ABSTRACT
In semiconductor device fabrication, metals are often deposited as electrodes onto the semiconductor surfaces The deposition of a metallic material onto a semiconductor results in an ohmic contact or it can result in another type of contact known as a Schottky contact The ohmic contact between a metallic material and a semiconductor is such that there is no energy barrier to block the flow of carriers in either direction at the metal-semiconductor junction In some cases, however, the contact between a metal and a semiconductor is rectifying; this type of contact is known as the Schottky contact
To better understand the origin of Schottky and ohmic contacts, recall that the work function of a material is the energy required to remove an electron from its Fermi energy level and set it free (Figure 61) Note that while there are electrons at E = EF for a metal, there are no electrons at E = EF for a semiconductor
Therefore we define the electron affinity of a semiconductor (qχS) as the energy needed to remove an electron from the conduction band and set it free (Figure 61) It is not the lowest energy required to remove an electron, because when an electron is removed from the conduction band, another electron must move from the valence band to conduction band, which requires additional energy
For semiconductors, we usually refer to the values of electron affinity, and not the work function, since electrons are present in the conduction band but not at E = EF The work function and electron affinity values for different metals and semiconductors are shown in Table 61 The values of the electron affinity and the work function are often expressed as the potential in volts (V) or as energy in electron volts
A Schottky contact is a rectifying contact between a metal and a semiconductor It can function as a diode, known as the Schottky diode (Figure 62)
The Schottky contact is formed if ϕM < ϕS for a p-type semiconductor or ϕM > ϕS for an n-type semiconductor The subscripts “m” and “s” stand for metal and semiconductor, respectively
Consider a metal-semiconductor system in which the work function of the metal (ϕM) is greater than that for an n-type semiconductor (ϕS; Figure 61a)
We will construct a band diagram for this metalsemiconductor junction using the principle of the invariance of Fermi energy We will follow steps similar to those used in Chapter 5 for creating a band diagram for a p-n junction At this metal-n-type semiconductor junction, where ϕM > χS, electrons flow from the higher-
energy states of the semiconductor conduction band to the lower-energy states of the metal This creates a positively charged depletion region in the n-type semiconductor A negative surface charge builds up on the metal Since the free electron concentration in a metal is very high, this charge is within an atomic distance from the surface A built-in electric field is directed from the n-type
TABLE 6.1 Some Metal Work Function (qϕM) and Semiconductor Electron Affinity (qχs) Values
semiconductor to the metal The associated built-in potential (V0) prevents the further flow of electrons from the n-type semiconductor to the metal (Figure 63)
As we can see in Figure 63, there is also a barrier (qϕB) to the flow of electrons from the metal to the n-type semiconductor:
q qφ φ χB M S= −q (61)
This barrier, called the Schottky barrier (qϕB), prevents any further injection of electrons into the n-type semiconductor from the metal When a metal is deposited onto a semiconductor, we may think that the electrons from the metal flow into the semiconductor easily However, this is not always the case
The magnitude of the built-in potential (qV0) for transferring an electron from the conduction band of the semiconductor to the Fermi energy level metal is given by
qV q qV0 = −φB n (62)
where qVn is the energy difference between Ec and EF of the n-type semiconductor (Figure 63) Substituting for the Schottky barrier from Equation 61 (qϕB) as (qϕM − qχS) in Equation 62,
we get
qV q q qV
qV q q q q
qV q
= − − ∴ = − − − ∴ =
φ χ φ χ φ χ
φ φM S− q
Thus, the built-in potential barrier (qV0) is equal to the difference between the two work functions of the materials forming the Schottky contact
qV q q0 = −φ φM S (63)
It may seem from Equation 61 that for different metals deposited on a given semiconductor (eg, silicon [Si]), the barrier height qϕB changes with the work function of the metal (qϕM) However, in practice the Schottky barrier height does not change appreciably for different metals deposited onto a given semiconductor (Table 62) As shown in Table 62, the Schottky barrier height of ∼08 eV is essentially independent of the metal deposited for n-type silicon For n-type gallium arsenide (GaAs), the Schottky barrier height is ∼09 eV
