs Þ nðV Þ For a metal–insulator–semiconductor (MIS) diode having interface states NSS in equilibrium with semiconductor, the ideality factor n becomes greater than unity and is given by

ð8Þ

where UBef(T = 0) is the flat-band barrier height extrapolated to zero temperature and a is the temperature coefficient of UBef(T = 0). Fig. 2 shows the variation of UBef as a function of temperature. It is evident that UBef is larger than UB0 in all temperatures. This is possible due to extremely high values of n. The barrier height of a Schottky diode depends on the electric field across the contact and consequently on the applied bias voltage. In Fig. 2, the fitting of the experimental UBef(T) data in Eq. (8) yields UBef(T = 0) = 0.686 eV and a = 3.64 · 104 eV/K. As shown in Fig. 1, the forward bias I–V characteristics are linear on a semi-logarithmic scale at low forward bias voltages but deviate considerably from linearity due to the effect of series resistance Rs. The values of Rs were achieved using a method developed by Cheung [40]. Cheung’s function   dV kT ¼ IRs þ n ð9Þ dðln IÞ q

1.40 1.30 1.20

d V /d L n (I ) ( V )

Ln(Io / T2)(A.K-2)

-21.7

945

1.10 1.00

200 K 250 K 300 K 315 K 335 K 350 K

0.90 0.80 0.70 0.60 0.50 0.40 1.E-03

2.E-03

3.E-03

4.E-03

5.E-03

6.E-03

I (A) Fig. 5. Plot of dV/d(ln I) vs I for Au/SnO2/n-Si (MIS) Schottky diode at various temperatures.

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

946

2.0E+14

145

200 K 295 K 350 K 200 K (with Rs) 295 K (with Rs) 350K (with Rs)

1.8E+14

125

1.6E+14 1.4E+14

65 45

-2

85

1.2E+14

-1

Nss (eV cm )

Rs ( )

105

1.0E+14

6.0E+13 4.0E+13

25 5 175

8.0E+13

2.0E+13

225

275

325

375

0.0E+00 0.15

T (K)

ð11Þ

This expression is identical to Eq. (18) of Card and Rhoderick [3]. The expression for the interface state density as deduced by Card and Rhoderick [3] is reduced to   1 ei es N SS ðV Þ ¼ ðnðV Þ  1Þ  ð12Þ q d WD where d is the thickness of interfacial insulator layer, WD is the width of the space charge region, ei and es are the permittivity of the interfacial insulator layer and the semiconductor, respectively. Furthermore, in n-type semiconductors, the energy of interface states ESS with respect to the conduction band edge, Ec, at the semiconductor surface, is given by

0.45

0.55

0.65

0.75

Fig. 7. The interface state energy distribution profiles of the Au/SnO2/n-Si (MIS) Schottky diode with and without taking into account the series resistance in the calculations.

3.2. Barrier height inhomogeneties Thermionic emission (TE) theory is normally used to extract the Schottky diode parameters [5,7,9,17,23,41]. However, there have been several reports of certain anomalies [5,7,17,23,41] at low temperature. According to [12,17,20,37], the ideality factor of an inhomogeneous Schottky barrier diode (SBD) with a distribution of low Schottky barrier heights (SBHs) may increase with a decrease in temperature. They found a linear correlation between the experimental zero-bias SBHs and the ideality factors. Fig. 8 shows a plot of the experimental BH vs ideality factor with temperature for the Au/SnO2/n-Si (MIS) Schottky diode. The straight line in Fig. 8 is the least

ð13Þ 0.8

( ) = (0,9712 - 0,1153n )

0.7 BO (eV)

where Ue is the effective barrier height of the n-type semiconductor (Si). For each temperature, substituting the values of the voltage dependent n(V) and variation of WD calculated from C2 vs V characteristics (not given here) ˚ , calculated from high-frequency in Eq. (12), and d = 35 A (1 MHz) C–V characteristics using the equation Cox = eie0A/d, where Cox is the capacitance of the interfacial layer, ei = 7e0, es = 11.8e0 [1] and e0 are the permittivity of the interfacial layer, semiconductor and free space, respectively. The values of interface states NSS with and without taking into account the Rs were obtained as a function of (Ec  Ess) and are given in Fig. 7. From Fig. 7 for all temperature, it is seen an exponential increase in the interface state density from midgap towards the bottom of conductance band. We have observed then that the values of NSS increases with decreasing temperature. This case is a result of molecular restructuring and reordering of the metal–semiconductor interface under the effect of temperature [41].

