Why mobility decreases when temperature increases

Connect and share knowledge within a single location that is structured and easy to search. Limiting for now the discussion to electrons, my intuition suggests that at a higher temperature without changing the electric field and the number of carriers , a single electron collides more frequently with the ions and so, on average, its velocity is reduced to zero more often.

That causes its drift velocity to be less than it would be at a lower temperature. I can't get an intuition of why an increased number of electrons at a constant temperature causes the mobility to decrease. That happens for every electron, that are assumed to be independent from one another. The way mobility depends on average scattering time of the carriers is given here:.

A simple model gives the approximate relation between scattering time average time between scattering events and mobility. It is assumed that after each scattering event, the carrier's motion is randomized, so it has zero average velocity. After that, it accelerates uniformly in the electric field, until it scatters again.

The resulting average drift mobility. The higher the temperature , i. So in a simple model the higher the temperature the smaller the mobility.

With increasing temperature, phonon concentration increases and causes increased scattering. Thus lattice scattering lowers the carrier mobility more and more at higher temperature. Theoretical calculations reveal that the mobility in non-polar semiconductors, such as silicon and germanium, is dominated by acoustic phonon interaction. A rough human size analogy for slow motion long scattering time, low temperature versus fast: A crowd in a square listening to a speaker.

They are still except for random mobility of changing places for friends or access to seats There will be no problem with mobility, i. If an explosion is heard , everybody will start running and hitting each other high temperature low mobility.

People die trampled in panic situations. Maybe I've found an intuitive answer myself to the remaining question: "why in an intrinsic semiconductor more carriers causes less mobility? Probably what the book means is in terms of probability for electrons to hit the targets ions. Thinking of one single electron moving in a lattice, it is likely that it travels all across a finite conductor without colliding with a ion.

At a concentration of 10 18 cm -3 , the mobility varied approximately 1. The results are similar to the model of solar cells found in the literature, with convenient use of the measured data or empirical formulas, for operations mobilities in K Si are well approximated [22] [22] R.

Pierret and W. This phenomenon occurs due to two physical processes that influence the mobility of the load carrier. The first process is the thermal scattering, due to the collisions of the electrons with phonons of the network, since the atoms of the vibratory network have determined thermal energy in temperatures above 0 K. A variation in the network temperature causes the atoms to randomly vibrate by the crystal and consequently interrupt the periodic potential that the crystalline lattice possesses.

The second process is scattering by ionizing impurities, since the dopants in the lattice will be ionized at room temperature. Coulomb interactions between free electrons in the network and the ionic nuclei of the impurities will be initiated, with this being an independent process of temperature oscillations as soon as it has values above the energy required for the ionization of the atoms [23] [23] C.

Jacoboni, C. Canali, G. Ottaviani and A. Quaranta, Solid-State Electronics 20, 77 In this work, the mobility variation for commercial Si-c cells, which have p-type dopant concentration of 10 15 cm -3 to 10 16 cm -3 and type n of 10 18 cm -3 to 10 19 cm -3 are presented in detail in Fig.

Even if mobility is not explicitly present in the equation, it is presented as the main factor considering that it is the fundamental parameter for diffusivity calculation, diffusion length and recombination time of charge carriers in the photovoltaic device. For a crystalline silicon p-n junction the saturation current density shows an increase of approximately a factor of 4 for every 10 K increase in temperature. Ideally the saturation current should be as low as possible. With the previous analyzes, we can analyze the spectral response as a function of temperature.

Thus, it can be said that the equations described play an important role both in determining the efficiency of the various types of semiconductors and in the choice of the best solutions in relation to the operating temperatures of the solar cells [24] [24] N. In the analysis of the influence of temperatures above NOCT Nominal Operating Cell Temperature in the production of photovoltaic solar energy, it is verified that the mobility of charge carriers, although presenting low changes in commercial cells, from the point of view of the temperature variation, caused a considerable change in the J s a t reverse saturation current density, thus substantially affecting the working efficiency of the photovoltaic device.

The data presented through the model opens space in the development of new methods that allow the modeling of the mobility in 2nd generation thin films and 3rd generation devices, organic cells, for a later analysis of the influence of temperature.

Ideally the saturation current should be as low as possible; its variation is a consequence of the change in mobility caused by the change in the concentration of ionized impurities and due to the increase of electron collisions with atoms of the vibration network. Both causes are directly connected to temperature variation. Among the analyzed parameters, the charge mobility, which is related to the current in the dark, showed to be a characteristic of extreme influence; the current in the dark, which is related to the charge mobility has proved to be a characteristic of extreme influence, since it defines the performance of the load carriers when moving through the material.

From the electrical parameters, the I-V curve can be determined, which characterizes the operation mode of solar cells in photovoltaic modules: open circuit voltage, short-circuit current, form factor and efficiency.

Due to the increase in the operating temperature of the device, the values indicate a power drop, because the drop of Voc to a photogenerated constant current means a drop in resistance and consequently in the power delivered by the device [25] [25] N. The model used presented a good approximation of the reality, allowing the analysis of the limitations of the silicon cell.

It is possible to work with new materials with absorption coefficients that take advantage of a larger range of the solar spectrum. This work has received honorable mention of the Brazilian Physics Society. Abrir menu Brasil. Abrir menu. Introduction The most commonly used energy models are being questioned as humanity is confronted with the consequences of expensive and less reliable energy systems [1] [1] M.

Figure 1 Ilustration of semiconductor structure of silicon. Figure 2 Equivalent circuit -1 diode model. Table 1 Parameters for calculation of the mobility, type n dopant: Phosphorus and type p dopant: Indium [15] [15] S. Dhar, H. Kosina, V. Palankovski, S. Ungersboeck and S. Figure 3 Variation of intrinsic concentration with temperature. Figure 4 Mobility of carriers of type n with different temperatures. Figure 5 Mobility of carriers of type p with different temperatures.

Figure 6 Mobility of n-type carriers with different doping at different temperatures. Figure 7 Mobility of p-type carriers with different doping at different temperatures. Figure 8 Mobility of the p-type charge carriers to a Si-c cell with commercial concentration of dopant at different temperatures. Figure 9 Mobility of n-type charge carriers to a Si-c cell with commercial concentration of dopant at different temperatures. Figure 10 Mobility of n-type charge carriers to a Si-c cell with commercial concentration of dopant at different temperatures.

References [1] M. Again the conductance of a semiconductor is. In the case of doped semiconductors, we note that at high temperatures they are intrinsic in behaviour and become pseudo-intrinsic at low temperature, with and energy gap equal to the gap between the impurity level and the band edge. Therefore on a plot similar to the one mentioned above we would expect two straight-line regions with different slopes.

In the region between these slopes the temperature is high enough to ionize the donors fully but not high enough to ionize an appreciable number of electrons from the lattice. Hence, in this temperature rage the carrier density will not be greatly influenced by temperature and the in mobility that were previously neglected will determined the shape of the curve. We know that where tau is the mean free time between collisions.

The mean free path may be written as proportional to Now consider that the mean free path is inversely proportional to the scattering probability, and that the scatting probability may be taken to be proportional to the energy of the lattice i.

These two effects operate simultaneously, with the total collision time equalling In general, ionized impurity scattering dominates at low temperatures, whilst at higher temperatures, phonon scattering dominates. The electrical conductivity of a semiconductor can be expressed in the following way: Note that both the carrier concentrations N e and N h and the mobilities depend on temperature, though with different functional forms.

As stated previously, the Hall voltage can be written as with only the current being temperature dependent. Determining the Energy Gap The variation of conductivity with temperature also allows us to measure the energy gap between the valence and conduction bands.