Many metals deposited on silicon are thermodynamically unstable, so that when the semiconductor-metal contact is exposed to high temperatures during processing, the metals react with the silicon and form a silicide intermetallic compound For example, platinum (Pt) reacts with silicon and forms platinum silicide (PtSi) This lowers the Schottky barrier by ∼006 eV, from 090 for platinum to 084 eV for PtSi Tantalum silicide (TaSi2) and titanium silicide (TiSi2) are the preferred materials for forming Schottky contacts in silicon semiconductor processing The values of the Schottky barrier for some silicides are listed in Table 62
The Schottky barrier is independent of the metal or alloy used to create it because of the surface pinning of the semiconductor’s Fermi energy level in the interface region (Figure 64)
At the semiconductor surface or its interface with another metal or material, additional energy levels are introduced into the otherwise forbidden bandgap The physical interface between the semiconductor and its surroundings (another metal, surrounding atmosphere, and so on) is not perfect; there are dangling or incomplete bonds, which means the atoms at the surface or interface are not fully coordinated with the other atoms For example, inside a single crystal of silicon, an atom of silicon should be coordinated with four other silicon atoms in a tetrahedral fashion However, this is not the case for silicon atoms at the surfaces or interfaces with other metals or materials The interface between a metal and a semiconductor is not sharp at an atomistic level There is a very small region at the interface in which it is unclear whether the material is a metal or a semiconductor Nanoscale oxide particles, intermetallic compounds, and so on may be present at this interface These surface atoms have incomplete bonds and other imperfections and introduce a large
TABLE 6.2 Schottky Barrier Heights (in Electron Volts) for Metals and Alloys on Different Semiconductors
number of energy states or available defect-related energy levels into the interface region of the semiconductor’s bandgap (Figure 64)
Thus, although theoretically there are no energy levels allowed in the bandgap, some energy levels occur in the bandgap near the surface or interface region in the bulk of the semiconductor These states effectively “pin” the Fermi energy level of the semiconductor in the interface region
Surface pinning means that the Fermi energy level in the surface region of the semiconductor is at a fixed level (ϕ0) that does not change with the addition or removal of electrons in the rest of the semiconductor (via doping) This also means that the position of the semiconductor’s conduction bandedge is fixed in the interfacial region Thus, regardless of the metal deposited, the Fermi energy level of the metal must align with the pinned Fermi energy level (ϕ0; Figure 64) When the Fermi energy level is pinned, the Schottky barrier height (qϕB) for the injection of electrons from a metal into the semiconductor is given by
q E qφ φB g= − 0 (64)
The Schottky barrier of different metals deposited on a given semiconductor is essentially constant (Table 62)
We now consider the ideal current-voltage (I-V) curve for a Schottky contact between an n-type semiconductor and a metal, such that qϕM > qχS When there is no applied bias, some electrons on the semiconductor side will have a high enough energy to overcome the built-in potential barrier (qV0) and flow onto the metal side This process of thermionic emission creates the thermionic current (IMS) If the n-type semiconductor is heavily doped, the depletion layer is thin, and it is possible for electrons to tunnel from the n-side semiconductor to the metal Thermionic emission and tunneling both create a flow of electrons from the semiconductor to the metal The resultant conventional current (IMS) is directed from the metal to the semiconductor (Figure 65) This current is balanced by the conventional current resulting from the flow of electrons from the metal to the semiconductor (ISM) These currents cancel each other out in a Schottky contact under equilibrium
A forward bias is applied to this Schottky contact by connecting the positive terminal of a power supply to the metal side The applied voltage is opposite the internal field, directed from the n-type semiconductor to the metal The potential barrier for the flow of electrons from the semiconductor to the metal is reduced from qV0 to q(V0 − VF) There is therefore an increased flow of electrons from the semiconductor to the metal This means that the current directed from the metal to the n-type semiconductor (IMS) increases This is represented in Figure 65b by the relatively thicker and longer arrow for IMS
Note that since the Schottky barrier does not change much for a given semiconductor (Table 62), the current due to the motion of electrons from the metal to the semiconductor (ISM) does not change Thus, the value of ISM does not change under an applied bias The net result is that under a forward bias, the overall conventional current flow from the metal to the semiconductor (ISM) increases
