Thank you for your useful information another thing is that can we find the fermi level and the dopant ionization energy from such data if we were given the work function of the metal?
Jan is almost correct. Yes, you have to plot C^-2 vs V and make the linear fit.
You can get the charge carrier density, either from the slope of the linear fit, if the slope is m, then the charge carrier density is given by n = - 2/(m*Epsilon*q*(A^2)), where epsilon is the dielectric permittivity of your semiconductor, A is the area of your Schottky diode and q is the absolute charge of electron, 1.6x10^(-19) Coulombs.... pay attention to put rightly all your units!
The second way is through the constant of your linear fit, lets call it b.
Then n = +2(Vbi)/(b*Epsilon*q*(A^2)), where Vbi is the built-in potential and all the other variables have the same meaning as before. In fact, the usual procedure is to use first the slope, you get n, and the you can determine Vbi, in case you can not get Vbi, for example using IV measurements.
You can find further details about all this in my Ph. D. thesis which you can donwload it from http://lib.tkk.fi/Diss/2007/isbn9789512286386.
And regarding the depletion region, remember that capacitance C is related with the depletion thickness d, by C = (Epsilon*A)/d.
And regarding your second question, use the expression Ec-Ef = - kT*ln(n/Nc), where Ec is the bottom of the conduction band, Ef the position of the Fermi level, k the Boltzmann constant, T the absolute temperature (in Kelvins!!!) and Nc the effective density of states.
As Jan mentioned, further details you can find them in the Sze book.
Regarding the dopant ionization energy, I find difficult that you can get it from a CV measurements, specially if it is only at one temperature and if it is homogenously dope.
Usually you use temperature dependent Hall measurement, DLTS, PL, or other technic to get the dopant ionization energy, absortion, etc...
thank you Victor but I assume that we can find N+D (ionized donor density) from the slop of 1/C2 vs V but I wanna find ND (dopant density). do you have any idea about the relation of these two? if I find these two then I can find the fermi level by N+D = ND(1-1/exp(Ed-Ef/kT) +1)
at some temperature, some of your dopants (which you call ND) will be ionized, and sure, you observe N+D (ionized donors density) from CV.... my advice is to make several CV at different temperatures.... you will get N+D at different T... the amount of dopants NOT ionized is given by ND*Ffd, where Ffd is the Fermi Dirac distribution, given by Ffd = 1 / ( 1 + EXP((Ed-Ef)/kT))... thus, the amount of ionized donors density is given by N+D = ND*(1-Ffd),.... if you make three measurements at three different temperatures, then you have three equations, with three unknown variables, ND and Ed and Ef.... you should be able to solve them at least numerically.... otherwise, from only one single CV measurement, at one temperature, I find if impossible to get ND and Ed at the same time....
To find the position of the fermi level with respect to the intrinsic fermi level( almost the mid gap position) one has to calculate the bulk potential (Phi.Bulk) (also called fermi potential) using the equation Phi.Bulk = Vt ln(Nd/ni). where Vt is the thermal voltage (approx. 26meV at 300K) Nd is the donor concentration and ni is the intrinsic carrier concentration (9.65x10^9 cm^-3 for Si at 300K). Extrinsic fermi level will be Phi.Bulk eV above mid gap for an n-type semiconductor. Jan has given you the technique to find the dopent density. Usually at room temperature (300K) almost all dopents will be ionised.
Depletion capacitance is given by Cdep=Epsi.s*A/Lambda where Epsi.s is silicon permitivity (approx 11.7 * Epsi.0), A-area of the cap, and Lamda is the Debye length
= Epsi.s *k*T/(q^2Nd) where k is Boltzmann const. q-electronic charge and Nd - doping concentration. (Ref. SM.Sze, Nicollian & Brews and Keithley application notes.)
Regards,
Thank you Rajeev but I wonder if I know the work function of the metal can I find the Fermi level and the dopant ionization energy ?
Dear Sina, In my knowledge you will have to find out Bulk potential (Phi.Bulk) to get the position of Fermi level. If your oxide is free of fixed charges and interface charges, then Vfb =Phi.ms where Vfb is flat band voltage and Phi.ms is the work function difference of the metal and Si. Knowing metal work function you can find out Si work fn from this. But for n-Si, Si.w.fn=Si.electron affinity +Eg/2 -Bulk potential of Si. Hence you can find out Bulk potential. For n-Si fermi level position is (Eg/2) - Bulk potential measured from Ec..
I am not sure about donor ionization energy Ed. May be you will have to take a low temperature I-V and find the activation energy from the Ln(sigma) vs 1/T Arrhenius plot. Hope somebody else can clarify this point. Regards.
The following article explain the procedure:
https://www.researchgate.net/publication/257482269_Extraction_of_Doping_Profile_in_Substrate_of_MNOS_capacitor_Using_Fast_Voltage_Ramp_Deep_Depletion_C-V_method
Regards
Article Extraction of Doping Profile in Substrate of MNOS capacitor ...
I would also recommend the following resources when analyzing MIS or MOS data:
Presentation at NanoHub: https://nanohub.org/resources/5363/play?resid=5405
Paper by Lubzens et. al.: D. Lubzens, A. Kolodny, and Y. J. Shacham-Diamand, “Automated measurement and analysis of MIS interfaces in narrow-bandgap semiconductors,” IEEE Trans. Electron Devices, vol. 28, no. 5, pp. 546–551, May 1981.
Book chapter 6 from Schroeder: D. K. Schroder and L. G. Rubin, “Semiconductor Material and Device Characterization,” Phys. Today, vol. 44, no. 4, p. 107, 1991.
Enjoy!
Article Automated Measurement and Analysis of MIS Interfaces in Narr...
Article Semiconductor Material And Device Characterization
As for the concern of linear fit for 1/C^2 vs V, what two points are chosen on voltage scale on which linear approximation are to be made?
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