Metal Semiconductor Contacts

Metal Semiconductor Contacts The investigation of rectification in metal-semiconductor contacts was first described by Braun [33-35], who discovered in 1874 the asymmetric nature of electrical conduction between metal contacts and semiconductors. However, the first step towards understanding the rectifying action of metal-semiconductor contacts was taken in 1931[33], when Schottky, Stormer and Waibel showed that if a current flows through a metal-semiconductor contact, then potential drop occurs almost entirely at the contact, implying the existence of a potential barrier. In 1938 Schottky and Mott, independently pointed out that the observed direction of rectification could be explained by supposing that the transport of electrons over the potential barrier took place through drift and diffusion [33]. This was the groundwork on which subsequent work done on Schottky and Ohmic contacts was based. This chapter reports the review of theory of M-S contacts operation. In this chapter brief introduction of ideal rectifying contacts, current conduction mechanism, current transport mechanism and barrier height measurement techniques are explained. 3.1 Ideal Metal-Semiconductor contacts A Metal-Semiconductor contact is formed when a metal and a semiconductor are brought into intimate contact with each other. fig.3.1 shows the energy band-diagram for an n- type semiconductor and metal, which are electrically neutral and isolated to each other, with the assumption that the work function of semiconductor ( s ) is less than that of the

metal work function ( m ). This is the most common case observed while forming Schottky contacts with the assumption that there are no surface states present. Fig. 3.1 Formation of Schottky barrier between metal and n-type semiconductor when neutral and electrically isolated. If the metal and semiconductor are electrically connected by a wire, electrons will pass from the semiconductor into the metal and the two Fermi levels are forced to align as shown in fig. 3.2. There is an electric field in the gap directed from semiconductor to metal and there is a negative charge on the surface of the metal, which is balanced by a positive charge in the semiconductor.

Fig. 3.2 Formation of Schottky barrier between metal and n-type semiconductor when electrically connected. If the metal and the semiconductor approach each other as shown in fig. 3.3, the potential difference between the electrostatic potentials of two surfaces tend to zero. When finally both surfaces touch, the barrier due to the vacuum vanishes in altogether and an ideal metal-semiconductor contact is formed and shown in fig. 3.4. Fig. 3.3 Formation of Schottky barrier between metal and n-type semiconductor separated by a narrow gap.

In most practical cases, the ideal situation as shown in fig. 3.4 is never reached because there is usually a thin insulating layer of oxide about 10-20Å thick on the surface of the semiconductor. Such an insulating layer is called an interfacial layer. A practical contact is thus more like that shown in fig. 3.3. However, the barrier presented to the electrons by the interfacial layer is usually so narrow that the electrons can tunnel through it quite easily. Fig. 3.4 Formation of Schottky barrier between metal and n-type semiconductor in perfect contact. Fig 3.5 illustrates barrier height for various combinations of the semiconductor type and the M-S work function difference (φ ms ). The cases shown in fig. 3.5 (b) and (c) are very uncommon in practice and the majority of the metal-semiconductor combinations form rectifying contacts.

Fig. 3.5 Barriers for semiconductors of different types and work functions; n-type :( a) m > s (rectifying), (b) m < s (ohmic). p-type:(c) m > s (ohmic), (d) m < s (rectifying). For the case shown in fig. 3.5(b) where s is greater than m, the electrons flowing from semiconductor to the metal, encounter no barrier and the current is determined by the bulk resistance of the semiconductor. Such contact is called an Ohmic contact and has sufficiently low resistance.

b) Schottky Barrier Height (SBH) i) Schottky Mott Limit [33] The semiconductor work function is given by: (3.1) s n where n is the energy difference between the E C and the Fermi level E F, and is given by: kt NC n E C E F ln( ) q N (3.2) D The potential difference between the work functions m and s is called the contact potential and is equal to the built-in potential at equilibrium when no bias is applied. This potential difference is given by: V (3.3) ms i m s Thus the barrier height, for the ideal case is given by: (3.4) bn m This equation is known as the Schottky-Mott Limit [33], and gives the limiting value for the barrier height in ideal metal-semiconductor contacts and is based on following assumptions: a) The surface dipole contributions to m and χ do not change when the metal and semiconductor are brought in contact with each other. b) There are no localized states present on the surface of the semiconductor. c) There is perfect contact between the metal and the semiconductor; i.e., there is no interfacial layer present between metal and semiconductor.

