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Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode
Accepted Manuscript Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode
R.K. Mamedov, A.R. Aslanova PII:
S0749-6036(18)30526-3
DOI:
10.1016/j.spmi.2018.04.034
Reference:
YSPMI 5648
To appear in:
Superlattices and Microstructures
Received Date:
15 March 2018
Accepted Date:
16 April 2018
Please cite this article as: R.K. Mamedov, A.R. Aslanova, Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode, Superlattices and Microstructures (2018), doi: 10.1016/j.spmi.2018.04.034
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ACCEPTED MANUSCRIPT Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode R.K. Mamedov*, A.R. Aslanova The Baku State University, Az 1148, Baku, Azerbaijan E-mail: [email protected]
Abstract. The trench MOS barrier Schottky diode (TMBS diode) under the influence of the voltage drop of the additional electric field (AEF) appearing in the near-contact region of the semiconductor are in a nonequilibrium state and their closed external circuit flows currents in the absence of an external voltage. When an external voltage is applied to the TMBS diode, the current transmission is described by the thermionic emission theory with a specific feature. Both forward and reverse I-V characteristics of the TMBS diode consist of two parts. In the initial first part of the forward I-V characteristic there are no forward currents, but reverse saturation currents flow, in its subsequent second part the currents increase exponentially with the voltage. In the initial first part of the reverse I-V characteristic, the currents increase in an abrupt way and in the subsequent second part the saturation currents flow under the action of the image force. The mathematical expressions for forward and reverse I-V characteristic of the TMBS diode and also narrow or nanostructure Schottky diode are proposed, which are in good agreement with the results of experimental and calculated I-V characteristics. Key words: TMBS diode, metal-semiconductor contact, Schottky diode, additional electric field, nonequilibrium SD, power diodes.
1. Introduction In connection with the development of modern measurement technology, especially scanning probe microscopy, there has been a growing interest in the study of electronic processes occurring in real Schottky diodes (SD), whose important electrophysical properties deviate in many real cases from the corresponding theoretical positions of idealized physical models and theories by Schottky, Bethe et al. [1-6]. The Schottky contacts (SC), i.e. the direct metal-semiconductor contacts (MSC) possessing either rectifier and ohmic properties, according to the Schottky model are characterized by the potential barrier height in the near-contact region of the semiconductor formed under the action of the electrostatic field of the contact potential difference of the contacting unlimited homogeneous surfaces of the metal and semiconductor [1,4 ]. As a result of comprehensive, intensive and systematic theoretical and experimental studies of instrumental characteristics and parameters of real MSC, it is established that many deviations between properties, parameters of real and ideal Schottky diodes (SD) are uniquely interpreted by the occurrence of an additional electric field (AEF) in real MSC [6,7]. A real SC has the contact surface with the potential barrier height of about 1 eV, limited to it adjacent free surfaces of the metal and semiconductor with a work function of the order of 4-6 eV. The presence of a potential difference between the contact surface and the free surfaces of the contacting materials causes the occurrence of the AEF around the contact [6-11]. The AEF intensity is quite commensurate with the electric field intensity of idealized SD and it is directed from the contact surface to the free surfaces of metal and semiconductor, covering the peripheral near-contact region. Under the action of the AEF, a rather wide transition region (aureole) is formed on the semiconductor surface around the contact, where the surface potential differs from the surface potentials of the metal and the semiconductor by the magnitude of their difference. The previously established AEF in real SC with such indirect methods as electrophysical, thermionic, constructive-technological [6], in recent years directly measured by Scanning Probe Microscopy [12-16]. In Ref.[13], the direct measurement of the AEF by the AFM method on the surface Au-nGaAs SC with different diameters (5-100 μ) was carried out. It is obtained that under the influence of AEF an expanded transition region (aureole) is formed along the entire perimeter of the contact with the potential, differing by 0.5-0.6 V from the potential of the free surface of nGaAs. As the contact diameter increases from 5 μ to 50 μ, the width of the aureole around the contact increases from 4 μ to 23 μ and then, with an increase in diameter to 100 μ, the width of the aureole remains almost unchanged. In Ref.[14] it was shown that under the influence of the AEF around Au - nGaAs SC with a rectangular
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contact surface the aureole with the potential different from the potential of the free surface nGaAs is formed and the width of the aureole along the rectilinear edge line of a metal with a large area reaches about 30 μ. An AFM study of two-dimensional (x, y) and one-dimensional (x) distributions of electrostatic potentials and electrostatic fields of the Au-nGaAs SC with different contact surface shape was carried out in Ref. [12]. It is established that the character of the distribution of the potential and the AEF intensity of the SC depend significantly on the geometric configurations and contact dimensions. The results of the AFM measurement of the two-dimensional and one-dimensional potential distribution and the AEF intensity of the SC with a rectangular (20 × 40 μ2) contact form are shown in Fig. 1a and b, respectively. It can be seen from the figures that the aureole with a thickness of about l m* 2 = 30μ is formed around the gold contact. The surface potential and the AEF intensity along the periphery of the contact have the maximum values and they decrease along the width of the aureole.
a)
b)
Fig.1. AFM images of two-dimensional (a) and one-dimensional (b) surface potential distributions (work function qφ-solid curve 1) and field intensity E * (dashed curve 2) of Au-nGaAs rectangular Schottky contact with dimensions 20 × 40 μ2.
Unlike other geometric configurations of SD, the TMBS diode structure widely used in modern power electronics [17-19], the AEF as a whole is formed in the near-contact region of the semiconductor. The TMBS diode has a structure consisting of a number of narrow bars (sections) of Schottky barriers (mesa diodes) of micron or submicron width, separated by trenches. The Schottky barrier in such structure is created on the planar surface of a part of the semiconductor between the trenches in which the MOS (metal-oxide-semiconductor) structure is formed on the side walls with a metal electrode located inside the trenches and connected to the barrier metal. In this case, due to the contact potential difference between the contact surface and adjacent to it free surfaces of the metal and the semiconductor, the AEF arises in the mesa region of the semiconductor. As a result of fundamental studies [20-26] of electrophysical properties of the TMBS diode, a number of effects were established (the nonlinearity of the dependence of the electric field intensity along the perpendicular line to the metal surface in the SCR, the strong decrease of the electric field intensity on the metal surface and the appearance of the electric field peak at a large distance from the interface into the SCR, the increase in the peak shift from the surface with increasing depth of the trench, the decrease in the potential barrier height and at the same time the decrease leakage, abrupt occurrence of reverse current with increasing voltage, does not match the saturation currents in the forward and reverse directions, the lack of forward current at initial voltages, etc.) which are difficult to be explained by classical theories and models of the SD. The results of investigations of the features of the AEF in the TMBS diode show that taking into account the influence of the AEF on electronic processes in the SCR makes a definite contribution to a clear understanding of these effects.
