5 Solid State Detectors
155
by the drain voltage. A resistive voltage drop along the channel is responsible for
the current saturation that occurs once this voltage drop equals the effective gate
voltage (voltage above the threshold necessary to create inversion).
Important parameters of the transistor to be used in noise considerations are
the transistor (output) conductance g = dI d /dV d and transconductance g m = dI d
/dV g . These and other parameters can be modelled using the graded channel
approximation which relies on the assumption that changes along the channel are
much smaller than those occurring in the transverse direction. It allows deriving
scaling laws for changes in geometry. However, for microelectronics with minimal
feature size these are of limited validity. Instead, two- and three-dimensional
numerical device simulations are needed.
Measurement precision is limited by noise. There are several noise mechanisms
present. Considering a resistor with resistance R for example, the thermal motion
of electrons will result in a statistical fluctuation of the charge distribution in the
conductor, leading to a noise voltage density of d
terminals of the resistor. The resistance of the MOSFET channel is a source of white
noise too. It is customary to represent this noise by a voltage at the gate d
= 4 kT(2/3)(1/g m ) for the operation of the transistor in the saturation region.
A further mechanism of noise is the capture and delayed release of single
charge carriers in the channel. While being captured the drain current decreases,
returning to the initial value when released. For a single trapping centre with
characteristic average capture and release times a Lorentzian noise spectrum as
function of frequency results. Having many different trapping centres, as is the
case for traps at the Si-SiO 2 interface where trapping and detrapping occurs by
means of tunnelling, the result of the superposition of Lorentzian noise spectra
is a 1/f spectrum dv n
2 /df = A f /f with A f a constant, which depends on the
technology and the geometric parameters of the transistor. A f is usually obtained
from measurements and parameterized as A f = K F /(WLC ox
2 ). K F characterizes the
technology, W and L are channel width and length, and C ox the oxide capacitance
per unit area. Note that the 1/f noise is independent of the transistor current.
5.7.2 The Measurement of Charge
The standard problem in the readout of a semiconductor detector is the low-noise
measurement of the signal charge, usually under severe constraints such as highspeed operation, low power consumption, restricted space and frequently high
radiation levels. In this section the general problems of charge measurement will
be addressed, while specific solutions for the electronics will be considered later.
The charge-sensitive amplifier (CSA), invented by Emilio Gatti [14] and represented in Fig. 5.14, consists of an inverting amplifying circuit which—in the ideal
case—delivers an output voltage proportional to the input (U out = −A U in ) and a
feedback capacitor C f . In addition, a high-resistance feedback or a switch is needed
in the feedback loop, in order to bring the circuit into its operating condition. C D
155
by the drain voltage. A resistive voltage drop along the channel is responsible for
the current saturation that occurs once this voltage drop equals the effective gate
voltage (voltage above the threshold necessary to create inversion).
Important parameters of the transistor to be used in noise considerations are
the transistor (output) conductance g = dI d /dV d and transconductance g m = dI d
/dV g . These and other parameters can be modelled using the graded channel
approximation which relies on the assumption that changes along the channel are
much smaller than those occurring in the transverse direction. It allows deriving
scaling laws for changes in geometry. However, for microelectronics with minimal
feature size these are of limited validity. Instead, two- and three-dimensional
numerical device simulations are needed.
Measurement precision is limited by noise. There are several noise mechanisms
present. Considering a resistor with resistance R for example, the thermal motion
of electrons will result in a statistical fluctuation of the charge distribution in the
conductor, leading to a noise voltage density of d
terminals of the resistor. The resistance of the MOSFET channel is a source of white
noise too. It is customary to represent this noise by a voltage at the gate d
= 4 kT(2/3)(1/g m ) for the operation of the transistor in the saturation region.
A further mechanism of noise is the capture and delayed release of single
charge carriers in the channel. While being captured the drain current decreases,
returning to the initial value when released. For a single trapping centre with
characteristic average capture and release times a Lorentzian noise spectrum as
function of frequency results. Having many different trapping centres, as is the
case for traps at the Si-SiO 2 interface where trapping and detrapping occurs by
means of tunnelling, the result of the superposition of Lorentzian noise spectra
is a 1/f spectrum dv n
2 /df = A f /f with A f a constant, which depends on the
technology and the geometric parameters of the transistor. A f is usually obtained
from measurements and parameterized as A f = K F /(WLC ox
2 ). K F characterizes the
technology, W and L are channel width and length, and C ox the oxide capacitance
per unit area. Note that the 1/f noise is independent of the transistor current.
5.7.2 The Measurement of Charge
The standard problem in the readout of a semiconductor detector is the low-noise
measurement of the signal charge, usually under severe constraints such as highspeed operation, low power consumption, restricted space and frequently high
radiation levels. In this section the general problems of charge measurement will
be addressed, while specific solutions for the electronics will be considered later.
The charge-sensitive amplifier (CSA), invented by Emilio Gatti [14] and represented in Fig. 5.14, consists of an inverting amplifying circuit which—in the ideal
case—delivers an output voltage proportional to the input (U out = −A U in ) and a
feedback capacitor C f . In addition, a high-resistance feedback or a switch is needed
in the feedback loop, in order to bring the circuit into its operating condition. C D