Temperature dependence of current–voltage characteristics

of Ag/p-SnS Schottky barrier diodes

Mehmet Sahina,*, Haluk Safaka, Nihat Tugluoglub, Serdar Karadenizb

aDepartment of Physics, Faculty of Sciences and Arts, Selcuk University, Kampus, Konya 42031, TurkeybDepartment of Materials Research, Ankara Nuclear Research and Training Center,

Besevler, Ankara 06100, Turkey

Received in revised form 3 September 2004; accepted 4 September 2004

Available online 12 October 2004

www.elsevier.com/locate/apsusc

Applied Surface Science 242 (2005) 412–418

Abstract

The current–voltage (I–V) measurements on Ag/p-SnS Schottky barrier diodes in the temperature range 100–300 K were

carried out. It has been found that all contacts are of Schottky type. The ideality factor and the apparent barrier height calculated

by using thermionic emission (TE) theory were found to be strongly temperature dependent. The I–V curves is fitted by the

equation based on thermionic emission theory, but the zero-bias barrier height (FB0) decreases and the ideality factor (n)

increases with decreasing temperature. The conventional Richardson plot exhibits non-linearity below 200 K with the linear

portion corresponding to activation energy of 0.32 eV. It is shown that the values of Rs estimated from Cheung’s method were

strongly temperature dependent and decreased with increasing temperature. From the reverse-bias I–V graphs, it is found that the

experimental carrier density (NA) values increased with increasing temperature.

# 2004 Elsevier B.V. All rights reserved.

PACS: 73.30.+y; 73.40.Qv

Keywords: Schottky barrier diode; IV–VI layered semiconductor compounds; I–V characteristics

1. Introduction

Tin sulphide (SnS) has attracted considerable

attention in recent years due to the possibility of its

application in photovoltaic devices. It has an optical

* Corresponding author. Tel.: +90 332 223 2598;

fax: +90 332 241 0106.

E-mail address: sahinm@selcuk.edu.tr, m.sahin@lycos.com

(M. Sahin).

0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved

doi:10.1016/j.apsusc.2004.09.017

band gap of 1.3 eV [1,2] with a high-light absorption

coefficient (>104 cm�1). Tin sulphide is a IV–VI

compounds whose constituent elements are abundant

in nature. It crystallizes in an orthorhombic structure

as a deformed sodium chloride structure and is a

layered material [3,4] that presents interesting semi-

conducting properties. SnS single crystals obtained by

Bridgman method exhibits p-type conductivity with

controllable electrical properties [5]. The SnS stru-

cture can be described, along the c-axis, as composed

.

M. Sahin et al. / Applied Surface Science 242 (2005) 412–418 413

of double layers of Sn and S atoms tightly bound,

while the binding between layers is of the van der

Walls type. This layer type character gives rise to

perfect cleavage along the {0 0 1} plane [4]. Its

electrical and optical characteristics have been

reported in several studies [1–15]. Thin films of

SnS have been also prepared by different techniques in

[6–12]. Although the structural, electrical, optical

absorption and photoelectric properties have been

widely investigated [1–15], it has been seen only

one study on the metal/p-SnS Schottky diodes [15].

In contrast to other layered semiconductors, to our

knowledge, the current–voltage characteristic para-

meters of metal/p-SnS Schottky barrier diodes in

the wide temperature range have not yet been reported.

Schottky diodes with low barrier height have found

applications in devices operating at cryogenic tempera-

tures as infrared detectors and sensors in thermal

imaging [15–27]. Therefore, analysis of I–V character-

istics of the Schottky barrier diodes only at room

temperature does not give detailed information about

their conduction process or the nature of barrier form-

ation at the MS interface. The temperature dependence

of the I–V characteristics allows us to understand

different aspects of conduction mechanisms. The I–V

characteristics of the Schottky barrier diodes usually

deviate from the ideal TE current model [18–27].

Generally, the ideality factor n was found to increase,

while the Schottky barrier height FB0 decreases, with

decreasing temperature [18–27]. The decrease in the

barrier height at low temperatures leads to non-linearity

in the activation energy ln(I0/T2) versus 1/T plot. In this

paper, for the first time, we report an investigation of the

temperature dependence of current–voltage character-

istics of Ag/p-SnS Schottky barrier diodes in the

temperature range of 100–300 K. The temperature

dependenceof the barrierheightand the ideality factor is

discussed using thermionic emission theory.

