Work Function of Metals - Revision history

Cmditradmin at 21:25, 21 July 2010

2010-07-21T21:25:46Z

← Older revision		Revision as of 14:25, 21 July 2010
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			Contributed by Michal Malicki - Georgia Tech- Thesis Introduction

	=== Work Function - Physical Description ===		=== Work Function - Physical Description ===

Cmditradmin at 19:47, 23 September 2009

2009-09-23T19:47:58Z

← Older revision		Revision as of 12:47, 23 September 2009
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	=== Work Function of Metallic Surfaces – Methods of Measurement ===		=== Work Function of Metallic Surfaces – Methods of Measurement ===

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

2009-09-23T18:50:24Z

Work Function of Metallic Surfaces – Methods of Measurement

← Older revision		Revision as of 11:50, 23 September 2009
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	Photoelectric-effect-based methods use light, typically in the UV range, as the source of energy for the electrons. As in other absolute methods, the resulting electric current (here called ''photocurrent'') is analyzed. Figure 2 shows the energetics of a photoelectric-effect-based measurement of the work function. In this experiment the electrons are provided with a known energy, ''hν'' (red arrows in Figure 2). Electrons with sufficient kinetic energy to overcome the barrier at the interface are able to escape the metal – these are represented with the blue box in Figure 2. These ''photoelectrons ''then travel away from the metal surface experiencing the potential depicted with the thick black line in Figure 2. As the electrons move further away from the surface their kinetic energy increases, according to Equation 1. The generated photocurrent is then measured as a function of the photoelectron kinetic energy. Two important features are present in a typical plot of photocurrent – kinetic energy. First, a sharp onset at low photoelectron kinetic energy, ''E<sub>min''</sub> is present. As already mentioned, this onset defines the lowest energy electrons able to overcome the work function of the surface.'''		Photoelectric-effect-based methods use light, typically in the UV range, as the source of energy for the electrons. As in other absolute methods, the resulting electric current (here called ''photocurrent'') is analyzed. Figure 2 shows the energetics of a photoelectric-effect-based measurement of the work function. In this experiment the electrons are provided with a known energy, ''hν'' (red arrows in Figure 2). Electrons with sufficient kinetic energy to overcome the barrier at the interface are able to escape the metal – these are represented with the blue box in Figure 2. These ''photoelectrons ''then travel away from the metal surface experiencing the potential depicted with the thick black line in Figure 2. As the electrons move further away from the surface their kinetic energy increases, according to Equation 1. The generated photocurrent is then measured as a function of the photoelectron kinetic energy. Two important features are present in a typical plot of photocurrent – kinetic energy. First, a sharp onset at low photoelectron kinetic energy, ''E<sub>min''</sub> is present. As already mentioned, this onset defines the lowest energy electrons able to overcome the work function of the surface.'''
	[[Image:photoelectric_workfunct.jpg\|thumb\|300px\|Figure 2. Energetics of electrons in a photoelectric-effect-based measurement of the work function. The photon energy, ''hν'', is shown as a red arrow. After ejection from the metal the electrons experience the potential shown with the thick black line. The kinetic energies of two ''photoelectrons'' originating from different energy levels in the metal are shown with thick green lines.In a real experiment the photoelectron-kinetic-energy analyzer causes an additional drop in the potential, which adds a rigid offset to the kinetic energy of the photoelectrons. More on this can be found in ~~Ref~~. 12. ''']]
			[[Image:photoelectric_workfunct.jpg\|thumb\|300px\|Figure 2. Energetics of electrons in a photoelectric-effect-based measurement of the work function. The photon energy, ''hν'', is shown as a red arrow. After ejection from the metal the electrons experience the potential shown with the thick black line. The kinetic energies of two ''photoelectrons'' originating from different energy levels in the metal are shown with thick green lines.In a real experiment the photoelectron-kinetic-energy analyzer causes an additional drop in the potential, which adds a rigid offset to the kinetic energy of the photoelectrons. More on this can be found in Nieuwenhuys 1974 <ref>Nieuwenhuys, B. E.; Van Aardenne, O. G.; Sachtler, W. M. H. Chem. Phys. 1974, 5, 418-28.</ref> ''']]


