# CV

From CV measurements we can determine several parameters, such us mobility, charge density, and charge inversion.

• ### Effective field (Eeff)

For example, in order to measure effective field, it is common to use Split CV. With this technique we are able to determine charge depletion and charge inversion which are need. (Figure a. reproduced from Dobbie.)

In the gate channel configuration, Cgc,the substrate is connected to Earth while we apply voltage at the gate. The capacitance will be measured through the drain and source. The charge inversion will determine integrating the CV curve from the flatband voltage:

$Q_{inv}=\frac{1}{WL}\int^{V_G}_{V_{FB}}C_{gc}dV_{G}$

In the gate body configuration, Cgb, the drain and the source are connected to the Earth while we apply voltage at the gate. the capacitance will now be measure through the substrate and the charge depletion will be determined integrating the CV curve, also, from the flatband voltage:

$Q_{dep}=\frac{1}{WL}\int^{V_G}_{V_{FB}}C_{gb}dV_{G}$

From the above expressions it can be perceive that another important parameter is the flatband voltage. This can be determined from the 1/C2 vs VG curve, by extrapolating the linear part to V=0.

The effective field is given by

$\varepsilon_{eff}=\frac{\eta Q_{int}+Q_{dep}}{\kappa \epsilon_0}$

with $\eta=1/2$ for electron mobility and $\eta=1/3$ for hole mobility.

Combining this measurements with IV measurements we can see how mobility changes with the effective field since the mobility can be obtained from the drain conductance in the linear region:

$\mu_{eff}=\frac{L}{W}\frac{g_D}{q.N_S}$

where q.NS is the inversion carrier density determined through the gate channel capacitance.

•  Effective mobility (µeff):

Mobility are affected by three kind of scattering surface roughness μsr, phonon scattering μph and columbic scattering μc,  so the total mobility could be defined by:

1/μ =1/μph + 1/μsr + 1 /μc

The following fig shows how these types of scattering have impacted mobility.To avoid the impact of the substrate impurity, substrate bias and oxide thickness should Plot mobility versus effective electric field which defined by equation in the last section  .By making  the approximation that Qinv (Vg) = Cox (Vg − Vt),where Qinv is the inversion charge  and initially assume that mobility is constant with gate voltage  so the effective mobility is

μeff  = Id L /W Vd Qinv

L gate channel length gate width, this equation is used to extract the effective mobility from experimental data that by using split CV method .

• ## Interface trap density (Dit):

Interface trap density is an important parameter that affect the performance of MOSFETs (following figure ), which accounted for the increase of  leakage current. There are many techniques to extract the interface trap density .However, two techniques will be emphasised:

  High-Low frequency technique:
Although, this method is convenient with experimental data more than others such  as Low  Frequency (Quasi-static) Methods, Terman Method, Deep  Level Transient
Spectroscopy and Charge  Pumping, it  is not  suitable  for low band gap semiconductor such as Ge  The  following equation  used to determine trap density by  applying  low and high frequency:

$Dit=Cox/q(Clf/cox/1-Clf/Cox-((Chf/Cox)/1-(Chf/Cox)))$

Which Clf low frequences capacitance  and Chf high frequencies capacitance,Cox oxide capacitance.

  Conductance method

This method is very sensitive and could measure 109 cm-2eV-1 interface trap densities .It  is based on measuring  (G-C)  as function of  different  frequencies in  the  equivalent  parallel circuit of MOSFET  so

Dit=(2.5/q) (Gpa/ω) max

which ω =2πf and Gpa is the conductance and this is preferred method for Ge MOSFET.

## Bibliography

1. A. DOBBIE “Investigation of the Electrical Properties of Si1-xGexchannel pMOSFETs with High-k Dielectrics” PhD Thesis University of Warwick (2007).

2. D. K. Schroder, Semiconductor material and device characterisation (3rd Ed.) John Wiley & Sons.

3. A. Ortiz-Condea , F.J. Garc ,S a ancheza, J.J. Liou b,1, A. Cerdeira c,M. Estrada c, Y. Yue d ,A review of recent MOSFET threshold voltage extraction methods,
Microelectronics eliability 42 (2002) 583–596.

4.  C. Beer, Fabrication and Characterization of novel Ge MOSFETs, PhD Thesis
University of Warwick 2007.