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The AEF in the TMBS diode is formed completely in the near-contact region of the semiconductor and extends over a sufficiently large distance from the contact surface into the interior of the semiconductor [9, 27, 28]. Under the action of the AEF, the free electrons of the semiconductor accumulate on the contact surface of the metal and in the near-contact region of the semiconductor the SCR is formed from the positive impurity ions. The metal is charged negatively, and the n-type semiconductor is positive, therefore, there are potential differences between them, i.e. voltage drop, and the real SD under this voltage is in a nonequilibrium state. Such a specific feature of SD with AEF, which is of great scientific and practical importance, is practically not covered in the literature. In this paper, we present the results of the investigation of the features of the current flow in the nonequilibrium TMBS diode with an additional electric field. 2. Nonequilibrium state of the Schottky contacts 2.1. Formation of the Schottky barrier In ideal SC with an unlimited homogeneous contact surface, according to the Schottky model [1], when direct contact of the contacting surfaces of the metal and the n-type semiconductor with different work functions (ФM and ФS) due to their contact potential difference, a redistribution of free electrons occurs in the near-contact region and this continues before the establishment of thermodynamic equilibrium state. The schematic structure of one section of the TMBS diode at thermodynamic equilibrium state is shown in Fig. 2a, where ФM > ФS and is formed the potential barrier height ФВ and the contact has a rectifying property. In this case, a depletion layer with thickness d is formed in the near-contact region of the semiconductor, in which the electric field intensity Ed has a maximum on the contact surface of the metal and linearly decreases to zero at a distance d along the line ox perpendicular to the interface (Fig. 2b). The energy structure of the TMBS diode according to the Schottky model acquires the form, as shown schematically in Fig. 2c. According to the thermionic emission theory [1], in the equilibrium state of the SD with the potential barrier height ФB, the saturation currents IS in opposite directions flowing through the interface are equal in modulus, which are described by the formula: (1) I S SAT 2 exp kT Here, S - is the contact area, A - is the Richardson constant, T- is the absolute temperature, k - is the Boltzman constant. When an external voltage U is applied, the SD goes out of equilibrium state and the current flowing through the contact in the forward direction (+ U) becomes larger than the flow in the reverse direction (-U) and the I-V characteristic of the SD is determined by the formula: qU I SAT 2 exp exp 1 kT kT
(2)
where, the change in the barrier height ΔФB of the SD under the action of the mirror image force is determined by the formula: 1/ 4 q 3 N D kT (3) B q 2 3 U D U q 8 S Here, ND -is the impurity concentration in the semiconductor, s - is the dielectric constant of the semiconductor, q - is the electron charge, UD – is the diffusion potential, the signs (+) and (-) correspond to the forward and reverse directions, respectively.
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Unlike an ideal SD, real SD are not in a thermodynamic equilibrium state in the absence of an external voltage, but are in a more or less nonequilibrium state under the action of the AEF in them [27, 28]. 2.2. Nonequilibrium state of the real Schottky diode In real SD having certain construction structures, the contact potential difference arises not only between the contact surface of the contacting metal and the semiconductor, but also between the contact surface with the ФB (where, ФВ=ФM – ФS) and the adjacent free surfaces of the metal with ФM and semiconductor with ФS. Because of this, the AEF is formed, encompassing the near-contact region of the semiconductor and directed from the contact surface to the free surfaces of the metal and semiconductor [6-16]. Under the action of the AEF in the near-contact region of a semiconductor, free electrons move to the contact surface of the metal and a certain amount of positive charges accumulate, in the depth of the semiconductor. Consequently, real SD with any constructive structure, including TMBS diode, are in a nonequilibrium state under the action of the voltage arising due to the AEF. ФM
ФВ
D
ФS
E
n+
∆ФB
Ed
o
d
FM
FS
xm
b) E
EA
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + +
d)
x
d
a)
m
FC
ФB
+ + + + + + + + + + + + + + + + + + ++ + + + + + + +
R
c) El Er
s
ФB
xm
o
lo
x
UC
FM
xm
EA
e)
l
FS
f)
Fig.2. Schematic representation of one section of a TMBS diode without AEF (a) and with AEF (d) in the absence of an external voltage; the distribution of the intensity Ed without AEF (b) and El, EA, Er with AEF (e); energy diagrams without AEF (c) and with AEF (f).
In the TMBS diode, the AEF completely concentrates in the near-contact region of the semiconductor and its propagation space is limited by the contact surface with the potential barrier height ФB and the internal surfaces of the metal electrodes with the work function ФM of the MOS structure in the trenches (Fig. 2d). In the near-contact region of an n-type semiconductor, under the action of the AEF with the intensity EA, the SCR is formed with an electric field intensity El directed to the contact surface of the metal. The width of SCR is commensurable with the depth lo of the trench (Fig.2e). In the SCR, the horizontal components of the AEF intensities directed oppositely compensate each other and the vertical components EA become effective. The EA of AEF and EI SCR along the axis ox are directed in the opposite, they have the maximum values at the origin of the axis on the contact surface of the metal and decrease with increasing distance x. As a result of the superposition of electric
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fields with the intensities EA and EI, the resulting electric field (REF) with the intensity Er in the SCR is formed. The dependence of Er on the distance x is represented by a curve line and it is at the origin of the coordinate of a low value and reaches a maximum at a sufficiently large distance in the depth of the semiconductor. As a result, the metal and semiconductor in the depth of the SCR acquire the potentials φm and φs (where φm <φs). Thus, the SD under the action of the resulting voltage UC due to the AEF becomes in the nonequilibrium state, where: U C s m (4) The potential barrier of the TMBS diode, which is in the nonequilibrium state under the action of a negative voltage (-UC), is formed in accordance with the REF and its energy diagram approximately has the form shown schematically in Fig.1f. In the case of a short-circuit with the wire the ends of the TMBS diode (Fig. 2c, dashed line), an electric current IO arises in the closed external circuit in the absence of an external voltage, that flows through the interface of the contact and is described by the thermionic emission theory:
I O SAT 2 exp(
qU C ) exp( ) 1 kT kT
(5)
2. The current flows in the nonequilibrium TMBS diode The arises of an electric current due to the AEF in the absence of an external voltage in a closed external circuit of a nonequilibrium TMBS diode manifests itself differently in the process of current flows when applying the forward and reverse external voltage. On the one hand, this is due to the fact that the effective component of the EA in the SCR is always directed from the contact surface of the metal to the interior of the semiconductor, and the external electric field intensity E direction depends on its sign. When the forward bias (U> 0) is applied to the TMBS diode, the directions of the E and EA intensities in the SCR are the same (Fig. 3a), and for the reverse bias (U <0) they are directed in the opposite (Fig. 3d). On the other hand, the AEF propagates beyond the width d of the SCR and under its influence a certain amount of free electrons (-Q) at a distance (l-d) accumulate on the contact surface of the metal and as many positive charges (+ Q) in the volume of the semiconductor. Consequently, the depth of the SCR becomes l greater than d, and an electric field intensity El directed to the interface. As a result of superposition of electric fields with EA and EI, the resulting electric field intensity Er and the potential barrier height ФВ are formed. Such characteristic parameters of the TMBS diode as El, Er and ФВ become sensitive to a change in the EA under the action of either structural shapes and dimensions or the applied external voltage. If the forward bias U (plus to the metal) is applied to the nonequilibrium TMBS diode with negative voltage (-UC), the external field intensity E and EA of the AEF in the SCR are directed in parallel (Fig.3a). The potential barrier height for electrons passing from the semiconductor to the metal decreases by qU. And the potential barrier height change due to the influence of the mirror image force increases (Fig. 3b) by the value of ΔФВ (where, ΔФВ = βqU and the proportionality coefficient β << 1). At the same time, the forward I-V characteristic of the TMBS diode according to the thermionic emission theory with allowance for (5) is expressed by the following formula:
I F SAT 2 exp(
qU C qU qU ) exp( ) 1 kT kT
qU C qU qU qU SAT exp( ) exp( ) exp( kT kT kT If, to make the following simple transformations n 1 1 1 1 n1 ; ; n2 n1 1
(6)
2
(7)
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then, the forward I-V characteristic expression is obtained:
I F SAT 2 exp(
Er
EA
E
n qU qU qU ) exp( 1 C ) exp( kT n1kT n2 kT ∆ФB
El
m
s
∆ФB (U-UC)q
ФB FM
(8)
FS
xm
(U-UC)q
ФB
FS
FM
xm
l
U
a) Er
EA
E
b)
0 ≤ /U/ ≤ / UC /
s
∆ФB (-UC+U)q
ФB FM
/U/ > / UC /
c)
∆ФB
El
m
l
FS
xm
(-U+UC)q
ФB FM
xm
l
U
d)
e)
0 ≤ /U/ ≤ / UC /
l
f)
FS
/
Fig.3. Schematic representation of a single section of the TMBS diode with the AEF at forward (a) and reverse (d) voltage; energy diagrams at the voltage of 0 ≤ / U / ≤ / UC / (b, e) and / U /> / UC / (c, f).
