nextnano.NEGF - Software for
Quantum Transport

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
===== Optical Gain =====

In this tutorial we calculate the optical gain upon optical irradiation.
The irradiation parameters are the
  * photon energy of the irradiation and the
  * line width.

==== Physics model ====
The transition rate per volume element can be expressed with the following sum,
\[
R = R_{ab} - R_{ba} = \frac{2}{V} \sum_{k_a} \sum_{k_b} \frac{2 \pi}{ \hbar} |H_{ba}| ^2 \delta(E_b - E_a -\hbar \omega)(f_a-f_b).
\]

In order to evaluate the sum much faster we calculate the $H_{ba}$ matrix element at $k_a = 0; k_b = 0$ (Remark: $k_a = k_b$), and we neglect the $k$ dependence of it. 
Then we can simplify the sum in the following form, if the irradiation has the $\gamma(E, w)$ broadening function, where $E$ is the irradiation energy, and $w$ is the line width. 

\[
R(E, w) = C_0(E)   \int \gamma(E_a-E, w) \cdot  H(E_a-E) \cdot  [n(E_a) - p(E_b)]  {\rm d}E_a {\rm d}E_b
\]

Here $C_0(E)$ is an energy dependent constant,
\[
C_0 = \frac{\pi e^2 \hbar}{n_{\rm r} c \epsilon_0 m_0^2 E}.
\] 

====Input file structure====

A new keyword has been introduced to handle an optical device, //opticaldevice{}//

<code>
opticaldevice{
	name = "quantum_region_name"
	line_broadening = 1            #Line broadening model (1: Lorentzian)
	photon_energy = 1              #Photon energy in (eV)
	line_width = 1                 #Line width in (eV)
}
</code>

An in the run paragraph you have to also add //solve_optical_device{}// in order to include it the simulation flow. 

