4.4 Temperature and voltage dependence of electron transport
3 min read•august 7, 2024
Electron transport in molecules is heavily influenced by temperature and voltage. These factors affect how electrons move through materials, impacting everything from to resistance changes.
Understanding these dependencies is crucial for designing and analyzing molecular electronic devices. We'll look at how temperature impacts electron emission and energy distributions, and how voltage drives current flow and reveals .
Thermionic Emission and Thermal Effects
Temperature-Dependent Electron Emission and Transport
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Thermionic emission occurs when electrons gain enough thermal energy to overcome the work function and escape from a material's surface
Governed by the Richardson-Dushman equation: J=AT2e−kBTW, where J is the emission current density, A is a material-specific constant, T is the temperature, W is the work function, and kB is the Boltzmann constant
Commonly observed in vacuum tubes and electron guns (cathode ray tubes)
of energy levels leads to a distribution of electron energies around the Fermi level
Described by the : f(E)=e(E−EF)/kBT+11, where f(E) is the probability of an electron occupying a state with energy E, EF is the Fermi energy, kB is the Boltzmann constant, and T is the temperature
Results in a smearing of the Fermi edge and a non-zero probability of finding electrons above the Fermi level at finite temperatures
Activation Energy and Temperature-Dependent Resistance
is the minimum energy required for a process to occur, such as electron transport or chemical reactions
Determines the temperature dependence of the rate of a process according to the : k=Ae−kBTEa, where k is the rate constant, A is a pre-exponential factor, Ea is the activation energy, kB is the Boltzmann constant, and T is the temperature
Can be extracted from the slope of an Arrhenius plot, which is a graph of ln(k) vs. 1/T
describes the relative change in resistance with temperature
Defined as α=R1dTdR, where α is the TCR, R is the resistance, and T is the temperature
Positive TCR (metals) indicates increasing resistance with temperature due to increased electron scattering
Negative TCR (semiconductors) indicates decreasing resistance with temperature due to increased from thermal excitation across the bandgap
Voltage-Dependent Transport
Current-Voltage Characteristics and Differential Conductance
is the potential difference applied across a device or junction
Drives current flow and determines the energy landscape for electron transport
Can be used to probe the and transport properties of materials and devices
I-V characteristics describe the relationship between current and voltage in a device
Provide information about the transport mechanism, such as ohmic (linear) or non-ohmic (non-linear) behavior
Can reveal the presence of energy barriers, such as in a Schottky diode or a tunnel junction
is the derivative of the current with respect to voltage: G=dVdI
Reflects the local density of states and the transmission probability at a given energy
Can be measured using lock-in techniques or numerical differentiation of I-V data
Peaks in differential conductance correspond to resonant tunneling through discrete energy levels (quantum dots, molecules)
Non-Linear Transport Phenomena
occurs when the current-voltage relationship deviates from ohmic behavior
Can arise from various mechanisms, such as voltage-dependent tunneling, space-charge limited current, or field emission
Examples include in resonant tunneling diodes and current saturation in field-effect transistors
leads to non-linear I-V characteristics in tunnel junctions
Described by the : I∝Ve−2dℏ22mϕ, where I is the current, V is the voltage, d is the barrier width, m is the electron mass, ϕ is the barrier height, and ℏ is the reduced Planck constant
Enables the study of electronic structure and transport mechanisms in and nanoscale devices