2. Experimental procedure

In this work, single crystals of SnS were grown by

Bridgman–Stockbarger technique and detailed infor-

mation about this preparing procedure given in Ref.

[13]. The sample prepared has been shown p-type

behaviour and the carrier density determined has been

reported as nearly 1017 to 1019 cm�3 in the temperature

range of 77–600 K. The samples used for current–

voltage measurements were obtained by cleavage along

{0 0 1} planes. The a and b crystallographic axes are

contained in the plane of cleavage. The cleavage

surfaces were mirror-like. The samples having about

4 mm� 4 mm area and 100–300 mm thickness were cut

from the freshly cleaved sheets with a razor blade (no

further polishing or cleaning treatments were required

because of the natural mirror-like cleavage faces of the

samples) and inserted into the deposition chamber

immediately. It is stated that In back contact exhibits

low resistance ohmic contact by Merdan [13]. Ohmic

contacts of low resistance on the backside of the

samples were formed by evaporating 2500 A thick

indium (In, 99.999%) followed by a temperature

treatment at 150 8C for 2 min in nitrogen atmosphere.

The Schottky contacts were formed on the other faces

by evaporating 2000 A thick silver (Ag, 99.999%) as

dots with diameters of about 1.0 mm. The evaporating

process was carried out in a vacuum-coating unit at

1 � 10�7 Torr. Metal layer thickness as well as the

deposition rates were monitored with the help of a

digital quartz crystal thickness monitor. The deposition

rates were about 5–10 A/s.

The I–V characteristics of the Ag/p-SnS Schottky

barrier diodes were studied in the temperature range of

100–300 K in the dark by using temperature con-

trolled Janes 475 cryostat. The I–V measurements

were performed by the use of a Keithley 220

programmable constant current source, a Keithley

614 electrometer. The device temperature was con-

trolled within an accuracy of �0.2 K by a Lakeshore

321 model temperature controller.

3. Results and discussion

The diode parameters are determined from the

forward bias current–voltage characteristics, which is

usually described within the thermionic emission

theory [17]:

I ¼ I0 expqV

nkT

� �1 � exp � qV

kT

� �� �(1)

where

I0 ¼ AA�T2 exp � qFB0

kT

� �(2)

M. Sahin et al. / Applied Surface Science 242 (2005) 412–418414

Fig. 1. Experimental forward-bias current–voltage characteristics

of Ag/p-SnS Schottky barrier diode in the temperature range of 100–

300 K.

Table 1

The experimentally obtained characteristic parameters of Ag/p-SnS

Schottky barrier diodes in the temperature range of 100–300 K

T (K) n FB0 (eV) Rs (V) NA (cm�3)

100 5.20 0.158 96.6 1.88 � 1018

125 4.23 0.241 76.4 2.67 � 1018

150 3.59 0.307 56.4 5.70 � 1018

175 3.27 0.360 45.5 1.32 � 1019

200 3.05 0.392 38.2 2.69 � 1019

225 2.83 0.424 34.6 3.60 � 1019

250 2.67 0.455 32.9 4.62 � 1019

275 2.58 0.473 31.1 6.96 � 1019

300 2.53 0.484 29.4 8.91 � 1019

is the saturation current derived from the straight line

intercept of semi-log forward I–V plot at V = 0, V the

forward-bias voltage, T the absolute temperature, q the

electronic charge, k the Boltzmann constant, A the

effective diode area, A* = 4pqm*k2/h3 the effective

Richardson constant of 24 A cm�2 K�2 for p-SnS,

where m* = 0.20m0 [28] the effective mass for the

holes perpendicular to the layer plane, FB0 the appar-

ent barrier height, and n is the ideality factor and is a

measure of conformity of the diode to pure thermionic

emission and it is determined from the slope of the

straight line region of the forward bias I–V character-

istics through the relation:

n ¼ q

kT

dV

dðln IÞ (3)

In the usual analyses of the experimental data on

Schottky contacts, the barrier height is determined

from the extrapolated . The apparent barrier height

FB0 is given by

FB0 ¼ kT

q

� �ln

AA�T2

I0

� �(4)