Under a reverse bias, that is, when the metal side is connected to the negative terminal of a DC power supply, the potential barrier for the flow of electrons from the semiconductor toward the metal increases from qV0 to q(V0 + Vr) This causes the resultant IMS to decrease, whereas the value of ISM remains unchanged (Figure 65c) The resultant I-V curve for a Schottky diode is shown in Figure 65d
We have considered a Schottky contact formed between an n-type semiconductor and a metal (Figure 66a and b) This type of rectifying contact can occur between a p-type semiconductor and a metal when ϕM < ϕS (Figure 66)
The current through a Schottky diode is given by the following equation:
I I qV
k T =
−
S
exp η
1 (65)
where IS is the reverse saturation current, V is the applied bias, and η is the ideality factor for a Schottky diode The value of η is between 1 and 2 and is closer to 1 for a Schottky diode The reverse-bias saturation current (IS) is given by
I A m qk
T q
k TS B
= × × × −
2π φ
(66)
where A is the area through which the Schottky current flows
The term m qk *
2 32π
is known as the effective Richardson constant (R*)
R m qk m
m *
= =
120 π
A K 2 (67)
where m* is the carrier effective mass and m0 is the carrier rest mass Instead of the saturation current (IS), we can write Equation 67 in the form of a saturation current
density (JS) as
J m qk
T q
= × × −
exp 2
2π φ
(68)
The values of the effective Richardson’s constant (R*), predicted from Equation 67, are high Values from more detailed calculations are shown in Table 63
The Schottky diode I-V curve (Figure 65) appears very similar to that for a p-n junction diode However, there are important differences in the magnitude of the currents, which are illustrated in Example 61 and Figure 67
SOLUTION
TABLE 6.3 Effective Richardson Constants for Semiconductors
The Schottky diode is considered a majority device, that is, minority carriers do not play an important role Therefore, Schottky diodes exhibit faster switching times The lower forward voltage means that a Schottky diode does not dissipate as much power Because of these advantages, Schottky diodes are used in high-speed computer circuits
The junction capacitance of a Schottky diode is lower compared to that of a typical p-n junction based on the same semiconductor Since the reverse saturation current is high, the voltage and current ratings of Schottky diode for a forward bias are lower
Silicon Schottky diodes have relatively smaller breakdown voltages The silicon diodes work well up to a breakdown voltage of ∼100 V The resistance of the diode increases significantly in silicon diodes that have larger breakdown voltages For any given forward voltage drop, the value of the current decreases significantly with higher breakdown voltage diodes This limits the use of silicon Schottky diodes to rectify relatively lower voltages (Figure 68)
We can use semiconductors with higher breakdown voltages to control currents and voltages in high-powered electronics For example, there is considerable interest in using silicon carbide (SiC) Schottky diodes The forward current characteristics for a form of silicon carbide (known as 4H-SiC) are shown in Figure 69
Compared to silicon diodes, these diodes have higher Schottky barrier height of ∼11 eV They can also be designed for higher breakdown voltages and still offer a lower resistance Thus, compared to silicon, Schottky diodes made using SiC are better suited for high-power applications that involve higher voltages and currents
Ohmic contacts are necessary in many semiconductor devices, such as solar cells and transistors Ohmic contacts are formed when ϕM < ϕS for an n-type semiconductor or ϕM > ϕS for a p-type semiconductor These contacts are nonrectifying, meaning that there is no energy barrier to block current flow in either direction The use of the word “ohmic” does not, however, mean that the resistance of the contact is constant with voltage
The band diagrams for a metal-semiconductor junction forming an ohmic contact are shown in Figure 610
Ohmic contacts can be formed on semiconductor surfaces using different strategies such as those shown in Figure 611 The usual approach is to make tunneling possible using a Schottky barrier of a lower height and then doping to reduce the depletion layer width