It follows from (8) that the forward I-V characteristic of the TMBS diode consists of two parts. When the voltage U is varied in the interval 0≤ /U/ ≤ /UC/ (Fig.3b), the I-V characteristic is determined by the reverse saturation current (mainly with the second summand), and for /U/>/UC/ (Fig. 3c) – by the forward current (mainly with the first summand). If the reverse bias (-U) (minus to the metal) is applied to the nonequilibrium TMBS diode with voltage (-UC), the external field intensity E and EA of the AEF in the SCR are directed in the opposite (Fig. 3d). With an increase in the reverse voltage, the external electric field E partially compensates for EA of the AEF, and consequently, the amount of accumulated charges (Q) and the intensity E1 decrease. The potential barrier height ФВ decrease by ΔФВ too (where, ΔФВ = βr1qU and the βr1 – is coefficient proportionality). In this case, according to the thermionic emission theory, taking into account the formula (5), the first initial part of the reverse I-V characteristic of the TMBS diode in the voltage range 0≤/U/
I R1 SAT 2 exp(
r1qU q (U C U ) ) exp( ) 1 kT kT
q (U C U ) r1qU qU SAT exp( ) exp( ) exp( r1 kT kT kT 2
(9)
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It follows from formula (9) that for a reverse voltage /U/=/UC/, the value of the current becomes zero (IR1 = 0) and the potential barrier height ФВ decreases by the value βr1qUС and becomes the ФВR, where: (10) R r1qU C и r1 R / U C With the reverse bias /U/ > /UC/ (Fig. 3f), the second part of the reverse I-V characteristic of the TMBS diode is expressed by the following formula::
I R 2 SAT 2 exp(
R r 2 qU qU ) exp( ) 1 kT kT
qU r 2 qU qU SAT exp( R ) exp( ) exp( r 2 kT kT kT
(11)
2
If, perform the following transformations for the image force factor r 2 n 1 1 1 nr1 r 2 r1 ; ; nr 2 , nr 1 r2 1 r2 then, the second part of the reverse I-V characteristic is obtained by the expression:
I R 2 SAT 2 exp(
R qU qU ) exp( ) exp( kT nr1kT nr 2 kT
(12)
(13)
Thus, the I-V characteristics of the nonequilibrium TMBS diode, as well as narrow and nanostructured SD in which the AEF completely covers the near-contact region of the semiconductor, both in the forward and reverse directions, consist of two parts, each of which is characterized by its specific feature. 4. Results and discussion From the direct measurements of the AEF of real SD by the AFM methods [5] it follows that it is formed around the contact with any geometric configuration and covers the peripheral near-contact region of the semiconductor. In SD with a sufficiently narrow contact area, the AEF completely covers the near-contact region, and with the TMBS diode structure it completely concentrates in the nearcontact region. In the SD structure with a wider contact area, the AEF covers the peripheral near-contact region and, consequently, the contact edge region becomes in the nonequilibrium state. Therefore, the study of the feature of current flows in the nonequilibrium narrow SD with the same contact area and various geometric configurations made in unified technological conditions is of great interest. The forward and reverse I-V characteristics of Au-nGaAs SD with a contact area of 7854 μ2 and various shapes were prepared by the methods of [14]. A thin gold films of thickness 0.1μ are electrochemically deposited onto the surface of an epitaxial layer 10μ thick and an impurity concentration ND=6.4∙1014 cm-3, grown on the (100) surface of a high-concentration n+GaAs substrate with ND = 2∙1018 cm-3, different shape of the contact surface. Their optical images with indices 1,2,3,4,5 and 6 are shown in Fig.4. The shapes and geometric dimensions of the contacts were: 1 - round with a diameter of 100μ, 2 - square 89х89μ2, rectangular (μ2): 3 - 40х196; 4 - 20x393; 5 - 10x785; 6 Fig.4. Optical image of gold contacts of the same 5x1571. 2 The forward and inverse I-V characteristics of area S = 7854μ by forms: 1 - 2round with a diameter of 100 μ, 2 - square 89х89 μ , rectangular (μ2): 3 Au-nGaAs SD with the different shape of the contact 40х196; 4 - 20x393; 5 - 10x785; 6 - 5x1571. surface are presented on a semilogarithmic scale in
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Fig.5. From this figure it can be seen that the forward I-V characteristic of the SD consists of two parts in accordance with formula (8). In the first initial part of the I-V characteristic of the SD, there are no forward currents (rather small reverse saturation currents are not noted). The subsequent second parts of the I-V characteristic of the SD on a semilogarithmic scale are well described by straight lines with close ideality coefficients (n = 1.05-1.09). This means that the mechanism of current flow in the SD is thermionic emission. The beginning of the straight lines I-V characteristics are shifted from the origin of the U axis by the value /-UC/=/ U if / (where, i = 1,2,3,4,5,6) for SD with different shapes with indices i, respectively. This shows that the currents of the second parts of the I-V characteristic of the SD with the indices i begin to flow after compensation by positive U if of the corresponding negative voltages (-UC) caused by the AEF. Therefore, in order to determine the effective potential barrier height of the SD by formula (8), the saturation currents ISf at zero voltage were determined by extrapolating the straight lines of the IV characteristic to the ordinate axis passing through their initial points, i.e. displaced by the value U if . It should be noted that due to the fact that the initial part of the I-V characteristic of the SD is determined by another formula, the saturation currents ISf can not be determined as shown in Fig. 5, where the differences in the saturation currents iSr would be of incredible great importance. The measured values of the electrophysical parameters UC( U if ), ISf, ФВ, n of the SD and their geometric parameters (diameter D of the circular contact, sides a and b of the rectangular contacts, perimeter P of the contact) are shown in the Table.
Fig.5. The forward If (Uf) and the reverse Ir (Ur) I-V characteristics of Au-nGaAs SD with a contact surface of different shapes: 1 - round with a diameter of 100 μ, 2 - square 89х89 μ2, rectangular (μ2): 3 40х196; 4 - 20x393; 5 - 10x785; 6 - 5x1571.
It can be seen from the Table that with an increase in the contact perimeter from 314 μ to 3158 μ, the effective potential barrier height of the SD decreases by a value of 0.069 eV, the ideality coefficient n increases from 1.05 to 1.09 and the voltage drop of the UC increases from 0.11 V to 0.21 V. This is explained by the fact that as the length P of the contact periphery increases, the contribution of the
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current flowing through the peripheral region, which has a relatively low barrier height due to the AEF, to the common contact current increases.
SD №
Table. axb (μ2)
P (μ)
1. 2. 3. 4. 5. 6.