14 dots (Schottky contact) on the same semiconductor

surface were performed for the Ag/p-SnS Schottky

barrier diodes. The variation of calculated parameters

is almost same with each other. We have introduced

only one diode in the different temperatures in this

paper. Fig. 1 shows the forward bias semi-log I–V

characteristics one of the Ag/p-SnS Schottky barrier

diodes in the temperature range of 100–300 K. The I0

was obtained by extrapolating the linear region of

these curves to V = 0 at each temperature and the FB0

values were calculated from Eq. (4). The values of

ideality factor n were also obtained from the slope of

linear region of semi-log forward I–V characteristics

according to Eq. (3). The change in n and FB0 with

temperatures is presented in Table 1. The experimental

values of n (denoted by closed circles) and FB0

(denoted by open circles) are also plotted as a function

of temperature in Fig. 2. As seen in Table 1 and Fig. 2,

the FB0 and n determined from semi-log forward I–V

plots were found to be a strong function of tempera-

ture. The ideality factor n was found to increase, while

the FB0 decrease with decreasing temperature. As

explained in [21–27], since current transport across

the metal/semiconductor (MS) interface is a tempera-

ture-activated process; electrons at low temperatures

are able to surmount the lower barriers and therefore

the current transport will be dominated by current

flowing through the patches of lower Schottky barrier

height and a larger ideality factor. As the temperature

increases, more and more electrons have sufficient

energy to surmount the higher barrier. As a result, the

dominant barrier height will increase with the tem-

perature and bias voltage. 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

M. Sahin et al. / Applied Surface Science 242 (2005) 412–418 415

Fig. 2. Temperature dependence of the ideality factor and zero-bias

apparent barrier height for Ag/p-SnS Schottky barrier diode in the

temperature range of 100–300 K.

Fig. 3. Zero-bias apparent barrier height vs. ideality factor of

Ag/p-SnS Schottky diode at various temperatures.

Fig. 4. Richardson plots of ln(I0/T2) vs. 103/T or 103/nT for Ag/p-

SnS Schottky diode.

non-uniformity of the interfacial charges. This gives

rise to an extra current such that the overall character-

istics still remains consistent with the TE process [27].

According to [23–26], the ideality factor of

Schottky barrier diode with a distribution of low

Schottky barrier heights may increase with a decrease

in temperature. Schmitsdorf et al. [26] used Tung’s

theoretical approach and they found a linear correla-

tion between the experimental zero-bias Schottky

barrier heights and the ideality factors. We prepared a

plot of the experimental barrier height versus the

ideality factor (Fig. 3). The straight line in Fig. 3 is the

least squares fit to the experimental data. As can be

seen from this figure, there is a linear relationship

between the experimental effective barrier heights and

the ideality factors of the Schottky contact. The extr-

apolation of the experimental barrier heights versus

ideality factor plot to n = 1 has given a homogeneous

barrier height of approximately 0.65 eV.

To determine the barrier height in another way,

Eq. (2) can be rewritten as

lnI0

T2

� �¼ ln ðAA�Þ � qFB0

kT(5)

The Richardson constant is usually determined from

the intercept of ln(I0/T2) versus 1000/T plot. Fig. 4

shows the conventional energy variation of ln(I0/T2)

against 103/T or 103/nT. The dependence of ln(I0/T2)

versus 1000/T is found to be non-linear in the tem-

perature measured; however, the dependence of ln

(I0/T2) versus 103/nT gives a straight line. The non-

M. Sahin et al. / Applied Surface Science 242 (2005) 412–418416

Fig. 6. Temperature dependence of the series resistance from the

experimental forward bias current–voltage characteristics of Ag/p-

SnS Schottky barrier diode.

linearity of the conventional ln(I0/T2) versus 103/T is

caused by the temperature dependence of the barrier

height and ideality factor. Similar results have also

been reported by several authors [21–27]. In addition,

it is impossible to fit the experimental data. The

experimental data are shown to fit asymptotically with

a straight line at higher temperatures only, yielding a

Richardson constant (A*) of 2.02 � 10�6 A cm�2

K�2, which is much lower than the known value of

24 A cm�2 K�2 for holes in p-SnS [28]. Moreover, if

ln(I0/T2) is plotted against 103/nT, straight line is

obtained with a slope giving an activation energy of

0.32 eV, as shown in Fig. 4. A value of 4.73 �10�5 A cm�2 K�2 for Richardson constant was obta-

ined from ln(I0/T2) versus 103/nT plot.