Barrier height,

Ec  Ess ¼ qðUe  V Þ

0.35

Ec-Ess (eV)

Fig. 6. Temperature dependence of series resistance obtained from the experimental forward bias I–V characteristics of the Au/SnO2/n-Si (MIS) Schottky diode.

  d es nðV Þ ¼ 1 þ þ qN SS ðV Þ ei W D

0.25

0.6

0.5

0.4

0.3

0.2 2

2.5

3

3.5

4

4.5

5

5.5

Ideality factor,n Fig. 8. The zero-bias apparent barrier height vs ideality factor for the Au/ SnO2/n-Si (MIS) Schottky diode.

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

where Uap and nap are the apparent barrier height and apparent ideality factor, respectively. The assumption of the Gaussian distribution for the BH yields the following equation for the barrier height [5,31] Uap ¼ UB0 

qr20 2kT

 ¼ q2 

qq3 2kT

ð19Þ

It is assumed that the mean SBH UB and rs are linearly bias dependent on Gaussian parameters such that UB ¼ UB0  q2 V and standard deviation rs = rso + q3V, which may depend on temperature and quantify the voltage deformation of the BH distribution. The temperature dependence of rs is usually small and can be neglected [12]. From Fig. 9, the apparent BH Uap vs q/2kT plot should produce a straight line that gives the intercept UB0 ðT ¼ 0Þ and the slope r20 . The values of UB0 ðT ¼ 0Þ and r0 are 1.101 eV, 0.158 V, respectively. Clearly, the diode with the best rectifying performance presents the best barrier homogeneity with the lower value of standard deviation. It was seen that the value of r0 = 0.158 V is not small compared to the mean value of UB0 ¼ 1:101 eV, and it indicates the presence of the interface inhomogeneities. Nevertheless, this inhomogeneity and potential fluctuation cause dramatically affects on low temperature I–V characteristics. Again, the (1/nap  1) vs q/2kT plot should be a straight line that gives voltage coefficient q2 and q3 from the intercept and slope, respectively (Fig. 9). The values of q2 =  0.337 V and q3 = 0.0167 were obtained from the experimental plot. The linear behavior of this plot demonstrates that the ideality factor does indeed express the voltage deformation of the Gaussian distribution of the SBH. Now, combining Eqs. (17) and (18), we get:    2 2 I0 q r0 qUB0 ln ð20Þ  ¼ lnðAA Þ  2 2 kT T2 2k T The plot of a modified ln(I 0 =T 2 Þ  q2 r20 =2k 2 T 2 vs q/kT plot according to Eq. (20) should give a straight line with the slope directly yielding the mean UB0 and the intercept -0.35

0.9 16.6

17.3

18.4

19.7

29.0 -0.4

0.8 -0.45 0.7

Bo

= (1.101+0.025(q/2kT) ) eV

-0.5 -0.55

0.6

-0.6 0.5

-0.65 -0.7

0.4

-0.75 0.3

-1

(n -1) = (-0.337+0.0167(q/2kT) )

ð18Þ

where UB0 is the mean SBH at zero bias and extrapolated towards zero temperature, r0 is the standard deviation at zero bias. In the ideal case (n = 1), the expression is obtained as following suggested by [5,42]

23.2

(n-1-1)

where I(UB, V) is the current at a bias V for a SBH based on ideal thermionic emission diffusion (TED) theory. Here the implicit assumption is that there exist a number of parallel diodes of different SBH, contributing to the current independently. The mean SBH and a standard deviation may be both bias and temperature dependent. The temperature dependence of SBH is approximately linear in the temperature range being measured [20] and the temperature dependence of rs is usually small and can be neglected [32]. Now, taking integration from 1 to +1, the current I(V) through a Schottky barrier at a forward bias V has a similar form Eqs. (1) and (2). But with the modified BH, we get    q  qr2 UB  S IðV Þ ¼ AA T 2 exp  ð16Þ kT 2kT     qV qV 1  exp  exp nap kT kT   qUap with I 0 ¼ AA T 2 exp  ð17Þ kT

1 1 nap

(eV)

1



Bo

squares fit to the experimental data. As can be seen from Fig. 8, there is linear relationship between the experimental effective BHs and the ideality factors of the Schottky contact that was explained by lateral inhomogeneities of the BHs in the Schottky diodes [12,20,37]. The extrapolation of the experimental BHs vs ideality factors plot to n = 1 has given a homogeneous BH of approximately 0.856 eV. Thus, it can be said that the significant decrease of the zero-bias BH and increase of the ideality factor especially at low temperature are possible caused by the BH inhomogeneities. The above abnormal behaviors can be explained by assuming a Gaussian distribution of BH with a mean value  B0 and a standard deviation rs, which can be given by of U [1,7,9–12,17] ! 2 1 ðUB  UB Þ P ðUB Þ ¼ pffiffiffiffiffiffi exp  ð14Þ 2r2S rS 2p pffiffiffiffiffiffi where 1/ rS 2p stands for the normalization constant of the Gaussian barrier height distribution. The total current through the SB at the forward bias then becomes Z þ1 IðV Þ ¼ IðUB ; V ÞP ðUB ÞdU ð15Þ

947

-0.8 -0.85

0.2

q/2kT (eV -1) Fig. 9. The zero-bias apparent barrier height and ideality factor vs 1/T curves for the Au/SnO2/n-Si (MIS) Schottky diode according to Gaussian distribution.