Aluminum (Al) metallization is often used to create an ohmic contact on silicon As we can see from Table 62, aluminum can form a Schottky contact on silicon by itself However, when an evaporated aluminum film on p-type silicon is heated to ∼450-550°C, the aluminum diffuses into the silicon and creates a heavily doped (p+) layer at the interface between the aluminum and p-type silicon Silicon can also diffuse out into aluminum and form an aluminum-silicon alloy The contact between the p+ layer of silicon and the aluminum-silicon alloy is ohmic in nature Similarly, gold (Au) containing a small concentration of antimony (Sb), when deposited on n-type silicon, can create an ohmic contact by diffusing some of the antimony into the n-type silicon and creating an n+ layer at the interface Electrons can tunnel through this barrier and create an ohmic contact The current-voltage (I-V) characteristics of an ohmic contact and a Schottky contact are compared in Figure 612
A solar cell is a p-n junction-based device that generates an electric voltage or current upon optical illumination Solar cells are useful in alternative energy technologies that are “greener” and utilize resources such as energy from the sun and wind The field of research and development converting light energy into electricity is known as photovoltaics
The sun emits most of its energy in the wavelength of 2 to 4 μm Solar cells are made using semiconductors that can absorb energy in this wavelength spectrum The bandgap of the semiconductors used is hν > Eg, where ν is the frequency of light Absorptivity is the ability of the semiconductor to absorb solar radiation This is also important to solar cells The semiconductors used in solar cells include crystalline silicon, amorphous silicon (a:Si:H), polycrystalline silicon, silicon ribbons, nanocrystalline silicon, and GaAs Polycrystalline silicon is the most widely used because it costs less than single-crystal silicon, the second most widely used (Green 2003) Amorphous silicon is attractive because it can be used for deposition on large areas Other compound semiconductors such as copper indium diselenide (CuInSe2, CIS) and cadmium telluride (CdTe) can also be used, and provide a very high absorption of incident light
A schematic of the structure of a solar cell is shown in Figure 613 Usually, the top layer is an n-type material and the bottom layer is a p-type semiconductor There
are other elements in solar cell structure, such as an antireflective coating (Figure 613) The coating helps capture as much of the light energy incident on the solar cell as possible by minimizing reflection losses Similarly, in addition to the p-n junction, electrical ohmic contacts are required for operating an electrical circuit The bottom contact is made using metals such as aluminum or molybdenum The top contact is in the form of metal grids or transparent conductive oxides such as indium tin oxide (ITO) so that light can still get through to the p-n junction The symbol for a solar cell in an electrical circuit is shown in Figure 614
A solar cell is basically an illuminated p-n junction that absorbs energy from light radiation (Figure 615) The absorption of light causes the creation of electron-hole pairs (EHPs) This effect is known as photogeneration or optical generation of carriers The photogenerated carriers within the diffusion distances of the depletion layer (Lp or Ln, for holes or electrons, respectively) are swept up by the internal, built-in electric field The photogenerated holes drift toward the p-side with the negatively charged space-charge region, in the direction of the built-in
electric field (E) Photogenerated electrons drift toward the positively charged space-charge region on the n-side Both of these motions result in a photocurrent (IL) that is directed from the n-side to the p-side (Figure 615)
The photocurrent (IL) is also known as the short circuit current (Isc) This is the maximum current that flows through an external circuit with zero external resistance The photocurrent magnitude depends upon the rate at which electron-hole pairs are created per unit volume (gop) If A is the area of the p-n junction and Lp and Ln are the diffusion lengths for holes and electrons, respectively, then the photocurrent (IL) is given by
I q A L L gL p n op= × × + ×( ) (610)
We assume in Equation 610 that only the carriers that are generated within the diffusion distances of the depletion layer will contribute to IL The rest of the carriers created in the semiconductor p-and n-regions will recombine, which will not result in the generation of a current We also assume that the number of carriers generated in the depletion layer itself is small compared to those created in the neutral region n-and p-sides of the junction
When an external resistance (R) is connected to a solar cell, the flow of the current creates a voltage drop (V) across the resistor This voltage drop, in turn, creates a forward bias for the p-n junction and results in a forward current (IF), which is directed in an opposite direction (compared
−
+
to IL) The appearance of this forward voltage across an illuminated p-n junction is known as the photovoltaic effect
Thus, the net current (I) flowing through the external circuit is