==== Results ====
<figure>
;#;
<dataplot xlabel="x(nm)" ylabel="1/s/m^3" ylegends="Gain">
-90	0
-85	0
-80	0
-75	0
-70	0
-69.8	0
-69.6	0
-69.4	0
-69.2	0
-69	0
-68.8	0
-68.6	0
-68.4	0
-68.2	0
-68	0
-67.8	0
-67.6	0
-67.4	0
-67.2	0
-67	0
-66.8	0
-66.6	0
-66.4	0
-66.2	0
-66	0
-65.8	0
-65.6	0
-65.4	0
-65.2	0
-65	0
-64.8	0
-64.6	0
-64.4	0
-64.2	0
-64	0
-63.8	0
-63.6	0
-63.4	0
-63.2	0
-63	0
-62.8	0
-62.6	0
-62.4	0
-62.2	0
-62	0
-61.8	0
-61.6	0
-61.4	0
-61.2	0
-61	0
-60.8	0
-60.6	0
-60.4	0
-60.2	0
-60	0
-59.8	0
-59.6	0
-59.4	0
-59.2	0
-59	0
-58.8	0
-58.6	0
-58.4	0
-58.2	0
-58	0
-57.8	0
-57.6	0
-57.4	0
-57.2	0
-57	0
-56.8	0
-56.6	0
-56.4	0
-56.2	0
-56	0
-55.8	0
-55.6	0
-55.4	0
-55.2	0
-55	0
-54.8	0
-54.6	0
-54.4	0
-54.2	0
-54	0
-53.8	0
-53.6	0
-53.4	0
-53.2	0
-53	0
-52.8	0
-52.6	0
-52.4	0
-52.2	0
-52	0
-51.8	0
-51.6	0
-51.4	0
-51.2	0
-51	0
-50.8	0
-50.6	0
-50.4	0
-50.2	0
-50	-1.5033862802743e+26
-49.8	-3.0058131421596e+26
-49.6	-3.0049128749147e+26
-49.4	-3.0038521706133e+26
-49.2	-3.0026309177626e+26
-49	-3.0012489773794e+26
-48.8	-2.9997061829158e+26
-48.6	-2.9980023401621e+26
-48.4	-2.996137227125e+26
-48.2	-2.9941105938819e+26
-48	-2.991922162411e+26
-47.8	-2.9895716263963e+26
-47.6	-2.9870586510084e+26
-47.4	-2.984382872659e+26
-47.2	-2.9815438987301e+26
-47	-2.9785413072768e+26
-46.8	-2.9753746467028e+26
-46.6	-2.972043435409e+26
-46.4	-2.9685471614133e+26
-46.2	-2.9648852819417e+26
-46	-2.9610572229891e+26
-45.8	-2.9570623788505e+26
-45.6	-2.952900111619e+26
-45.4	-2.948569750652e+26
-45.2	-2.9440705920034e+26
-45	-2.9394018978205e+26
-44.8	-2.9345628957043e+26
-44.6	-2.9295527780323e+26
-44.4	-2.9243707012415e+26
-44.2	-2.9190157850706e+26
-44	-2.9134871117591e+26
-43.8	-2.9077837252019e+26
-43.6	-2.901904630057e+26
-43.4	-2.8958487908041e+26
-43.2	-2.8896151307522e+26
-43	-2.8832025309931e+26
-42.8	-2.8766098292984e+26
-42.6	-2.8698358189569e+26
-42.4	-2.8628792475499e+26
-42.2	-2.85573881566e+26
-42	-2.8484131755109e+26
-41.8	-2.8409009295333e+26
-41.6	-2.8332006288536e+26
-41.4	-2.8253107717006e+26
-41.2	-2.8172298017251e+26
-41	-2.8089561062276e+26
-40.8	-2.8004880142882e+26
-40.6	-2.791823794793e+26
-40.4	-2.7829616543503e+26
-40.2	-2.7738997350888e+26
-40	-2.7646361123322e+26
-39.8	-2.7551687921389e+26
-39.6	-2.7454957087013e+26
-39.4	-2.7356147215913e+26
-39.2	-2.7255236128452e+26
-39	-2.7152200838731e+26
-38.8	-2.7047017521829e+26
-38.6	-2.6939661479039e+26
-38.4	-2.6830107100953e+26
-38.2	-2.6718327828236e+26
-38	-2.6604296109922e+26
-37.8	-2.648798335901e+26
-37.6	-2.6369359905184e+26
-37.4	-2.6248394944392e+26
-37.2	-2.6125056485048e+26
-37	-2.5999311290566e+26
-36.8	-2.5871124817914e+26
-36.6	-2.5740461151846e+26
-36.4	-2.5607282934439e+26
-36.2	-2.5471551289497e+26
-36	-2.5333225741365e+26
-35.8	-2.5192264127625e+26
-35.6	-2.5048622505093e+26
-35.4	-2.490225504844e+26
-35.2	-2.4753113940718e+26
-35	-2.4601149254893e+26
