1 Introduction

We attempt to model the frequency response of the silicon vertex detector for BaBar with a network of capacitors and resistors using PSPICE and compare to measurements. Specifically we measure the impedances and phases of a 1B3 part which is a Layer 1 backward part. The important capacitances and resistances are the capacitances between the AC metal strip and the implant $C_{AC}$, the bias resistance $R_b$, the bulk capacitance from one strip to a single strip on the backplane $C_{b\_ one}$, and the interstrip capacitance between implants $C_{is}$. In addition, each strip also sees an effective resistance to ground after going through $C_{b\_ one}$ to the backplane. If $n$ is the number of strips, then each strip sees $n$ $C_{b\_ one}$ capacitors and $n$ $R_b$ resistors in series (see Fig. 1). The equivalent circuit for this is a single capacitor with value $nC_{b\_ one}$ in series with a resistor with value $R_b/n$. From now on, we will define $C_b\equiv nC_{b\_ one}$ while still referring to the resistance as $R_b/n$.

Figure 1: The capacitances and resistances to the backplane, which can be simplified to a single resistance and capacitance

We study the frequency response of the detector with an LCR probe between the AC metal strip and the implant for frequencies between about 10 Hz and 1 MHz with an amplitude of 1V for the input frequency. For actual measurements, there are many parasitic elements between the probe and the detectors, such as those of the relay boards. We will see that the data does not agree very well with the SPICE simulations, although there are some ways of compensating for the parasitic elements.

The values we use for the detector are

$$\begin{array}{ccc} C_{AC} &=& 24 \textrm{pF/cm for the n-si... ...}\\ n &=& 798 \textrm{total strips on two wafers} \end{array}$$ (1)

Each wafer is 4 cm by 4 cm and there are two wafers placed side by side. On the p-side, there are $n$ strips on each wafer running along the short side. On the n-side, the strips run along the long side and so there are $n$ strips on each wafer that are linked by AC metal strips that are connected between wafers. Both sides still end up seeing $C_b$ and $Rb/n$ to the backplane assuming that the interaction between strips on different wafers is negligible. So on each side, we multiply by 4cm to get the total values. The values we get for the p-side are

$$\begin{array}{ccc} C_{AC} &=& 184 \textrm{pF}\\ R_b &=& 5\... ...0.68 \textrm{pF}\\ C_{is} &=& 4.2 \textrm{pF}\\ \end{array}$$ (2)

while the values for the n-side are

$$\begin{array}{ccc} C_{AC} &=& 96 \textrm{pF}\\ R_b &=& 5 ... ...0.68 \textrm{pF}\\ C_{is} &=& 4.2 \textrm{pF}\\ \end{array}$$ (3)