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	Table 1 shows experimentally measured work-function values for a variety of metallic surfaces. The presented data show a variation of the work function in the range of 2.7 – 5.65 eV, revealing that the chemical composition of the surface has a large effect on the work function value. '''		Table 1 shows experimentally measured work-function values for a variety of metallic surfaces. The presented data show a variation of the work function in the range of 2.7 – 5.65 eV, revealing that the chemical composition of the surface has a large effect on the work function value. '''


	=== Work Function Values ===		=== Work Function Values ===

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

2009-09-23T18:49:01Z

Work Function of Metallic Surfaces – Methods of Measurement

← Older revision		Revision as of 11:49, 23 September 2009
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	Table 1 shows experimentally measured work-function values for a variety of metallic surfaces. The presented data show a variation of the work function in the range of 2.7 – 5.65 eV, revealing that the chemical composition of the surface has a large effect on the work function value. '''		Table 1 shows experimentally measured work-function values for a variety of metallic surfaces. The presented data show a variation of the work function in the range of 2.7 – 5.65 eV, revealing that the chemical composition of the surface has a large effect on the work function value. '''


			=== Work Function Values ===


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	{\| class="prettytable" border = "1"		{\| class="prettytable" border = "1"
	\| <center>'''Element'''</center>		\| <center>'''Element'''</center>
	\| <center>'''?<sub>m</sub><nowiki> [eV]</nowiki>'''</center>		\| <center>'''φ<sub>m</sub><nowiki> [eV]</nowiki>'''</center>
	\| <center>'''Element'''</center>		\| <center>'''Element'''</center>
	\| <center>'''?<sub>m</sub><nowiki> [eV]</nowiki>'''</center>		\| <center>'''φ<sub>m</sub><nowiki> [eV]</nowiki>'''</center>
	\| <center>'''Element'''</center>		\| <center>'''Element'''</center>
	\| <center>'''?<sub>m</sub><nowiki> [eV]</nowiki>'''</center>		\| <center>'''φ<sub>m</sub><nowiki> [eV]</nowiki>'''</center>

	\|-		\|-

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

2009-09-23T18:47:23Z

Work Function of Metallic Surfaces – Methods of Measurement

← Older revision		Revision as of 11:47, 23 September 2009
Line 31:		Line 31:

	Photoelectric-effect-based methods use light, typically in the UV range, as the source of energy for the electrons. As in other absolute methods, the resulting electric current (here called ''photocurrent'') is analyzed. Figure 2 shows the energetics of a photoelectric-effect-based measurement of the work function. In this experiment the electrons are provided with a known energy, ''hν'' (red arrows in Figure 2). Electrons with sufficient kinetic energy to overcome the barrier at the interface are able to escape the metal – these are represented with the blue box in Figure 2. These ''photoelectrons ''then travel away from the metal surface experiencing the potential depicted with the thick black line in Figure 2. As the electrons move further away from the surface their kinetic energy increases, according to Equation 1. The generated photocurrent is then measured as a function of the photoelectron kinetic energy. Two important features are present in a typical plot of photocurrent – kinetic energy. First, a sharp onset at low photoelectron kinetic energy, ''E<sub>min''</sub> is present. As already mentioned, this onset defines the lowest energy electrons able to overcome the work function of the surface.'''		Photoelectric-effect-based methods use light, typically in the UV range, as the source of energy for the electrons. As in other absolute methods, the resulting electric current (here called ''photocurrent'') is analyzed. Figure 2 shows the energetics of a photoelectric-effect-based measurement of the work function. In this experiment the electrons are provided with a known energy, ''hν'' (red arrows in Figure 2). Electrons with sufficient kinetic energy to overcome the barrier at the interface are able to escape the metal – these are represented with the blue box in Figure 2. These ''photoelectrons ''then travel away from the metal surface experiencing the potential depicted with the thick black line in Figure 2. As the electrons move further away from the surface their kinetic energy increases, according to Equation 1. The generated photocurrent is then measured as a function of the photoelectron kinetic energy. Two important features are present in a typical plot of photocurrent – kinetic energy. First, a sharp onset at low photoelectron kinetic energy, ''E<sub>min''</sub> is present. As already mentioned, this onset defines the lowest energy electrons able to overcome the work function of the surface.'''
	[[Image:photoelectric_workfunct.jpg\|thumb\|300px\|Figure 2. Energetics of electrons in a photoelectric-effect-based measurement of the work function. The photon energy, ''h~~<ref>~~nu~~</ref>~~'', is shown as a red arrow. After ejection from the metal the electrons experience the potential shown with the thick black line. The kinetic energies of two ''photoelectrons'' originating from different energy levels in the metal are shown with thick green lines.In a real experiment the photoelectron-kinetic-energy analyzer causes an additional drop in the potential, which adds a rigid offset to the kinetic energy of the photoelectrons. More on this can be found in Ref. 12. ''']]		[[Image:photoelectric_workfunct.jpg\|thumb\|300px\|Figure 2. Energetics of electrons in a photoelectric-effect-based measurement of the work function. The photon energy, ''hν'', is shown as a red arrow. After ejection from the metal the electrons experience the potential shown with the thick black line. The kinetic energies of two ''photoelectrons'' originating from different energy levels in the metal are shown with thick green lines.In a real experiment the photoelectron-kinetic-energy analyzer causes an additional drop in the potential, which adds a rigid offset to the kinetic energy of the photoelectrons. More on this can be found in Ref. 12. ''']]

Cmditradmin: /* Work Function of Definition */

2009-09-23T18:46:16Z

Work Function of Definition

← Older revision		Revision as of 11:46, 23 September 2009
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	=== Work Function ~~of Definition~~ ===		=== Work Function - Physical Description ===

	Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''E<sub>tot''</sub>, of such an electron is equal to its potential energy, which can be defined after Cahen and Kahn as the ''vacuum level at infinity'', ''E<sub>vac</sub>(∞)''.<ref>Cahen, D.; Kahn, A. Adv. Mater. 2003, 15, 271-277</ref>. Let us supply the electron with some kinetic energy, ''E<sub>k''</sub>, and allow it to travel towards the surface. The total energy of the electron outside the metal can be expressed as the sum of its potential energy, ''E<sub>V''</sub>, and kinetic energy, ''E<sub>k''</sub>:'''		Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''E<sub>tot''</sub>, of such an electron is equal to its potential energy, which can be defined after Cahen and Kahn as the ''vacuum level at infinity'', ''E<sub>vac</sub>(∞)''.<ref>Cahen, D.; Kahn, A. Adv. Mater. 2003, 15, 271-277</ref>. Let us supply the electron with some kinetic energy, ''E<sub>k''</sub>, and allow it to travel towards the surface. The total energy of the electron outside the metal can be expressed as the sum of its potential energy, ''E<sub>V''</sub>, and kinetic energy, ''E<sub>k''</sub>:'''
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	=== Work Function of Metallic Surfaces – Methods of Measurement ===		=== Work Function of Metallic Surfaces – Methods of Measurement ===
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Cmditradmin at 18:45, 23 September 2009

2009-09-23T18:45:28Z

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 === Work Function of Definition ===
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 === References ===
 <references/>

Cmditradmin: New page: === Work Function of Definition === Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''E_tot'...

2009-09-23T18:44:35Z

New page: === Work Function of Definition === Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''Etot'...