I I I= −( )L F (611)
Note that the photocurrent (IL) and the net solar cell current (I) are always in the reverse-bias direction
The maximum value of the solar cell current (I) is IL; when there is no resistance (R = 0), it is also known as the short-circuit current (Isc) The minimum value of the solar cell current (I) is zero when the resistance is infinite (R = ∞) and is known as the open-circuit condition
We now derive expressions for the solar cell current (I) and open-circuit voltage (Voc) starting with the diode equation
I I qV
kTF S =
−
exp 1 (612)
The saturation current (Is) in Equation 612 can be written as
I q A D p
L
D n
= × × +
n (613)
The product of the hole and electron concentrations is a constant for a given semiconductor at fixed temperature T Therefore, pn × nn = ni2 and pp × np = ni2 or pn × Nd = ni2 and np × Na = ni2 Recall that subscripts for the electron and hole concentrations refer to the side of the p-n junction; for example, pn is the concentration of holes on the n-side Thus, Equation 613 can be written as
I q A n D
L N
D
= × × +
2 (614)
where Dp and Dn are the diffusion coefficients for holes and electrons, respectively, and Na and Nd are the dopant concentrations for the p-and n-sides, respectively
Substituting the expression for IS in Equation 612, we can write IF as
I q A n
D
L N
D
L N
qV
k TF p
= × × +
i
exp2 −
1
(615)
The diffusion lengths for a carrier are related to the lifetime of the carrier (τ) by the following equations:
L Dn n n= τ (616)
L Dp p p= τ (617)
The longer the lifetime (τ) of a carrier, the higher the diffusion length (L) The longer the carrier can survive without recombining, the higher the probability of it contributing to the photocurrent
Sometimes, we prefer to write IF without directly involving diffusion coefficients For example, using Equations 616 and 617 and substituting them into Equation 615 and rearranging, we get
I q A L
p L
n qV
k TF p
= × × +
−τ τ exp 1
(618)
Now, substituting Equation 610 for IL and Equation 618 for IF in the expression for total current I (Equation 611), we get
I q A L
p L
n qV
k T = × × +
−
p
exp 1 − × × × +q A g L Lop p n( ) (619)
For the limiting case of I = 0 (ie, open circuit), when the photocurrent (IL) is equal and opposite to the forward current (IF), we get the open-circuit voltage (Voc):
V k T q I
ln= +
( / ) 1
(620)
Voc is the maximum voltage that can be generated from the p-n junction forming a solar cell We can see the appearance of this voltage on a band diagram upon the illumination of a p-n junction, called the photovoltaic effect (Figure 616)
We can rewrite Equation 620 as follows:
V k T
q
L L
L p L n oc
=
+ +( )
( ) + ( )ln 1 / /τ τ p op
×
g
(621)
If the rate of the optical generation of carriers (gop) is large compared to their rate of thermal generation (gth) and the p-n junction is symmetric, that is, pn = np and τp = τn, then
V k T q
g
=
( / ) ln
(622)
As the intensity of the illumination increases, the optical generation rate increases on both sides of the p-n junction This leads to an increase in the open-circuit voltage (Voc) We can see this in the I-V curves for a solar cell in Figure 617
The open-circuit voltage (Voc) cannot keep increasing indefinitely with the increasing gop As the optical rate of the carrier generation increases, the minority carrier concentration increases This causes the lifetime (τ) of the carriers to become shorter Thus, more carriers recombine, which prevents the voltage from exceeding the built-in potential (V0)
Example 62 illustrates the calculation of the open-circuit voltage (Voc) for a solar cell
SOLUTION a. We rewrite Equation 6.20 current densities as
The maximum voltage from the solar cell is Voc for zero current in the external circuit The minimum voltage is zero when the current is maximum under a short-circuit condition (Isc) This gives us the diode current (I) as a function of the diode voltage generated as shown in Figure 618
The power a solar cell delivers to a load is obtained by calculating the value of I × V Note that since the current generated is in the reverse-bias direction, the sign of I is negative, and since the
voltage is positive, the product I × V is negative This means that the power is being generated but not consumed
This can be written as
P I V I V I qV
k T V= × = × −
−
×
( ) expL S B
1
(626)
We can calculate the current (Im) and voltage (Vm) that will result in maximum power (Pmax) by equating dP/dV = 0 From Equation 626,
dP
dV I I
qV
k T I V
q
k T = −
−
−
exp 1
=exp qV
k T m
1 1+
=
× +
I
I
qV
k T
qV
k T L
exp
or
1 1+
=
× +
I
I
qV
k T
V
V L
exp
(627)
In Equation 627, Vt = (kBT/q) = 0026 V at T = 300 K Since the right-hand side is known for a given p-n junction, we can solve for Vm by trial and error for a given IL The Vm and corresponding value of Im are shown in Figure 619
