Density of India
As a result of the gradual increase in the population of India with the passing of each day, the population density of India per square km is also quickly on the rise. A survey of the Indian population density 2011 shows quite a considerable rise in the figures of population density in India. The records of population density 2011 of India state that the density 2011 has increased from a figure of 324 to that of 382 per square kilometre, which is considerably higher than the average population density of the world 2011, which are 46 per square kilometre. Records reveal that along with the wide difference with the population density of the world, there are also a lot of differences in the population density of the various states of India.
While the National Capital Region area of Delhi possesses the highest of the population density 2011 among the states of India having a statistics of 11,297 per square kilometre, the state of Arunachal Pradesh has the lowest record of population density having just 17 per square kilometre.
It is very obvious that a higher density of population of a region would essentially mean that it is an urban area with high buildings and other modern aspects, while the low density of population of region would mean that it is a rural area with a probability there might be lack of modern amenities in the region.
The recent population of India in the year of 2012 is 1.22 billion or 1,220,200,000 if viewed in numerical terms. India is the second among the most populous nations of the world and is just under China which has a population of 1.35 billion people or 1,350,044,605. This is quite an increase from the population which India had in 2001 which was 1.02 billion. Records reveal the fact that males constitute 628.8 billion of the population whereas their female counterparts consist of 591.4 million of the population of India and 50% of the population of India consists of people within the age of 25 years and 65% consists of people below the age of 35 years. It has also been noted that India consists 17.31% of the population of the world. This stands for the fact that out of six people of this world one lives in India. Statistics also reveal that by the year of 2030 India would become the most populous country of the world leaving China behind. One of the primary causes of the steep increase in India's population is illiteracy.
Area Sq. Km
Density 2011
Density 2001
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band structure and density of state 性能计算?
请问有些性质如band structure and density of state，在几何优化后从.castep可以直接输出，这时候得到的结果和再次进行性质计算得到的结构有何不同？
性质计算通常应该取多大的超包呢？文献上很好用单包进行计算，原理上，castep计算单包结果不是更快吗？
本人刚学习理论计算，很希望多认识一些同领域的朋友，方便讨论互相学习，欢迎加QQ，
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最好的禅语是：该吃饭的时候好好吃饭，该睡觉的时候好好睡觉。
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08:29:25sunyang1988: 金币+1, 谢谢交流
再次进行性质计算得到的结构实在上一次优化的结果上进行的，得到的图会更加准确
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单包原子数太少！而实际材料是有很多原子组成的。故超胞更能模拟真实材料的性能，因为原子数相对多！
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引用回帖:: Originally posted by 漫天飘雪 at
再次进行性质计算得到的结构实在上一次优化的结果上进行的，得到的图会更加准确 你好，那请问我设置的K-Point为fine,结果不同的体系，显示的kpoint不同，有的是5*5*1有的是9*9*1，这时候，我是不是要把kpoints 设置为custom grid parameters呢？然后再手动固定grid parameter呢？
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最好的禅语是：该吃饭的时候好好吃饭，该睡觉的时候好好睡觉。
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引用回帖:: Originally posted by jondan at
单包原子数太少！而实际材料是有很多原子组成的。故超胞更能模拟真实材料的性能，因为原子数相对多！ 你好，请问我设置的K-Point为fine,结果不同的体系，显示的kpoint不同，有的是5*5*1有的是9*9*1，这时候，我是不是要把kpoints 设置为custom grid parameters呢？然后再手动固定grid parameter呢？
无标题.png
最好的禅语是：该吃饭的时候好好吃饭，该睡觉的时候好好睡觉。
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★ ★ ★ purplesdd: 金币+2, ★★★★★最佳答案
11:35:39sunyang1988: 金币+1, 谢谢交流
引用回帖:: Originally posted by purplesdd at
你好，那请问我设置的K-Point为fine,结果不同的体系，显示的kpoint不同，有的是5*5*1有的是9*9*1，这时候，我是不是要把kpoints 设置为custom grid parameters呢？然后再手动固定grid parameter呢？
无标题.png
... KPOINTS的设置需要判断它的收敛性，同时也要看你所计算的体系，正交晶格和六方晶格的设置当然有所区别，你可以手动进行设置
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引用回帖:: Originally posted by 漫天飘雪 at
KPOINTS的设置需要判断它的收敛性，同时也要看你所计算的体系，正交晶格和六方晶格的设置当然有所区别，你可以手动进行设置... 模仿文献中的设置可以吗？
最好的禅语是：该吃饭的时候好好吃饭，该睡觉的时候好好睡觉。
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★ ★ 感谢参与，应助指数 +1purplesdd: 金币+1, ★有帮助
14:43:47sunyang1988: 金币+1, 谢谢交流
再次进行性质计算得到的要准确
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引用回帖:: Originally posted by purplesdd at
模仿文献中的设置可以吗？... 如果是模仿别人的，那设置尽量和别人的一样，这样才能得到相似的结果
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引用回帖:: Originally posted by 漫天飘雪 at
如果是模仿别人的，那设置尽量和别人的一样，这样才能得到相似的结果... 不知道尊下用的是什么计算软件？我用的是castep,我在建立超包的时候，达到了64个原子，8个分子而已，2*2的超包，这样计算会不会过大呢？
最好的禅语是：该吃饭的时候好好吃饭，该睡觉的时候好好睡觉。
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i请填写生词本名称!Density of states
Chapter 2:&Semiconductor Fundamentals
2.4&Density of states
Before we can calculate the density of carriers in a semiconductor, we have to find the number of available states at each energy. The number of electrons at each energy is then obtained by multiplying the number of states with the probability that a state is occupied by an electron. Since the number of energy levels is very large and dependent on the size of the semiconductor, we will calculate the number of states per unit energy and per unit volume.