New page

=== Work Function of Definition ===

Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''Etot'', of such an electron is equal to its potential energy, which can be defined after Cahen and Kahn as the ''vacuum level at infinity'', ''Evac(∞)''.<ref>Cahen, D.; Kahn, A. Adv. Mater. 2003, 15, 271-277</ref>. Let us supply the electron with some kinetic energy, ''Ek'', and allow it to travel towards the surface. The total energy of the electron outside the metal can be expressed as the sum of its potential energy, ''EV'', and kinetic energy, ''Ek'':'''

:<math>E_{tot} = E_V + E_k\,\!</math> Equation 1'''

As the distance between the electron and the metal surface decreases the potential energy of the electron will increase, thus slowing it down, according to Equation 1 (see Figure 1b). If the kinetic energy is sufficiently large to overcome the potential barrier at the metal / vacuum interface the electron will go over the barrier and then will rapidly lose its potential energy due to the interaction with the positively charged ion lattice within the metal, resulting in the increase of kinetic energy. Once the electron is within the metal Equation 1 no longer holds as the interactions with other electrons and the ion lattice result in energy dissipation and thermal equilibration. The electron is now trapped within the metal. '''

A similar thought experiment can be performed in the opposite direction. Let us choose an electron from one of the highest occupied energy levels at the particular temperature of the system. The potential energy of this electron is approximately at the ''Fermi level'','' EF''. In terms of Fermi – Dirac statistics the Fermi level is defined as the energy at which the probability of finding an electron is 0.5 for a system at thermal equilibrium. For metals at room temperature the probability of finding an electron below the Fermi level is close to unity.'''I<ref>shii, H.; Sugiyama, K.; Ito, E.; Seki, K. Adv. Mater. 1999, 11, 605-625.</ref> <ref>Ishii, H.; Sugiyama, K.; Ito, E.; Seki, K. Adv. Mater. 1999, 11, 605-625.
</ref>

The electron is then supplied with some kinetic energy, ''E'k'', sufficiently large to overcome the potential barrier existing at the metal surface. Right after escaping the metal, the greatly slowed-down electron has a potential energy which can be defined as the ''vacuum level close to the surface'', ''Evac(s)''.1 The drop in the kinetic energy of the electron caused by the potential energy barrier is defined as the work function of the metal surface, ''φm'': 1,2'''

:<math>\Phi_m = E_{vac}(s) - E_F\,\!</math> Equation 2
 
After escaping from the metal the electron is moving away further from the surface experiencing acceleration as the potential drops to the value of ''Evac(∞)''.'''

[[Image:PE_workfunct.jpg|thumb|400px|Figure 1. a) Potential energy of an electron in vacuum at an infinite distance from a metal surface, ''Evac(∞)'', and the Fermi level of the metal, ''EF''. b) Potential landscape the electron experiences along a travel path towards the metal surface (thick line). The difference between the electron energy just outside the metal surface, ''Evac(s)'', and ''EF'' defines the work function of the metal surface, ''φm = Evac(s) - EF''.''']]

It is important to describe the physical origin of the potential landscape illustrated in the above thought experiment. As already mentioned, the sharp potential drop the electron experiences when it enters the metal is related to the electrostatic attraction force between the negative charge of the electron and the positively charged ion lattice of the metal. However, at the vacuum / metal interface the electron experiences a potential energy barrier. This implies that in that region of space there must be a repulsive force that acts upon the electron. Indeed, the lack of positively charged metal ions on the vacuum side of the aforementioned interface causes a negative charge to exist just outside of the metal and, conversely, an uncompensated positive charge within the metal. The spilling of the electronic density outside of the solid causes a formation of a sheet of dipoles, which are often referred to as ''the surface dipoles''.1-3 '''

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=== References ===
<references/>

Work Function of Metals - Revision history

Cmditradmin at 21:25, 21 July 2010

Cmditradmin at 19:47, 23 September 2009

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

Cmditradmin: /* Work Function of Metallic Surfaces – Methods of Measurement */

Cmditradmin: /* Work Function of Definition */

Cmditradmin at 18:45, 23 September 2009

Cmditradmin: New page: === Work Function of Definition === Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''Etot'...

Cmditradmin: New page: === Work Function of Definition === Let us consider an electron at rest in a vacuum at an infinite distance from a metal surface, as depicted in Figure 1a. The total energy, ''E_tot'...