D=100 89x89 40x196 20x393 10x785 5x1571
314 355 473 825 1591 3158
Geometric and electrophysical parameters of Au-nGaAs Schottky diodes βr1 I n Ф I J Ф U (∆Ufi) sf
(A) 7.0∙10-11 9.0∙10-11 1.0∙10-10 2.0∙10-10 4.0∙10-10 1.0∙10-9
B
1,05 1,06 1,06 1,07 1,08 1,09
(eV) 0.783 0.777 0.774 0.756 0.738 0.714
C
(V) 0.11 0.13 0.14 0.15 0.17 0.21
sr
(A) 3.0∙10-8 4.5∙10-8 5.5∙10-8 8.0∙10-8 1.5∙10-7 2.5∙10-7
lr
(A/μ) 9.5∙10-11 1.3∙10-10 1.2∙10-10 9.7∙10-11 9.4∙10-11 7.9∙10-11
BR
(eV) 0.627 0.614 0.609 0.6 0.586 0.578
1.4 1.3 1.2 1.0 0.9 0.6
βr2 0.01 0.01 0.01 0.01 0.01 0.01
The reverse I-V characteristic of the Au-nGaAs SD is also well described by formulas (9) and (13). It can be seen from Fig.5 that the reverse I-V characteristics of the SD also consists of two parts: the initial first part in the voltage range 0≤/U//UC/). In the initial part of the I-V characteristic of the SD, the external electric field intensity E and the EA of the AEF are directed oppositely in the near-contact region of the semiconductor (Fig.3d). Therefore, with increasing voltage U, the potential barrier height decreases from the ФВ by the value (βr1qU) and the voltage drop of the AEF decreases and becomes equal to (UC-U), and the I-V characteristic of the SD is determined by the formula (9). At the voltage /U/=/UC/, the effective potential barrier height becomes equal to the ФВR (10) and the reverse current IR1 of the first part of the I-V characteristic becomes zero. In the further increase of the voltage /U/>/UC/, the second part of the I-V characteristic of the SD is determined by the formula (13). The saturation currents ISr were determined by extrapolating the straight lines of the I-V characteristic at a semilogarithmic scale to the ordinate axis and the potential barrier height of the ФВR was calculated. In addition, the current densities of JPr along the length of the contacts periphery and the coefficients βr1 and βr2 were calculated. The values of ISr, JPr, ФВR , βr1 and βr2 are listed in the Table. It can be seen from the Table that with an increase in the length P of the contact perimeter of the SD, the barrier height of the ФВR decreases by 0.049 eV, the linear current density JPr remains almost unchanged, the coefficient βr1 related with the AEF decreases from 1.4 to 0.6 and the coefficient βr2 related the mirror image force remains unchanged. The independence of JPr from the length P and the increase in the saturation current ISr by one order with increasing P by one order means that the currents of the second part of the reverse I-V characteristic of the SD of different shapes consist almost of currents flowing along the periphery of the contact covered by the AEF. To verify the correspondence between the experimentally measured I-V characteristic (Fig.5) of the Au-nGaAs SD and the I-V characteristic curves (Fig.6) calculated from Eqs. (8) - (13), an I-V characteristic was calculated using the same formulas. In this case, all the necessary values of the parameters of the SD with a contact area of 7854 μ2, presented in the table, were used. Comparison of the curves shows that there is good agreement between them. Both the measured and calculated forward I-V characteristic curves of the SD contain two parts. In the first initial part of the I-V characteristic in the voltage range 0≤/U/ /UC/, the forward currents of the SD begin to be noticeable. The calculated reverse I-V characteristics of the SD, as well as the measured I-V characteristics, consists of two parts. In the first part of the I-V characteristic, with an increase in the voltage in the interval 0≤/U/
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1,0E-02
I, A 1,0E-03
K1r K2r K3r K4r K5r K6r K1 K2 K3 K4 K5 K6
1,0E-04 1,0E-05 1,0E-06 1,0E-07 1,0E-08 1,0E-09 1,0E-10 1,0E-11 1,0E-12 1,0E-13
-0,5
-0,4
-0,3
-0,2
-0,1
0
U, V
0,1
0,2
0,3
0,4
0,5
Fig.6. Forward (U) and reverse (-U) I-V characteristics of the SD with a contact area of 7854μ2 in different shapes calculated with the formulas (6) - (13) according to the data in the Table: K1 - round with a diameter of 100 μ, K2 - square 89х89 μ2, rectangular (μ2 ): К3 - 40х196; K4 - 20x393; K5 - 10x785; K6 - 5x1571.
It should be noted that the above features of the I-V characteristics of the nonequilibrium TMBS diode are in good agreement with the results of numerous experimentally measured I-V characteristics of both the TMBS diode and the SD with a narrow or nanostructured contact surface [17-26, 29-34]. 5. Conclusion The AEF in the TMBS diode is formed completely in the near-contact region of the semiconductor and extends over a sufficiently large distance from the contact surface into the interior of the semiconductor. Under the action of the AEF, the free electrons of the semiconductor n-type accumulate on the contact surface of the metal and in the near-contact region of the semiconductor the SCR is formed from the positive impurity ions. The metal is charged negatively, and the semiconductor is positive, therefore, there are potential differences between them, i.e. voltage drop (-UC). The TMBS diode under this voltage drop is in the nonequilibrium state and its external closed electrical circuit flows currents in the absence of an external voltage. The current flow in a nonequilibrium TMBS diode is determined by the thermionic emission theory with some peculiarity. Mathematical expressions for the forward and inverse I-V characteristic of the TMBS diode are proposed, as well as narrow or nanostructural SD, which are found in good agreement with the results of the experimental and the calculated I-V characteristics. The forward I-V characteristic of the Au-nGa SD consists of two parts: in the first initial part of the I-V characteristic, in the voltage range 0≤/U/ /UC/ I-V characteristics are well described by straight lines on the semilogarithmic scale. The beginning of the straight lines I-V characteristics are shifted from the ordinate axis by certain values of the voltage UC for the SD with different shapes. The reverse I-V characteristic of the Au-nGa DS also consists of two parts: the first initial part in the voltage range 0≤ /U/ /UC/. In the initial part of the I-V characteristic, the external electric field intensity E and the EA of the AEF are directed oppositely in the near-contact region of the semiconductor. With increasing voltage to /UC/, the effective potential barrier height decreases by (βr1qU) and the voltage drop due to the AEF decreases and becomes equal to (UC-U). At voltage /U/ = /UC/, the potential barrier height becomes equal to the ФВR, less than
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the effective barrier height of the ФВ. In the second part of the I-V characteristic curve at /U/> /UC/, the saturation currents flow under the image force action. References [1] S.M. Sze, Physics of Semiconductor Devices, New York, 1981. [2]. Bardeen J. Surface states and rectification at a metal semi-conductor contact. Phys.Rev. 71(10). (1947). 717. [3] Uzi Landman, R.N.Barner, A.G. Scherbacov Metal-Semiconductor Nanocontacts: Silicon Nanowires, Physical Review Letters 85 (9) (2000) 1958-1961. [4] Rhoderick E.H., Williams R.H. Metall-semiconductor contacts. 2nd ed. Clarendon,Oxford (1988) 345.. [5]. N.A.Torkhov, V.G.Boshkov, I.V.Ivanov, V.A.Novikov, Issledovaniye raspredeleniya potensiala na poverxnosti metalnGaAs metodom ASM, J. Poverxnost, 1 (2009) 57-66. [6] R.K. Mamedov, “Contacts metal–semiconductor with an electric spots field”, Baku, BSU, 2003 [7] R.K.Mamedov, Features of additional electric field in real metal - semiconductor contacts, News of BSU: series of physico-mathematical sciences, 4 (2013)128–163. [8] M. Yeganeh., N. Balkanian, and Sh. Rahmatallahpur, Nanoscale potential barrier distributions and their effect on current transport in Ni/n type Si Schottky diode, Journal of Semiconductors, 36 (12) (2015) 124001-7. [9] R.K. Mamedov, A.R. Aslanova, Additional electric field in TMBS diode, Superlattices and Microstructures, 92 (2016) 1–9. [10] R.K. Mamedov, M.A. Yeganeh, Current Transport and Formation of Energy Structures in Narrow Schottky Diodes, J. Microelectronics Reliability, 52 (2) (2012). 418 – 424. [11] R.K.Mamedov, Features of the potential barrier and current flow in the narrow Schottky diodes, Superlattices and Microstructures, 60 (4) (2013) 300–310. [12] N.A.Torkhov Vliyanie elektrostaticeskogo polya periferii ha ventilniy fotoeffect v kontakte metal-poluprovodnik c baryerom Schottki, Izvestiya BUZov Fizika, Deponirovano v VINITI 126-V2017 10.10.2017. [13] N.A.Torkhov, V.A. Novikov, The influence of periphery of Shottky barrier metal–semiconductor contacts on their electrophysical characteristics, FTP, 45 (1) (2011) 70-86. [14] N.A. Torkhov, Vliyanie fotoeds na tokoproxojdeniye v diodax Shottky, FTP, 45 (7) (2011) 965 –973 [15] M.O. Nikoloyevich, “Modeling of electrosistem of contackt Shottky. Actual Problems of Science XXI. Sb.2 Int. Conference. Maxachkala”, (2013) 36-40 [16] N.A.Torkhov, V.G.Bozhkov, V.A.Novikov, I.V.Ivonin, Investigation of electric fields in Ni/GaN metal-semiconductor contacts with a Schottky barrier by atomic-force microscopy, 25th Int. Crimean Conference “Microwave & Telecommunication Technology” (CriMiCo’2015). Sevastopol, (2015) 611-612. [17] M. Mehrotra, B.J. Baliga, Trench MOS barrier Schottky (TMBS) rectifier, Solid State Electron, 38 (1995) 801-806. [18] B.J. Baliga, Advanced power rectifier concepts, Springer, 2009. [19] N.F.Golubev, V.V. Tocarev, S.Shpacovski, Primenenie submicronnoy technology dlya sozdaniya visokoeffektivnich diodov Shottky. Silavaya Electronika, 4 (2005) 4 -7. [20] Max Chen, Sr. Director, Henry Kuo, et.al. High-Voltage TMBS Diodes Challenge Planar Schottkys. Power Electronics Technology, (2006) 22 -32. [21] Davide Chiola, Stephan Oliver, Marco Soldano, Increased Efficiency and Improved Reliability in “ORing” functions using Trench Schottky Technology, International Rectifier. As presented at PCIM Europe, 2002. [22] V. Khemka, R.Patel, T.P.Chow, R.J.Gutmann, Design considerations and experimental analysis for silicon carbide power rectifiers, Solid State Electron, 43 (1999) 1945-1962. [23] V. Khemka, A. Ananthan, T.P. Chow, A fully planarized 4H-SiC trench MOS barrier Schottky (TMBS) rectifier, In: IEEE Int. Symp. Power Semicond. Dev. ICs, Toronto, Canada, (1999)165-168. [24] V.S.