2.4.1&Calculation of the density of states
The density of states in a semiconductor equals the density per unit volume and energy of the number of solutions to Schr鰀inger's equation. We will assume that the semiconductor can be modeled as an infinite quantum well in which electrons with effective mass, m*, are free to move. The energy in the well is set to zero. The semiconductor is assumed a cube with side L. This assumption does not affect the result since the density of states per unit volume should not depend on the actual size or shape of the semiconductor.
The solutions to the wave equation (equation ) where V(x) = 0 are sine and cosine functions:
Where A and B are to be determined. The wavefunction must be zero at the infinite barriers of the well. At x = 0 the wavefunction must be zero so that only sine functions can be valid solutions or B must equal zero. At x = L, the wavefunction must also be zero yielding the following possible values for the wavenumber, kx.
This analysis can now be repeated in the y and z direction. Each possible solution then corresponds to a cube in k-space with size np/L as indicated on Figure .
Figure 2.4.1:Calculation of the number of states with wavenumber less than k.
The total number of solutions with a different value for kx, ky and kz and with a magnitude of the wavevector less than k is obtained by calculating the volume of one eighth of a sphere with radius k and dividing it by the volume corresponding to a single solution, , yielding:
A factor of two is added to account for the two possible spins of each solution. The density per unit energy is then obtained using the chain rule:
The kinetic energy E of a particle with mass m* is related to the wavenumber, k, by:
And the density of states per unit volume and per unit energy, g(E), becomes:
The density of states is zero at the bottom of the well as well as for negative energies.
The same analysis also applies to electrons in a semiconductor. The effective mass takes into account the effect of the periodic potential on the electron. The minimum energy of the electron is the energy at the bottom of the conduction band, Ec, so that the density of states for electrons in the conduction band is given by:
Example 2.3Calculate the number of states per unit energy in a 100 by 100 by 10 nm piece of silicon (m* = 1.08 m0) 100 meV above the conduction band edge. Write the result in units of eV-1.
SolutionThe density of states equals:
So that the total number of states per unit energy equals:
2.4.2& Calculation of the density of states in 1, 2 and 3 dimensions
We will here postulate that the density of electrons in k杝pace is constant and equals the physical length of the sample divided by 2p and that for each dimension. The number of states between k and k + dk in 3, 2 and 1 dimension then equals:
We now assume that the electrons in a semiconductor are close to a band minimum, Emin and can be described as free particles with a constant effective mass, or:
Elimination of k using the E(k) relation above then yields the desired density of states functions, namely:
for a three-dimensional semiconductor,
For a two-dimensional semiconductor such as a quantum well in which particles are confined to a plane, and
For a one-dimensional semiconductor such as a quantum wire in which particles are confined along a line.
An example of the density of states in 3, 2 and 1 dimension is shown in the figure below:
Figure 2.4.2:Density of states per unit volume and energy for a 3-D semiconductor (blue curve), a 10 nm quantum well with infinite barriers (red curve) and a 10 nm by 10 nm quantum wire with infinite barriers (green curve). m*/m0 = 0.8.
The above figure illustrates the added complexity of the quantum well and quantum wire: Even though the density in two dimensions is constant, the density of states for a quantum well is a step function with steps occurring at the energy of each quantized level. The case for the quantum wire is further complicated by the degeneracy of the energy levels: for instance a two-fold degeneracy increases the density of states associated with that energy level by a factor of two. A list of the degeneracy (not including spin) for the 10 lowest energies in a quantum well, a quantum wire and a quantum box, all with infinite barriers, is provided in the table below:
Figure 2.4.3:Degeneracy (not including spin) of the lowest 10 energy levels in a quantum well, a quantum wire with square cross-section and a quantum cube with infinite barriers. The energy E0 equals the lowest energy in a quantum well, which has the same size
Next, we compare the actual density of states in three dimensions with equation (). While somewhat tedious, the exact number of states can be calculated as well as the maximum energy. The result is shown in Figure . The number of states in an energy range of 20 E0 are plotted as a function of the normalized energy E/E0. A dotted line is added to guide the eye. The solid line is calculated using equation (). A clear difference can be observed between the two, while they are expected to merge for large values of E/E0.
Figure 2.4.4:Number of states within a range DE = 20 E0 as a function of the normalized energy E/E0. (E0
is the lowest energy in a 1-dimensional quantum well). See text for more detail.
A comparison of the total number of states illustrates the same trend as shown in Figure . Here the solid line indicates the actual number of states, while the dotted line is obtained by integrating equation ().
Figure 2.4.5:Number of states with energy less than or equal to E as a function of E0 (E0 is the lowest energy in an 1-dimensional quantum well). Actual number (solid line) is compared with the integral of equation () (dotted line).
ece.colorado.edu/~bart/bookBoulder, August 2007