-34.8	-2.4446308825403e+26
-34.6	-2.4288538108459e+26
-34.4	-2.4127780029437e+26
-34.2	-2.3963974814679e+26
-34	-2.3797059802115e+26
-33.8	-2.362696921273e+26
-33.6	-2.3453633770948e+26
-33.4	-2.3276980113892e+26
-33.2	-2.30969372225e+26
-33	-2.2913421188166e+26
-32.8	-2.2726347415231e+26
-32.6	-2.253562661862e+26
-32.4	-2.2341164446594e+26
-32.2	-2.2142861062241e+26
-32	-2.1940610678017e+26
-31.8	-2.1734301036676e+26
-31.6	-2.152381283084e+26
-31.4	-2.130901905203e+26
-31.2	-2.1089784258365e+26
-31	-2.08659637481e+26
-30.8	-2.0637402623725e+26
-30.6	-2.0403934728324e+26
-30.4	-2.0165381432169e+26
-30.2	-1.9921550242898e+26
-30	-1.9672233206825e+26
-29.8	-1.9417205061654e+26
-29.6	-1.9156221091625e+26
-29.4	-1.8889014624294e+26
-29.2	-1.8615294092939e+26
-29	-1.8334739568762e+26
-28.8	-1.8046998641085e+26
-28.6	-1.775168148923e+26
-28.4	-1.7448354943525e+26
-28.2	-1.7136535270079e+26
-28	-1.6815679327569e+26
-27.8	-1.6485173623753e+26
-27.6	-1.6144320628552e+26
-27.4	-1.5792321454181e+26
-27.2	-1.542825365068e+26
-27	-1.5051042321597e+26
-26.8	-1.4659421928915e+26
-26.6	-1.4251884837016e+26
-26.4	-1.3826610498372e+26
-26.2	-1.338136556592e+26
-26	-1.2913358870651e+26
-25.8	-1.2419023530843e+26
-25.6	-1.1893675747436e+26
-25.4	-1.133095251242e+26
-25.2	-1.0721823048588e+26
-25	-1.0052696739016e+26
-24.8	-9.301351236507e+25
-24.6	-8.4264964517585e+25
-24.4	-7.3317129051003e+25
-24.2	-5.6004484131293e+25
-24	-4.0995424263874e+25
-23.8	-4.064803234231e+25
-23.6	-4.0295356276604e+25
-23.4	-3.9937288598541e+25
-23.2	-3.9573718195143e+25
-23	-3.9204530135609e+25
-22.8	-3.8829605484896e+25
-22.6	-3.8448821102299e+25
-22.4	-3.8062049423196e+25
-22.2	-3.7669158221759e+25
-22	-3.7270010352124e+25
-21.8	-3.6864463465068e+25
-21.6	-3.6452369696736e+25
-21.4	-3.6033575325367e+25
-21.2	-3.5607920391215e+25
-21	-3.5175238274015e+25
-20.8	-3.4735355221224e+25
-20.6	-3.4288089818994e+25
-20.4	-3.3833252396154e+25
-20.2	-3.3370644349403e+25
-20	-3.2900057375128e+25
-19.8	-3.2421272589146e+25
-19.6	-3.1934059508238e+25
-19.4	-3.1438174846916e+25
-19.2	-3.0933360971401e+25
-19	-3.0419342089316e+25
-18.8	-2.9895839291424e+25
-18.6	-2.936253527989e+25
-18.4	-2.8819098061644e+25
-18.2	-2.8265170450409e+25
-18	-2.7700366414307e+25
-17.8	-2.7124266662199e+25
-17.6	-2.6536413271499e+25
-17.4	-2.5936303098787e+25
-17.2	-2.5323379630465e+25
-17	-2.4697022813808e+25
-16.8	-2.405653624422e+25
-16.6	-2.3401130848853e+25
-16.4	-2.2729903863474e+25
-16.2	-2.2041811389571e+25
-16	-2.1335632044443e+25
-15.8	-2.0609918012609e+25
-15.6	-1.9862927880558e+25
-15.4	-1.9092532457521e+25
-15.2	-1.8296079343952e+25
-15	-1.7470192296567e+25
-14.8	-1.6610463215772e+25
-14.6	-1.571095828917e+25
-14.4	-1.4763382068556e+25
-14.2	-1.3755560635529e+25
-14	-1.2668421533896e+25
-13.8	-1.1469139389756e+25
-13.6	-1.0092096239525e+25
-13.4	-8.3622058035193e+24
-13.2	-4.572873617073e+24
-13	-4.4703966445059e+24