The high values of the ideality factor show that

there is a deviation from TE theory for current mech-

anism. The increase in ideality factor with decreasing

temperature is known as T0 effect [29]. As shown in

Fig. 5, n was found to be inversely proportional with

temperature as

nðTÞ ¼ n0 þT0

T(6)

where the n0 and T0 are constants which were found to

be 1.08 and 398 K, respectively.

Fig. 6 shows the experimental series resistance

values from forward-bias I–V characteristics as a

Fig. 5. Temperature dependence of the ideality factor for Ag/p-SnS

Schottky barrier diode in the temperature range of 100–300 K.

function of temperature. The values of series

resistance Rs have been also obtained using a method

developed by Cheung and Cheung [30]. The series

resistance values range from 29.4 V at 300 K to

96.6 V at 100 K. The increase of Rs with the fall of

temperature is believed to appear from the factors

responsible for increase of n and/or lack of free carrier

concentration at low temperatures [23].

On the other hand, if reverse-bias case is

considered, the main effect is the lowering of Schottky

barrier height with the applied voltage [16]. In this

case the reverse-current expression can be written as

IR ¼ I0 expq

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqE=4pes

pkT

" #(7)

with I0 being the same as above (Eq. (2)). Here, the E

quantity is defined as [16]

E ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2qNA

esV þ Vbi �

kT

q

� �s(8)

where es is dielectric constant, es = 14e0 for p-SnS [13–

15]. NA is the acceptor concentration in p-type semi-

conductor (ND for n-type material) and Vbi is the built-

in potential. In the case of V þ Vbi kT=q, reverse

M. Sahin et al. / Applied Surface Science 242 (2005) 412–418 417

Fig. 7. The variation of reverse current log(IR) with V1=4eff for

Ag/p-SnS structure. By means of these curves, a parameter were

determined.

current expression might be given approximately as

IR ffi I0 exp ½aðV þ VbiÞ1=4� (9)

Here a parameter is defined as follows [15]:

a ¼ q

kT

q

4pes

� �1=22qNA

es

� �1=4

(10)

Vbi, built-in potential for any contact can be deter-

mined by means of the variation of ln(I) with the

inverse temperature, 1/T. Therefore, an effective

potential, Veff = V + Vbi can be introduced and the

reverse-bias current density might be written as

IR ¼ I0 exp ½aV1=4eff � (11)

Thus, the a parameter in the above equation, and

hence NA carrier densities can be estimated by plotting

the ln ðIRÞ � V1=4eff graph, which were given in Fig. 7.

The a parameters found by slopes of curves for each

temperature were shown on relevant figure. The values

of NA concentrations obtained by the a values by

means of Eq. (10) are listed in Table 1 for Ag/p-

SnS Schottky barrier diode. The carrier density values

were found in agreement with these given in Refs.

[13,15].

4. Conclusions

The I–V characteristics of Ag/p-SnS Schottky

barrier diode have been measured over the tempera-

ture range of 100–300 K. While the zero-bias barrier

height FB0 decreases, the ideality factor n increases

with decrease in temperature, the changes are quite

significant at low temperatures. The non-ideal forward

bias I–V behaviour observed in the Ag/p-SnS Schottky

diode was attributed to a change in the metal-

semiconductor barrier height due to the interface

states and the series resistance. Therefore, the

concavity of the forward bias I–V characteristics

increases with increasing series resistance value. It is

shown that the series resistance value decreased as the

temperature is increased. The conventional Richard-

son plot, ln(I0/T2) versus 103/T, shows a deviation from

linearity at low temperatures. However, the depen-

dence of ln(I0/T2) versus 103/nT gives a straight line.

The zero-bias barrier height of Ag/p-SnS Schottky

barrier diode at the absolute zero is found to be

0.32 eV. A value of 4.73 � 10�5 A cm�2 K�2 was

obtained for the Richardson constant from this plot.

The significant decrease of the zero-bias barrier height

and increase of the ideality factor at low temperatures

cannot be caused by a process such as tunneling and

image force lowering effects. Moreover, the carrier

density values were found in agreement with those

given in the literature for p-SnS. It has been found that

all contacts are of Schottky type.

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