For an ideal contact between a metal and a p-type semiconductor, the barrier height bp is given by Equ. (3.5) and energy band diagram for ideal is shown in fig. 3.6. E ( ) (3.5) bn g m Fig. 3.6 Energy band diagram of ideal Schottky contact. 3.2.2 Bardeen Limit [36] The Schottky-Mott theory suggests that the barrier height is a function of the metal work function and the electron affinity of the semiconductor. However, it is practically found that the barrier height is a less sensitive function of the metal work function and in some situation is almost independent of m [36]. A possible cause of this discrepancy was given by Bardeen in 1947, who suggested that the discrepancy may be due to the effect of surface states. fig. 3.7 illustrates a Schottky contact with the presence of a thin interfacial

and there is a continuous distribution of surface states present at the surface of semiconductor and characterized by a neutral level 0. Fig. 3.7 M/S contact with surface states. The occupancy of the surface states is determined by the Fermi level which is constant throughout the barrier region in the absence of applied bias. If the neutral level 0 is above the Fermi level E F, the surface states contain a net positive charge. On the other hand, if 0 is below E F, then the surface states have a net negative charge. The surface states behave like a negative feedback loop, the error signal of which is the deviation of 0 from E F. If the density of surface states becomes very large, the error signal will be very small and 0 E F. As a result, the barrier height is determined by the property of the semiconductor surface and not the metal work function. When this state is

reached, the barrier height is said to be pinned by the high density of the surface states. This is called the Bardeen Limit and when it is reached, the surface states screen the semiconductor from the electric field in the insulating layer so that the amount of charge in the depletion region and the barrier height is independent of the metal work function m. The Bardeen Limit is given by: E (3.6) b g 0 The Schottky-Mott Limit and the Bardeen Limit are the two limiting cases for the barrier height, b, for M/S contacts. Usually, the actual Schottky Barrier Height falls somewhere between the Schottky-Mott Limit and the Bardeen Limit. In general, surface states can be both intrinsic and extrinsic. The extrinsic surface states result due to damage caused to the surface of the semiconductor during the metal deposition process. It can also be as a result of chemical reactions between metals and semiconductors. The knowledge behind the origin and nature of extrinsic interface states is limited because it is very difficult to measure them experimentally. The chemical reactions can occur just within a few atomic layers which may be difficult to measure. Intrinsic surface states arise due to the presence of dangling bonds at the surface [34, 35]. The dangling bonds are referred to the presence of unpaired electrons in the localized orbital at the surface because atoms at the surface do not have neighboring atoms to bond on one side of the interface. Heine [37] in 1965 proposed that metal induced gap states (MIGS) could exist at metal-semiconductor interface. According to Heine, wave functions of the electrons from the metal can decay into the semiconductor in the energy range where metal conduction band overlaps with the semiconductor band gap. The

exponentially decaying electron wave-functions from the metal into the semiconductor are analyzed based on virtual gap states of the semiconductor band structure. Louie [38] in 1977 carried out extensive theoretical analysis to show that the intrinsic surface states which existed in the fundamental gaps of these semiconductors are removed by the presence of the metals and a new type of interface states (MIGS) appear in this energy range and are responsible for the pinning of Fermi level. Monch [39] gave the physical and chemical concept regarding the barrier heights of Schottky contacts. He divides the concept of barrier heights into two contributions: the zero charge transfer barrier height and a dipole term. Dipole term is equal to the product of slope parameter and difference in electronegativities of metal and semiconductor. The density of states and charge decay length of the MIGS at their branch point determine slope parameter. If metal and semiconductor have same electronegativity then no charge transfer occurs at the interface and Fermi level will coincide with branch point of MIGS. The zero charge transfer barrier height thus equal to the energy distance from the MIGS branch point to the edge of corresponding majority carrier band. As a result Monch concluded that the MIGS are fundamental mechanism of the barrier formation and attributed the lowering of barrier heights to fabrication induced defects. Interface states in Schottky diodes work as the traps of electrons, and as a result degrade the I-V characteristics i.e. barrier heights of the Schottky diodes. 3.3 Current Conduction Mechanism The principal current transport mechanisms which determine the conduction in the Schottky contacts are illustrated in fig. 3.8 and are described below:

a) Emission of electrons over the top of the barrier into the metal. b) Quantum-mechanical tunneling through the barrier. c) Electron-hole recombination in the space-charge region. d) Electron-hole recombination in the neutral region of the semiconductor. Fig. 3.8 Current transport mechanisms in a forward-biased Schottky Barrier. 3.3.1 Electron Emission over the Barrier Before the emission of electrons over the barrier into the metal, electrons must first be transported through the space charge region. There have been two theories for this phenomenon. One is the diffusion theory of Wagner (1931) and Schottky and Spenke (1939), and the other is the theory of thermionic emission [33, 40]. According to diffusion theory the current is limited by the mechanism of drift and diffusion in the depletion region and concentration of conduction electrons in the semiconductor is not

