Boltzmann constant in formulas

[aarnes]

Hi, I see that Boltzmann constant comes in different forms like: k=8.62*10^-5 eV/K and also k=1.38*10^-23J/K.
Which one should I use in , say formula for intrinsic carrier concentration n_i = sqrt(N_c*N_v)*e^-E_g(T)/2kT ?

 

[Bob S]

kT has units of energy; Joules or electron volts. Always remember that an exponent has to be unitless. If the numerator has volts, then kT is in eV.

Sometimes you will see kTB which is noise power times bandwidth.

The noise power is kTB where k= 1.38 x 10^-20 millijoules per deg kelvin, T=293 kelvin, and B(bandwidth in Hz)= 1 MHz

So noise power is 1.38 x 10^-20 x 293 x 10⁶ Hz= 4 x 10^-12milliwatts per MHz = -114 dBm per MHz.

Add 3 dB noise figure to get -111 dBm per MHz

 

[aarnes]

Thank you, Bob! I used the eV form before but I saw some different results on the web and just wasn't sure why is there always a slightly different value for ni, depending on which website you look.

 

[Dickfore]

Instead of $k_ B = 8.62 \times 10^{-5} \, \frac{\mathrm{eV}}{\mathrm{K}}$, people usually find it convenient to remember the following number:
$$k_B = \frac{1 \, \mathrm{eV}}{11600 \, \mathrm{K}}$$

(notice that $(8.62 \times 10^{-5})^{-1} = 1.16 \times 10^4$, so the above are equivalent)

 

[Dickfore]

At room temperature $T \approx 293 \, \mathrm{K}$, the value $k_B \, T \approx 25 \, \mathrm{meV}$.

 

[aarnes]

At room temperature $T \approx 293 \, \mathrm{K}$, the value $k_B \, T \approx 25 \, \mathrm{meV}$.

On the web you usually see 300K as room temperature. I guess it depends on one's preference? :D

 

[Dickfore]

On the web you usually see 300K as room temperature. I guess it depends on one's preference? :D

Right, that is why i used only 2 significant figures in the final result and the approximate sign.

 

[rbj]

Hi, I see that Boltzmann constant comes in different forms like: k=8.62*10^-5 eV/K and also k=1.38*10^-23J/K.
Which one should I use in , say formula for intrinsic carrier concentration n_i = sqrt(N_c*N_v)*e^-E_g(T)/2kT ?

boy, you sure are good at using HTML markup. i never knew you could get a subscript in the superscript. anyway, it might look better with LaTeX

$$n_i \ = \ \sqrt{N_c N_v} e^{-\frac{E_g(T)}{2 k T}}$$


now, to answer your question, you want you $kT$ quantity to be in the same units as the $E_g$ quantity. if $k=8.62 \times 10^5$ eV/K then $T$ better be in Kelvin and $E_g$ better be in eV.