¨ zer et al. / Solid-State Electronics 51 (2007) 941–949 M. O

948

Ln(I o / T 2 ) - (q 2

2 2 2 o /2 k T )

( A. K - 2 )

-30 -35 -40 -45 -50 -55

y = -1.116x + 1.39

-60 -65 -70 30

35

40

45

q/kT (eV -1)

50

55

60

Fig. 10. Modified Richardson ln(I0/T2)  q2 r20 /2k2T2 vs 1/T plot for the Au/SnO2/n-Si (MIS) Schottky diode according to Gaussian distribution of the barrier heights.

(=lnAA*) at the ordinate determining A* for a given diode area A. In Fig. 10, the modified ln(I 0 =T 2 Þ  q2 r20 =2k 2 T 2 vs q/kT plot gives UB0 and A* as 1.116 eV and 127.86 A/ cm2 K2, respectively. As can be seen, the value of UB0 ðT ¼ 0Þ ¼ 1:116 eV from this plot is in close agreement with the value of UB0 ðT ¼ 0Þ ¼ 1:101 eV from the plot of Uap vs q/2kT. Also the Richardson constant value 127.86 A/cm2 K2 obtained from ln(I 0 =T 2 Þ  q2 r20 =2k 2 T 2 vs q/kT plot is much closer to theoretical value of 120 A/ cm2 K2 than the values of Amodified obtained earlier.

in an empirical manner by introducing the so-called T0 and n0 parameters, with an optimum value here of 1253 K and 1.122, respectively. Also, the ideality factor n and series resistance Rs were found to be strongly temperature dependent and changed linearly with the inverse temperature. It is shown that series resistance values decreased with increasing temperature; the changes being quite important at high voltages and at low temperature ranges. In order to obtain evidence of a Gaussian distribution of the BHs, we have drawn a UB0 vs q/2kT plot, and the values of UB0 ¼ 1:101 eV and r0 = 0.158 V for the mean barrier height and standard deviation at zero-bias. After then the values of rB0 and A* were obtained from a modified ln(I 0 =T 2 Þ  q2 r20 =2k 2 T 2 vs q/kT plot as 1.116 eV and 127.86 A/cm2 K2, respectively. This value of the Richardson constant 127.86 A/cm2 K2 is very close to the theoretical value of 120 A/cm2 K2. From the above results it is suggested that the forward bias I–V characteristics of Au/ SnO2/n-Si (MIS) Schottky diode in the temperature range of 200–350 K can be satisfactorily interpreted on the basis of the thermionic-emission (TE) mechanism with Gaussian distribution of barrier heights. Acknowledgement This work is partly supported by Turkish of Prime Ministry State Planning Organization Project Number 2001K120590 and Gazi University Scientific Research Project (BAP)-FEF.05/2005/53.

4. Conclusion

References

The current conduction mechanism across Au/SnO2/nSi (MIS) Schottky diode have been investigated using forward bias I–V measured in the temperature range of 200– 350 K. It is found that while the zero-bias barrier height UB0(I–V) increases, the ideality factor n decreases with increasing temperature. Therefore, for these Schottky diodes, the usual activation energy plot of ln(I0/T2) vs 1/ T in accordance with the thermionic emission (TE) do not give a straight line due to the temperature dependence of n and UB(I–V). In addition, there is a consistent disagreement between the values of barrier height UB(I–V) obtained from forward bias I–V characteristics. It is concluded that a better result has been possible simply by including the ideality factor n in the expression for reverse bias saturation current I0. The non-ideal forward bias I–V behavior observed in the Au/SnO2/n-Si (MIS) Schottky diodes was attributed to a change in the metal–semiconductor barrier height due to the interfacial layer, interfaces states and series resistance. The UBef, a fundamental parameter of the Schottky barrier which eliminates the effects of image force lowering, is calculated from I–V–T data to be UBef(T = 0) = 0.686 eV with a negative temperature coefficient, a = 3.64 · 104 eV K1. The curvature of the basic Richardson plot may be substantially remedied

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