affected by the applied bias. Hence, the quasi Fermi level in the semiconductor coincides with the Fermi level in the metal at the junction as shown in fig. 3.9. Since the gradient of the quasi Fermi level is the driving force for the electrons to move from the semiconductor to the metal, the transportation of electrons in the space charge region is the reason for the current flow [41]. Diffusion theory Thermionic emission theory Fig. 3.9 Electron quasi-fermi level in a forward-biased Schottky barrier. Thermionic emission theory suggests that the current is limited by emission of electrons over the barrier. The electrons emitted from the semiconductor into the metal are not in thermal equilibrium with the electrons in the metal, but have an energy which equals the sum of the Fermi energy of the metal and the barrier height. These are referred to as hot electrons. When these hot electrons penetrate into the metal, they lose energy by collisions with the conduction electrons and eventually become in equilibrium with

them. This indicates that the quasi- Fermi level falls in the metal until it coincides with the metal Fermi level and the gradient of the quasi-fermi level is finally the driving force for electrons. According to the diffusion theory the main obstacle to the current flow is the combined effects of drift and diffusion in the depletion region while according to the thermionic-emission theory the bottleneck lies in the process of emission of electrons into the metal. In practice however, the true behavior of the current transport lies somewhere between the two extremes of the diffusion theory and the thermionic emission theory. 3.3.2 Quantum-mechanical tunneling through the barrier Quantum mechanical tunneling of carriers though the barrier is another important current conduction mechanism. It has a significant effect at low temperatures and heavy doping (10 19 cm -3 ). In the case of heavily doped semiconductors, the depletion region and the barrier width become narrow and therefore allow carriers to readily tunnel through the barrier. In the case of degenerate semiconductors at low temperature, current may arise from tunneling of electrons close to the Fermi level and this is called field emission. Field emission is of considerable importance for Ohmic contacts. As the temperature is increased, electrons acquire higher energies and the tunneling probability increases since they face a thin barrier. However, the number of excited electrons decreases rapidly with the increase in energy and there will be an optimum energy at which the excited electrons contribute maximum to the current. This is called thermionic-field emission. If the temperature is further increased, more and more electrons will be energized to go over the top of the barrier, until the effect of tunneling as compared to the pure thermionic emission become negligible.

3.3.3 Electron-hole recombination in the space-charge region The recombination in the depletion region usually takes place due to the presence localized states in the semiconductor. The localized states are often referred to as traps since they act as trapping centre for the minority carriers. The localized states are formed due to defects, surface states, dangling bonds and impurities. These traps have an energy level which is usually located in the forbidden energy gap. The most effective trap centers are those with energies lying near the center of the forbidden gap. The theory of current due to such recombination centers is similar to that for p-n junctions, and is predicted by the S-H-R (Shockley, Hall and Read) model [33, 34]. The Recombination current is a common cause of departure from ideal behavior in Schottky diodes. 3.3.4 Hole Injection in the neutral region of semiconductor When the height of the Schottky barrier on n-type material is higher than half of the energy band gap, the semiconductor region at and near the surface becomes p-type and contains a high-density of holes. These holes diffuse into the neutral region of the semiconductor under the influence of forward bias and thus giving rise to the injection of the holes. If hole concentration exceeds that of the electrons, the surface is inverted and forms a p-n junction with the bulk. This effect is only noticeable in large barrier heights with weakly doped semiconductors. Since SiC has a large bandgap and has a very low intrinsic carrier concentration so, the hole injection is negligible in SiC devices.

3.4 Schottky diode forward bias operation In the case of moderately or low doped semiconductors the current transport through the Schottky junctions is dominated by emission of majority carriers over the potential barrier from the semiconductor into the metal contact. If the Schottky barrier is significantly higher than the thermal energy q b >>kt, the thermionic emission theory describes the current-voltage characteristic of the Schottky junction as [9]: J J s / (exp qv F kt 1) (3.7) where V F is the applied voltage and Js is the saturation current density. Js * 2 / AT exp b kt (3.8) Where A* is the effective Richardson constant and is proportional to the effective mass of the majority carriers m* and can be given as: A * * 2 4 qm kb 3 (3.9) h In real Schottky diodes the thermionic emission theory does only describe the forward current-voltage characteristic for a limited range of current densities. At higher diode currents the deviations from ideal diode characteristics are observed as an additional voltage drop through the device. Depending upon the design of the diode major contribution to this voltage drop is generally found in series resistance R s of the neutral regions of the semiconductor and diode equation can be written as: I AJ s qv ( IRs )/ kt exp (3.10) where A is the area of the Schottky contact