Кotov, N.F.Golubev, V.V.Tocarev, Modeling TMBS diode, Prakticheskaya Silavaya Electronika, 50 (2) (2013) 1-7. [25] Li Wei-Yi, Ru Guo-Ping, Jiang Yu-Long, Ruan Gang, Trapezoid mesa trench metal oxide semiconductor barrier Schottky rectifier: an improved Schottky rectifier with better reverse characteristics, Chin. Phys. B. 20 (8) (2011) 087304-087315. [26] Zhai Dong-Yuan, Zhu Jun, Zhao Yi, High performance trench MOS barrier Schottky diode with high-k gate oxide, Chin. Phys. B 24 ( 7) (2015) 077201-077203 [27] R.K. Mamedov, A.R. Aslanova, Electrical current in metal-semiconductor contact with additional electric field, X International Conference Modern Problems of Physic, Baku, (2015) 212-214. [29] H.R.Chang, C.Winderhalter, R.Gupta, Trench Oxide PIN Schottky diode, IEEE, (1999) 353-358. [30] Min-Seak Kang, Yung-Joon Ahn, Kyoung-Sonk Moon, Metal work-function=dependent barrier height of Ni contacts with metal-embedded nanoparticles to 4H-SiC, Nanoskale Research Letters, 7 (2012) 1-8. [31] T. Sato, S.Kasa, H.Hasegawa, Electric Propertes of Nanometer-Sized Schottky Contacts for Gate Control of III-V Single Electron Devices and Quantum Devices, Jpn. J.Appl.Phys. 40 (2001) 2021-2025. [32] J Q Song, T Ding, J. Li, et al. Scanning tunneling microscope study of nano sized metal–semiconductor contacts between ErSi2 nano islands and Si (001) substrate. Surf Sci, (2010) 604: 361. [33] A Alberti, F.Giannazzo, Nanoscale study of the current transport through transrotational NiSi/n-Si contacts by conductive atomic force microscopy. Appl Phys Lett, (2012)101: 261906. [34] T.H.Ismailov, A.R.Aslanova, Influence of Peripheral Effects on the Electro Physical Properties of Schottky Diodes, International Journal of Innovative Technology and Exploring Engineering, 5 (2) (2015)1-7.
ACCEPTED MANUSCRIPT Highlights
In TMBS diode is formed voltage drop due to additional electric field .
TMBS diode with additional voltage drop becomes in the nonequilibrium state.
The nonequilibrium TMBS diode has I-V characteristic with specific features.
R.K. Mamedov, A.R. Aslanova PII:
S0749-6036(18)30526-3
DOI:
10.1016/j.spmi.2018.04.034
Reference:
YSPMI 5648
To appear in:
Superlattices and Microstructures
Received Date:
15 March 2018
Accepted Date:
16 April 2018
Please cite this article as: R.K. Mamedov, A.R. Aslanova, Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode, Superlattices and Microstructures (2018), doi: 10.1016/j.spmi.2018.04.034
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ACCEPTED MANUSCRIPT Features of current-voltage characteristic of nonequilibrium trench MOS barrier Schottky diode R.K. Mamedov*, A.R. Aslanova The Baku State University, Az 1148, Baku, Azerbaijan E-mail: [email protected]
Abstract. The trench MOS barrier Schottky diode (TMBS diode) under the influence of the voltage drop of the additional electric field (AEF) appearing in the near-contact region of the semiconductor are in a nonequilibrium state and their closed external circuit flows currents in the absence of an external voltage. When an external voltage is applied to the TMBS diode, the current transmission is described by the thermionic emission theory with a specific feature. Both forward and reverse I-V characteristics of the TMBS diode consist of two parts. In the initial first part of the forward I-V characteristic there are no forward currents, but reverse saturation currents flow, in its subsequent second part the currents increase exponentially with the voltage. In the initial first part of the reverse I-V characteristic, the currents increase in an abrupt way and in the subsequent second part the saturation currents flow under the action of the image force. The mathematical expressions for forward and reverse I-V characteristic of the TMBS diode and also narrow or nanostructure Schottky diode are proposed, which are in good agreement with the results of experimental and calculated I-V characteristics. Key words: TMBS diode, metal-semiconductor contact, Schottky diode, additional electric field, nonequilibrium SD, power diodes.
1. Introduction In connection with the development of modern measurement technology, especially scanning probe microscopy, there has been a growing interest in the study of electronic processes occurring in real Schottky diodes (SD), whose important electrophysical properties deviate in many real cases from the corresponding theoretical positions of idealized physical models and theories by Schottky, Bethe et al. [1-6]. The Schottky contacts (SC), i.e. the direct metal-semiconductor contacts (MSC) possessing either rectifier and ohmic properties, according to the Schottky model are characterized by the potential barrier height in the near-contact region of the semiconductor formed under the action of the electrostatic field of the contact potential difference of the contacting unlimited homogeneous surfaces of the metal and semiconductor [1,4 ]. As a result of comprehensive, intensive and systematic theoretical and experimental studies of instrumental characteristics and parameters of real MSC, it is established that many deviations between properties, parameters of real and ideal Schottky diodes (SD) are uniquely interpreted by the occurrence of an additional electric field (AEF) in real MSC [6,7]. A real SC has the contact surface with the potential barrier height of about 1 eV, limited to it adjacent free surfaces of the metal and semiconductor with a work function of the order of 4-6 eV. The presence of a potential difference between the contact surface and the free surfaces of the contacting materials causes the occurrence of the AEF around the contact [6-11]. The AEF intensity is quite commensurate with the electric field intensity of idealized SD and it is directed from the contact surface to the free surfaces of metal and semiconductor, covering the peripheral near-contact region. Under the action of the AEF, a rather wide transition region (aureole) is formed on the semiconductor surface around the contact, where the surface potential differs from the surface potentials of the metal and the semiconductor by the magnitude of their difference. The previously established AEF in real SC with such indirect methods as electrophysical, thermionic, constructive-technological [6], in recent years directly measured by Scanning Probe Microscopy [12-16]. In Ref.[13], the direct measurement of the AEF by the AFM method on the surface Au-nGaAs SC with different diameters (5-100 μ) was carried out. It is obtained that under the influence of AEF an expanded transition region (aureole) is formed along the entire perimeter of the contact with the potential, differing by 0.5-0.6 V from the potential of the free surface of nGaAs. As the contact diameter increases from 5 μ to 50 μ, the width of the aureole around the contact increases from 4 μ to 23 μ and then, with an increase in diameter to 100 μ, the width of the aureole remains almost unchanged. In Ref.[14] it was shown that under the influence of the AEF around Au - nGaAs SC with a rectangular
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contact surface the aureole with the potential different from the potential of the free surface nGaAs is formed and the width of the aureole along the rectilinear edge line of a metal with a large area reaches about 30 μ. An AFM study of two-dimensional (x, y) and one-dimensional (x) distributions of electrostatic potentials and electrostatic fields of the Au-nGaAs SC with different contact surface shape was carried out in Ref. [12]. It is established that the character of the distribution of the potential and the AEF intensity of the SC depend significantly on the geometric configurations and contact dimensions. The results of the AFM measurement of the two-dimensional and one-dimensional potential distribution and the AEF intensity of the SC with a rectangular (20 × 40 μ2) contact form are shown in Fig. 1a and b, respectively. It can be seen from the figures that the aureole with a thickness of about l m* 2 = 30μ is formed around the gold contact. The surface potential and the AEF intensity along the periphery of the contact have the maximum values and they decrease along the width of the aureole.