From Figure 619, we can see that the product Vm × Im is less than Voc × Ioc The ratio of these two products is called the fill factor (Ff) of a solar cell:
F
V I
= × ×
(628)
Most solar cells have a fill factor of ∼07 Please note that the subscript “m” in Vm and Im does not stand for maximum voltage and maximum current The subscripts instead represent the values of voltage and current, respectively, that lead to the maximum power
Experimental data for a silicon solar cell I-V curve is shown in Figure 620 Note that the opencircuit voltage is slightly less than 07 V and the contact potential (V0) for silicon is ∼07 V
Solar cell conversion efficiency (ηconv) is defined as the ratio of maximum power delivered to the incident power (Pin):
= ×I V P
(629)
If the incident photons have an energy (hν) less than the bandgap energy (Eg), then no electron-hole pairs are produced and the incident energy is wasted, that is, it is not used for conversion into electrical energy Similarly, if the incident photon energy (hν) is too high compared to Eg, then electronhole pairs are created, and the difference (hν−Eg) will appear as heat This will also make the solar cell inefficient Thus, the efficiency of the solar cell conversion is maximized by better matching the semiconductor bandgap with the solar spectrum By this principle, GaAs is a better material; however, it is more expensive than silicon and is thus used only in specialized applications Many polycrystalline silicon-based solar cells offer a conversion efficiency of ∼15%
Note that both direct and indirect bandgap semiconductors can be used in solar cells Recall that in LEDs, electrons and holes recombine and cause the emission of light, so we must use direct bandgap semiconductors In some ways, the solar cell and the LED make use of opposite effects Currently, CuInSe2 solar cells offer some of the highest conversion efficiencies, approaching ∼15% More complex solar cells based on multiple layers of different semiconductors offer higher efficiencies, up to 40%, because as the bandgap varies across the thickness of the solar cell, we can capture photons of different energies (Figure 620b) However, the cost of these solar cells is relatively high There is also a growing interest in using the nanoparticles of semiconductors and organic materials for solar cell applications
An LED normally uses a direct bandgap semiconductor in which the process of electron-hole recombination results in spontaneous emission of light The symbol for an LED is shown in Figure 621
The first practical LED was reported by Nick Holonyak, Jr, working at General Electric in 1962
This principle underlying the operation of an LED has already been mentioned in Chapter 5 in the discussion of indirect and direct bandgap semiconductors as well as the processes of radiative and nonradiative electron-hole recombination (Figure 622) The recombination dynamics, that is, how rapidly the electrons and holes can recombine and produce light, determine the speed at which an LED can be turned on and off The speed with which an LED can be turned on and off is important in some fiber optics applications
Most LEDs are made using direct bandgap materials However, as has been noted in Chapter 5, it is possible to use indirect bandgap materials to make LEDs, provided a defect energy level can be introduced by doping (see Section 653) This defect level provides an intermediate state in which radiative recombination is possible
LEDs are constructed as forward-biased p-n junctions made most often from direct bandgap semiconductors (Figure 623) When the p-n junction forming an LED is forwardbiased, the electrons with a high energy can overcome the
built-in potential barrier and arrive at the p-side of the junction These minority carriers then combine with the holes (ie, the majority carriers) on the p-side
Similarly, some of the holes from the p-side of the junction also make it across the depletion layer onto the n-side and recombine with the electrons there These recombination processes result in the emission of light in direct bandgap materials (Figure 623) For indirect bandgap materials such as silicon or germanium, the recombination process also leads to the generation of heat Thus, no LEDs are made using silicon or germanium Note that even in direct bandgap materials, some nonradiative recombination occurs and has a negative effect on the efficiency of an LED
The light emitted from an LED may be in the visible, infrared, or ultraviolet ranges LEDs that emit in the visible range are widely used in displays and many other consumer applications Figure 624 shows some of the materials used for making LEDs
The response of the eye to different wavelengths corresponding to various colors is also shown in this figure The wavelength of light emitted (λ) is related to the bandgap of the semiconductor (Eg) by the following equation:
λ µ= =h E E
ν g g in eV
m 1 24.