3.5 Schottky diode reverse bias operation Thermionic theory predicts a constant current density for a reverse biased Schottky diode of the same order of the saturation current density which can be given as: J J AT * 2 / exp b kt s (3.11) Experimental measurements show however a significant increase of several orders of magnitude in the leakage current with increasing reverses bias. Important contributions due to the leakage current are explained as follows: 3.5.1 Image force barrier lowering of the Schottky barrier Under the influence of reverse bias, there is a reduction in the Schottky barrier height due to the image force barrier lowering. When an electron is at a distance x from the metal, a positive charge will be induced on the surface of metal. The force of attraction between the electron and induced positive charge is equivalent to the force that would exist between electron and an equal positive charge located at position x, which is referred to as image charge shown in fig.3.10. The force of attraction between electron and its image charge can be expressed as: 2 q Fx ( ) (3.12) 2 4 (2 x) d and potential energy is: 2 q Ex ( ) 16 d x (3.13) This electron has potential energy relative to that of an electron at infinity. So total potential energy will be:

2 q PE( x) qe( x) 16 d x (3.13) and x m q (3.14) 16 0 So, image force barrier lowering can be given as: qe B 2 Ex ( m) (3.15) 4 d 3 qn d B 2 2 V i 8 d s 1/4 ] (3.16) where d and s are image force permittivity and static permittivity. The image force permittivity may be different from the static permittivity because when the electron transit time through the barrier region is small compared to the dielectric relaxation time, semiconductor does not get fully polarized. However in most cases the transit time is sufficiently large and we can write d = s. Fig. 3.10 Image force barrier lowering in Schottky barrier diodes.

3.5.2 Space charge Generation In the depletion region there are some deep levels in the band-gap which act like generation-recombination centers. If U is the generation rate related to the carrier emission from deep levels with capture cross-section of n,p and E t the energy position in the bandgap, then time constant e can be defined as [9] : U p nvthn t ni ni Et Ei Ei Et e nexp pexp kt kt (3.17) Where n i and E i are intrinsic carrier concentration and Fermi level respectively, and v th is the thermal velocity. Therefore leakage current contributed by generation can be given as: J gen w qni w q( U) dx (3.18) 0 e where w is the width of depletion region. 3.6 Method of measurement of barrier height The Schottky barrier height ( b ) and ideality factor (n) are important parameters for characterization of the Schottky diodes. In general, there are four measurement methods for estimating the barrier height of metal-semiconductor contacts such as the current voltage (I-V) measurement, the capacitance-voltage (C-V) measurement, photoelectric measurement, and activation energy [9, 33, 35]. In this work only two methods are used which are described briefly below.

2.7.1 Current -Voltage (I-V) Measurement Schottky diodes made from high mobility semiconductor possess I-V (current -voltage) characteristics under the thermionic emission theory, provided forward bias is not too large. According to this theory, J qv Js [exp( ) 1] (3.19) kt where J s * q 2 b AT exp( ) kt represents the reverse saturation current density, q is the electronic charge, A * is the Richardson s constant, b is the barrier height, k is the Boltzmann constant, T is temperature in K and V is the forward voltage. Practically diodes never satisfy the ideal equation (3.19) exactly, but always a modified equation J qv Js [exp( ) 1] (3.20) nkt If the applied voltage V is larger than 3kT/q, exponential term in equation 3.17 dominates and J can be approximated as: J qv Js exp( ) (3.21) nkt where n is ideality factor and is equal to 1 for thermionic emission theory. A plot of ln(j) versus V in the forward direction give a straight line except for the region where V<3kT/q. The ideality factor can be calculated from the slope of the linear region of the forward bias J-V characteristics using the relation:

q dv n kt d(ln J ) (3.22) The reverse saturation current density J s can be calculated from the extrapolated value of the current density to zero voltage and barrier height can be obtained from the relation * 2 kt A T b ln( ) q J (3.23) s 3.6.2 Capacitance Voltage (C-V) measurement Capacitance-voltage (C-V) measurements were also used for the extraction of SBH and doping concentration. When a small ac signal is superimposed upon a dc bias, charges of one type are induced on metal surface and charges of other type on semiconductor. The depletion region capacitance can be expressed as [35, 42] C q 0 snd 2[ V V ( kt / q)] bi R (3.24) where N D is the donor concentration; q, is the electronic charge; k, the Boltzman s constant; s, is the permittivity of the semiconductor: V bi, the built in voltage; and V R the applied voltage. The slope of the 1/C 2 vs. V plot is given by

d 2 (1/ C ) 2 2 dv A ND s 0 (3.25) The donor concentration is calculated from the measured slope as N D 2 Aqs 2 d 2 (1/ ) C dv (3.26) The barrier height is calculated from the measured intercept on the voltage axis [35]. Thus we obtain kt b Vbi Vn (3.27) q Where V bi represents the intercept on the voltage axis;, the image force barrier lowering; and V n is the depth of the Fermi level below the conduction band. 3.7 Summary In this Chapter the formation of m/s contacts were reviewed. Schottky barrier height and theories related to the origin of the barrier height were discussed. The different current conduction mechanisms operating in Schottky contacts were reviewed followed by the discussion on forward and reverse biased operation of the Schottky diodes. Most commonly used method of measurement of barrier height is also discussed.