a)
b)
Fig.1. AFM images of two-dimensional (a) and one-dimensional (b) surface potential distributions (work function qφ-solid curve 1) and field intensity E * (dashed curve 2) of Au-nGaAs rectangular Schottky contact with dimensions 20 × 40 μ2.
Unlike other geometric configurations of SD, the TMBS diode structure widely used in modern power electronics [17-19], the AEF as a whole is formed in the near-contact region of the semiconductor. The TMBS diode has a structure consisting of a number of narrow bars (sections) of Schottky barriers (mesa diodes) of micron or submicron width, separated by trenches. The Schottky barrier in such structure is created on the planar surface of a part of the semiconductor between the trenches in which the MOS (metal-oxide-semiconductor) structure is formed on the side walls with a metal electrode located inside the trenches and connected to the barrier metal. In this case, due to the contact potential difference between the contact surface and adjacent to it free surfaces of the metal and the semiconductor, the AEF arises in the mesa region of the semiconductor. As a result of fundamental studies [20-26] of electrophysical properties of the TMBS diode, a number of effects were established (the nonlinearity of the dependence of the electric field intensity along the perpendicular line to the metal surface in the SCR, the strong decrease of the electric field intensity on the metal surface and the appearance of the electric field peak at a large distance from the interface into the SCR, the increase in the peak shift from the surface with increasing depth of the trench, the decrease in the potential barrier height and at the same time the decrease leakage, abrupt occurrence of reverse current with increasing voltage, does not match the saturation currents in the forward and reverse directions, the lack of forward current at initial voltages, etc.) which are difficult to be explained by classical theories and models of the SD. The results of investigations of the features of the AEF in the TMBS diode show that taking into account the influence of the AEF on electronic processes in the SCR makes a definite contribution to a clear understanding of these effects.
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The AEF in the TMBS diode is formed completely in the near-contact region of the semiconductor and extends over a sufficiently large distance from the contact surface into the interior of the semiconductor [9, 27, 28]. Under the action of the AEF, the free electrons of the semiconductor accumulate on the contact surface of the metal and in the near-contact region of the semiconductor the SCR is formed from the positive impurity ions. The metal is charged negatively, and the n-type semiconductor is positive, therefore, there are potential differences between them, i.e. voltage drop, and the real SD under this voltage is in a nonequilibrium state. Such a specific feature of SD with AEF, which is of great scientific and practical importance, is practically not covered in the literature. In this paper, we present the results of the investigation of the features of the current flow in the nonequilibrium TMBS diode with an additional electric field. 2. Nonequilibrium state of the Schottky contacts 2.1. Formation of the Schottky barrier In ideal SC with an unlimited homogeneous contact surface, according to the Schottky model [1], when direct contact of the contacting surfaces of the metal and the n-type semiconductor with different work functions (ФM and ФS) due to their contact potential difference, a redistribution of free electrons occurs in the near-contact region and this continues before the establishment of thermodynamic equilibrium state. The schematic structure of one section of the TMBS diode at thermodynamic equilibrium state is shown in Fig. 2a, where ФM > ФS and is formed the potential barrier height ФВ and the contact has a rectifying property. In this case, a depletion layer with thickness d is formed in the near-contact region of the semiconductor, in which the electric field intensity Ed has a maximum on the contact surface of the metal and linearly decreases to zero at a distance d along the line ox perpendicular to the interface (Fig. 2b). The energy structure of the TMBS diode according to the Schottky model acquires the form, as shown schematically in Fig. 2c. According to the thermionic emission theory [1], in the equilibrium state of the SD with the potential barrier height ФB, the saturation currents IS in opposite directions flowing through the interface are equal in modulus, which are described by the formula: (1) I S SAT 2 exp kT Here, S - is the contact area, A - is the Richardson constant, T- is the absolute temperature, k - is the Boltzman constant. When an external voltage U is applied, the SD goes out of equilibrium state and the current flowing through the contact in the forward direction (+ U) becomes larger than the flow in the reverse direction (-U) and the I-V characteristic of the SD is determined by the formula: qU I SAT 2 exp exp 1 kT kT
(2)
where, the change in the barrier height ΔФB of the SD under the action of the mirror image force is determined by the formula: 1/ 4 q 3 N D kT (3) B q 2 3 U D U q 8 S Here, ND -is the impurity concentration in the semiconductor, s - is the dielectric constant of the semiconductor, q - is the electron charge, UD – is the diffusion potential, the signs (+) and (-) correspond to the forward and reverse directions, respectively.
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Unlike an ideal SD, real SD are not in a thermodynamic equilibrium state in the absence of an external voltage, but are in a more or less nonequilibrium state under the action of the AEF in them [27, 28]. 2.2. Nonequilibrium state of the real Schottky diode In real SD having certain construction structures, the contact potential difference arises not only between the contact surface of the contacting metal and the semiconductor, but also between the contact surface with the ФB (where, ФВ=ФM – ФS) and the adjacent free surfaces of the metal with ФM and semiconductor with ФS. Because of this, the AEF is formed, encompassing the near-contact region of the semiconductor and directed from the contact surface to the free surfaces of the metal and semiconductor [6-16]. Under the action of the AEF in the near-contact region of a semiconductor, free electrons move to the contact surface of the metal and a certain amount of positive charges accumulate, in the depth of the semiconductor. Consequently, real SD with any constructive structure, including TMBS diode, are in a nonequilibrium state under the action of the voltage arising due to the AEF. ФM
ФВ
D
ФS
E
n+
∆ФB
Ed
o
d
FM
FS
xm
b) E
EA
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + +
d)
x
d
a)
m
FC
ФB
+ + + + + + + + + + + + + + + + + + ++ + + + + + + +
R
c) El Er
s
ФB
xm
o
lo
x
UC
FM
xm
EA
e)
l
FS
f)
Fig.2. Schematic representation of one section of a TMBS diode without AEF (a) and with AEF (d) in the absence of an external voltage; the distribution of the intensity Ed without AEF (b) and El, EA, Er with AEF (e); energy diagrams without AEF (c) and with AEF (f).