-12.8	-4.3662384815115e+24
-12.6	-4.2604003599215e+24
-12.4	-4.1528885086092e+24
-12.2	-4.0437148281445e+24
-12	-3.932897636917e+24
-11.8	-3.8204624944808e+24
-11.6	-3.7064431077916e+24
-11.4	-3.5908823256879e+24
-11.2	-3.4738332263152e+24
-11	-3.3553603010887e+24
-10.8	-3.2355407370657e+24
-10.6	-3.1144657970532e+24
-10.4	-2.9922422931408e+24
-10.2	-2.8689941442753e+24
-10	-3.2290809750222e+27
-9.8	-6.3902612554379e+27
-9.6	-6.3246820923317e+27
-9.4	-6.2585513676534e+27
-9.2	-6.1918465747605e+27
-9	-6.1245442714799e+27
-8.8	-6.0566199819354e+27
-8.6	-5.9880480906042e+27
-8.4	-5.9188017272171e+27
-8.2	-5.8488526409284e+27
-8	-5.7781710619057e+27
-7.8	-5.7067255480436e+27
-7.6	-5.6344828135582e+27
-7.4	-5.5614075331256e+27
-7.2	-5.4874620956008e+27
-7	-5.4126061274423e+27
-6.8	-5.2850294406087e+27
-6.6	-5.0222477800373e+27
-6.4	-4.8499360151842e+27
-6.2	-4.6979825203457e+27
-6	-4.5561542274138e+27
-5.8	-4.4203667356121e+27
-5.6	-4.2884702483473e+27
-5.4	-4.1591473481682e+27
-5.2	-4.0315041621689e+27
-5	-3.9048859026943e+27
-4.8	-3.778782001287e+27
-4.6	-3.6527723123691e+27
-4.4	-3.5264940498546e+27
-4.2	-3.3996199154406e+27
-4	-3.271842513288e+27
-3.8	-3.1428623093088e+27
-3.6	-3.0123774580893e+27
-3.4	-2.880074348306e+27
-3.2	-2.7456179511612e+27
-3	-2.6086410983436e+27
-2.8	-2.4687316953594e+27
-2.6	-2.3254165689105e+27
-2.4	-2.178140069379e+27
-2.2	-2.0262345200843e+27
-2	-1.8688777522704e+27
-1.8	-1.7050295062745e+27
-1.6	-1.5333316701069e+27
-1.4	-1.3519429659526e+27
-1.2	-1.1582456359355e+27
-1	-9.4827638686186e+26
-0.8	-7.154768782015e+26
-0.6	-4.4738673839211e+26
-0.4	-1.1348404929519e+26
-0.2	4.5272528273396e+26
-4.4408920985006e-16	7.6062858814698e+26
0.2	7.913126196159e+26
0.4	8.2179513263573e+26
0.6	8.520907762704e+26
0.8	8.8221356753489e+26
1	9.1217697413077e+26
1.2	9.4199399023299e+26
1.4	9.7167720659164e+26
1.6	1.0012388760631e+27
1.8	1.0306909755747e+27
2	1.0600452654509e+27
2.2	1.0893133470026e+27
2.4	1.1185067193386e+27
2.6	1.1476368367654e+27
2.8	1.1767151711294e+27
3	1.205753298838e+27
3.2	1.6714718557684e+27
3.4	2.895999859911e+27
3.6	3.5595102435165e+27
3.8	4.0808635707771e+27
4	4.5268935122948e+27
4.2	4.9243102755744e+27
4.4	5.2870183987246e+27
4.6	5.6233553826254e+27
4.8	5.938790935326e+27
5	6.2371459625719e+27
5.2	6.5212170027833e+27
5.4	6.7931263214249e+27
5.6	7.0545320806019e+27
5.8	7.3067614955154e+27
6	7.5508989889201e+27
6.2	7.7878467542437e+27
6.4	8.0183677319037e+27
6.6	8.2431170245994e+27
6.8	8.4626655389527e+27
7	8.6775183372705e+27
7.2	8.8881294104693e+27
7.4	9.0949141333057e+27
7.6	9.2982604325952e+27
7.8	9.4985396507599e+27
8	9.6961182428315e+27
8.2	9.8913719122031e+27
8.4	1.0084704851113e+28
8.6	1.0276579124344e+28
8.8	1.0467564886685e+28
9	1.0658437163041e+28
9.2	1.0850391994684e+28
9.4	1.104564350423e+28
9.6	1.124984127174e+28
9.8	1.1512129308502e+28
10	5.832613854467e+27
10.2	-5.7147249229296e+22