In the TMBS diode, the AEF completely concentrates in the near-contact region of the semiconductor and its propagation space is limited by the contact surface with the potential barrier height ФB and the internal surfaces of the metal electrodes with the work function ФM of the MOS structure in the trenches (Fig. 2d). In the near-contact region of an n-type semiconductor, under the action of the AEF with the intensity EA, the SCR is formed with an electric field intensity El directed to the contact surface of the metal. The width of SCR is commensurable with the depth lo of the trench (Fig.2e). In the SCR, the horizontal components of the AEF intensities directed oppositely compensate each other and the vertical components EA become effective. The EA of AEF and EI SCR along the axis ox are directed in the opposite, they have the maximum values at the origin of the axis on the contact surface of the metal and decrease with increasing distance x. As a result of the superposition of electric
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fields with the intensities EA and EI, the resulting electric field (REF) with the intensity Er in the SCR is formed. The dependence of Er on the distance x is represented by a curve line and it is at the origin of the coordinate of a low value and reaches a maximum at a sufficiently large distance in the depth of the semiconductor. As a result, the metal and semiconductor in the depth of the SCR acquire the potentials φm and φs (where φm <φs). Thus, the SD under the action of the resulting voltage UC due to the AEF becomes in the nonequilibrium state, where: U C s m (4) The potential barrier of the TMBS diode, which is in the nonequilibrium state under the action of a negative voltage (-UC), is formed in accordance with the REF and its energy diagram approximately has the form shown schematically in Fig.1f. In the case of a short-circuit with the wire the ends of the TMBS diode (Fig. 2c, dashed line), an electric current IO arises in the closed external circuit in the absence of an external voltage, that flows through the interface of the contact and is described by the thermionic emission theory:
I O SAT 2 exp(
qU C ) exp( ) 1 kT kT
(5)
2. The current flows in the nonequilibrium TMBS diode The arises of an electric current due to the AEF in the absence of an external voltage in a closed external circuit of a nonequilibrium TMBS diode manifests itself differently in the process of current flows when applying the forward and reverse external voltage. On the one hand, this is due to the fact that the effective component of the EA in the SCR is always directed from the contact surface of the metal to the interior of the semiconductor, and the external electric field intensity E direction depends on its sign. When the forward bias (U> 0) is applied to the TMBS diode, the directions of the E and EA intensities in the SCR are the same (Fig. 3a), and for the reverse bias (U <0) they are directed in the opposite (Fig. 3d). On the other hand, the AEF propagates beyond the width d of the SCR and under its influence a certain amount of free electrons (-Q) at a distance (l-d) accumulate on the contact surface of the metal and as many positive charges (+ Q) in the volume of the semiconductor. Consequently, the depth of the SCR becomes l greater than d, and an electric field intensity El directed to the interface. As a result of superposition of electric fields with EA and EI, the resulting electric field intensity Er and the potential barrier height ФВ are formed. Such characteristic parameters of the TMBS diode as El, Er and ФВ become sensitive to a change in the EA under the action of either structural shapes and dimensions or the applied external voltage. If the forward bias U (plus to the metal) is applied to the nonequilibrium TMBS diode with negative voltage (-UC), the external field intensity E and EA of the AEF in the SCR are directed in parallel (Fig.3a). The potential barrier height for electrons passing from the semiconductor to the metal decreases by qU. And the potential barrier height change due to the influence of the mirror image force increases (Fig. 3b) by the value of ΔФВ (where, ΔФВ = βqU and the proportionality coefficient β << 1). At the same time, the forward I-V characteristic of the TMBS diode according to the thermionic emission theory with allowance for (5) is expressed by the following formula:
I F SAT 2 exp(
qU C qU qU ) exp( ) 1 kT kT
qU C qU qU qU SAT exp( ) exp( ) exp( kT kT kT If, to make the following simple transformations n 1 1 1 1 n1 ; ; n2 n1 1
(6)
2
(7)
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then, the forward I-V characteristic expression is obtained:
I F SAT 2 exp(
Er
EA
E
n qU qU qU ) exp( 1 C ) exp( kT n1kT n2 kT ∆ФB
El
m
s
∆ФB (U-UC)q
ФB FM
(8)
FS
xm
(U-UC)q
ФB
FS
FM
xm
l
U
a) Er
EA
E
b)
0 ≤ /U/ ≤ / UC /
s
∆ФB (-UC+U)q
ФB FM
/U/ > / UC /
c)
∆ФB
El
m
l
FS
xm
(-U+UC)q
ФB FM
xm
l
U
d)
e)
0 ≤ /U/ ≤ / UC /
l
f)
FS
/
Fig.3. Schematic representation of a single section of the TMBS diode with the AEF at forward (a) and reverse (d) voltage; energy diagrams at the voltage of 0 ≤ / U / ≤ / UC / (b, e) and / U /> / UC / (c, f).
It follows from (8) that the forward I-V characteristic of the TMBS diode consists of two parts. When the voltage U is varied in the interval 0≤ /U/ ≤ /UC/ (Fig.3b), the I-V characteristic is determined by the reverse saturation current (mainly with the second summand), and for /U/>/UC/ (Fig. 3c) – by the forward current (mainly with the first summand). If the reverse bias (-U) (minus to the metal) is applied to the nonequilibrium TMBS diode with voltage (-UC), the external field intensity E and EA of the AEF in the SCR are directed in the opposite (Fig. 3d). With an increase in the reverse voltage, the external electric field E partially compensates for EA of the AEF, and consequently, the amount of accumulated charges (Q) and the intensity E1 decrease. The potential barrier height ФВ decrease by ΔФВ too (where, ΔФВ = βr1qU and the βr1 – is coefficient proportionality). In this case, according to the thermionic emission theory, taking into account the formula (5), the first initial part of the reverse I-V characteristic of the TMBS diode in the voltage range 0≤/U/
I R1 SAT 2 exp(
r1qU q (U C U ) ) exp( ) 1 kT kT
q (U C U ) r1qU qU SAT exp( ) exp( ) exp( r1 kT kT kT 2
(9)
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It follows from formula (9) that for a reverse voltage /U/=/UC/, the value of the current becomes zero (IR1 = 0) and the potential barrier height ФВ decreases by the value βr1qUС and becomes the ФВR, where: (10) R r1qU C и r1 R / U C With the reverse bias /U/ > /UC/ (Fig. 3f), the second part of the reverse I-V characteristic of the TMBS diode is expressed by the following formula::
I R 2 SAT 2 exp(
R r 2 qU qU ) exp( ) 1 kT kT
qU r 2 qU qU SAT exp( R ) exp( ) exp( r 2 kT kT kT
(11)
2
If, perform the following transformations for the image force factor r 2 n 1 1 1 nr1 r 2 r1 ; ; nr 2 , nr 1 r2 1 r2 then, the second part of the reverse I-V characteristic is obtained by the expression:
I R 2 SAT 2 exp(
R qU qU ) exp( ) exp( kT nr1kT nr 2 kT
(12)
(13)
Thus, the I-V characteristics of the nonequilibrium TMBS diode, as well as narrow and nanostructured SD in which the AEF completely covers the near-contact region of the semiconductor, both in the forward and reverse directions, consist of two parts, each of which is characterized by its specific feature. 4. Results and discussion From the direct measurements of the AEF of real SD by the AFM methods [5] it follows that it is formed around the contact with any geometric configuration and covers the peripheral near-contact region of the semiconductor. In SD with a sufficiently narrow contact area, the AEF completely covers the near-contact region, and with the TMBS diode structure it completely concentrates in the nearcontact region. In the SD structure with a wider contact area, the AEF covers the peripheral near-contact region and, consequently, the contact edge region becomes in the nonequilibrium state. Therefore, the study of the feature of current flows in the nonequilibrium narrow SD with the same contact area and various geometric configurations made in unified technological conditions is of great interest. The forward and reverse I-V characteristics of Au-nGaAs SD with a contact area of 7854 μ2 and various shapes were prepared by the methods of [14]. A thin gold films of thickness 0.1μ are electrochemically deposited onto the surface of an epitaxial layer 10μ thick and an impurity concentration ND=6.4∙1014 cm-3, grown on the (100) surface of a high-concentration n+GaAs substrate with ND = 2∙1018 cm-3, different shape of the contact surface. Their optical images with indices 1,2,3,4,5 and 6 are shown in Fig.4. The shapes and geometric dimensions of the contacts were: 1 - round with a diameter of 100μ, 2 - square 89х89μ2, rectangular (μ2): 3 - 40х196; 4 - 20x393; 5 - 10x785; 6 Fig.4. Optical image of gold contacts of the same 5x1571. 2 The forward and inverse I-V characteristics of area S = 7854μ by forms: 1 - 2round with a diameter of 100 μ, 2 - square 89х89 μ , rectangular (μ2): 3 Au-nGaAs SD with the different shape of the contact 40х196; 4 - 20x393; 5 - 10x785; 6 - 5x1571. surface are presented on a semilogarithmic scale in
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Fig.5. From this figure it can be seen that the forward I-V characteristic of the SD consists of two parts in accordance with formula (8). In the first initial part of the I-V characteristic of the SD, there are no forward currents (rather small reverse saturation currents are not noted). The subsequent second parts of the I-V characteristic of the SD on a semilogarithmic scale are well described by straight lines with close ideality coefficients (n = 1.05-1.09). This means that the mechanism of current flow in the SD is thermionic emission. The beginning of the straight lines I-V characteristics are shifted from the origin of the U axis by the value /-UC/=/ U if / (where, i = 1,2,3,4,5,6) for SD with different shapes with indices i, respectively. This shows that the currents of the second parts of the I-V characteristic of the SD with the indices i begin to flow after compensation by positive U if of the corresponding negative voltages (-UC) caused by the AEF. Therefore, in order to determine the effective potential barrier height of the SD by formula (8), the saturation currents ISf at zero voltage were determined by extrapolating the straight lines of the IV characteristic to the ordinate axis passing through their initial points, i.e. displaced by the value U if . It should be noted that due to the fact that the initial part of the I-V characteristic of the SD is determined by another formula, the saturation currents ISf can not be determined as shown in Fig. 5, where the differences in the saturation currents iSr would be of incredible great importance. The measured values of the electrophysical parameters UC( U if ), ISf, ФВ, n of the SD and their geometric parameters (diameter D of the circular contact, sides a and b of the rectangular contacts, perimeter P of the contact) are shown in the Table.