10.4	-4.9596044711296e+22
10.6	-4.2969072824105e+22
10.8	-3.7168746797997e+22
11	-3.2103955279151e+22
11.2	-2.7690689268744e+22
11.4	-2.3852280889996e+22
11.6	-2.0519366473135e+22
11.8	-1.7629646924061e+22
12	-1.5127510806083e+22
12.2	-1.2963572590525e+22
12.4	-1.1094166442479e+22
12.6	-9.4808253920204e+21
12.8	-8.0897670381919e+21
13	-6.8914000041869e+21
13.2	-5.8598600180276e+21
13.4	-4.9725804771795e+21
13.6	-4.2098993932773e+21
13.8	-3.5547024314741e+21
14	-2.9921000802968e+21
14.2	-2.5091354881204e+21
14.4	-2.0945176938479e+21
14.6	-1.7383718904734e+21
14.8	-1.4319915631565e+21
15	-1.1675595673302e+21
15.2	-9.3775018197209e+20
15.4	-7.3490990287716e+20
15.6	-5.4828632294183e+20
15.8	-3.3705437988418e+20
16	-2.2494468134638e+20
16.2	-1.9511887096407e+20
16.4	-1.6922580071961e+20
16.6	-1.4674945790594e+20
16.8	-1.2724118730874e+20
17	-1.1031095501032e+20
17.2	-9.5619734116421e+19
17.4	-8.2872870893054e+19
17.6	-7.1814306999274e+19
17.8	-6.2221548785622e+19
18	-5.3901288159467e+19
18.2	-4.6685591463842e+19
18.4	-4.0428583335376e+19
18.6	-3.5003561751546e+19
18.8	-3.0300488588568e+19
19	-2.6223807117976e+19
19.2	-2.2690544089663e+19
19.4	-1.9628659487142e+19
19.6	-1.6961955102625e+19
19.8	-1.4656114287649e+19
20	-1.2658397369305e+19
20.2	-1.0927282739712e+19
20.4	-9.427031756854e+18
20.6	-8.1267083787815e+18
20.8	-6.9994908302834e+18
21	-6.0221157590868e+18
21.2	-5.1744001865334e+18
21.4	-4.4388309649028e+18
21.6	-3.8002096783317e+18
21.8	-3.2453448999777e+18
22	-2.7627852351459e+18
22.2	-2.3425876263364e+18
22.4	-1.9761162018976e+18
22.6	-1.6558676068944e+18
22.8	-1.3753193061654e+18
23	-1.1287978193544e+18
23.2	-9.113642512659e+17
23.4	-7.1871482913277e+17
23.6	-5.4709445964235e+17
23.8	-3.9322157958407e+17
24	-2.5422280031622e+17
24.2	-1.2757604260063e+17
24.4	-1.1061028709922e+16
24.6	9.7283853509352e+16
24.8	1.9919917181501e+17
25	2.9623730223796e+17
25.2	3.8979116362588e+17
25.4	4.8111940197526e+17
25.6	5.7136852213701e+17
25.8	6.6159240563072e+17
26	7.5276960619019e+17
26.2	8.4581878128761e+17
26.4	9.4161260395087e+17
26.6	1.0409905192217e+18
26.8	1.144770801328e+18
27	1.2537626372951e+18
27.2	1.3687797494775e+18
27.4	1.4906596701e+18
27.6	1.6203036970485e+18
27.8	1.7588245451379e+18
28	1.9097926805291e+18
28.2	2.0636970928785e+18
28.4	2.2290417373803e+18
28.6	2.4067177327278e+18
28.8	2.5976767637574e+18
29	2.8029360983978e+18
29.2	3.0235838842453e+18
29.4	3.2607847549977e+18
29.6	3.5157857777756e+18
29.8	3.7899227733835e+18
30	4.0846270428074e+18
30.2	4.4014325347038e+18
30.4	4.7419834903108e+18
30.6	5.108042604099e+18
30.8	5.5014997405852e+18
31	5.9243812500567e+18
31.2	6.3788599285036e+18
31.4	6.8672656698409e+18
31.6	7.3920968615231e+18
31.8	7.9560325779303e+18
32	8.5619456294403e+18
32.2	9.2129165289105e+18
32.4	9.9122484413969e+18
32.6	1.0663483187338e+19
32.8	1.1470418374159e+19
33	1.2337125736316e+19
33.2	1.3267970769228e+19
33.4	1.4267633748348e+19
33.6	1.5341132230841e+19
33.8	1.6493845143954e+19
34	1.7731538571306e+19
34.2	2.6102791190001e+19
34.4	3.3680495518877e+19
34.6	4.024204778331e+19
34.8	4.6696724981377e+19
35	5.33136060908e+19
35.2	6.0229591063294e+19
35.4	6.7535868495545e+19
35.6	7.5304381313219e+19
35.8	8.3598455211246e+19
36	9.2477871435918e+19
36.2	1.0200162143131e+20
36.4	1.1222957371972e+20
36.6	1.2322358640242e+20
36.8	1.3504832055503e+20
37	1.4777188663989e+20
37.2	1.6146639690226e+20
37.4	1.7620846638476e+20
37.6	1.9207968878743e+20
37.8	2.0916710412647e+20
38	2.2756366970928e+20
38.2	2.4736874266337e+20
38.4	2.6868858023301e+20
38.6	2.9163686279086e+20
38.8	3.1633524371456e+20
39	3.4291392978122e+20
39.2	3.7151229543081e+20
39.4	4.0227953407972e+20
39.6	4.353753495855e+20
39.8	4.7097069094669e+20
40	5.0924853334973e+20
40.2	5.5040470873577e+20
40.4	5.9464878914527e+20
40.6	6.422050262013e+20
40.8	6.9331335020914e+20
41	7.4823043247572e+20
41.2	8.072308145859e+20
41.4	8.7060810850942e+20
41.6	9.3867627155149e+20
41.8	1.0117709602979e+21
42	1.090250967841e+21
42.2	1.1744997487008e+21
42.4	1.2649270359773e+21
42.6	1.3619705553773e+21
42.8	1.4660978408522e+21
43	1.5778081566558e+21
43.2	1.6976345306828e+21
43.4	1.8261459039646e+21
43.6	1.9639494011887e+21
43.8	2.1116927270492e+21
44	2.2700666931334e+21
44.2	2.4398078798886e+21
44.4	2.6217014379889e+21
44.6	2.8165840331219e+21
44.8	3.0253469378291e+21
45	3.2489392735562e+21
45.2	3.4883714054732e+21
45.4	3.7447184919127e+21
45.6	4.0191241894243e+21
45.8	4.3128045134315e+21
46	4.627051853305e+21
46.2	4.9632391393008e+21
46.4	5.3228241572359e+21
46.6	5.7073540049833e+21
46.8	6.1184696828197e+21
47	6.5579108073587e+21
47.2	7.0275204362099e+21
47.4	7.5292499876199e+21
47.6	8.0651642361429e+21
47.8	8.6374463618553e+21
48	9.2484030267551e+21
48.2	9.900469447759e+21
48.4	1.0596214431143e+22
48.6	1.1338345328351e+22
48.8	1.2129712867856e+22
49	1.2973315812189e+22
49.2	1.3872305383423e+22
49.4	1.4829989394338e+22
49.6	1.5849836016214e+22
49.8	1.6935477107901e+22
50	9.0503277327804e+21
50.2	0
50.4	0
50.6	0
50.8	0
51	0
51.2	0
51.4	0
51.6	0
51.8	0
52	0
52.2	0
52.4	0
52.6	0
52.8	0
53	0
53.2	0
53.4	0
53.6	0
53.8	0
54	0
54.2	0
54.4	0
54.6	0
54.8	0
55	0
55.2	0
55.4	0
55.6	0
55.8	0
56	0
56.2	0
56.4	0
56.6	0
56.8	0
57	0
57.2	0
57.4	0
57.6	0
57.8	0
58	0
58.2	0
58.4	0
58.6	0
58.8	0
59	0
59.2	0
59.4	0
59.6	0
59.8	0
60	0
60.2	0
60.4	0
60.6	0
60.8	0
61	0
61.2	0
61.4	0
61.6	0
61.8	0
62	0
62.2	0
62.4	0
62.6	0
62.8	0
63	0
63.2	0
63.4	0
63.6	0
63.8	0
64	0
64.2	0
64.4	0
64.6	0
64.8	0
65	0
65.2	0
65.4	0
65.6	0
65.8	0
66	0
66.2	0
66.4	0
66.6	0
66.8	0
67	0
67.2	0
67.4	0
67.6	0
67.8	0
68	0
68.2	0
68.4	0
68.6	0
68.8	0
69	0
69.2	0
69.4	0
69.6	0
69.8	0
70	0
75	0
80	0
85	0
90	0

</dataplot>
;#;
</figure>
nextnano.NEGF - Software for Quantum Transport

User Tools

Site Tools

Page Tools

nextnano.NEGF - Software for
Quantum Transport