Fig.5. The forward If (Uf) and the reverse Ir (Ur) I-V characteristics of Au-nGaAs SD with a contact surface of different shapes: 1 - round with a diameter of 100 μ, 2 - square 89х89 μ2, rectangular (μ2): 3 40х196; 4 - 20x393; 5 - 10x785; 6 - 5x1571.
It can be seen from the Table that with an increase in the contact perimeter from 314 μ to 3158 μ, the effective potential barrier height of the SD decreases by a value of 0.069 eV, the ideality coefficient n increases from 1.05 to 1.09 and the voltage drop of the UC increases from 0.11 V to 0.21 V. This is explained by the fact that as the length P of the contact periphery increases, the contribution of the
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current flowing through the peripheral region, which has a relatively low barrier height due to the AEF, to the common contact current increases.
SD №
Table. axb (μ2)
P (μ)
1. 2. 3. 4. 5. 6.
D=100 89x89 40x196 20x393 10x785 5x1571
314 355 473 825 1591 3158
Geometric and electrophysical parameters of Au-nGaAs Schottky diodes βr1 I n Ф I J Ф U (∆Ufi) sf
(A) 7.0∙10-11 9.0∙10-11 1.0∙10-10 2.0∙10-10 4.0∙10-10 1.0∙10-9
B
1,05 1,06 1,06 1,07 1,08 1,09
(eV) 0.783 0.777 0.774 0.756 0.738 0.714
C
(V) 0.11 0.13 0.14 0.15 0.17 0.21
sr
(A) 3.0∙10-8 4.5∙10-8 5.5∙10-8 8.0∙10-8 1.5∙10-7 2.5∙10-7
lr
(A/μ) 9.5∙10-11 1.3∙10-10 1.2∙10-10 9.7∙10-11 9.4∙10-11 7.9∙10-11
BR
(eV) 0.627 0.614 0.609 0.6 0.586 0.578
1.4 1.3 1.2 1.0 0.9 0.6
βr2 0.01 0.01 0.01 0.01 0.01 0.01
The reverse I-V characteristic of the Au-nGaAs SD is also well described by formulas (9) and (13). It can be seen from Fig.5 that the reverse I-V characteristics of the SD also consists of two parts: the initial first part in the voltage range 0≤/U/
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1,0E-02
I, A 1,0E-03
K1r K2r K3r K4r K5r K6r K1 K2 K3 K4 K5 K6
1,0E-04 1,0E-05 1,0E-06 1,0E-07 1,0E-08 1,0E-09 1,0E-10 1,0E-11 1,0E-12 1,0E-13
-0,5
-0,4
-0,3
-0,2
-0,1
0
U, V
0,1
0,2
0,3
0,4
0,5
Fig.6. Forward (U) and reverse (-U) I-V characteristics of the SD with a contact area of 7854μ2 in different shapes calculated with the formulas (6) - (13) according to the data in the Table: K1 - round with a diameter of 100 μ, K2 - square 89х89 μ2, rectangular (μ2 ): К3 - 40х196; K4 - 20x393; K5 - 10x785; K6 - 5x1571.
It should be noted that the above features of the I-V characteristics of the nonequilibrium TMBS diode are in good agreement with the results of numerous experimentally measured I-V characteristics of both the TMBS diode and the SD with a narrow or nanostructured contact surface [17-26, 29-34]. 5. Conclusion The AEF in the TMBS diode is formed completely in the near-contact region of the semiconductor and extends over a sufficiently large distance from the contact surface into the interior of the semiconductor. Under the action of the AEF, the free electrons of the semiconductor n-type accumulate on the contact surface of the metal and in the near-contact region of the semiconductor the SCR is formed from the positive impurity ions. The metal is charged negatively, and the semiconductor is positive, therefore, there are potential differences between them, i.e. voltage drop (-UC). The TMBS diode under this voltage drop is in the nonequilibrium state and its external closed electrical circuit flows currents in the absence of an external voltage. The current flow in a nonequilibrium TMBS diode is determined by the thermionic emission theory with some peculiarity. Mathematical expressions for the forward and inverse I-V characteristic of the TMBS diode are proposed, as well as narrow or nanostructural SD, which are found in good agreement with the results of the experimental and the calculated I-V characteristics. The forward I-V characteristic of the Au-nGa SD consists of two parts: in the first initial part of the I-V characteristic, in the voltage range 0≤/U/ /UC/ I-V characteristics are well described by straight lines on the semilogarithmic scale. The beginning of the straight lines I-V characteristics are shifted from the ordinate axis by certain values of the voltage UC for the SD with different shapes. The reverse I-V characteristic of the Au-nGa DS also consists of two parts: the first initial part in the voltage range 0≤ /U/ /UC/. In the initial part of the I-V characteristic, the external electric field intensity E and the EA of the AEF are directed oppositely in the near-contact region of the semiconductor. With increasing voltage to /UC/, the effective potential barrier height decreases by (βr1qU) and the voltage drop due to the AEF decreases and becomes equal to (UC-U). At voltage /U/ = /UC/, the potential barrier height becomes equal to the ФВR, less than
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the effective barrier height of the ФВ. In the second part of the I-V characteristic curve at /U/> /UC/, the saturation currents flow under the image force action. References [1] S.M. Sze, Physics of Semiconductor Devices, New York, 1981. [2]. Bardeen J. Surface states and rectification at a metal semi-conductor contact. Phys.Rev. 71(10). (1947). 717. [3] Uzi Landman, R.N.Barner, A.G. Scherbacov Metal-Semiconductor Nanocontacts: Silicon Nanowires, Physical Review Letters 85 (9) (2000) 1958-1961. [4] Rhoderick E.H., Williams R.H. Metall-semiconductor contacts. 2nd ed. Clarendon,Oxford (1988) 345.. [5]. N.A.Torkhov, V.G.Boshkov, I.V.Ivanov, V.A.Novikov, Issledovaniye raspredeleniya potensiala na poverxnosti metalnGaAs metodom ASM, J. Poverxnost, 1 (2009) 57-66. [6] R.K. 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ACCEPTED MANUSCRIPT Highlights
In TMBS diode is formed voltage drop due to additional electric field .
TMBS diode with additional voltage drop becomes in the nonequilibrium state.
The nonequilibrium TMBS diode has I-V characteristic with specific features.